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Ultrafast multi-directional devices for optical wireless communications Jin, Xian 2016

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  ULTRAFAST MULTI-DIRECTIONAL DEVICES  FOR OPTICAL WIRELESS COMMUNICATIONS by Xian Jin  M.A.Sc., The University of British Columbia, 2010 B.Eng., Nanjing University of Science & Technology, P. R. China, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE COLLEGE OF GRADUATE STUDIES (Electrical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)  June 2016  © Xian Jin, 2016   								The	undersigned	certify	that	they	have	read,	and	recommend	to	the	College	of	Graduate	Studies	for	acceptance,	a	thesis	entitled:				Ultrafast	Multi-directional	Devices	for	Optical	Wireless	Communications		Submitted	by																															Xian	Jin																														in	partial	fulfillment	of	the	requirements	of			The	degree	of																																	Doctor	of	Philosophy																																	.		 		Dr.	Jonathan	F.	Holzman,	School	of	Engineering,	The	University	of	British	Columbia	Supervisor,	Professor	(please	print	name	and	faculty/school	above	the	line)		Dr.	Kenneth	Chau,	School	of	Engineering,	The	University	of	British	Columbia	Supervisory	Committee	Member,	Professor	(please	print	name	and	faculty/school	in	the	line	above)		Dr.	Richard	Klukas,	School	of	Engineering,	The	University	of	British	Columbia								Supervisory	Committee	Member,	Professor	(please	print	name	and	faculty/school	in	the	line	above)		Dr.	Murray	Neuman,	Physics,	The	University	of	British	Columbia																													University	Examiner,	Professor	(please	print	name	and	faculty/school	in	the	line	above)		Dr.	Lawrence	R.	Chen,	Department	of	Electrical	and	Comuputer	Engineering,	McGill	University	External	Examiner,	Professor	(please	print	name	and	university	in	the	line	above)			June	15,	2016	(Date	submitted	to	Grad	Studies)					 	iii  Abstract  Optical wireless communications (OWC) has become an increasingly attractive technology for dense urban environments, as it merges the high-speed capability of optical communications with the mobility of wireless operation. Early generations of OWC systems are now emerging as indoor (e.g., Li-Fi) networks and outdoor (e.g., free-space optical) links. Unlike contemporary point-to-point fibre-optic networks, however, these OWC systems typically demand bi-/multi-directional operations between distributed transceivers. With this in mind, various forms of multi-directional optical wireless transceivers are presented in this dissertation. A corner-cube (CC) optical wireless transceiver is introduced first, with orthogonal photoconductive (PC) switches facilitating OWC operation over a solid angle of π/2 steradians. The CC-PC transceiver is capable of simultaneous photodetection (via PC switches operating at a gigahertz bandwidth), optical retroflection (via a CC architecture operating over a solid angle of π/2 steradians), and optical modulation (via a liquid crystal modulator operating at a kilohertz bandwidth). The capabilities of the multi-directional optical wireless transceiver are then extended through the introduction of a spherical (SP) optical wireless transceiver. The SP-PC transceiver offers improved performance over that of the CC-PC transceiver. It is capable of simultaneous photodetection (via PC switches operating at a gigahertz bandwidth), optical retroflection (via refraction over a solid angle of 4π steradians), and optical modulation (via all-optical modulation at a terahertz bandwidth). The proposed optical wireless transceivers are well-suited to the demands of bi-directional OWC networks, with active downlink and passive uplink operation, and they yield great potential for future implementations of OWC networks.  iv  Preface      All of the presented research work was conducted in the Integrated Optics Laboratory and the Applied Micro and Nanosystems Facility, in the School of Engineering, at the University of British Columbia's, Okanagan campus under the supervision of Dr. Jonathan F. Holzman. Portions of this dissertation have appeared in published work.  This dissertation is largely based on my work [J4, J5, J9, J10, J13], for which I was principal investigator under the supervision of Dr. Jonathan F. Holzman. I was responsible for the relevant manuscript preparation and revisions. The following statements explain the co-authorship of the publications incorporated in this dissertation. Chapter 2 contains my work from three journal articles [J9, J10, J13]. For journal article [J13], I fabricated and assembled the device, acquired the experimental results, and interpreted the results according to theoretical modeling. For journal article [J10], I fabricated and assembled the device, designed the system with a DC-shifted AC-three-phase biasing mechanism and carried out the theoretical and experimental investigations, with the assistance of D. Guerrero. For journal article [J9], I fabricated and assembled the device, experimentally tested the material impulse response and theoretically analyzed the input response, with the assistance of C. M. Collier, J. J. A. Garbowski, and B. Born. C. M. Collier and B. Born were involved in the material impulse response measurements, and J. J. A. Garbowski was involved in the device fabrication. Chapter 3 contains my work from one journal article [J4]. I carried out the theoretical and experimental investigations for ultrafast retro-modulation characterization of spherical optical wireless transceivers, with the assistance of B. A. Hristovski, C. M. Collier, S. Geoffroy-Gagnon, and B. Born. B. A. Hristovski and C. M. Collier were involved in the ultrafast retro-modulation v  experiment, and S. Geoffroy-Gagnon and B. Born were involved in the MIE theory simulations. Appendix B contains my work from one journal article [J5]. I fabricated the microlenses used for optical wireless imaging characterization and carried out the theoretical and experimental investigations, with the assistance of D. Guerrero. D. Guerrero was involved in the fabrication of the microlens.    Publication List Book Chapters B1. X. Jin and J. F. Holzman, "Multi-directional optical sensing using differential triangulation," in: Smart Sensors for Industrial Applications, Part I Photonic and Optoelectronics Sensors: Chapter 10, pp. 155–175, K. Iniewski, Eds.: CRC Press, May 2013. (Invited) (reprinted in Advances in Imaging and Sensing, Part II Imaging Sensors and Systems: Chapter 14, S. Tang, S. Daryoosh, and K. Iniewski, Eds.: CRC Press, Sept. 2016. (Invited))  B2. X. Jin, A. Arafa, B. A. Hristovski, R. Klukas, and J. F. Holzman, "Differential photosensors for optical wireless communication and location technologies," in Optical Imaging Devices: New Technologies and Applications, Chapter 9, pp. 207–234, A. Khosla and D. Kim, Eds.: CRC Press, Oct. 2015. (Invited)  Refereed Journal Articles J1. Z. Wang, X. Jin, R. Dai, J. F. Holzman, and K. Kim, "An ultrafast hydrogel photocrosslinking method for direct laser bioprinting," RSC Advances, vol. 6, pp. 21099–211104, Feb. 2016. vi  J2. M. H. Bergen, A. Arafa, X. Jin, R. Klukas, and J. F. Holzman, "Characterization of angular precision and dilution of precision for optical wireless positioning," IEEE/OSA J. Lightwave Technol., vol. 33, no. 20, pp. 4253–4260, Oct. 2015.  (Front cover of the journal) J3. A. Arafa, X. Jin, M. Bergen, R. Klukas, and J. F. Holzman, "Characterization of image receivers for optical wireless location technology," IEEE Photonics Technol. Lett., vol. 27, no. 18, pp. 1923–1926, Sept. 2015. J4. X. Jin, B. A. Hristovski, C. M. Collier, S. Geoffroy-Gagnon, B. Born, and J. F. Holzman, "Ultrafast all-optical technologies for bi-directional optical wireless communications," Opt. Lett., vol. 40, no. 7, pp. 1583–1586, Apr. 2015.  J5. X. Jin, D. Guerrero, R. Klukas, and J. F. Holzman, "Microlenses with tuned focal characteristics for optical wireless imaging," Appl. Phys. Lett., vol. 105, no. 3, 031102, Jul. 2014.  J6. M. H. Bergen, J. Nichols, C. M. Collier, X. Jin, B. Raja, D. J. Roberts, P. Ruchhoeft, R. C. Willson, and J. F. Holzman, "A retroreflective imaging system for optical labelling and detection of microorganisms," Appl. Opt., vol. 53, no. 17, pp. 3647–3655, Jun. 2014. (reprinted in the Virtual J. Biomed. Opt., vol. 9, no. 8, pp. 3647–3655, Jul. 2014) J7. C. M. Collier, B. Born, X. Jin, and J. F. Holzman, "Ultrafast charge-carrier and phonon dynamics in GaP," Appl. Phys. Lett., vol. 103, 072106, Aug. 2013.  J8. C. M. Collier, B. Born, M. Bethune-Waddell, X. Jin, and J. F. Holzman, "Ultrafast photoexcitation and transient mobility of GaP for photoconductive terahertz emission," IEEE J. Quantum Electron., vol. 49, no. 8, pp. 691–696, Aug. 2013.  J9. X. Jin, C. M. Collier, J. J. A. Garbowski, B. Born, and J. F. Holzman, "Ultrafast transient characteristics of optical wireless communication sensors," Appl. Opt., vol. 52, no. 20, pp. vii  5042–5049, Jul. 2013.  J10. X. Jin, D. Guerrero, and J. F. Holzman, "Enhanced link directionality for optical wireless communications," IEEE Photonics Technol. Lett., vol. 24, no. 24, pp. 2225–2228, Dec. 2012.  J11. C. M. Collier, X. Jin, and J. F. Holzman, "Ultrafast refractometry for nanocomposite material systems," IEEE Photonics Technol. Lett., vol. 24, no. 7, pp. 590–592, Apr. 2012.  J12. A. Arafa, X. Jin, and R. Klukas, "Wireless optical positioning with a differential photosensor," IEEE Photonics Technol. Lett., vol. 24, no. 12, pp. 1027–1029, Jun. 2012.  J13. X. Jin and J. F. Holzman, "Multitone photoconductive sensors for free-space optics," IEEE Photonics J., vol. 2, no. 4, pp. 659–669, Aug. 2010.  J14. X. Jin and J. F. Holzman, "Differential retro-detection for remote sensing applications," IEEE Sensors J., vol. 10, no. 12, pp. 1875–1883, Dec. 2010. (Front cover of the journal)  J15. X. Jin, J. E. Barg, and J. F. Holzman, "Retro-detective control structures for free-space optical communication links," Opt. Express, vol. 17, no. 26, pp. 23867–23872, Dec. 2009.  J16. C. M. Collier, X. Jin, J. F. Holzman, and J. Cheng, "Omni-directional characteristics of composite retroreflectors," J. Opt. A: Pure Appl. Opt., vol. 11, no. 8, 085404, Aug. 2009.  Refereed Conference Proceedings C1. M. H. Bergen, D. Guerrero, X. Jin, B. A. Hristovski, H. Chaves, R. Klukas, and J. F. Holzman, "Design and optimization of indoor optical wireless positioning systems," SPIE Proceedings of Photonics West, vol. 9754, 97540A, San Francisco, USA, Feb. 2016. C2. X. Jin, B. A. Hristovski, C. M. Collier, S. Geoffroy-Gagnon, B. Born, and J. F. Holzman, "Spherical transceivers for ultrafast optical wireless communications," SPIE Proceedings of Photonics West, vol. 9744, 97440F, San Francisco, USA, Feb. 2016. viii  C3. M. H. Bergen, J. Nichols, C. M. Collier, X. Jin, and J. F. Holzman, "Retroreflective imaging systems for enhanced optical biosensing," SPIE Proceedings of Photonics Europe, vol. 9129, 912914, Brussels, Belgium, Apr. 2014. C4. A. Arafa, X. Jin, D. Guerrero, R. Klukas, and J. F. Holzman, "Imaging sensors for optical wireless location technology," Proceedings of Institute of Navigation GNSS, pp. 1020–1023, Nashville, USA, Sept. 2013. C5. X. Jin, D. Guerrero, R. Klukas, and J. F. Holzman, "Micro-optical elements for optical wireless applications," SPIE Proceedings of Optics + Photonics, vol. 8841, 88410, San Diego, USA, Aug. 2013. C6. X. Jin, C. M. Collier, J. J. A. Garbowski, B. Born, and J. F. Holzman, "Ultrafast transient characteristics of photoconductive elements for optical wireless communications," SPIE Proceedings of Optics + Photonics, vol. 8847, 884710, San Diego, USA, Aug. 2013. C7. C. M. Collier, B. Born, X. Jin, T. M. Westgate, M. Bethune-Waddell, M. H. Bergen, and J. F. Holzman, "Transient mobility and photoconductive terahertz emission with GaP," SPIE Proceedings of Optics + Photonics, vol. 8846, 884616, San Diego, USA, Aug. 2013. C8. C. M. Collier, B. Born, X. Jin, and J. F. Holzman, "Ultrafast spectroscopy of hot electron and hole dynamics in GaP," SPIE Proceedings of Optics + Photonics, vol. 8845, 88450U, San Diego, USA, Aug. 2013.  C9. A. Arafa, R. Klukas, X. Jin, and J. F. Holzman, "Towards a practical indoor lighting positioning system," Proceedings of Institute of Navigation GNSS, pp. 2450–2453, Nashville, USA, Sept. 2012.   C10. X. Jin, C. M. Collier, B. W. D. Veerman, and J. F. Holzman, "Enhanced field of view and speed characteristics for optical wireless devices," Proceedings of IEEE Photonics ix  Society Summer Topical Meetings, pp. 136–137, Seattle, USA, Jul. 2012. C11. X. Jin, D. Guerrero, and J. F. Holzman, "Three-phase photoconductive elements for directional optical sensing," SPIE Proceedings of Photonics West, vol. 8257, 82570R, San Francisco, USA, Jan. 2012. C12. C. M. Collier, X. Jin, B. Born, and J. F. Holzman, "Ultrafast optical analyses and characteristics of nanocomposite media," SPIE Proceedings of Photonics West, vol. 8260, 826012, San Francisco, USA, Jan. 2012. C13. A. Arafa, X. Jin, and R. Klukas, "A differential photosensor for indoor optical wireless positioning," Proceedings of GNSS 24th International Technical Meeting of the Satellite Division of The Institute of Navigation, pp. 1758–1763, Portland, USA, Sept. 2011. C14. J. E. Barg, X. Jin, M. Wiltshire, M. Abolhasani, and J. F. Holzman, "Photoconductive sensors for distributed optical sensing," Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, pp. 1–4, Calgary, Canada, May 2010. C15. X. Jin, J. E. Barg, and J. F. Holzman, "An integrated optical control and communication system for free-space environments," SPIE Proceedings of International conference on Optical Instrument and Technology, vol. 7506, 75060M, Shanghai, China, Oct. 2009. C16. X. Jin, C. M. Collier, J. F. Holzman, and J. Cheng, "Modulation and directionality characteristics of free-space optical transmission Links," IEEE Proceedings of International Conference on Electro/Information Technology, pp. 3–8, Windsor, Canada, Jun. 2009.   Presentations P1. Z. Wang, X. Jin, R. Dai, R. Samanipour, J. F. Holzman, and K. Kim, "Laser diode-based ultrafast crosslinking of cell-encapsulated gelatin methacrylate hydrogels," 10th World x  Biomaterials Congress, Montreal, Canada, May 2016.  P2. X. Jin and J. F. Holzman, "Ultrafast photoconductive sensors for optical wireless technologies," Presentation at Communications Microelectronics Optoelectronics Sensors Emerging Technologies Research Symposium, Whistler, Canada, Jul. 2013. (Invited) P3. X. Jin, C. M. Collier, B. Born, M. Beaudoin, S. K. O'Leary, and J. F. Holzman, "Semiconductor-polymer nanocomposite materials for ultrafast photodetectors," Presentation at Canadian Institution of Photonic Innovations (CIPI) Annual General Meeting (AGM), Ottawa, Canada, May 2011.   Thesis T1. Xian Jin, "Integrated optical devices for free-space optical (FSO) communications," Master’s Thesis, The University of British Columbia, Dec. 2009.	       xi  Table of Contents  Abstract ......................................................................................................................................... iii	Preface ........................................................................................................................................... iv	Table of Contents ......................................................................................................................... xi	List of Tables .............................................................................................................................. xiv	List of Figures ...............................................................................................................................xv	List of Abbreviations ............................................................................................................. xxviii	Acknowledgements ....................................................................................................................xxx	Dedication ................................................................................................................................ xxxii	Chapter 1: Introduction ................................................................................................................1	1.1	 Background and motivation ............................................................................................ 1	1.2	 Scope of this dissertation ................................................................................................ 8	Chapter 2: Multi-directional Corner-Cube Photoconductive Transceivers ..........................11	2.1	 Transceiver design ........................................................................................................ 11	2.2	 Transceiver analyses: Photodetection ........................................................................... 14	2.2.1	 Theoretical analyses ................................................................................................ 14	2.2.2	 Experimental analyses of the directionality characteristics ..................................... 42	2.2.2.1   Multitone photoconductive sensing ................................................................ 42	2.2.2.2   Three-phase photoconductive sensing ............................................................ 51	2.2.3	 Experimental analyses of the ultrafast transient characteristics .............................. 59	2.2.3.1   Material impulse response .............................................................................. 60	2.2.3.2   Geometrical input response ............................................................................. 63	xii  2.2.3.3   Overall device response .................................................................................. 67	2.3	 Transceiver analyses: Retro-modulation ....................................................................... 72	2.3.1    Theoretical analyses ................................................................................................ 73	2.3.2    Experimental analyses ............................................................................................. 75	2.4	 Summary ....................................................................................................................... 77	Chapter 3: Multi-directional Spherical Optical Wireless Transceivers .................................80	3.1	 Transceiver design ........................................................................................................ 80	3.2	 Transceiver analyses: Photodetection ........................................................................... 83	3.2.1   Theoretical analyses ................................................................................................... 83	3.2.2   Experimental analyses of the directionality characteristics ....................................... 85	3.2.3   Experimental analyses of the ultrafast transient characteristics ................................ 88	3.2.3.1   Material impulse response .............................................................................. 88	3.2.3.2   Geometrical input response ............................................................................. 89	3.2.3.3   Overall device response .................................................................................. 95	3.3	 Transceiver analyses: Retro-modulation ..................................................................... 100	3.3.1   Theoretical analyses ................................................................................................. 103	3.3.2   Experimental analyses ............................................................................................. 107	3.4	 Summary ..................................................................................................................... 113	Chapter 4: Conclusion ...............................................................................................................114	4.1	 Summary of contributions ........................................................................................... 114	4.2	 Future work ................................................................................................................. 117	Bibliography ...............................................................................................................................120	Appendices ..................................................................................................................................134	xiii  Appendix A Integrated Corner-cube Photosensor .................................................................. 134	Appendix B Microlenses with Tuned Focal Characteristics for Optical Wireless Imaging ... 136	Appendix C Ray-tracing Model for a Spherical Microlens .................................................... 148	Appendix D Three-phase AC Circuit Design ......................................................................... 152	Appendix E Photoconductive Device Microfabrication Processes ........................................ 155	Appendix F Time-resolved Pump-probe Reflectivity Measurement ...................................... 157	Appendix G Mathematical Expressions of Incident Optical Power for Individual PCs ......... 160	Appendix H Matlab Ray-tracing Code for Retroreflected Power of a CC-PC Transceiver ... 162	Appendix I Derivation of Transient Optical Power of the CC-PC Transceiver ..................... 167	xiv  List of Tables   Table 2.1 Theoretical incident optical power expressions for the PC1, PC2, and PC3 switches                   are tabulated for illumination directional cosine conditions that have azimuthal                   and polar angles in the range of 0° < φ < 90° and 0° < θ < 90°, respectively. The                   expressions shown here are normalized. ...................................................................... 41	Table 2.2 Theoretical incident optical power expressions for the PC1, PC2, and PC3 switches                   are tabulated for a polar angle of θ ≈ 54.7° and azimuthal angles in the range of                   0° < φ < 90°. The illumination cases lead to the two displayed illumination                   directional cosine conditions. The expressions shown here are normalized. .............. 46	Table B.1 Theoretical vs. experimental comparison of focal length and NA for the                   acute-angle microlens, α = 30°, right-angle microlens, α = 90°, and obtuse-angle                        microlens, α = 120°, normalized by r. ....................................................................... 145	Table C.1 Parameters defined for the ray-tracing model of a general spherical microlens are                    listed. .......................................................................................................................... 149	 xv  List of Figures   Figure 1.1 Schematics are shown for OWC systems using the (a) point-to-point                    implementation and (b) broadcasting implementation. The outdoor point-to-point                    implementation typically employs lasers, while the indoor broadcasting                    implementation typically employs LEDs. ..................................................................... 3	Figure 1.2 The two operational modes for OWC systems are shown as the (a) active                    downlink operational mode and (b) passive uplink operational mode. ........................ 4	Figure 1.3 The flowchart that is shown depicts the organization of this dissertation. .................. 10	Figure 2.1 Schematics are shown in an exploded view (left) and an assembled view (right)                    for the CC-PC transceiver. The CC-PC transceiver consists of three mutually-                   orthogonal PC switches that are biased via three external bias voltages. ................... 13	Figure 2.2 The schematic (left) and photograph (right) of the CC-PC transceiver are shown.                   Illumination by light rays is shown for an AOA along the central axis of                    symmetry, i.e., an azimuthal angle of φ = 45° and a polar angle of θ ≈ 54.7°. ......... 14	Figure 2.3 Schematics are shown for the internal reflection process of PC1 onto PC2 onto PC3                    occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow                    (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in                    blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds                     as (a) 2n1 ≥ (n2 + n3), (b) (n3 - 2n2) ≤ 2n1 < (n2 + n3), (c) 2n1 < (n3 - 2n2). ............. 19 Figure 2.4 Schematics are shown for the internal reflection process of PC1 onto PC3 onto PC2                    occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow xvi                    (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in                   blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds                    as (a) 2n1 ≥ (n2 + n3), (b) (n3 - 2n2) ≤ 2n1 < (n2 + n3), (c) 2n1 < (n3 - 2n2). .............. 22	Figure 2.5 Schematics are shown for the internal reflection process of PC2 onto PC1 onto PC3                   occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow                   (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in                   blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds                    as (a) 2n2 ≥ (n1 + n3), (b) (n3 - 2n1) ≤ 2n2 < (n1 + n3), (c) 2n2 < (n3 - 2n1). .............. 27	Figure 2.6 Schematics are shown for the internal reflection process of PC2 onto PC1 onto PC3                    occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow                   (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in                    blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds                    as (a) 2n2 ≥ (n1 + n3), (b) (n3 - 2n1) ≤ 2n2 < (n1 + n3), (c) 2n2 < (n3 - 2n1). .............. 31	Figure 2.7 Schematics are shown for the internal reflection process of PC3 onto PC1 onto PC2                   occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow                    (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in                   blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds                    as (a) 2n3 ≥ (n1 + n2), (b) (n2 - 2n1) ≤ 2n3 < (n1 + n2), (c) 2n3 < (n2 - 2n1). .............. 36	Figure 2.8 Schematics are shown for the internal reflection process of PC3 onto PC2 onto PC1                    occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow                     (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in                    blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds  xvii                    as (a) 2n3 ≥ (n1 + n2), (b) (n2 - 2n1) ≤ 2n3 < (n1 + n2), (c) 2n3 < (n2 - 2n1). .............. 40	Figure 2.9 Schematics are shown for the CC-PC transceiver's (a) biasing arrangement and (b)                    electronic processing system. The CC-PC transceiver consists of three mutually-                   orthogonal PC switches that are biased as shown in (a) with three distinct                    frequencies, f1-3. The resulting output photocurrents are then amplified (via a                   feedback resistor RL) and electronically filtered with the system shown in (b). ........ 45	Figure 2.10 Theoretical photocurrent amplitudes, I1(φ,θ), I2(φ,θ) and I3(φ,θ), are plotted for the                    CC-PC transceiver, for a polar angle of θ ≈ 54.7° and azimuthal angles in the                    range of 0° < φ < 90°. Experimental data points, given a 5 m optical link, are                    shown as solid circles for a polar angle of θ ≈ 54.7°and azimuthal angles of                    φ ≈ 20°, φ ≈ 45° and φ ≈ 70°. The results are normalized. ...................................... 47	Figure 2.11 The experimental setup used to record the output photocurrent from a distant                    optical source is shown. The collimated laser beam is expanded to uniformly                    illuminate the CC-PC transceiver. The biasing is provided at three distinct                    frequencies, and the output photocurrent, iout(t), is recorded and processed by a                    DAQ system with an oscilloscope interface. .............................................................. 49	Figure 2.12 Experimental frequency-domain photocurrents for the CC-PC transceiver are                    shown for PC1, PC2, and PC3. Misaligned results are shown for (a) φ ≈ 20°,                   θ ≈ 54.7° and (b) φ ≈ 70°, θ ≈ 54.7°, with differing signal strengths, while well-                   aligned results are shown for (c) φ = 45°, θ ≈ 54.7°, with the balanced/equal signal                    strengths. The insets show the CC-PC transceiver as viewed from the source for                    the respective orientations. .......................................................................................... 50	xviii  Figure 2.13 Three DC-shifted AC3φ waveforms bias the CC-PC transceiver. The incident                    optical beam (with an AOA into the page for the shown orientation) forms output                    photocurrents on the recessed vertex electrode. HP and LP filters are applied to                    extract the respective AC, IAC(φ,θ), and DC, IDC(φ,θ), output photocurrent                    amplitudes, and the mixer yields an output photocurrent. Representative HP and                    LP filtered output photocurrent waveforms are shown for (a) well-aligned and (b)                    misaligned orientations. .............................................................................................. 52	Figure 2.14 Theoretical results are shown as surface plots as a function of the azimuthal angle,                    φ, and polar angle, θ, for the (a) DC output photocurrent amplitudes, IDC(φ,θ), and                     (b) AC output photocurrent amplitudes, IAC(φ,θ). The results are normalized. ......... 55	Figure 2.15 Output photocurrent amplitude profiles are shown for (a) θ ≈ 54.7° and (b) φ =                    45°. Theoretical output photocurrent amplitudes, IAC(φ,θ) and IDC(φ,θ), are                    displayed as dotted and dashed lines, respectively. The theoretical output                    photocurrent amplitudes, Iout(φ,θ), is shown as a solid line. Experimental AC, DC                    and output photocurrent amplitudes are shown as discrete data points. The results                   are normalized. ............................................................................................................ 56	Figure 2.16 Theoretical output photocurrent amplitudes, Iout(φ,θ), are shown versus azimuthal                    φ and polar θ angles. The results are normalized. ....................................................... 57	Figure 2.17 AC and DC output photocurrents of the CC-PC transceiver are shown for (a) an                    optimal orientation at φ = 45° and θ ≈ 54.7°, (b) a slight misaligned orientation                    at φ ≈ 55° and θ ≈ 54.7°, and (c) a severe misaligned orientation at φ ≈ 65° and                    θ ≈ 54.7°. The figure insets show the CC-PC transceiver as viewed from the  xix                    illumination source at the respective orientations. The results are normalized. ......... 58	Figure 2.18 The time-resolved pump-probe setup for the differential transmissivity                    measurements is shown with a pump beam wavelength of (a) 390 nm and                     (b) 780 nm. ................................................................................................................. 62 Figure 2.19 Material impulse responses are shown as normalized transient photoconductivity,                    σ(t), for (a) 390 nm (violet) and (b) 780 nm (red) pump photoexcitation, with                    respective pump fluences of 20 µJ/cm2  and 40 µJ/cm2 on the GaAs PC gaps. The                    GaAs electronic bandstructure is shown in the insets, with the relevant                    photoexcitation transitions and intervalley scattering processes. ............................... 63	Figure 2.20 Responses are shown for a CC-PC transceiver with a side-length of a = 5 mm.                    The geometrical input response is shown as the normalized transient optical power,                    P(t), on the PC gaps for (a) 390 nm (violet) and (b) 780 nm (red) photoexcitation.                    The resulting overall response is shown as the normalized output photocurrent,                    iout(t), for (c) 390 nm (violet) and (d) 780 nm (red) photoexcitation. The figure                    inset at the lower right corner of each figure shows the CC-PC transceiver as                    viewed from the optical source. .................................................................................. 66	Figure 2.21 Responses are shown for a CC-PC transceiver with a side-length of a = 1 mm.                    The geometrical input response is shown as the normalized transient optical power,                    P(t), on the PC gaps for (a) 390 nm (violet) and (b) 780 nm (red) photoexcitation.                    The resulting overall response is shown as the normalized output photocurrent,                    iout(t), for (c) 390 nm (violet) and (d) 780 nm (red) photoexcitation. The figure                    inset at the lower right corner of each figure shows the CC-PC transceiver as                    viewed from the optical source. .................................................................................. 68	xx  Figure 2.22 Responses are shown for a CC-PC transceiver with a side-length of a = 10 mm.                    The geometrical input response is shown as the normalized transient optical power,                   P(t), on the PC gaps for (a) 390 nm (violet) and (b) 780 nm (red) photoexcitation.                    The resulting overall response is shown as the normalized output photocurrent,                    iout(t), for (c) 390 nm (violet) and (d) 780 nm (red) photoexcitation. The figure                    inset at the lower right corner of each figure shows the CC-PC transceiver as                    viewed from the optical source. .................................................................................. 69	Figure 2.23 Overall response times for the CC-PC transceiver are shown for a side-length, a,                    ranging from 1 to 10 mm, with triangles and diamonds demarcating 390 nm                     (violet) and 780 nm (red) photoexcitation, respectively. The inset in the lower                    right corner shows the CC-PC transceiver as viewed from the source. ...................... 70	Figure 2.24 The retroreflection process is shown with the CC-PC transceiver. The incident                    light rays enter the CC-PC transceiver along (-n1, -n2, -n3), and the retroreflected                    light rays exit the CC-PC transceiver along (n1, n2, n3), anti-parallel to the incident                   direction. ..................................................................................................................... 73	Figure 2.25 The (a) 3-D view and (b) 2-D view of the theoretical normalized retroreflected                    power are shown as a surface varying with azimuthal, φ, and polar, θ, angles. Both                    figures are produced from the Matlab ray-tracing model shown in Appendix H. ...... 76	Figure 2.26 A schematic of the retro-modulation experimental setup is shown. The CC-PC                    transceiver is illuminated by a uniform laser beam with a Pi-cell LC optical                    modulator mounted over its entrance interface. The encoded and retroreflected                    beam is then sampled by a beamsplitter and photodetector. ....................................... 77	Figure 2.27. Experimental (a) time-domain and (b) frequency-domain waveforms for the  xxi                    retroreflected optical power level returned to the optical source are shown for                    continuous laser illumination with a Pi-cell LC optical modulator on the CC-PC                    transceiver. The results are shown for the optimal alignment with φ  = 45° and θ ≈                    54.7° given a 5 m optical link. The insets show the CC-PC transceiver as viewed                    from the source. .......................................................................................................... 78	Figure 3.1 Schematics are shown as (a) an oblique view and (b) a top view of the SP-PC                    transceiver (not to scale).  The SP-PC transceiver consists of three radial and                    equally-spaced PC switches, a SP-RR, and a substrate, which also acts as an                    aperture. Each PC switch is activated with a bias voltage, and each has a gap width                    of w and a gap length of l. The distance from the geometrical centre of each PC                    gap to the geometrical centre of the SP-RR is defined as a∆. The incident optical                    beams illuminate the SP-PC transceiver along azimuthal angle, φ, and polar angle,                    θ, as defined by the xyz-coordinate system in the figure. ........................................... 82	Figure 3.2 Transmittance is shown as a function of wavelength, λ, for N-BK7 (n = 1.51), N-                   LASF9 (n = 1.85), and S-LAH79 (n = 2.00) materials (from left to right). The                    figure inset shows refractive indices as a function of wavelength, λ, for N-BK7 (n                    = 1.51) [90], N-LASF9 (n = 1.85) [91], and S-LAH79 (n = 2.00) [92] materials. ..... 83	Figure 3.3 Theoretical incident power on each PC gap is shown as a function of the polar                    angle, θ, ranging from 0º to 90º. The results are normalized. ..................................... 85	Figure 3.4 A schematic of the experimental setup for photodetection is shown with the SP-                   PC transceiver. Three power supplies are connected to the three PC switches to                    provide voltage biasing. The output photocurrent, iout(t), is sampled by way of the  xxii                    common inner electrode through the substrate and processed by a DAQ system                    with an oscilloscope. ................................................................................................... 86	Figure 3.5 Proof-of-principle results for the SP-PC transceiver with DC voltage biasing are                    shown. Individual photocurrents and the summed output photocurrent, iout(t), are                    shown on the primary vertical axis and secondary vertical axis as a function of                    time, respectively. The figure inset shows the SP-PC transceiver (not to scale) as                    viewed from the source. .............................................................................................. 87	Figure 3.6 The material impulse response is shown as the normalized transient                    photoconductivity, σ(t), for (a) 390 nm (violet) and (b) 780 nm (red) pump                    photoexcitation, with respective pump fluences of 20 µJ/cm2  and 40 µJ/cm2 on the                    GaAs PC gaps of SP-PC transceiver. The GaAs electronic bandstructure is shown                    in the insets with the relevant photoexcitation transitions and intervalley                    scattering processes. .................................................................................................... 91	Figure 3.7 Responses are shown for the SP-PC transceiver, having any distance, a∆, from the                    geometrical centre of each PC gap to the geometrical centre of the SP-RR, with                    illumination along φ  = 0° and θ = 0°. The geometrical input response is shown in                     (a) as the incident optical power, P(t), on the PC gaps for both 390 nm (violet)                    and 780 nm (red) photoexcitation. The resulting overall response is shown as the                    output photocurrent, iout(t), for (b) 390 nm (violet) and (c) 780 nm (red)                    photoexcitation. The results are normalized. The figure inset shows the SP-PC                    transceiver (not to scale) as viewed from the source. ................................................. 92	Figure 3.8 Responses are shown for the SP-PC transceiver, having a distance of a∆ ≈ 4.33                    mm from the geometrical centre of each PC gap to the geometrical centre of the  xxiii                    SP-RR, with illumination along φ  = 45° and θ ≈ 54.7°. The geometrical input                    response is shown in (a) as the incident optical power, P(t), on the PC gaps for                    both 390 nm (violet) and 780 nm (red) photoexcitation. The resulting overall                    response is shown as the output photocurrent, iout(t), for (b) 390 nm (violet) and (c)                    780 nm (red) photoexcitation. The results are normalized. The figure inset shows                    the SP-PC transceiver (not to scale) as viewed from the source. ................................ 93	Figure 3.9 Responses are shown for the SP-PC transceiver, having a distance of a∆ ≈ 0.17                    mm from the geometrical centre of each PC gap to the geometrical centre of the                    SP-RR, with illumination along φ  = 45° and θ ≈ 54.7°. The geometrical input                    response is shown in (a) as the incident optical power, P(t), on the PC gap for both                    390 nm (violet) and 780 nm (red) photoexcitation. The resulting overall response is                    shown as the output photocurrent, iout(t), for (b) 390 nm (violet) and (c) 780 nm                    (red) photoexcitation. The results are normalized. The figure inset shows the SP-                   PC transceiver (not to scale) as viewed from the source. ........................................... 94	Figure 3.10 The overall response time of the SP-PC transceiver is shown for a SP-PC                     transceiver having a distance from the geometrical centre of each PC gap to the                     geometrical centre of the SP-RR, a∆, ranging from 0.17 mm to 4.33 mm, with                     triangles and diamonds for the respective 390 nm (violet) and 780 nm (red)                     photoexcitation. The figure inset shows the SP-PC transceiver (not to scale)                     as viewed from the source. ......................................................................................... 99	Figure 3.11 Schematics are shown of the SP-PC transceiver, as (a) an oblique view and (b) a                     cross-sectional view. A collimated incident signal beam illuminates the SP-RR,  xxiv                     at an azimuthal angle, φ, and polar angle, θ, with respect to the xyz-coordinate                     system. This forms a retroreflected signal beam that returns to the source. A local                     control beam illuminates the SP-RR's rear interface to apply all-optical modulation                     to the signal beam. A bandpass dichroic filter (not shown) passes the 1550 nm                     signal beam and blocks the 780 nm local control beam. In this design, the                     substrate in the xy-plane acts as an aperture. ........................................................... 102	Figure 3.12 The ray-tracing model is shown for the characterization of the SP-RR with                     respect to the refractive index, n. An incident light ray runs parallel to the OA,                     and it is focused by the entrance interface, reflected by the rear interface, and re-                    collimated by the entrance interface for return to the source (being anti-parallel to                     the incident light ray). .............................................................................................. 105 Figure 3.13 The (a) incident signal intensity, Is(z = –a), at the rear interface of the SP-RR,                     and (b) retroreflected signal intensity, Is(z = L), following propagation back                     toward the source, are shown versus the SP-RR refractive index, n. Ray-tracing                     model simulations are shown as figure insets for N-BK7 (n = 1.51), N-LASF9                      (n = 1.85), and S-LAH79 (n = 2.00) SP-RRs. ........................................................ 109	Figure 3.14 A schematic of the time-resolved impulsive excitation setup is shown (not to                     scale). The retroreflected signal intensity, Is(t), is recorded as a function of the                     time delay, t, between pulses in the signal beam (yellow) and control beam (red).                     The figure shows the 1550/780 nm pulsed laser source, delay stage,                     neutral-density variable filter, photodetector, dichroic filter, beamsplitter,                     and SP-PC transceiver. ............................................................................................. 110 Figure 3.15 Retroreflected signal intensity, Is(t), versus time, t, is shown for retro-modulation  xxv                     with the N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00) SP-                     RRs, listed here from the weakest signal intensity (bottom) to the strongest (top).. 111	Figure 3.16 Modulation on the retroreflected signal power, ΔPs, is shown in a function of the                     (peak) local control beam intensity, Ic, with squares, triangles, and diamonds                     denoting N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00) SP-                    RRs, respectively. .................................................................................................... 112	Figure A.1 A bi-directional OWC system is shown in (a) with an LED as the light source.                    The CC-based photosensor is shown in the inset. The OWL system is shown in                     (b) with two optical sources. .................................................................................... 135	Figure B.1 Schematics of the (a) electro-dispensing system and (b) microlens configuration                    above the CMOS image sensor. SEM images are shown in (b) of the acute-angle                     (α = 30°), right-angle (α = 90°), and obtuse-angle (α = 120°) microlenses,                    left to right, and the CMOS image sensor array, with a pixel size of 6 × 6 µm2                     and a representative 25 µm diameter focal spot. ...................................................... 138	Figure B.2 Cross-sectional profile of the spherical microlens. Optical rays are incident at an                    angle, θ, off the OA. The focal point of the rays is defined by an axial focal                    length, f(θ), and off-axial focal deflection, ρ(θ). The image on the image sensor is                    defined by an axial focal contraction, ∆f(θ), and off-axial focal spot size, ∆ρ(θ). ... 141	Figure B.3 Theoretical ray-tracing results, versus incident angle, θ, for the (a) axial focal                    length, f(θ), and (b) axial focal contraction, ∆f(θ). Experimental axial focal length                    results are shown in (a) as a discrete cross, circle and star at θ = 0°for the acute-,                    right-, and obtuse-angle microlenses, respectively. All results are normalized  xxvi                    with respect to the microlens radius, r. ..................................................................... 142	Figure B.4 Theoretical ray-tracing results, versus incident angles, θ, for the (a) off-axial                    focal deflection, ρ(θ), and (b) off-axial focal spot size, ∆ρ(θ). Experimental off-                   axial focal deflection results are shown in (a) as discrete crosses, circles and stars                    for the acute-, right-, and obtuse-angle microlenses, respectively. All results are                    normalized with respect to the microlens radius, r. .................................................. 143	Figure C.1 Cross-sectional profile of a spherical microlens is shown with the ray-tracing                    model solutions. Optical rays are incident at a polar angle, θ, off the OA, and                    contact angle, α, of a spherical microlens is defined from 30° to 120° in this                    model. ........................................................................................................................ 148	Figure D.1 AC3φ circuit is designed. The generated AC3φ voltages are delivered to individual                    PC switches via respective op-amps. ........................................................................ 152	Figure D.2 The LTspice schematic of the AC3φ circuit is shown with the calculated values for                    resistors and capacitors. (Op-amps are not shown.) ................................................. 153	Figure D.3 Photograph of the AC3φ circuit. (Op-amps are not shown.) ..................................... 153	Figure D.4 The LTspice simulation results of the designed AC3φ circuit. .................................. 154	Figure D.5 Photograph of the oscilloscope display of the output of the built AC3φ circuit.                    All three outputs are seen to have the identical frequency and amplitude. ............... 154	Figure F.1 A time-resolved pump-probe reflectivity setup is shown for probing the ultrafast                    carrier dynamics in a GaAs wafer. ............................................................................ 158	Figure F.2 The Labview user interface is shown for the time-resolved pump-probe                    reflectivity experiment. The semi-insulating GaAs material response is shown in  xxvii                    the top Channel 1 window. ....................................................................................... 158	Figure F.3 The A block diagram of the Labview program is shown for the time-resolved                    pump-probe reflectivity measurement. ..................................................................... 159	Figure I.1 A schematic is shown for the direct illumination on PC2 gap. The optical beams                    are incident along the central axis of symmetry and passing through the entrance                    interface along the line B1B2 (shown as a blue dashed triangular) to strike the                    entire PC2 gap. The illuminated PC2 gap is shown in green. .................................... 168	Figure I.2 Schematics are shown for the single-reflection illumination on PC2 gap as a two-                   step illustration. The incident optical beams, along the central axis of symmetry,                    first strike the PC1 Au surface along the line B3B4 (shown in (a)) and then reflect                    off the PC1 Au surface to strike the PC2 gap along B4B5 (shown in (b)).                    The illuminated PC2 gap is shown in green. ............................................................. 171	Figure I.3 Schematics are shown for the double-reflection illumination on PC2 gap as a three-                   step illustration. The incident optical beams, along the central axis of symmetry,                    first strike the PC3 surface along the line B6B7 (shown in (a)), reflected onto PC1                    surface along the line B7B8 (shown in (b)), and ultimately partially illuminate the                    PC2 gap along the line B8B9 (shown in (c)). The illuminated PC2 gap is shown in                    green, and the unilluminated PC2 gap is shown in grey. .......................................... 172	 xxviii  List of Abbreviations  Abbreviations                                    Definitions 2-D     Two-Dimensional 3-D     Three-Dimensional AC     Alternating Current AOA     Angle-of-Arrival CC     Corner-Cube  CMOS     Complementary Metal–Oxide–Semiconductor CW     Continuous Wave DAQ     Data Acquisition DC     Direct Current FOV     Field-of-View FWHM    Full-Width-at-Half-Maximum GaAs                               Gallium Arsenide HP     High Pass LC     Liquid Crystal  LED     Light-Emitting Diode LOS                                                     Line-of-Sight LP     Low Pass            MEMS    Micro-Electro-Mechanical Systems MQW      Multiple-Quantum-Well  NA     Numerical Aperture xxix  NOA     Norland Optical Adhesive OA     Optical Axis OWC                                                   Optical Wireless Communications PC     Photoconductive PD     Photodiode RR     Retroreflector SEM     Scanning Electron Microscope SNR     Signal-to-Noise Ratio SP     Spherical UV     Ultraviolet  xxx  Acknowledgements      I am very deeply grateful to many individuals. Without their support, the projects could not possibly have been completed.     I am deeply grateful to thank my dissertation supervisor, Dr. Jonathan F. Holzman, for his encouragement, support, enthusiasm, guidance and friendship. His helpful suggestions and patience throughout my graduate studies have made this dissertation possible. I will continue to be influenced by his rigorous scholarship, clarity in thinking, and professional integrity.  I would like to thank Dr. Lawrence R. Chen, from McGill University, for his willingness to serve as my external examiner. It is my great honour to have such an expert on my committee. I would also like to thank Drs. Kenneth Chau, Richard Klukas, and Murray Neuman for their willingness to serve on the committee. I have appreciated their time and constructive comments over the past few years. I would also like to express my thanks to Dr. Julian Cheng for his constructive comments and valuable suggestions during my graduate studies at the University of British Columbia.  Many thanks to the technical support from David J. Arkinstall, Marc Nadeau, Tim Giesbrecht, Emily Zhang, and School of Engineering for providing the facilities and research spaces to fabricate and test the devices presented in this dissertation.  Special thanks go to Xuegui Song and Christopher M. Collier for being good friends and for their insightful comments and suggestions on my Ph.D. researches. I would also like to thank my dear colleagues, Mingbo Niu, Luanxia Yang, Arafa Ahmed, Brandon Born, Xuan Gao, Wenbo Zheng, Jackie Nichols, Zongjie Wang, Changle Zhu, Mark H. Bergen, Daniel Guerrero, Jamie J. A. Garbowski, Mitch Westgate, and Niu Liu, for sharing their expertise and viewpoints with me. xxxi  I would also like to thank my dear friends, Blago A. Hristovski, Ilija Hristovski, Simon Geoffroy-Gagnon, Max Bethune-Waddell, Hugo Chaves, Trevor Stirling, Cong Xu, Kai Zhang, Zhenlin Tian, and Hao Liu, at the University of British Columbia for all of their assistance, insight, encouragement and support during my Ph.D. journey.      Finally, special thanks are owed to my parents and parents-in-law for their understanding, patience and support over all these years of education, both morally and financially. I wish to acknowledge my dear wife, Yiwen Wu, for her invaluable and thoughtful support over all these years. Without their support and encouragement, all of my achievements would not be possible. xxxii  Dedication                                   To my loving wife, Yiwen,    and loving sons, Aiden and Evan         1  Chapter 1: Introduction 1.1 Background and motivation This dissertation depicts a paradigm shift that is underway in optical communications. Optical communication systems in prior generations have been dominated largely by optical fibres [1–4]. Such fibres have been integrated with optical transmitters and receivers in a straightforward manner—mainly because typical fibre-based systems operate over a narrow spectrum (spanning wavelengths of 1490 to 1650 nm [5]) with minimal directional dependence (because lasers and photodetectors simply require focusing [6, 7] or butt-coupling [8]). For this reason, the predominant metric for fibre-based systems has been operational speed. However, this is changing with the introduction of optical wireless technologies. Optical wireless systems make use of visible and infrared links to support communication through free-space. These links have great potential—given that the high carrier frequencies of visible and infrared waves support broadband (and unlicensed)1 data transmission and the use of free-space connectivity allows for mobile operation. However, it should be noted that optical wireless systems have added considerations. First, optical wireless transceivers are often designed to support multi-wavelength operation. Multi-wavelength operation enables wavelength division multiplexing for higher aggregate bit rates [9–12] and diversity reception for reduced bit error rates [13–17], but it can also impact the overall performance. This is especially true for emerging visible light communication systems that use wavelengths across the visible spectrum [18–21]). Second, optical wireless receivers must be designed to support multi-directional operation. This consideration emerges from the decentralized nature of the wireless communication environment [22–25]. Transmitters can be spread across the environment, and it                                                 1 These optical wireless links are also less susceptible to multipath fading and co-channel interference [24]. 2  is necessary for the receiver to maintain a line-of-sight link to these transmitters. Third, and finally, it is necessary for the optical wireless systems to support high-speed operation. This is an ever-present demand for communication systems. Advancements have been made over the years to develop optical wireless technologies that can meet the above demands. The remainder of this chapter summarizes these optical wireless technologies. The (arguably) first optical wireless communication (OWC) system was introduced in 1880 by way of Alexander Graham Bell's Photophone. The Photophone made use of intensity-modulated light to transmit sounds over a distance of 213 m through the air [26, 27]. In 1957, Braunstein, from Radio Corporation of American, took this one step further by implementing a simple OWC system with a GaAs light-emitting diode (LED) sending modulated audio from a record player to a distant PbS photodiode [28, 29]. With the invention of laser in 1960s, OWC technology saw dramatic improvements because of the coherent and collimated nature of laser beams. Many OWC links were demonstrated [30, 31]. For example, at M.I.T.'s Lincoln Labs, a television signal was transmitted by way of a GaAs diode over a distance of 30 miles through free-space [30–32]. Developments of OWC technology stalled in the 1970s, however, with the invention of low-loss optical fibre. With this fibre, it became straightforward to implement long-haul optical data transmission [31]. Demands have changed in recent years, however, as there is exponential growth in the use of wireless systems [33, 34] and with this growth we see a resurgence of interest in OWC technology. The OWC systems that are being developed have two common implementations. The first form for OWC links uses a point-to-point implementation [35–37]. It is shown in Figure 1(a). These (typically) outdoor links are applicable to dense urban environments. The links are a solution to the "last-mile problem" [38], for which there is a reluctance to install 3  optical fibre networks over short distances. In addition, the links are effective for remote environments, for which there is little existing communication infrastructure. These laser-based links typically operate through the air over kilometre-long distances. For this reason, they are subject to eye-safety restrictions [24] as well as atmospheric turbulence [39–41].  The second form for OWC links uses a broadcasting implementation. It is shown in Figure 1(b). These (typically) indoor links use LEDs as transmitters [19, 42–44] that broadcast optically-encoded data to distributed receivers [21, 45]. Visible [46] or infrared [47] links can be used here, but there is particularly strong interest in operating these systems with visible LEDs—as it then becomes possible to piggyback the data onto existing LED-based lighting [43, 45, 48]. The second (broadcasting) implementation employed for OWC systems is the major focus of this dissertation. It has two operational modes [49]. The first operational mode is the active downlink mode. It is shown in Figure 1.2(a). In this case, optical information is encoded on optical                                          (a)                (b) Figure 1.1 Schematics are shown for OWC systems using the (a) point-to-point implementation and (b) broadcasting implementation. The outdoor point-to-point implementation typically employs lasers, while the indoor broadcasting implementation typically employs LEDs.  4          (a)  (b) Figure 1.2 The two operational modes for OWC systems are shown as the (a) active downlink operational mode and (b) passive uplink operational mode.   beams being sent from the optical transmitters to the remote receivers. This uni-directional operation is practically challenging for mobile systems, however, as misalignment by the remote receivers can lead to link failures. Furthermore, if bi-directional operation is desired, it becomes necessary for the remote receiver to transmit an optical beam back to the transmitter. Unfortunately, such operation yields high power consumption for the remote receivers, which are typically battery-operated. The second operational mode is the passive uplink mode. It is shown in Figure 1.2(b). This bi-directional system has the remote receivers detect the incident optical signals coming from the optical transmitters, using a simple photodetector, and at the same time retroreflect and modulate a portion of the incident optical beam for its return back to the optical transmitters with the encoded data. This bi-directional passive uplink is attractive, as it can have the remote receivers operate with minimal directional dependence (as retroreflection is largely insensitive to the incident beam's orientation [50]) and low power consumption (as there is no need for the receivers to emit optical power to send data back to the optical transmitters [51].     It is important to note that the technologies for active downlink and passive uplink operations 5  become particularly challenging when the transceivers are integrated as compact devices. The attempts to overcome these challenges can be seen in the development of "Smart Dust" technology [52]. This technology was first proposed by Pister, Kahn, and Boser from the University of California, Berkeley, in 1997. The millimetre-scale "Smart Dust" motes carried out communications via three elements: a photodetector for signal photodetection, a micro-electro-mechanical systems (MEMS) corner-cube-retroreflector (CC-RR) for passive signal retroreflection, and a MEMS beam-deflection element for mechanical beam modulation. The mote could provide multi-directional communications in a multitude of OWC active downlink and passive uplink applications [53]. More recently, O'Brien from the University of Oxford proposed an alternative form [54, 55]. The team's "Smart Dust" mote consisted of a photodetector for signal photodetection, CC-RRs for passive signal retroreflection, and a liquid crystal (LC) shutter for signal modulation. All of these millimetre-scale components were assembled on an integrated chip to form an OWC transceiver that could support photodetection for active downlinks and modulated retroreflection for passive uplinks. Since these early works, there have been major efforts to analyze and improve the performance of OWC transceivers. The efforts have targeted the three fundamental processes of OWC transceivers: photodetection (for active downlinks), retroreflection (for passive uplinks), and modulation (for passive uplinks). The following paragraphs elaborate on these processes. The first fundamental process for an OWC transceiver is photodetection. It is critical to the operation of active downlinks, and operational speed is its key metric. Reverse biased photodiodes (PDs) are commonly employed for this to convert the incident optical power to measurable electrical photocurrents [56–58]. These PDs typically have large active areas, to collect as much incident optical power as possible and form an appreciable signal level, but these 6  large active areas also lead to large junction capacitances, being on the order of picofarads [24, 59]. This diminishes the operational speed and bandwidth, which has remained on the gigahertz scale for active downlinks [60]. As an alternative, photoconductive (PC) switches have been considered for multi-directional OWC active downlinks. These light-activated optoelectronic devices can convert incident optical power into electrical photocurrents with high responsivities [61] and ultrashort (picosecond) response times [62]. The PC switches operate in a non-rectified (i.e., voltage-biased) manner with two metal electrodes on either side of a semi-insulating semiconductor gap. The electrodes have a bias voltage applied across them. Thus, with photoexcitation, the semiconductor gap is "shorted" and a voltage pulse is formed on the output electrode of the PC gap. The operational speed of such PC switches (neglecting the external electrical response times) is limited mainly by the electron-hole lifetime, which is set by the rate of electron-hole recombination. With this in mind, there has been a great deal of effort to develop ultrafast semiconductor materials with ultrashort lifetimes, including low-temperature grown GaAs [63–65] and radiation-damaged Silicon [66, 67]). In this dissertation, photodetection is considered specifically for OWC systems—for which it becomes necessary to understand the effects (if any) of the multi-wavelength and multi-directional operation. The second fundamental process for an OWC transceiver is retroreflection. It is critical to the operation of passive uplinks, and directionality is its key metric. A likely candidate to employ for this is the simple CC-RR. It has three mutually-orthogonal reflective surfaces (typically mirrors) that form an interior corner. The structure can reflect incident light beams back to their sources, as the incident rays' Cartesian components are reversed by each of the three reflective surfaces [68]. Retroreflection in the CC-RR is largely independent of incident angles as long as its operation is restricted to a solid angle of π/2 steradians, i.e., it is illuminated into the interior 7  corner spanning one-eighth of the full 4π solid angle. The CC-RR has been the main structure used by OWC researchers. O'Brien et al. at the University of Oxford integrated a CC-RR into their "Smart Dust" mote with an external optical modulator to implement OWC operation in bi-directional passive uplinks [54]. Zhou et al. at the University of California, Berkeley, fabricated quadruple MEMS CC-RRs, with a structure-assisted assembly technique, to form a transceiver for their "Smart Dust" mote [69]. Won et al., from Yonsei University, Korea, recently developed a piezoelectrically-actuated quadruple MEMS CC-RR that is packaged within a multichip module for use in OWC networks [70]. It is also worthnoting an alternative form of the RR, being the "cat's eye" RR, that has been tested in OWC systems. The cat's eye RR consists of multiple refractive optical elements and a reflective surface to implement retroreflection. The cat's eye RR has increased directionality over that of the CC-RR, being 2π/3 steradians [71], but its implementation to OWC systems may suffer from diffraction and aberration—as well as the significant complexity of its fabrication. Nonetheless, Rabinovich et al. from the U. S. Naval Research Laboratory have applied the cat's eye RR with an electro-absorption modulator to demonstrate OWC operation with an effective directionality of π/6 steradians [72]. In this dissertation, a completely different form of RR will be considered. It is the spherical- (SP-) RR [73–76]. The SP-RR refracts an incoming optical beam at its entrance interface, reflects the focused optical beam at its rear interface, and re-collimates the reflected optical beam at its entrance interface to return the beam back to its source. The key to this operation is the selection of an appropriate refractive index. If the design is successful, the SP-RR can be made to support retroreflection over the full 4π steradians of the sphere. The third fundamental process for an OWC transceiver is modulation. It is critical to the operation of passive uplinks, and modulation speed is the key metric. Modulation is used to 8  encode the optical data at the remote transceiver for its return back to the source, and several techniques have been utilized to accomplish this. Kahn et al. at the University of California, Berkeley, demonstrated mechanically-deflected mirrors on the remote transceivers to inhibit retroreflection and thereby modulate the light being reflected back to the source [69, 77, 78]. O'Brien et al. at the University of Oxford used a LC modulator [55] for low-power modulation. However, it should be noted that the modulation speeds of these mechanical and LC modulators are restricted to a millisecond timescale, i.e., operate up to kilohertz data rates, and this is well below the potential of high-speed OWC links. With this in mind, an electrical modulator was used by Rabinovich et al. from U. S. Naval Research Laboratory [79, 80]. The researchers demonstrated an OWC link operating at a wavelength of 1550 nm over a distance of 2 km by using a multiple-quantum-well (MQW) absorber to modulate the retroreflected beam at rates up to 5 Mbit/s [81]. The major success of this project was its demonstration of modulation on a nanosecond timescale, which ultimately came about from the use of electrical (rather than mechanical) switching of the absorber. This system was the state-of-the-art implementation for bi-directional OWC links. There is interest to further improve the modulation speed, however, and that is a major pursuit of this dissertation. In this dissertation, all-optical switching will be employed for ultrafast optical modulation in bi-directional OWC links. The work here will have a local control beam modulate the incident signal beam during the retroreflection process to encode optical data on a femtosecond timescale. This implementation has the potential to facilitate OWC operation at terabit-per-second rates.  1.2 Scope of this dissertation In this dissertation, two architectures for OWC transceivers are developed for use in OWC 9  systems. Efforts are made to ensure that the developed compact OWC transceivers support multi-wavelength and multi-directional operation in active downlinks (via photodetection with PC switches) and passive uplinks (via retroreflection and modulation). The structure of this dissertation is shown as a flowchart in Figure 1.3 and described here.     Chapter 1 presents the background of OWC systems. Details are given on the major developments and key metrics for OWC systems. Chapter 2 introduces a new architecture for OWC transceivers, being the CC-PC transceiver. The architecture has a CC form with integrated PC switches. The photodetection capabilities of the CC-PC transceiver are characterized first for uni-directional OWC operation in active downlinks. The complete theoretical analysis on the directional-dependent photodetection is presented, followed by the demonstration of two PC sensing techniques, being multitone PC sensing and three-phase PC sensing. These two techniques are implemented to enhance the directionality of the transceiver. The transient characteristics of photodetection for the CC-PC transceiver are also investigated, and design considerations are given for use of this transceiver in future ultrafast OWC implementations (that will seek broad spectral and directional characteristics). The retroreflection and modulation capabilities of the CC-PC transceiver are demonstrated next for bi-directional OWC operation in passive uplinks. The retroreflective nature of the CC-PC transceiver is used to retroreflect the encoded signal back to its source with an external LC modulator. Theoretical and experimental analyses of the retroreflection are carried out to characterize the directionality of this transceiver in passive uplinks. Chapter 3 introduces a second architecture for OWC transceivers, being the SP-PC transceiver. This architecture has three PC switches integrated with a SP-RR. The photodetection capability of the SP-PC transceiver is characterized first for uni-directional OWC operation in 10  active downlinks. Theoretical analyses on the directional-dependent photodetection are carried out, followed by proof-of-principle experimental analyses at the optimal orientation. The transient characteristics of photodetection for the SP-PC transceiver are also characterized, and design considerations are given on the use of the SP-PC transceiver in future ultrafast OWC implementations (that will seek broad spectral and directional characteristics). The retroreflection and modulation capabilities of the SP-PC transceiver are characterized next for bi-directional OWC operation in passive uplinks. The SP-RR and its all-optical modulation scheme are shown to facilitate the desired broad retroreflection and ultrafast modulation. Chapter 4 concludes the dissertation. A summary is given on the contributions of this dissertation, as well as suggestions for future work.    Figure 1.3 The flowchart that is shown depicts the organization of this dissertation. 11  Chapter 2: Multi-directional Corner-Cube Photoconductive Transceivers  A new form of CC-PC transceiver is introduced in this chapter for OWC applications. This new transceiver extends the capability of the PD-based CC-RR from my Master's work [23]. The employment of the PC switches improves the detected signal levels and the device response time over the PDs, and at the same time, its high-reflectivity metal coating enhances the retroreflected power over the silicon surface of the PDs. The architecture consists of three independent and mutually orthogonal PC switches arranged in an interior corner. It is shown to support photodetection, for uni-directional OWC operation in active downlinks, as well as retroreflection and modulation, for bi-directional OWC operation in passive uplinks. The requirements of retroreflection and modulation are associated with each other and will simply be referred to as retro-modulation in the remainder of this dissertation. The following subsections show the design and analyses of the proposed CC-PC transceiver. Section 2.1 presents its design. Section 2.2 analyzes its photodetection characteristics. Section 2.3 analyzes its retro-modulation characteristics. Section 2.4 summarizes the overall findings.  2.1 Transceiver design  The CC-PC transceiver's design must extend the capabilities of traditional PC switches to multi-directional OWC applications, and it can do this by integrating three PC switches. The three integrated PC switches are displayed in the exploded and assembled views of Figure 2.1. The exploded view of Figure 2.1 shows three independent right-angled PC switches, with PC1 in the y-z plane, PC2 in the x-z plane, and PC3 in the x-y plane. Each PC switch has a side length of a = 5 mm and is comprised of two separate metal electrodes, being sputtered 150-nm-thick Au layers over 50-nm-thick Cr adhesion layers. Au is selected for the electrodes because of its excellent electrical conductivity (4.1 × 107 Sm-1) and high surface reflectivity (96.9% for light at 12  a wavelength of 780 nm). The centre of the PC gap is at a distance2  of b = a/2 = 2.5 mm along the side as measured from the interior vertex. The light-induced photocurrent flows from the bias electrode, across the PC gap, and is measured on the recessed vertex electrode. A small PC gap width of w = 200 µm and a large PC gap length of l ≈ 3.5 mm are selected here to achieve a sufficiently large photocurrent. Semi-insulating GaAs is selected for the semiconductor in the PC gap, because it has a subnanosecond material response time (i.e., charge-carrier lifetime). We have measured the material response time to be approximately τ = 160 ps.3 The measurement used a 780 nm, 100 fs pump-probe reflectivity analysis, according to the experimental details in Appendix F. Semi-insulating GaAs is also selected because of its high resistivity (beyond 107 Ω·cm) and high electron mobility (approximately 8500 cm2V-1s-1). These properties yield a large dark resistance (beyond 40 MΩ) and strong light-induced photocurrent—which ultimately yield a high signal-to-noise ratio (SNR).4  To assemble the device, each right-angled PC switch is bonded with Norland Optical Adhesive (NOA 68) to form an interior corner. The NOA 68 adhesive is cured under an ultraviolet (UV) light while monitoring retroreflection from the structure. The retroreflected beam is monitored over a range of 5 m, and the CC-PC transceiver is adjusted, as needed, during the curing. The final assembled view is shown in Figure 2.1, and a photograph is shown in Figure 2.2. The resulting CC-PC transceiver has three electrically-isolated input bias electrodes,                                                   2 The PC gap is designed to be sufficiently far from the vertex electrodes (seen from Figure 2.1) to avoid reducing the retroreflected power from the CC-PC transceiver. More details can be found later in Section 2.3.1.      3 This charge-carrier lifetime, measured via a pump-probe reflectivity analysis, is lower than the often-reported charge-carrier lifetime of 300 ps [82]. This is because the reflectivity measurements of the probe beam are preferentially sensitive to the pump-induced variations of the refractive index at the surface (for which there will be a hastening of recombination due to surface states).     4 A 100 mW, 780 nm laser diode was employed to characterize the SNR responses for the CC-PC transceiver. The SNRs were found to range from 16 dB to 35 dB for incident optical intensities increasing from 1 mW/cm2 to 40 mW/cm2 [83]. A dark current of 12 nA was measured for a 2 V DC bias during the SNR measurements (without applying any electronic filters).  13  displayed as PC1, PC2, and PC3 bias electrodes, and one common recessed vertex electrode for the summed photocurrent output. The CC-PC transceiver is fixed on a planar substrate (not shown) and mounted on a gyroscope for testing under various optical illumination conditions.     Uniform optical illumination is directed onto the structure along a prescribed angle-of-arrival (AOA), which is defined by an azimuthal angle, φ, and polar angle, θ, as shown in Figure 2.2. Transmission lines are patterned onto the surface of the structure to route electrical biasing to the three input PC bias electrodes. An electrical via-hole is used to extract the output photocurrent, iout(t), from the recessed vertex electrode out the back of the structure. Given a uniform intensity incident over the entire CC-PC transceiver, the individual PC switches respond with increased photoconductivity and this forms three photocurrents, in proportion to (and synchronized with) the three external bias voltages. In general, a PC switch with a given illumination intensity will respond with a proportional conductance and photocurrent across its gap.   Figure 2.1 Schematics are shown in an exploded view (left) and an assembled view (right) for the CC-PC transceiver. The CC-PC transceiver consists of three mutually-orthogonal PC switches that are biased via three external bias voltages.  14   Figure 2.2 The schematic (left) and photograph (right) of the CC-PC transceiver are shown. Illumination by light rays is shown for an AOA along the central axis of symmetry, i.e., an azimuthal angle of φ = 45° and a polar angle of θ ≈ 54.7°.   2.2 Transceiver analyses: Photodetection  The CC-PC transceiver's capabilities for photodetection are analyzed in this subsection. The analyses are motivated by a desire to optimize the directionality and speed of the transceiver, as this will enable effective uni-directional OWC operation in active downlinks. Subsection 2.2.1 presents theoretical analyses on the directionality of the transceiver. Subsections 2.2.2 and 2.2.3 present respective experimental analyses on its directionality characteristics (pertaining to field-of-view (FOV)) and ultrafast transient characteristics (pertaining to speed).   2.2.1 Theoretical analyses     The photodetection process for the CC-PC transceiver will have a directional dependence. The directional dependence can be analyzed by assuming that the incident optical light has a uniform intensity of I0 across the CC-PC transceiver. This leads to three PC photocurrents with (typically) distinct amplitudes. The disparity between the amplitudes is fundamentally due to the imbalances 15  between the incident light rays' directional cosine components, n1 = cosφsinθ, n2 = sinφsinθ, and n3 = cosθ, in the x, y, and z direction, respectively. Each PC gap will capture a distinct power from the optical source: incident light rays with a larger n1 component along the x-axis will preferentially illuminate PC1 gap; incident light rays with a larger n2 component along the y-axis will preferentially illuminate PC2 gap; incident light rays with a larger n3 component along the z-axis will preferentially illuminate PC3 gap. However, quantifying these relationships is complicated by the fact that the incident optical power upon each PC gap will also have contributions from the light rays undergoing the primary and secondary internal reflections from neighbouring PC switches. During these internal reflections, the incident light rays' directional cosine components, n1, n2, and n3, are reversed in the x, y, and z directions, respectively. The complete theoretical response for the incident powers, including contributions from the primary and secondary internal reflections onto each PC gap, is developed here. There is an assumption of an angular-independent surface reflectivity, R, for the Au electrodes. This is deemed to be a good assumption because the angular reflectivity of a Au surface changes by only approximately 1% for incident AOA angles ranging from 0° to 90°.5 The power levels illuminating each PC gap are investigated for primary and secondary internal reflections occurring with six different orders: (1) PC1 onto PC2 onto PC3, (2) PC1 onto PC3 onto PC2, (3) PC2 onto PC1 onto PC3, (4) PC2 onto PC3 onto PC1, (5) PC3 onto PC1 onto PC2, (6) PC3 onto PC2 onto PC1. Each of these cases is also characterized by three subcases. All of these eighteen cases are analyzed here.                                                   5 It is also worth noting that there is a balancing of reflectivities during multiple reflections. The reflection from one Au surface at a glancing angle will be balanced by a reflection at a near-normal angle on the next Au surface.  16      The first case corresponds to the internal reflection order of PC1 onto PC2 onto PC3, which means that the incident light strikes PC1, reflects onto PC2, and then reflects onto PC3. Light rays having undergone these reflections then exit the transceiver to return to the source.     For the first subcase, 2n1 ≥ (n2 + n3), the light rays' unit-normal vectors that are incident on PC1, PC2, and PC3 are             1 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − − , 12 1 2 3ˆ ˆ ˆ ˆr n x n y n z= + − − ,                                                                                                                                                                                                                                                           123 1 2 3ˆ ˆ ˆ ˆr n x n y n z= + + − , (1) respectively, where the unit-normal vectors' subscripts indicate the successive illumination and reflection sequences. Figure 2.3(a) shows the illumination for this subcase with PC1 fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The two corner points in the yz-plane are projected along 12rˆ onto the xz-plane, and the resulting illumination area of PC2 (shown in blue) is defined as the overlap between this projected area and the PC2 surface. For this subcase, the PC2 gap is fully illuminated by the primary reflection (shown in red). Similarly, the PC2 illumination area is projected along 123rˆonto the xy-plane, and the illumination area of PC3 (shown in blue) is defined as the overlap between this projected area and the PC3 surface. For this subcase, the PC3 gap is partially illuminated by the secondary reflection (shown in red). The resulting normal vectors for the illuminated PC gap areas can now be defined for this subcase as                      12 ˆ2A awx= ,      122 ˆ2A awy= ,      17    21231 22 ˆ2nA awzn n=+, (2) where, a is the side length of each PC switch and w is the PC gap width. The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (2) onto the respective light rays' unit-normal vectors in (1). The result is   1 0 1 1 1 02ˆ2P I r A awn I= − ⋅ = ,      12 0 12 12 2 02ˆ2P I r A awn RI= − ⋅ = ,                     22123 0 123 123 3 01 22ˆ2nP I r A awn R In n= − ⋅ =+.  (3) For the second subcase, (n3 – 2n2) ≤ 2n1 < (n2 + n3), the light rays' unit-normal vectors remain the same as those shown in (1). Figure 2.3(b) shows the illumination for this subcase with PC1 still fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The successive reflection illumination areas are referred onto their respective adjoining neighbours. For this subcase, the PC2 gap is partially illuminated by the primary reflection (shown in red) from PC1, which ultimately results in partial illumination onto the PC3 gap (shown in red) from the secondary reflection. The resulting normal vectors for the illuminated PC gap areas can then be defined for this subcase as  12 ˆ2A awx= ,      1122 3 12 ˆ2nA awyn n n=+ −,         2 3 121231 2 1 2 322 ˆ( )2n n nnA awzn n n n n+ −= −+ + +. (4) 18  The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (4) onto the respective light rays' unit-normal vectors in (1). The result is  1 0 1 1 1 02ˆ2P I r A awn I= − ⋅ = ,      112 0 12 12 2 02 3 12ˆ2nP I r A awn RIn n n= − ⋅ =+ −,   22 3 12123 0 123 123 3 01 2 1 2 322ˆ ( )2n n nnP I r A awn R In n n n n+ −= − ⋅ = −+ + +. (5)     For the third subcase, 2n1 < (n3 – 2n2), the light rays' unit-normal vectors remain the same as those shown in (1). Figure 2.3(c) shows the illumination for this subcase. For this subcase, the PC3 gap is completely unilluminated (shown in grey), while the PC1 gap is still fully illuminated (shown in red) and the PC2 gap is partially illuminated (shown in red). The resulting normal vectors for the illuminated PC gap areas can then be written for this subcase as 12 ˆ2A awx= ,     1122 3 12 ˆ2nA awyn n n=+ −,    123 0A = . (6) The resulting incident power levels for PC1, PC2 and PC3 gaps for this subcase are then found from (1) and (6) to be 1 0 1 1 1 02ˆ2P I r A awn I= − ⋅ = ,     19   Figure 2.3 Schematics are shown for the internal reflection process of PC1 onto PC2 onto PC3 occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds as (a) 2n1 ≥ (n2 + n3), (b) (n3 - 2n2) ≤ 2n1 < (n2 + n3), (c) 2n1 < (n3 - 2n2). 20    112 0 12 12 2 02 3 12ˆ2nP I r A awn RIn n n= − ⋅ =+ −,     123 0 123 123ˆ 0P I r A= − ⋅ = . (7) The second case corresponds to the internal reflection order of PC1 onto PC3 onto PC2, which means that the incident light strikes PC1, reflects onto PC3, and then reflects onto PC2. Light rays having undergone these reflections then exit the transceiver to return to the source. For the first subcase, 2n1 ≥ (n2 + n3), the light rays' unit-normal vectors that are incident on PC1, PC3, and PC2 are               1 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − − ,      13 1 2 3ˆ ˆ ˆ ˆr n x n y n z= + − − ,   132 1 2 3ˆ ˆ ˆ ˆr n x n y n z= + − + , (8) respectively, where the unit-normal vectors' subscripts indicate the successive illumination and reflection sequences. Figure 2.4(a) shows the illumination for this subcase with the PC1 fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The two corner points in the yz-plane are projected along 13rˆ onto the xy-plane, and the resulting illumination area of PC3 (shown in blue) is then defined as the overlap between this projected area and the PC3 surface. For this subcase, the PC3 gap is fully illuminated by the primary reflection (shown in red). Similarly, the PC3 illumination area is projected along 132rˆ onto the xz-plane, and the illumination area of PC2 (shown in blue) is then defined as the overlap between this projected area and the PC2 surface. For this subcase, the PC2 gap is partially illuminated by the secondary reflection (shown in red). The resulting normal vectors for the illuminated PC gap area can now be defined for this subcase as 21   12 ˆ2A awx= ,      132 ˆ2A awz= ,    31321 32 ˆ2nA awyn n=+. (9) The corresponding incident power levels associated with each PC gap are then found by projecting the component of these normal vectors in (9) onto the respective reflected light rays' unit-normal vectors in (8). The result is   1 0 1 1 1 02ˆ2P I r A awn I= − ⋅ = ,      13 0 13 13 3 02ˆ2P I r A awn RI= − ⋅ = ,    23132 0 132 132 2 01 32ˆ2nP I r A awn R In n= − ⋅ =+. (10) For the second subcase, (n3 – 2n2) ≤ 2n1 < (n2 + n3), the light rays' unit-normal vectors remain the same as shown in (8). Figure 2.4(b) shows the illumination for this subcase with PC1 still fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The successive reflection illumination areas are referred onto their adjoining neighbours. For this subcase, the PC3 gap is partially illuminated by the primary reflection (shown in red), which ultimately results in a partially illumination onto the PC2 gap (shown in red) from the secondary reflection. The resulting normal vectors for the illuminated PC gap area can then be defined for this subcase as   12 ˆ2A awx= ,     22   Figure 2.4 Schematics are shown for the internal reflection process of PC1 onto PC3 onto PC2 occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds as (a) 2n1 ≥ (n2 + n3), (b) (n3 - 2n2) ≤ 2n1 < (n2 + n3), (c) 2n1 < (n3 - 2n2). 23    1132 3 12 ˆ2nA awzn n n=+ −,     3 2 3 11321 3 1 2 322 ˆ( )2n n n nA awyn n n n n+ −= −+ + +. (11) The corresponding incident power levels associated with each PC gap are then found by projecting the component of these normal vectors in (11) onto the respective reflected light rays' unit-normal vectors in (8). The result is  1 0 1 1 1 02ˆ2P I r A awn I= − ⋅ = ,      113 0 13 13 3 02 3 12ˆ2nP I r A awn RIn n n= − ⋅ =+ −,   23 2 3 1132 0 132 132 2 01 3 1 2 322ˆ ( )2n n n nP I r A awn R In n n n n+ −= − ⋅ = −+ + +. (12) For the third subcase, 2n1 < (n3 – 2n2), the light rays' unit-normal vectors remain the same as those shown in (8). Figure 2.4(c) shows the illumination for this. For this subcase, the PC2 gap is completely unilluminated (shown in grey), while the PC1 gap is still fully illuminated (shown in red) and the PC3 gap is partially illuminated (shown in red). The resulting normal vectors for the illuminated PC gap areas can then be written for this subcase as  12 ˆ2A awx= ,      1132 3 12 ˆ2nA awzn n n=+ −,    132 0A = . (13) The resulting incident power levels for PC1, PC3 and PC2 gaps for this subcase are then found from (8) and (13) to be 24   1 0 1 1 1 02ˆ2P I r A awn I= − ⋅ = ,      113 0 13 13 3 02 3 12ˆ2nP I r A awn RIn n n= − ⋅ =+ −,    132 0 132 132ˆ 0P I r A= − ⋅ = . (14) The third case corresponds to the internal reflection order of PC2 onto PC1 onto PC3, which means that the incident light strikes PC2, reflects onto PC1, and then reflects onto PC3. Light rays having undergone these reflections then exit the transceiver to return to the source.  For the first subcase, 2n2 ≥ (n1 + n3), the light rays' unit-normal vectors that are incident on PC2, PC1, and PC3 are               2 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − − ,       21 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − + − ,   213 1 2 3ˆ ˆ ˆ ˆr n x n y n z= + + − , (15) respectively, where the unit-normal vectors' subscripts indicate the successive illumination and reflection sequences. Figure 2.5(a) shows the illumination for this subcase with PC2 fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The two corner points in the xz-plane are projected along 21rˆ  onto the yz-plane, and the resulting illumination area of PC1 (shown in blue) is then defined as the overlap between this projected area and the PC1 surface. For this subcase, the PC1 gap is fully illuminated by the primary reflection (shown in red). Similarly, the PC1 illumination area is projected along 213rˆonto the xy-plane, and the illumination area of PC3 (shown in blue) is then defined as the overlap between this projected area and the PC3 surface. For this subcase, the PC3 gap is partially 25  illuminated by the secondary reflection (shown in red). The resulting normal vectors of the illuminated PC gap areas can now be defined for this subcase as  22 ˆ2A awy= ,      212 ˆ2A awx= ,   12131 22 ˆ2nA awzn n=+. (16) The corresponding incident power levels associated with each PC gap are then found by projecting the component of these normal vectors in (16) onto the respective reflected light rays' unit-normal vectors in (15). The result is   2 0 2 2 2 02ˆ2P I r A awn I= − ⋅ = ,      21 0 21 21 1 02ˆ2P I r A awn RI= − ⋅ = ,   21213 0 213 213 3 01 22ˆ2nP I r A awn R In n= − ⋅ =+. (17)     For the second subcase, (n3 – 2n1) ≤ 2n2 < (n1 + n3), the light rays' unit-normal vectors remain the same as those shown in (15). Figure 2.5(b) shows the illumination for this subcase with PC2 still fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The successive reflection illumination areas are referred onto their adjoining neighbours. For this subcase, the PC1 gap is partially illuminated by the primary reflection (shown in red), which ultimately results in partial illumination on the PC3 gap (shown in red) from the secondary reflection. The resulting normal vectors for the illuminated PC gap areas can then be defined for this subcase as 26   22 ˆ2A awy= ,      2211 3 22 ˆ2nA awxn n n=+ −,   1 3 212131 2 1 2 322 ˆ( )2n n nnA awzn n n n n+ −= −+ + +. (18) The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (18) onto the respective reflected light rays' unit-normal vectors in (15). The result is  2 0 2 2 2 02ˆ2P I r A awn I= − ⋅ = ,      221 0 21 21 1 01 3 22ˆ2nP I r A awn RIn n n= − ⋅ =+ −,    21 3 21213 0 213 213 3 01 2 1 2 322ˆ ( )2n n nnP I r A awn R In n n n n+ −= − ⋅ = −+ + +. (19) For the third subcase, 2n2 < (n3 – 2n1), the light rays' unit-normal vectors remain the same as those shown in (15). Figure 2.5(c) shows the illumination for this subcase. For this subcase, the PC3 gap is completely unilluminated (shown in grey), while the PC2 gap is still fully illuminated (shown in red) and the PC1 gap is partially illuminated (shown in red). The resulting normal vectors for the illuminated PC gap areas can then be written for this subcase as  22 ˆ2A awy= ,      27   Figure 2.5 Schematics are shown for the internal reflection process of PC2 onto PC1 onto PC3 occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds as (a) 2n2 ≥ (n1 + n3), (b) (n3 - 2n1) ≤ 2n2 < (n1 + n3), (c) 2n2 < (n3 - 2n1). 28  2211 3 22 ˆ2nA awxn n n=+ −,    213 0A = . (20)     The resulting incident power levels for PC1, PC3 and PC2 gaps for this subcase are then found from (15) and (20) to be  2 0 2 2 2 02ˆ2P I r A awn I= − ⋅ = ,      221 0 21 21 1 01 3 22ˆ2nP I r A awn RIn n n= − ⋅ =+ −,   213 0 213 213ˆ 0P I r A= − ⋅ = . (21) The fourth case corresponds to the internal reflection order of PC2 onto PC3 onto PC1, which means that the incident light strikes PC2, reflects onto PC3, and then reflects onto PC1. Light rays having undergone these reflections then exit the transceiver to return to the source.  For the first subcase, 2n2 ≥ (n1 + n3), the light rays' unit-normal vectors that are incident on PC2, PC3, and PC1 are               2 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − − ,      23 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − + − ,   231 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − + + , (22) respectively, where the unit-normal vectors' subscripts indicate the successive illumination and reflection sequences. Figure 2.6(a) shows the illumination for this subcase with PC2 fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The two corner points in the xz-plane are projected along 23rˆ  onto the xy-plane, and the resulting illumination area of PC3 (shown in blue) is then defined as the overlap between this 29  projected area and the PC3 surface. For this subcase, the PC3 gap is fully illuminated by the primary reflection (shown in red). Similarly, the PC3 illumination area is projected along 231rˆonto the yz-plane, and the illumination area of PC1 (shown in blue) is defined as the overlap between this projected area and the PC1 surface. For this subcase, the PC1 gap is partially illuminated by the secondary reflection (shown in red). The resulting normal vector for the illuminated PC gap area can now be defined for this subcase as 22 ˆ2A awy= ,     232 ˆ2A awz= ,  32312 32 ˆ2nA awxn n=+. (23) The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (23) onto the respective reflected light rays' unit-normal vectors in (22). The result is   2 0 2 2 2 02ˆ2P I r A awn I= − ⋅ = ,      23 0 23 23 3 02ˆ2P I r A awn RI= − ⋅ = ,   23231 0 231 231 1 02 32ˆ2nP I r A awn R In n= − ⋅ =+. (24)     For the second subcase, (n3 – 2n1) ≤ 2n2 < (n1 + n3), the light rays' unit-normal vectors remain the same as those shown in (22). Figure 2.6(b) shows the illumination for this subcase with PC2 fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is 30  shown in red. The successive reflection illumination areas are referred onto their adjoining neighbours. For this subcase, the PC3 gap is partially illuminated by the primary reflection (shown in red) from PC2, which ultimately results in partial illumination onto the PC1 gap (shown in red) from the secondary reflection from PC3. The resulting normal vectors for the illuminated PC gap areas can then be defined for this subcase as  22 ˆ2A awy= ,      2231 3 22 ˆ2nA awzn n n=+ −,   3 1 3 22312 3 1 2 322 ˆ( )2n n n nA awxn n n n n+ −= −+ + +. (25) The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (25) onto the respective reflected light rays' unit-normal vectors in (22). The result is  2 0 2 2 2 02ˆ2P I r A awn I= − ⋅ = ,      223 0 23 23 3 01 3 22ˆ2nP I r A awn RIn n n= − ⋅ =+ −,   23 1 3 2231 0 231 231 1 02 3 1 2 322ˆ ( )2n n n nP I r A awn R In n n n n+ −= − ⋅ = −+ + +. (26) For the third subcase, 2n2 < (n3 – 2n1), the light rays' unit-normal vectors remain the same as those shown in (22). Figure 2.6(c) shows the illumination for this subcase. For this subcase, the PC1 gap is completely unilluminated (shown in grey), while the PC2 gap is still fully illuminated  (shown in red) and the PC3 gap is partially illuminated (shown in red). The resulting normal  31   Figure 2.6 Schematics are shown for the internal reflection process of PC2 onto PC1 onto PC3 occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds as (a) 2n2 ≥ (n1 + n3), (b) (n3 - 2n1) ≤ 2n2 < (n1 + n3), (c) 2n2 < (n3 - 2n1). 32  vectors for the illuminated PC gap areas can then be written as  22 ˆ2A awy= ,      2231 3 22 ˆ2nA awzn n n=+ −,   231 0A = . (27)     The resulting incident power levels for PC1, PC3 and PC2 gaps for this subcase are then found from (22) and (27) to be  2 0 2 2 2 02ˆ2P I r A awn I= − ⋅ = ,      223 0 23 23 3 01 3 22ˆ2nP I r A awn RIn n n= − ⋅ =+ −,          231 0 231 231ˆ 0P I r A= − ⋅ = . (28) The fifth case corresponds to the internal reflection order of PC3 onto PC1 onto PC2, which means that the incident light strikes PC3, reflects onto PC1, and then reflects onto PC2. Light rays having undergone these reflections then exit the transceiver to return to the source. For the first subcase, 2n3 ≥ (n1 + n2), the light rays' unit-normal vectors that are incident on PC3, PC1, and PC2 are              3 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − − ,      31 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − + ,   312 1 2 3ˆ ˆ ˆ ˆr n x n y n z= + − + , (29) respectively, where the unit-normal vectors' subscripts indicate the successive illumination and reflection sequences. Figure 2.7(a) shows the illumination for this subcase with PC3 fully 33  illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The two corner points in the xy-plane are projected along 31rˆ  onto the yz-plane, and the resulting illumination area of PC1 (shown in blue) is then defined as the overlap between this projected area and the PC1 surface. For this subcase, the PC1 gap is fully illuminated by the primary reflection (shown in red). Similarly, the PC1 illumination area is projected along 312rˆonto the xz-plane, and the illumination area of PC2 (shown in blue) is defined as the overlap between this projected area and the PC2 surface. For this subcase, the PC2 gap is partially illuminated by the secondary reflection (shown in red). The resulting normal vectors for the illuminated PC gap areas can now be defined for this subcase as  32 ˆ2A awz= ,      312 ˆ2A awx= ,   13121 32 ˆ2nA awyn n=+. (30) The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (30) onto the respective reflected light rays' unit-normal vectors in (29). The result is  3 0 3 3 3 02ˆ2P I r A awn I= − ⋅ = ,     31 0 31 31 1 02ˆ2P I r A awn RI= − ⋅ = ,  21312 0 312 312 2 01 32ˆ2nP I r A awn R In n= − ⋅ =+. (31) 34  For the second subcase, (n2 – 2n1) ≤ 2n3 < (n1 + n2), the light rays' unit-normal vectors remain the same as those shown in (29). Figure 2.7(b) shows the illumination for this subcase with PC3 fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The successive reflection illumination areas are referred onto their adjoining neighbours. For this subcase, the PC1 gap is partially illuminated by the primary reflection (shown in red) from PC3, which ultimately results in partial illumination onto the PC2 gap (shown in red) from the secondary reflection from PC1. The resulting normal vectors for the illuminated PC gap areas can then be defined for this subcase as  32 ˆ2A awz= ,      3311 2 32 ˆ2nA awxn n n=+ −,   1 2 313121 3 1 2 322 ˆ( )2n n nnA awyn n n n n+ −= −+ + +. (32) The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (32) onto the respective reflected light rays' unit-normal vectors in (29). The result is  3 0 3 3 3 02ˆ2P I r A awn I= − ⋅ = ,      331 0 31 31 1 01 2 32ˆ2nP I r A awn RIn n n= − ⋅ =+ −,   21 2 31312 0 312 312 2 01 3 1 2 322ˆ ( )2n n nnP I r A awn R In n n n n+ −= − ⋅ = −+ + +. (33) For the third subcase, 2n3 < (n2 – 2n1), the light rays' unit-normal vectors remain the same as those shown in (29). Figure 2.7(c) shows the illumination for this subcase. For this subcase, the 35  PC2 gap is completely unilluminated (shown in grey), while the PC3 gap is still fully illuminated (shown in red) and the PC1 gap is partially illuminated (shown in red). The resulting normal vectors for the illuminated PC gap areas can then be written for this subcase as  32 ˆ2A awz= ,      3311 2 32 ˆ2nA awxn n n=+ −,     312 0A = . (34)     The resulting incident power levels for PC1, PC3 and PC2 gaps for this subcase are then found from (29) and (34) to be  3 0 3 3 3 02ˆ2P I r A awn I= − ⋅ = ,      331 0 31 31 1 01 2 32ˆ2nP I r A awn RIn n n= − ⋅ =+ −,   312 0 312 312ˆ 0P I r A= − ⋅ = . (35) The sixth case corresponds to the internal reflection order of PC3 onto PC2 onto PC1, which means that the incident light strikes PC3, reflects onto PC2, and then reflects onto PC1. Light rays having undergone these reflections then exit the transceiver to return to the source.  For the first subcase, 2n3 ≥ (n1 + n2), the light rays' unit-normal vectors that are incident on PC3, PC2, and PC1 are  3 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − − ,      32 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − + ,   321 1 2 3ˆ ˆ ˆ ˆr n x n y n z= − + + , (36) 36   Figure 2.7 Schematics are shown for the internal reflection process of PC3 onto PC1 onto PC2 occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds as (a) 2n3 ≥ (n1 + n2), (b) (n2 - 2n1) ≤ 2n3 < (n1 + n2), (c) 2n3 < (n2 - 2n1). 37  respectively, where the unit-normal vectors' subscripts indicate the successive illumination and reflection sequences. Figure 2.8(a) shows the illumination for this subcase with PC3 fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The two corner points in the xy-plane are projected along 32rˆ  onto the xz-plane, and the resulting illumination area of PC2 (shown in blue) is then defined as the overlap between this projected area and the PC2 surface. For this subcase, the PC2 gap is fully illuminated by the primary reflection (shown in red). Similarly, the PC2 illumination area is projected along 321rˆonto the yz-plane, and the illumination area of PC1 (shown in blue) is then defined as the overlap between this projected area and the PC1 surface. For this subcase, the PC1 gap is partially illuminated by the secondary reflection (shown in red). The resulting normal vectors for the illuminated PC gap areas can now be defined for this subcase as  32 ˆ2A awz= ,      322 ˆ2A awy= ,   23212 32 ˆ2nA awxn n=+. (37) The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (37) onto the respective reflected light rays' unit-normal vectors in (36). The result is   3 0 3 3 3 02ˆ2P I r A awn I= − ⋅ = ,      32 0 32 32 2 02ˆ2P I r A awn RI= − ⋅ = , 38    22321 0 321 321 1 02 32ˆ2nP I r A awn R In n= − ⋅ =+. (38) For the second subcase, (n2 – 2n1) ≤ 2n3 < (n1 + n2), the light rays' unit-normal vectors remain the same as those shown in (36). Figure 2.8(b) shows the illumination for this subcase with PC3 still fully illuminated. The illuminated Au area is shown in blue and the illuminated PC gap area is shown in red. The successive reflection illumination areas are referred onto their adjoining neighbours. For this subcase, the PC2 gap is partially illuminated by the primary reflection (shown in red) from PC3, which ultimately results in partial illumination onto the PC1 gap (shown in red) from the secondary reflection from PC2. The resulting normal vectors for the illuminated PC gap areas can then be defined for this subcase as  32 ˆ2A awz= ,      3321 2 32 ˆ2nA awyn n n=+ −,   1 2 323212 3 1 2 322 ˆ( )2n n nnA awxn n n n n+ −= −+ + +. (39) The corresponding incident power levels associated with each PC gap are then found by projecting the component of the normal vectors in (39) onto the respective reflected light rays' unit-normal vectors in (36). The result is  3 0 3 3 3 02ˆ2P I r A awn I= − ⋅ = ,      332 0 32 32 2 01 2 32ˆ2nP I r A awn RIn n n= − ⋅ =+ −,   21 2 32321 0 321 321 1 02 3 1 2 322ˆ ( )2n n nnP I r A awn R In n n n n+ −= − ⋅ = −+ + +. (40) 39  For the third subcase, 2n3 < (n2 – 2n1), the light rays' unit-normal vectors remain the same as those shown in (36). Figure 2.8(c) shows the illumination for this subcase. For this subcase, the PC1 gap is completely unilluminated (shown in grey), while the PC3 gap is still fully illuminated (shown in red) and the PC2 gap is partially illuminated (shown in red). The resulting normal vectors for the illuminated PC gap areas can then be written as  32 ˆ2A awz= ,      3321 2 32 ˆ2nA awyn n n=+ −,    321 0A = . (41) The resulting incident power levels for PC1, PC3 and PC2 gaps for this subcase are then found from (36) and (41) to be 3 0 3 3 3 02ˆ2P I r A awn I= − ⋅ = ,   332 0 32 32 2 01 2 32ˆ2nP I r A awn RIn n n= − ⋅ =+ −,  321 0 321 321ˆ 0P I r A= − ⋅ = . (42)     The illumination cases are well-defined for six orders of internal reflections, though each case differs in its three directional cosines. The ultimate incident optical power observed for each PC switch is a result of all the permutations of reflections that accumulate on the PC gaps. For example, the total incident optical power forming the PC1 photocurrent includes five components: (1) the direct incident power, P1, onto the PC1 gap; (2) the reflected power, P21, due to a primary reflection off PC2 onto the PC1 gap; (3) the reflected power, P31, due to a primary reflection off PC3 onto the PC1 gap; (4) the reflected power, P231, due to a primary reflection off  40   Figure 2.8 Schematics are shown for the internal reflection process of PC3 onto PC2 onto PC1 occurring in the CC-PC transceiver. Unilluminated PC areas are shown with yellow (for Au surfaces) and grey (for the GaAs gap). Illuminated PC areas are shown in blue (for Au surfaces) and red (for the GaAs gap). The illumination proceeds as (a) 2n3 ≥ (n1 + n2), (b) (n2 - 2n1) ≤ 2n3 < (n1 + n2), (c) 2n3 < (n2 - 2n1). 41  Table 2.1 Theoretical incident optical power expressions for the PC1, PC2, and PC3 switches are tabulated for illumination directional cosine conditions that have azimuthal and polar angles in the range of 0° < φ < 90° and 0° < θ < 90°, respectively. The expressions shown here are normalized. Illumination directional  cosine conditions Incident optical power on PC1 Incident optical power on PC2 Incident optical power on PC3 1 2 32 ( )n n n< +  1 3 22 ( 2 )n n n< −  1n  12 22 3 1nn Rnn n n++ − 13 32 3 1nn Rnn n n++ − 1 3 22 ( 2 )n n n≥ −  1n  12 22 3 12 321 32 3 11 2 3(2)nn Rnn n nnR nn nn n nn n n++ −+++ −−+ + 13 32 3 12 231 22 3 11 2 3(2)nn Rnn n nnR nn nn n nn n n++ −+++ −−+ + 1 2 32 ( )n n n≥ +  1n  2 32 2 21 3nn Rn R nn n+ ++ 2 23 3 31 2nn Rn R nn n+ ++ 2 1 32 ( )n n n< +  2 1 32 ( 2 )n n n< −  21 11 3 2nn Rnn n n++ − 2n  23 31 3 2nn Rnn n n++ − 2 1 32 ( 2 )n n n≥ −  21 11 3 22 312 31 3 21 2 3(2)nn Rnn n nnR nn nn n nn n n++ −+++ −−+ + 2n  23 31 3 22 131 21 3 21 2 3(2)nn Rnn n nnR nn nn n nn n n++ −+++ −−+ + 2 1 32 ( )n n n≥ +  2 31 1 12 3nn Rn R nn n+ ++ 2n  2 13 3 31 2nn Rn R nn n+ ++ 3 1 22 ( )n n n< +  3 2 12 ( 2 )n n n< −  31 11 2 3nn Rnn n n++ − 32 21 2 3nn Rnn n n++ − 3n  3 2 12 ( 2 )n n n≥ −  31 11 2 32 212 31 2 31 2 3(2)nn Rnn n nnR nn nn n nn n n++ −+++ −−+ + 32 21 2 32 121 31 2 31 2 3(2)nn Rnn n nnR nn nn n nn n n++ −+++ −−+ + 3n  3 1 22 ( )n n n≥ +  2 21 1 12 3nn Rn R nn n+ ++ 2 12 2 21 3nn Rn R nn n+ ++ 3n   42  PC2 followed by a secondary reflection off PC3 onto the PC1 gap; (5) the reflected power, P321, due to a primary reflection off PC3 followed by a secondary reflection off PC2 onto the PC1 gap. Thus, the total incident optical powers, defined by summing the incident optical powers of the subcases in  (3) to (42), are  P1-total = P1 + P21 + P31 + P231 + P321, P2-total = P2 + P12 + P32 + P132 + P312,  P3-total = P3 + P13 + P23 + P123 + P213. (43) The three photocurrents will be proportional to the total incident optical power shown in (43). The expressions for the incident optical powers on each PC gap are normalized with respect to awI0/21/2 and are summarized in Table 2.1 for all the illumination cosine conditions. Appendix G gives a piecewise representation of these incident optical power expressions. The following subsections make use of these incident optical power expressions, with various forms of voltage biasing, to characterize the PC photocurrents.  2.2.2 Experimental analyses of the directionality characteristics It can be seen from the previous subsection that the CC-PC transceiver exhibits directional dependence in its photodetection. The directional dependence must be carefully considered, as sub-optimal alignment of the transceiver towards the source will lead to degraded photodetection in OWC active downlinks. With this in mind, experimental analyses of the CC-PC transceiver are carried out in this subsection on multitone PC sensing and three-phase PC sensing. Both techniques offer a means to mitigate the degradation of photodetection from misalignment.  2.2.2.1   Multitone photoconductive sensing  Multitone PC sensing is investigated first. The technique makes use of distinct frequencies for 43  the three bias voltages of the CC-PC transceiver. This allows the frequency characteristics of the output photocurrent to be used to quantify the level of misalignment in the system. Thus, if desired, the alignment of the CC-PC transceiver can be adjusted to maximize the photodetection. For this study, the CC-PC transceiver is mounted onto an electrically-isolated planar substrate that can be rotated to vary the azimuthal angle, φ, and polar angle, θ, and electrical biasing is applied by way of the arrangement shown in Figure 2.9(a). Transmission lines on the surface of the substrate provide electrical biasing to the three input bias electrodes, each of which is biased by an alternating current (AC) waveform with a distinct frequency of f1, f2, or f3. An electrical via-hole is used to extract photocurrents from the recessed vertex electrode through the back of the transceiver. There will be three distinct photocurrents, defined according to   ii(t) = Ii(φ,θ)cos(2πfit + γi), (44) where Ii(φ,θ) are the directionally-dependent amplitudes and γi = 0° are the phases, for photocurrent flowing through the ith PC gap. The output photocurrent, being the sum of these three photocurrents, is   ∑==31out )()(ii titi  (45) An operational amplifier (op-amp), a data acquisition (DAQ) system and electronic filters are used to extract the broadband frequency signal. The post-detection amplification, digital DAQ, and filtering stages are shown in Figure 2.9(b). Given a uniform intensity over the CC-PC transceiver, the capture cross-section of incident photons for each PC gap (i.e., its incident power) will change as the device is rotated. For example, incident light at a small polar angle, θ ≈ 0°, would yield high photoconductivity in PC3 and a strong photocurrent signal on the recessed vertex electrode at the bias frequency of f3, while the photoconductivity and output signals of PC1 and PC2 would be negligible. Such 44  photoconductive responses will be linear, so the three AC bias signals will appear undistorted and DC-background-free on the recessed vertex electrode—with their photocurrent amplitudes, Ii(φ,θ), weighted in proportion to the incident optical powers on PC1, PC2, and PC3. For expository purposes, the CC-PC transceiver is presented here for a polar angle of θ ≈ 54.7°, being the optimal polar angle for retroreflection and detection, while the azimuthal angle, φ, is varied. The incident optical power expressions for the cases and sub-cases in Table 2.1, for the PC1, PC2, and PC3 switches, are simplified and shown in Table 2.2. Note that the polar angle of θ ≈ 54.7° restricts the illumination directional cosine conditions to only two direct-ray conditions, n1 ≤ n3 ≤ n2 and n2 ≤ n3 ≤ n1, and one reflected-ray condition, 2n3 > (n1 + n2).6  Theoretical photocurrents, being proportional to the incident optical powers with and without internal reflection contributions, are calculated for the use of multitone bias AC voltages, and the theoretical curve sets of three photocurrent amplitudes, I1(φ,θ), I2(φ,θ), and I3(φ,θ), are shown as solid lines (with internal reflection contributions) and dashed lines (without internal reflection contributions) in Figure 2.10, for a polar angle of θ ≈ 54.7° and azimuthal angles ranging over 0° < φ  < 90°. The mapping of the structure's alignment to the PC1, PC2, and PC3 photocurrent amplitudes is apparent in the figure. Given light incident along the x-axis, with φ ≈ 0°, the photocurrent amplitude I2(φ,θ) is negligible, the photocurrent amplitude I1(φ,θ) is maximal, and the photocurrent amplitude I3(φ,θ) is at an intermediate level. Likewise, given light incident along the y-axis, with φ ≈ 90°, the photocurrent amplitude I2(φ,θ) is maximal, the photocurrent amplitude I1(φ,θ) is negligible, and the photocurrent amplitude I3(φ,θ) is at an intermediate level. At both extremes, individual photocurrent amplitudes on solid and dashed lines are overlapped,                                                    6 The other reflected-ray condition, 2n3 < (n1 + n2), is not valid for the polar angle of θ ≈ 54.7° and is ignored.  45   (a)  (b) Figure 2.9 Schematics are shown for the CC-PC transceiver's (a) biasing arrangement and (b) electronic processing system. The CC-PC transceiver consists of three mutually-orthogonal PC switches that are biased as shown in (a) with three distinct frequencies, f1-3. The resulting output photocurrents are then amplified (via a feedback resistor RL) and electronically filtered with the system shown in (b). 46  as there are no internal reflection contributions. Between these extremes there exists the desired balanced condition, at φ = 45°, where all of the photocurrent amplitudes are equal and the total output photocurrent amplitude is a maximum. Individual photocurrent amplitudes on solid and dashed lines are also overlapped, as the internal reflection contributions are balanced at this balanced condition. In between the balanced condition and the extremes, the internal reflection contributions are clearly seen to affect the individual photocurrent amplitudes. The generalized process to align the system to this balanced and optimal state is accomplished in the frequency-domain by way of the multitone frequency biasing arrangement.     The multitone frequency biasing arrangement makes use of a 5 m indoor bi-directional OWC testbed. A continuous wave (CW) 100 mW, 780 nm laser diode is employed as a point-to-point test-source. Such a source provides above-bandgap photon absorption for the 1.43-eV-bandgap of the semi-insulating GaAs. The CC-PC transceiver is activated with AC voltage waveforms on the PC1, PC2, and PC3 bias electrodes using the configuration shown in Figure 2.9(a). The bias  Table 2.2 Theoretical incident optical power expressions for the PC1, PC2, and PC3 switches are tabulated for a polar angle of θ ≈ 54.7° and azimuthal angles in the range of 0° < φ < 90°. The illumination cases lead to the two displayed illumination directional cosine conditions. The expressions shown here are normalized.  Illumination directional cosine conditions           for θ ≈ 54.7° Incident optical power on PC1 Incident optical power on PC2 Incident optical power on PC3 1 3 2n n n≤ ≤  3 1 22 ( )n n n≥ +  21 1 12n Rn R n+ +  32121213212223nnnnnRnnnnnRRnn+++−+++ 32131213231333nnnnnRnnnnnRRnn+++−+++ 2 3 1n n n≤ ≤  3 1 22 ( )n n n≥ +  32121223121113nnnnnRnnnnnRRnn+++−+++ 22 2 22n Rn R n+ +  32132223132333nnnnnRnnnnnRRnn+++−+++  47   Figure 2.10 Theoretical photocurrent amplitudes, I1(φ,θ), I2(φ,θ) and I3(φ,θ), are plotted as solid lines (with internal reflection contributions) and dashed lines (without internal reflection contributions) for the CC-PC transceiver, for a polar angle of θ ≈ 54.7° and azimuthal angles in the range of 0° < φ < 90°. Experimental data points are shown as discrete dots for a polar angle of θ ≈ 54.7° and azimuthal angles of φ ≈ 20°, φ ≈ 25°, φ ≈ 35°, φ ≈ 45°, φ ≈ 55°, φ ≈ 65° and φ ≈ 70°. The results are normalized.  signal for PC1 is Vb1, at a frequency of f1 = 3.3 kHz, the bias signal for PC2 is Vb2, at a frequency of f2 = 1.5 kHz, and the bias signal for PC3 is Vb3, at a frequency of f3 = 2.4 kHz. The biasing frequencies are selected to avoid aliasing between the f1, f2, and f3 fundamental signals and all harmonics. The resulting individual PC photocurrents are then summed at the recessed vertex electrode to produce the output photocurrent defined by (45). The output photocurrent is processed by the electronic amplifier and broadband/narrowband filters shown in Figure 2.9(b). The bandwidth of the narrowband filters is chosen to pass the signal of interest while blocking the neighbouring signals. At the same time, this narrowband filtering blocks extraneous optical noise and background light. 48  To test the photodetection and sensing capabilities of the CC-PC transceiver, the device is uniformly illuminated by the laser diode with an intensity of approximately 45 mW/cm2, and the photocurrents are monitored while the device is rotated in a gyroscope as shown in Figure 2.11. Independent rotations of φ and θ are used, and three representative results are displayed in the frequency-domain in Figure 2.12. Figure 2.12(a) shows results for an orientation with incident light entering at φ ≈ 20° and θ ≈ 54.7°. The CC-PC transceiver, as viewed by the source, is shown in the inset. The imbalance in this misalignment (with PC1 having the greatest illumination and PC2 having the lowest illumination) is apparent in the results. The PC1 photocurrent is the largest peak, followed by the PC3 and PC2 photocurrents which reach 82% and 44% of the PC1 maximum, respectively. The experimental photocurrent amplitudes, i.e., photocurrent peaks at their respective frequencies, are plotted with the theoretical photocurrent amplitudes in Figure 2.10 and are seen to better agree with the solid lines (within 3% error) in comparison with the dashed lines. Figure 2.12(b) shows the results for an orientation of φ ≈ 70° and θ ≈ 54.7°. In this new case, PC2 has the greatest illumination and PC1 the lowest. The imbalance is apparent in the frequency-domain, as the PC3 and PC1 photocurrents reach 88% and 54% of the PC2 maximum. The experimental photocurrent amplitudes are plotted with the theoretical photocurrent amplitudes in Figure 2.10 and are again seen to better agree with the solid lines (within 3% error) in comparison with the dashed lines. More misaligned experimental photocurrent amplitudes are obtained and plotted with the theoretical photocurrent amplitudes in Figure 2.10 at various azimuthal angles of φ ≈ 25°, φ ≈ 35°, φ ≈ 55°, and φ ≈ 65°, with θ ≈ 54.7°. Those experimental results are again seen to better agree with the solid lines (within 2% error) in comparison with the dashed lines.     The alignment-balancing procedure for the CC-PC transceiver is performed by noting 49  disparities in the photocurrent amplitudes and rotating the structure to eliminate these disparities. This process is carried out with the CC-PC transceiver mounted in a gyroscope. Rotations are used to balance the photocurrent amplitudes, and the structure is ultimately left in the well-aligned orientation with θ ≈ 54.7° and φ = 45°. The frequency-domain signal for this orientation is shown in Figure 2.12(c). In this orientation, the structure (shown as viewed by the source in the inset) is balanced, and the photocurrents produced by PC1, PC2, and PC3 are approximately equal (within a 0.2% difference). Such an orientation corresponds to an optical alignment with the incident light rays entering the device along the (-n1, -n2, -n3) = (-1/√3, -1/√3, -1/√3) direction. This orientation is optimal for both maximal signal reception during uni-directional OWC operation in active downlinks (as it can be shown that the output photocurrent is maximized in this balanced orientation [84]) and maximal retroreflection in OWC passive uplinks (as will be shown in section 2.3).  Figure 2.11 The experimental setup used to record the output photocurrent from a distant optical source is shown. The collimated laser beam is expanded to uniformly illuminate the CC-PC transceiver. The biasing is provided at three distinct frequencies, and the output photocurrent, iout(t), is recorded and processed by a DAQ system with an oscilloscope interface. 50                 (a)                                       (b) (c) Figure 2.12 Experimental frequency-domain photocurrents for the CC-PC transceiver are shown for PC1, PC2, and PC3. Misaligned results are shown for (a) " ! 20°, ! ! 54.7° and (b) " ! 70°, ! ! 54.7°, with differing signal strengths, while well-aligned results are shown for (c) " = 45°, ! ! 54.7°, with the balanced/equal signal strengths. The insets show the CC-PC transceiver as viewed from the source for the respective orientations. 05101520251.0 1.5 2.0 2.5 3.0 3.5 4.0Photocurrents (a. u.)Frequency (kHz)Misalignment (! ! 54.7° & " ! 20°) PC2 PC1PC3i2i3i105101520251.0 1.5 2.0 2.5 3.0 3.5 4.0Photocurrents (a. u.)Frequency (kHz)Misalignment (! ! 54.7° & " ! 70°) PC2 PC1PC3i2i3i105101520251.0 1.5 2.0 2.5 3.0 3.5 4.0Photocurrents (a. u.)Frequency (kHz)Optimal alignment (! ! 54.7° &"= 45°)i2 i3 i1PC2 PC1PC351  2.2.2.2   Three-phase photoconductive sensing  A three-phase PC sensing technique is investigated next. The three-phase PC sensing technique is similar to the multitone PC sensing technique in that it wishes to establish effective photodetection during uni-directional OWC operation in active downlinks, but it differs in its implementation. The three-phase PC sensing technique uses a single frequency with three distinct phase shifts to establish photodetection with reduced directional dependence. For the three-phase PC sensing technique, the CC-PC transceiver is fixed to an electrically-isolated substrate, which is subsequently mounted onto a gyroscope facilitating rotation over an azimuthal angle, φ, and polar angle, θ. Transmission lines deliver DC-shifted AC-three-phase (AC3φ) voltage waveforms to the three input bias electrodes: Vb1(t) = Vb [1 + S⋅cos(2πft – 120°)] to PC1, Vb2(t) = Vb [1 + S⋅cos(2πft – 0°)] to PC2, and Vb3(t) = Vb [1 + S⋅cos(2πft + 120°)] to PC3. The bias voltage amplitude is Vb = 1 V, the AC3φ bias voltage frequency is f = 1 kHz, and the scaling factor between the AC and DC bias voltages, S, will be discussed shortly. This yields three distinct photocurrents on the recessed vertex electrode, that are defined as  ii(t) = Ii(φ,θ)[1 + S·cos(2πft + γi)],             (46) where Ii(φ,θ) are the directionally-dependent amplitudes, and γ1 = – 120°, γ2 = 0°, and γ3 = + 120° are the phases, for the photocurrents in the PC gaps denoted by i = 1, 2, and 3. The photocurrents on the recessed vertex electrode are then filtered by high-pass (HP) and low-pass (LP) electronic filters to define an AC output photocurrent amplitude of  ∑=+⋅⋅=31AC )2cos(),(),(iii ftSII γπθφθφ ,            (47) and a DC output photocurrent amplitude of   ∑==31DC ),(),(iiII θφθφ . (48) 52  Representative bias input waveforms and their related AC and DC output photocurrent waveforms are shown in Figures 2.13(a) and (b). Figure 2.13(a) illustrates the contrasting AC and DC output photocurrent amplitudes for a well-    (a)   (b) Figure 2.13 Three DC-shifted AC3φ waveforms bias the CC-PC transceiver. The incident optical beam (with an AOA into the page for the shown orientation) forms output photocurrents on the recessed vertex electrode. HP and LP filters are applied to extract the respective AC, IAC(φ,θ), and DC, IDC(φ,θ), output photocurrent amplitudes, and the mixer yields an output photocurrent. Representative HP and LP filtered output photocurrent waveforms are shown for (a) well-aligned and (b) misaligned orientations. 53  aligned orientation of φ = 45°, θ ≈ 54.7°, corresponding to symmetric illumination about the structure's central axis of symmetry. All PC1-3 gaps capture equal photon flux with the total captured photon flux being a maximum. Thus, the resulting AC individual photocurrents have identical amplitudes, and their three-phase output photocurrent sums to IAC(φ,θ) = 0. At the same time, the DC output photocurrent amplitude, IDC(φ,θ), reaches its maximum value.  Figure 2.13(b) shows contrasting AC and DC output photocurrent amplitudes for a misaligned orientation of φ = 65°, θ ≈ 54.7°, corresponding to asymmetric illumination about the structure's central axis of symmetry. The AC output photocurrent here produces a heightened amplitude IAC(φ,θ). At the same time, a lowered DC output photocurrent amplitude IDC(φ,θ) is observed due to the reduced overall photon flux being captured by the PC1-3 gaps. To quantify the directional dependency of the DC and AC output photocurrents, DC output photocurrents (LP filtered) and AC output photocurrents (HP filtered) are developed by way of the theoretical incident optical powers (in Table 2.1) and the DC-shifted AC3φ bias voltages. The resulting DC output photocurrent amplitudes, IDC(φ,θ), and AC output photocurrent amplitudes, IAC(φ,θ), are shown as a function of the azimuthal angle, φ, and polar angle, θ, in Figures 2.14(a) and (b), respectively. It is seen that the well-aligned orientation of φ = 45° and θ ≈ 54.7°, with symmetric illumination about the structure's central axis of symmetry gives a minimum AC output photocurrent amplitude of IAC(φ,θ) = 0, as the 120°-phase-offset of the AC3φ bias voltages have the photocurrents sum to zero, and a maximum DC output photocurrent amplitude, IDC(φ,θ). As the optical illumination moves away from the well-aligned orientation, the normalized AC output photocurrent amplitudes, IAC(φ,θ), increase while the normalized DC output photocurrent amplitudes, IDC(φ,θ), decrease. To more closely quantify this trend, the normalized AC output photocurrent amplitudes, IAC(φ,θ), (dotted lines) and DC output photocurrent amplitudes, 54  IDC(φ,θ), (dashed lines) are shown at cross-sections for θ  ≈ 54.7° and φ  = 45° in Figures 2.15(a) and (b), respectively. At the well-aligned orientation, with θ  ≈ 54.7° and φ = 45°, the CC-PC transceiver symmetry establishes negligible IAC(φ,θ) and maximal IDC(φ,θ). As the incident AOA deviates from this well-aligned point, the AC and DC output photocurrent amplitudes show monotonic rising and falling trends, respectively. It is desirable to have the CC-PC transceiver operate with minimal directional dependency, i.e., operate independent of φ and θ over a wide range of angles. This would avoid the need to optimize the alignment and reposition the transceiver—as was proposed in the subsection on multitone PC sensing. The negative and positive concavities of the surfaces seen in Figures 2.14(a) and (b), for DC and AC output photocurrent amplitudes, respectively, give a clue on how this may be realized. The CC-PC transceiver can be biased with an appropriate scaling between the DC and AC bias voltages to create a superposition of IDC(φ,θ) and IAC(φ,θ) that has a reduced dependency on φ and θ. This reduced directional dependency is possible only because of the opposing polarities of the DC and AC output photocurrent amplitudes in Figures 2.14(a) and (b). (When these surfaces are appropriately scaled and added, the superimposed surface can be made sufficiently flat.) With this in mind, the aforementioned scaling factor between the AC and DC bias voltages, S, is chosen to form an output photocurrent amplitude, Iout(φ,θ) = IAC(φ,θ) + IDC(φ,θ), that is constant over as wide of a range of angles as possible. Curve fitting is applied in this process, and it is found that S = 2 is the optimal choice, as it yields a flattened response with an R-squared coefficient of 0.999. This output photocurrent amplitude is shown (normalized) as a surface plot in Figure 2.16 versus φ and θ. It is seen here that the CC-PC transceiver achieves a constant output photocurrent amplitude, with a standard deviation of less than 2%, over the ranges 15° < φ < 75° and 35° < θ < 75°.  55   (a)  (b) Figure 2.14 Theoretical results are shown as surface plots as a function of the azimuthal angle, φ, and polar angle, θ, for the (a) DC output photocurrent amplitudes, IDC(φ,θ), and (b) AC output photocurrent amplitudes, IAC(φ,θ). The results are normalized. 56                                               (a)                                                            (b) Figure 2.15 Output photocurrent amplitude profiles are shown for (a) $ ! 54.7° and (b) " = 45°. Theoretical output photocurrent amplitudes, IAC(",$) and IDC(",$), are displayed as dotted and dashed lines, respectively. The theoretical output photocurrent amplitudes, Iout(",$), is shown as a solid line. Experimental AC, DC and output photocurrent amplitudes are shown as discrete data points. The results are normalized.  Experimental tests of the CC-PC transceiver are considered first for a nominal case with equal AC and DC bias voltage amplitudes, i.e., S = 1. A CW 780 nm laser diode is used to direct a uniform intensity of approximately 45 mW/cm2, over the structure for various " and $ angles. Representative AC and DC output photocurrent waveforms are shown in Figure 2.17, for three different azimuthal angles, " = 45°, 55°, and 65°, and a fixed polar angle of ! ' 54.7°. Figure 2.17(a) shows the AC and DC output photocurrent waveforms for the well-aligned orientation of " ' 55° and ! ' 54.7°, and the figure inset shows the orientation of the CC-PC transceiver as viewed from the laser diode. It is clear that the DC output photocurrent amplitude, IDC(",$), is large, while the ,C output photocurrent amplitude, IAC(",$), is negligible.  Figure 2.17(b) shows 0.00.51.015 30 45 60 75Output photocurrent  amplitudes (a. u.) Azimuthal angles (degrees)Exp ComExp ACExp DCIout(!,")IAC(!,")IDC(!,") ! ! 54.7°0.00.51.035 45 55 65 75Output photocurrent  amplitudes (a. u.)Polar angles (degrees)Exp COMexp acexp dcIout(!,")IAC(!,")IDC(!,") ! = 45°57  the AC and DC output photocurrent waveforms at the slightly misaligned orientation of φ ≈ 55° and θ ≈ 54.7°, and the figure inset here shows the misaligned CC-PC transceiver as viewed from the laser diode. For this orientation, the DC output photocurrent amplitude, IDC(φ,θ), has decreased, while the ΑC output photocurrent amplitude, IAC(φ,θ), has increased. Figure 2.17(c) shows the AC and DC output photocurrents at the severely misaligned orientation of φ ≈ 65° and θ ≈ 54.7°, and the figure inset shows the severely-misaligned CC-PC transceiver as viewed from the laser diode. The IDC(φ,θ) has decreased significantly and IAC(φ,θ) has increased significantly, compared to the values achieved with the well-aligned orientation. The extracted AC  and DC output photocurrent amplitudes, IAC(φ,θ) and IDC(φ,θ), are shown in Figure 2.15 as triangles and diamonds, respectively. Figure 2.15(a) shows the output photocurrent amplitudes as a function of    Figure 2.16 Theoretical output photocurrent amplitudes, Iout(φ,θ), are shown versus azimuthal φ and polar θ angles. The results are normalized. 58        (a)                                                                                    (b)     (c) Figure 2.17 AC and DC output photocurrents of the CC-PC transceiver are shown for (a) an optimal orientation at " = 45° and ! ! 54.7°, (b) a slight misaligned orientation at " ! 55° and ! ! 54.7°, and (c) a severe misaligned orientation at " ! 65° and ! ! 54.7°. The figure insets show the CC-PC transceiver as viewed from the illumination source at the respective orientations. The results are normalized. -0.4-0.20.00.20.40.60.81.00.0 1.0 2.0 3.0 4.0Output photocurrents (a. u.)Time (ms)iDC(t)PC2 PC1PC3Optimal alignment(! ! 54.7° & " ! 45°) iAC(t)-0.4-0.20.00.20.40.60.81.00.0 1.0 2.0 3.0 4.0Output photocurrents  (a. u.)Time (ms)Slight misalignment(! ! 54.7° & " ! 55°) PC2 PC1PC3iDC(t)iAC(t)-0.4-0.20.00.20.40.60.81.00.0 1.0 2.0 3.0 4.0Output photocurrents  (a. u.)Time (ms)Severe misalignment(! ! 54.7° & " ! 65°) PC2 PC1PC3iDC(t)iAC(t)59  the azimuthal angle, φ, for a fixed polar angle of θ ≈ 54.7°. Figure 2.15(b) shows the output photocurrent amplitudes as a function of the polar angle, θ, for a fixed azimuthal angle of φ = 45°. It is readily apparent from Figure 2.15 that the well-aligned orientation of φ = 45° and θ ≈ 54.7° gives a negligible ΑC output photocurrent amplitude and maximal DC output photocurrent amplitude. As the incident beam deviates from the well-aligned orientation, along either the azimuthal or polar angles, the respective ΑC and DC output photocurrent amplitudes are seen to rise and fall as predicted. The individual AC and DC theoretical and experimental trends are found to agree, within the system's measurement error of less than 10%. Experimental tests of the CC-PC transceiver are considered next for the case with unequal AC and DC bias voltage amplitudes, i.e., S = 2. The output photocurrent amplitudes are recorded by the mixer as the simple sum of the AC and DC output photocurrent amplitudes, i.e., Iout(φ,θ) = IAC(φ,θ) + IDC(φ,θ). The results for Iout(φ,θ) are shown in Figure 2.15 as discrete squares. It is clear here that the output photocurrent amplitudes, Iout(φ,θ), show a nearly-constant behaviour, with a deviation from the theoretical values of less than 3.5% over the ranges 15° < φ < 75° and 35° < θ < 75°. This directional independency will facilitate photodetection over an especially wide FOV, defined by the ranges 15° < φ < 75° and 35° < θ < 75° and a solid angle of 60° × 40°.  2.2.3 Experimental analyses of the ultrafast transient characteristics The directionality characteristics of the CC-PC transceiver were investigated theoretically and experimentally in the previous subsection for effective OWC operation in active downlinks. Within this subsection the ultrafast transient characteristics of the CC-PC transceiver are studied for photodetection in such OWC active downlinks. The transient characteristics of the CC-PC transceiver are complicated—given that OWC 60  transceivers are often operated with incident light having broadband illumination (potentially spanning the visible spectrum) and multi-directional illumination (in terms of both φ and θ). With this in mind, the CC-PC transceiver is analyzed here by decomposing its operation into a material impulse response and a geometrical input response. The material impulse response is subject to the effects of broadband illumination. This manifests itself as wavelength-dependent time delays in the transient photoconductivity of the semiconductor. The geometrical input response is subject to the effects of multi-directional illumination. This manifests itself as dimension-dependent transit time delays in the illuminating optical power. Delay times associated with the subsequent electrical response, due to transmission lines, cables, and measurement equipment are not considered in this work. The CC-PC transceiver, introduced in section 2.1, is uniformly illuminated by incident optical beams from surrounding optical transmitters, and bias voltages are applied to the three input electrodes. The output photocurrent, iout(t), is collected at the recessed vertex electrode. The overall response of the CC-PC transceiver is a single output photocurrent, and it will be the convolution of the material impulse response and the geometrical input response. The details of these responses are shown in the following subsections.  2.2.3.1   Material impulse response     The material impulse response is defined by the transient photoconductivity of the GaAs PC gaps upon illumination by an ultrafast optical pulse. This transient photoconductivity is studied here with a pump-probe differential transmission analysis, by way of an ultrashort-pulse laser system (FemtoFiber Laser, Toptica Photonics, 100 fs, 90 MHz). The time-resolved pump-probe experimental setup is shown in Figures 2.18(a) and (b), respectively. The GaAs PC gap's 61  photoconductivity is probed with a 1550 nm probe beam and is photoexcited by pump beams with wavelengths of 390 nm (having a fluence of 20 µJ/cm2) and 780 nm (having a fluence of 40 µJ/cm2). The pump wavelengths, corresponding to photon energies of 3.2 eV and 1.6 eV, respectively, are chosen to span the visible spectrum from violet to red. These photon energies are sufficient for resonant absorption with the 1.43 eV bandgap of GaAs.     The pump-induced transient photoconductivity, σ(t), is characterized by measurements of differential transmission of the probe beam's power as it passes through the GaAs. Results are shown in Figures 2.19(a) and (b) for 390 nm (violet) and 780 nm (red) pump photoexcitation, respectively. Photoexcitation commences at 4.8 ps in both figures to have the zero-time coincide with the incident laser pulse passing through the entrance interface of the CC, i.e., the plane defined by (a, a, a). Figure 2.19(a) shows the normalized transient photoconductivity, σ(t), of the GaAs PC gap for 390 nm (violet) photoexcitation. Processes of charge-carrier photogeneration and intravalley/intervalley scattering are shown on the electronic bandstructure in the figure inset. (The photoconductivity of GaAs is dominated by its high-mobility electrons rather than its low-mobility holes.) During the 100 fs pump photoexcitation, electrons transition to high states within the central Γ valley. These hot electrons then undergo rapid scattering, over a 100 fs timescale, into the neighbouring X6 and X7 sidevalleys [85]. This is because intervalley scattering to the X sidevalleys dominates over that of the L sidevalley [86]. The majority of scattered hot electrons populate the X6 sidevalley, and their return to the central Γ valley is seen as a risetime of 3 ps. This corresponds to a 1/e time constant of approximately 2 ps, agreeing with prior observations and interpretations of this scattering process [85]. It is also apparent from this figure that a small fraction of scattered hot electrons populates the X7 sidevalley and subsequently 62  scatters into the X6 sidevalley, over 0.8 ps, for eventual return to the Γ valley. This scattering process to and from the X7 sidevalley is seen as the photoconductivity's local maximum at 6 ps in Figure 2.19(a). Such observations and interpretations are also in agreement with the literature [85]. A slow decrease in transient photoconductivity is seen over 250 ps and is attributed to electron-hole recombination. Figure 2.19(b) shows the normalized transient photoconductivity, σ(t), of the GaAs PC gap for 780 nm (red) photoexcitation. The material impulse response shown here is far faster than that of the 390 nm (violet) photoexcitation. A rapid photoconductivity increase is seen in Figure 2.19(b), over a risetime of 200 fs, as electrons are photoexcited low in the Γ valley and their small excess energy is rapidly thermalized. These hot electrons do not have sufficient energy to scatter to sidevalleys, so the observed 200 fs risetime with 780 nm (red) photoexcitation is exceptionally fast. Overall, it is important to note that the material impulse response for short wavelength photoexcitation is τd ≈ 3 ps longer than that for long wavelength photoexcitation.          (a)                                                                            (b) Figure 2.18 The time-resolved pump-probe setup for the differential transmissivity measurements is shown with a pump beam wavelength of (a) 390 nm and (b) 780 nm.  63         (a)                                           (b) Figure 2.19 Material impulse responses are shown as normalized transient photoconductivity, "(t), for (a) 390 nm (violet) and (b) 780 nm (red) pump photoexcitation, with respective pump fluences of 20 µJ/cm2  and 40 µJ/cm2 on the GaAs PC gaps. The GaAs electronic bandstructure is shown in the insets, with the relevant photoexcitation transitions and intervalley scattering processes.  2.2.3.2   Geometrical input response     The geometrical input response of the CC-PC transceiver is characterized in general by the dimensions of the structure and the directionality of the illumination—as these attributes lead to varying transit time delays. The geometrical impulse response is defined for the output photocurrent, iout(t), on the recessed vertex electrode. As discussed in section 2.2.1, the incident optical power on each PC gap is comprised of three distinct photoexcitation contributions: direct illumination by the incident optical beam, single-reflection illumination following redirection off a neighbouring surface, and double-reflection illumination following redirection off two neighbouring surfaces. All direct, single-reflection and -0.20.00.20.40.60.81.01.21.40 5 10 15 20Transient photoconductivity, !(t) (a. u.)Time (ps)-0.20.00.20.40.60.81.01.21.40 5 10 15 20Transient photoconductivity, !(t) (a. u.)Time (ps)64  double-reflection contributions must be considered for both clockwise and counterclockwise permutations of reflections around the structure. The optimal alignment for photodetection and retroreflection is oriented with the incident optical intensity along the central axis of symmetry (φ = 45°, θ ≈ 54.7°) and is theoretically studied here, although the same analysis can be applied for other alignments. The incident optical intensity, Iop(t), is characterized by a laser pulse with a Gaussian envelope [87]. The full-width-at-half-maximum (FWHM) of the Gaussian laser pulse is first measured by a nonlinear autocorrelation measurement to be τp = 100 fs, and this result is used to create an expression for the transient optical power P(t, λ) on the three PC gaps. Details on the derivations can be found in Appendix I. The resulting transient optical power is   ( )( )( ) ( )( )( )00 122, 2 ( ) (3 ) ,2 ( )optP t R u t u t I t A dR tφδ τλ λ τ τ τ τλ δ τ∞−∞⎧ ⎫−⎪ ⎪⎪ ⎪= + − − − − ×⎡ ⎤⎨ ⎬⎣ ⎦⎪ ⎪+ −⎪ ⎪⎩ ⎭∫  (49) where Aφ is the area of one PC gap, and R(λ) is the wavelength-dependent Au surface reflectivity for which R(λ = 390 nm) = 40.2% and R(λ = 780 nm) = 96.9%. In this expression, δ(·) is a delta function, u(·) is a unit-step function, and the zero-time is defined by the arrival of the incident optical pulse at the entrance interface, i.e., at the plane of (a, a, a). The integrand of Eqn. (49) reveals distinct contributions to the geometrical input response. The first term in the braces corresponds to a direct illumination pulse at a time delay of t0 = (a–b)/(31/2c), where c is the free-space speed of light. The second term in the braces corresponds to single-reflection illumination and is characterized by a single-reflection turn-on time at t0 and a single-reflection turn-off time at t1 = 3t0. The third term in the braces corresponds to double-reflection illumination and manifests itself as a pulse at a time delay of t2 = 31/2(a–65  2b)/(3c)+31/2b/c. A factor of two is included in the second and third terms to account for clockwise and counterclockwise internal reflections. The transient optical power illuminating the PC gaps, for a τp = 100 fs incident optical intensity pulse, is    ( ) ( )( ) ( )( )200 12222 ln2, exp2 ln2 2 ln22 ( ) erf erf2 ln22 ( ) exp ,pp ppt tP t At t t tBRt tCRλτλτ τλτ⎡ ⎤⎛ ⎞−⎢ ⎥= −⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦⎡ ⎤⎛ ⎞ ⎛ ⎞− −+ ⎢ − ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦⎡ ⎤⎛ ⎞−⎢ ⎥+ −⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦ (50) where A = (I021/2wb)/31/2, B = (I0wcτp)/(8ln2)1/2, and C = (I0wb)/61/2 are the coefficients after integration for direct, single-reflection, and double-reflection illumination, respectively. Note that this geometrical input response has timescales that are subject to the device geometry, and it has amplitudes that are subject to both the material reflectivity and the device geometry. The geometrical input response is shown by way of the normalized transient optical powers in Figures 2.20(a) and (b) for wavelengths of 390 nm and 780 nm, respectively. The geometrical input response of the CC-PC transceiver shown here differs from that of a standard photodetector, for which illumination at normal incidence simply follows the optical pulse envelope. Instead, multiple pulses and steps are seen in Figures 2.20(a) and (b). For both wavelengths, an initial peak is seen at t0 = 4.81 ps and is attributed to direct illumination. At the same moment in time, a unit-step response is initiated as the single-reflection illumination begins to sweep across the PC gaps. The single-reflection unit-step is lower in amplitude than the initial peak, as one would expect from energy conservation, and it terminates at t1 = 14.43 ps. At t2 = t1 = 14.43 ps, a final peak is observed and is attributed to the double-reflection illumination. It is interesting to note that the investigated case of the optimal illumination along the central axis of  66     (a)                                     (b)               (c)                                 (d)Figure 2.20 Responses are shown for a CC-PC transceiver with a side-length of a = 5 mm. The geometrical input response is shown as the normalized transient optical power, P(t), on the PC gaps for (a) 390 nm (violet) and (b) 780 nm (red) photoexcitation. The resulting overall response is shown as the normalized output photocurrent, iout(t), for (c) 390 nm (violet) and (d) 780 nm (red) photoexcitation. The figure inset at the lower right corner of each figure shows the CC-PC transceiver as viewed from the optical source. 0.00.20.40.60.81.01.21.40 10 20 30Transient optical power, P(t) (a. u.)Time (ps)t0 = 4.81 pst 1 = t2 = 14.43 ps0.00.20.40.60.81.01.21.40 10 20 30Transient optical power, P(t) (a. u.)Time (ps)t0 = 4.81 pst 1 = t2 = 14.43 ps0.00.20.40.60.81.01.21.40 5 10 15 20 25 30 35 40Output photocurrent, i out(t) (a. u.)Time (ps)0.00.20.40.60.81.01.21.40 5 10 15 20 25 30 35 40Output photocurrent, i out(t)(a. u.)Time (ps)67  symmetry leads to a condition for which the double-reflection illumination creates a discrete pulse. This result only occurs for the optimal alignment with symmetric illumination and b ≤ a/2 for the dimensions.7   2.2.3.3   Overall device response     The overall response of the CC-PC transceiver is seen as an output photocurrent on the recessed vertex electrode, and it is defined by the convolution of the material impulse response and geometrical input response. Figures 2.20(c) and (d) show the overall responses of the CC-PC transceiver having a = 5 mm as normalized output photocurrents for 390 nm (violet) and 780 nm (red) photoexcitation, respectively. Differing overall response times are immediately apparent for the two wavelengths, with 13.73 ps for 390 nm (violet) and 10.40 ps for 780 nm (red) photoexcitation. This difference is attributed to the role of the material impulse response times in this structure with a = 5 mm.  To distinguish the differing roles of material impulse response and geometrical input response, a comparison is carried out for two CC-PC transceiver structures having opposing extremes of the side-length, a. A CC-PC transceiver with a = 1 mm is studied first, and its geometrical input responses are shown in Figures 2.21(a) and (b) as transient optical power with 390 nm (violet) and 780 nm (red) photoexcitation, respectively. It is apparent that the reduction in the dimensions, from that of the prior study, has reduced the t0, t1, and t2 times (as well as the zero-time). This leads to shorter geometrical input response times and faster overall responses, as seen by the output photocurrents in Figures 2.21(c) and (d) for 390 nm (violet) and 780 nm (red) photoexcitation, respectively. The overall response times are 6.44 ps for 390 nm (violet) and 2.90                                                    7 For b > a/2, a narrow step response will be created, but this does not apply to our CC-PC transceiver.     68       (a)                                    (b)          (c)                                    (d) Figure 2.21 Responses are shown for a CC-PC transceiver with a side-length of a = 1 mm. The geometrical input response is shown as the normalized transient optical power, P(t), on the PC gaps for (a) 390 nm (violet) and (b) 780 nm (red) photoexcitation. The resulting overall response is shown as the normalized output photocurrent, iout(t), for (c) 390 nm (violet) and (d) 780 nm (red) photoexcitation. The figure inset at the lower right corner of each figure shows the CC-PC transceiver as viewed from the optical source. 0.00.20.40.60.81.01.21.40 1 2 3 4 5 6Transient optical power, P(t) (a. u.)Time (ps)t0 = 0.96 pst 1 = t2 = 2.88 ps0.00.20.40.60.81.01.21.40 1 2 3 4 5 6Transient optical power, P(t) (a. u.)Time (ps)t0 = 0.96 pst 1 = t2 = 2.88 ps0.00.20.40.60.81.01.21.40 5 10 15 20 25 30Output photocurrent, i out(t) (a. u.)Time (ps)0.00.20.40.60.81.01.21.40 5 10 15 20 25 30Output photocurrent, i out(t)(a. u.)Time (ps)69  (a)                                    (b)     (c)                                    (d) Figure 2.22 Responses are shown for a CC-PC transceiver with a side-length of a = 10 mm. The geometrical input response is shown as the normalized transient optical power, P(t), on the PC gaps for (a) 390 nm (violet) and (b) 780 nm (red) photoexcitation. The resulting overall response is shown as the normalized output photocurrent, iout(t), for (c) 390 nm (violet) and (d) 780 nm (red) photoexcitation. The figure inset at the lower right corner of each figure shows the CC-PC transceiver as viewed from the optical source. 0.00.20.40.60.81.01.21.40 10 20 30 40 50 60Transient optical power, P(t) (a. u.)Time (ps)t0 = 9.6 pst 1 = t2 = 28.86 ps0.00.20.40.60.81.01.21.40 10 20 30 40 50 60Transient optical power, P(t) (a. u.)Time (ps)t0 = 9.6 pst 1 = t2 = 28.86 ps0.00.20.40.60.81.01.21.40 10 20 30 40 50 60Output photocurrent, i out(t) (a. u.)Time (ps)0.00.20.40.60.81.01.21.40 10 20 30 40 50 60Output photocurrent, i out(t)(a. u.)Time (ps)70 Figure 2.23 Overall response times for the CC-PC transceiver are shown for a side-length, a, ranging from 1 to 10 mm, for 390 nm (violet) and 780 nm (red) photoexcitation, respectively. The trendlines are shown as the dashed lines, and the inset in the lower right corner shows the CC-PC transceiver as viewed from the source.  ps for 780 nm (red) photoexcitation. Clearly, the dimensions associated with a = 1 mm lead to overall responses that are dominated by the difference in material impulse response times, (d ' 3 ps. The opposite extreme is seen for a larger CC-PC transceiver, with a = 10 mm, whose geometrical input responses are shown in Figures 2.22(a) and (b) as transient optical power with 390 nm (violet) and 780 nm (red) photoexcitation, respectively. It is apparent that the increased dimensions here lead to increased times for t0, t1, and t2 times (as well as the zero-time). The longer time delays impact the overall responses of the output photocurrents in Figures 2.22(c) and (d) for 390 nm (violet) and 780 nm (red) photoexcitation, respectively. The overall response times for the output photocurrents, being 20.42 ps for 390 nm (violet) and 20.36 ps for 780 nm 0.05.010.015.020.025.00 1 2 3 4 5 6 7 8 9 10 11Overall response times (ps)Side-length, a (mm)71  (red) photoexcitation, are nearly identical for this structure with a = 10 mm. The increased dimensions here diminish the importance of the material impulse responses, and the overall responses are dominated by the similar geometrical input responses.          To facilitate future design processes with CC-PC transceivers, the overall response times are investigated for a series of CC-PC transceivers with the side-length, a, varying from 1 to 10 mm. The overall response times are shown in Figure 2.23 for 390 nm (violet) and 780 nm (red) photoexcitations. Two distinct dimensional regimes are apparent for the overall response times. In the large-dimension regime, beyond a ≈ 8 mm, the material impulse response plays a negligible role in comparison to the geometrical input response. The larger device dimensions lead to geometrical input response times that are five or more times larger than the τd ≈ 3 ps difference for the material impulse response times. The overall response times in this large-scale regime are beyond 15 ps and are largely dictated by the long geometrical input response times. Differing material impulse responses can be neglected in this large-dimension regime.     In the small-dimension regime, below a ≈ 8 mm, the material impulse response dominates over the geometrical input response. This effect is seen as two distinct trendlines in the overall response times. The slower overall response times, for the upper trendline, correspond to 390 nm (violet) photoexcitation, while the faster overall response times, for the lower trendline, correspond to 780 nm (red) photoexcitation. Both of these overall response time trendlines are largely linear, with the vertical separation between the trendlines corresponding to the approximately τd ≈ 3 ps difference in material impulse response times. The upper and lower trendlines exhibit slopes of 1.7 ps/mm and 1.9 ps/mm, respectively, given R-squared fitting coefficients of 0.977 and 0.999 for the respective 390 nm (violet) and 780 nm (red) photoexcitation. The slope of the upper trendline is slightly smaller than that of the lower 72  trendline, and this difference is attributed to the wavelength-dependence of the Au surface reflectivity. The Au surface reflectivity for 390 nm (violet) photoexcitation is lower than that of 780 nm (red) photoexcitation. Thus, the transit time delays of single- and double-reflections have slightly less impact on the overall response times of 390 nm (violet) photoexcitation, compared to that of 780 nm (red) photoexcitation. This yields a slightly smaller slope for the shorter wavelength results. Some fundamental design principles can be established from this investigation of the CC-PC transceivers. The difference in material response times, being τd ≈ 3 ps between the short and long wavelengths in our study, must be considered in relation to geometrical transit time delays. Larger device geometries with large transit time delays, being larger than 5τd ≈ 15 ps in our study, lead to overall response times that are dictated by geometrical (i.e., dimensional) constraints. Smaller device geometries lead to overall response times that are dictated by both wavelength and geometrical constraints. In general, it is possible to identify the large- and small-dimension regimes for any OWC transceivers, by comparing the wavelength-dependent material responses with the dimension-dependent geometrical responses, and apply the appropriate material and geometry modifications for optimal device performance.   2.3 Transceiver analyses: Retro-modulation  In the previous subsection, the photodetection capabilities of the CC-PC transceiver were presented for OWC active downlinks in terms of the directionality characteristics and ultrafast transient characteristics. In this subsection, the retro-modulation capabilities of the CC-PC transceiver are demonstrated for OWC passive uplinks by exploiting its retroreflective response, with external modulation provided by a Pi-cell LC optical modulator.  73  2.3.1    Theoretical analyses The first step to establish bi-directional operation in OWC passive uplinks is to apply retroreflection. Retroreflection can be accomplished by the proposed CC-PC transceiver because of its CC architecture. As shown in Figure 2.24, incident light rays, with normalized directional cosine components of -n1, -n2, and -n3 in the respective x, y, and z directions, undergo three internal reflections within the corner and have each of the directional cosine components flipped by the Au surfaces in the y-z plane, x-z plane, and x-y plane, respectively [88]. For this process in the CC-PC transceiver, retroreflection is carried out by the recessed vertex electrodes, the three input bias electrodes, and (to a lesser extent) the three PC gaps. A wavelength of 780 nm is selected for the beam in the bi-directional link, given that this wavelength allows the Au electrodes to have a large and angular-independent reflectivity of R(λ = 780 nm) = 96.9%. This will maximize the retroreflected power. Moreover, the retroreflection contributions from the PC gaps—being less reflective than their surrounding Au surfaces—are minimized through the use    Figure 2.24 The retroreflection process is shown with the CC-PC transceiver. The incident light rays enter the CC-PC transceiver along (-n1, -n2, -n3), and the retroreflected light rays exit the CC-PC transceiver along (n1, n2, n3), anti-parallel to the incident direction.     74  of a sufficiently small PC gap area, i.e., lw = 0.7 mm2 << 12.5 mm2. This ensures that the effective retroreflection area of the device is dominated by the highly reflective Au surfaces. The retroreflection efficiency of the structure, being defined as the retroreflected power from the device versus the incident power on the device, will be a function of the incident light ray orientations on the CC-PC transceiver. The orientation for optimal retroreflection efficiency can be found by a straightforward ray-based analysis of the CC-PC transceiver. A Matlab ray-tracing model8 is developed to accomplish this, by illuminating the device with a sufficiently large and dense array of incident optical rays and recording the number of successfully retroreflected optical rays. The resulting theoretical retroreflected power from the CC-PC transceiver is shown as normalized surface distributions, as a function of the azimuthal angle, φ, and polar angle, θ, in the three-dimensional (3-D) and two-dimensional (2-D) views of Figure 2.25. As expected, the retroreflected power is diminished at orientations with glancing incidence upon any Au electrode in the CC-PC transceiver (seen as dark blue). The retroreflected power is maximized when φ = 45° and θ ≈ 54.7° (seen as the central dark red region). In this case, approximately 2.35% of the incident light rays are retroreflected. Thus, for optimal operation in a bi-directional optical link, the CC-PC transceiver should be aligned along this balanced orientation, i.e., along the central axis of symmetry, with the incident light beams entering along the (-n1, -n2, -n3) = (-1/√3, -1/√3, -1/√3) direction. The multitone PC sensing technique in section 2.2.2.1 can help facilitate the alignment to this optimal orientation. For the next step of establishing bi-directional operation for OWC passive uplinks, the retroreflective structure is made capable of optical modulation. This is accomplished through the employment of an external Pi-cell LC optical modulator. The Pi-cell LC optical modulator is                                                   8 The complete Matlab ray-tracing code can be found in Appendix H.    75  mounted over the triangular entrance interface of the CC-PC transceiver. An external electrical signal is used to provide optical loss modulation in the shutter and encode information onto the incident/retroreflected beams for their eventual return to their respective remote transceivers. Such retro-modulation is considered in the following experimental subsection.   2.3.2    Experimental analyses To test the retro-modulation capability of the CC-PC transceiver, the device is mounted onto the aforementioned gyroscope and 5 m indoor testbed. A CW 780 nm, 100 mW laser diode is employed as the point-to-point optical source. Approximately 1.3% of the incident optical power is retroreflected back to the laser from the uniformly-illuminated CC-PC transceiver. This percentage for the experimental power is smaller than that predicted theoretically, being 2.3%, and this discrepancy is attributed to the edges and imperfections of the Au surfaces in the CC architecture. The complete experimental setup is shown in Figure 2.26. A Pi-cell LC optical modulator is mounted over the entrance interface of the CC-PC transceiver to encode data onto the incident and retroreflected optical beams. The encoded and retroreflected optical beam is ultimately sampled by a beamsplitter and photodetector.  The CC-PC transceiver is adjusted to the well-aligned orientation of φ = 45° and θ ≈ 54.7°, which is optimized for both OWC active downlinks and passive uplinks. Uniform illumination is applied to the transceiver. The Pi-cell LC optical modulator is modulated at a 100 Hz frequency9, while the signal returning to the optical source is monitored. The retroreflected results are shown in Figures 2.27(a) and (b) as time- and frequency-domain curves, respectively. The LC modulation                                                   9 A Pi-cell LC optical modulator is selected here for proof-of-principle purposes. Higher modulation speeds can be achieved by way of a high-speed (sub-MHz) LC optical modulator [55] or a multiple-quantum-well (sub-GHz) absorber [81]. 76                     (a)                                                                                  (b) Figure 2.25 The (a) 3-D view and (b) 2-D view of the theoretical normalized retroreflected power are shown as a surface varying with azimuthal, φ, and polar, θ, angles. Both figures are produced from the Matlab ray-tracing model shown in Appendix H.  77   Figure 2.26 A schematic of the retro-modulation experimental setup is shown. The CC-PC transceiver is illuminated by a uniform laser beam with a Pi-cell LC optical modulator mounted over its entrance interface. The encoded and retroreflected beam is then sampled by a beamsplitter and photodetector.   applied on the CC-PC transceiver and measured at the optical source is evident in the signals. The 100 Hz modulation frequency is observed with an SNR beyond 30 dB. The ultimate strength of the signal seen here is attributed to the use of narrowband electronic filtering of extraneous noise in the environment and the enhanced signal power resulting from the CC-PC transceiver alignment-balancing procedure.  2.4 Summary In this chapter, a multi-directional CC-PC transceiver was introduced for OWC applications. The CC-PC transceiver incorporated three right-angled PC switches, with Au-coated electrodes and GaAs gaps, assembled into a CC architecture. The device was analyzed for photodetection, in uni-directional OWC operation in active downlinks, and retro-modulation, for bi-directional OWC operation in passive uplinks.  78  (a)                                    (b) Figure 2.27. Experimental (a) time-domain and (b) frequency-domain waveforms for the retroreflected optical power level returned to the optical source are shown for continuous laser illumination with a Pi-cell LC optical modulator on the CC-PC transceiver. The results are shown for the optimal alignment with "  = 45° and ! ! 54.7° given a 5 m optical link. The insets show the CC-PC transceiver as viewed from the source. The photodetection capabilities of the CC-PC transceiver were investigated first. The directional-dependence of the photodetection was carried out theoretically. It was found that the nominal structure exhibited a high level of directional dependence. With this in mind, multitone PC sensing and three-phase PC sensing techniques were introduced. Multitone PC sensing was applied to allow the transceiver to quantify and compensate for its misalignment, with respect to the optimal alignment along the central axis of symmetry. As an alternative to the realignment needed for multitone PC sensing, three-phase PC sensing was introduced. Three-phase PC sensing used the superposition of AC and DC output photocurrents to create a reduction in the 0510150 10 20 30 40Retroreflected power (!W)Time (ms)Optimal alignment(! " 54.7° & " = 45°) PC2 PC1PC30510152025300.00 0.05 0.10 0.15 0.20Retroreflected Power (a. u.)Frequency (kHz)Optimal alignment(! ! 54.7° &" = 45°) PC2 PC1PC379  directional dependency. A roughly constant output photocurrent was achieved over a FOV of 60° × 40°. The transient characteristics of the photodetection for the CC-PC transceiver were also investigated, in terms of the material impulse response and geometrical input response. It was found that these two responses must be considered together for ultrafast OWC active downlinks seeking broad spectral and directional characteristics.     The retro-modulation capabilities of the CC-PC transceiver were investigated next. A Pi-cell LC optical modulator was mounted on the CC-PC transceiver to encode data on the retroreflected beam. It was theoretically shown that the optimal retroreflection of the device is achieved for illumination along the central axis of symmetry, i.e., φ = 45° and θ ≈ 54.7°. Bi-directional communication was carried out for this optimal alignment with a 5 m experimental testbed. The capabilities of this system for bi-directional communication were deemed to be successful, as the transceiver could achieve an SNR of 30 dB over this link length.    80  Chapter 3: Multi-directional Spherical Optical Wireless Transceivers In the previous chapter, a multi-directional CC-PC transceiver was introduced for photodetection, in uni-directional OWC active downlinks, and retro-modulation, in bi-directional OWC passive uplinks. The CC-PC transceiver supported photodetection with operation well into the gigahertz range, but its retro-modulation capabilities were limited by its retroreflection, being within a solid angle of π/2 steradians, i.e., 1/8th of a sphere. At the same time its modulation was limited to the kilohertz operational range of the LC optical modulator. With this in mind, an alternative form of the transceiver is introduced in this chapter. A SP-PC transceiver is considered here for OWC applications. It integrates three PC switches with a SP-RR. The PC switches enable ultrafast photodetection, like that of the CC-PC transceiver, while the introduction of the SP-RR supports retroreflection over a solid angle of up to 2π steradians. More importantly, the SP-RR supports all-optical modulation well into the terahertz operational range. The following subsections show the design and analyses of the SP-PC transceiver. Section 3.1 presents its physical design. Section 3.2 analyzes its photodetection characteristics. Section 3.3 analyzes its retro-modulation characteristics. Section 3.4 draws some conclusions.   3.1 Transceiver design The proposed SP-PC transceiver is shown in Figure 3.1(a). The SP-PC transceiver consists of three PC switches, mounted radially and equally-spaced on a substrate. A SP-RR protrudes through the centre of the substrate. Each PC switch has a gap width of w = 200 µm and gap length of l = 3 mm. The PC gap is comprised of two separate metal electrodes, being sputtered 150-nm-thick Au layers on 50-nm-thick Cr adhesion layers, separated by a gap of semi-insulating GaAs. The dimensions and materials are selected to yield strong light-induced 81  photocurrents, as discussed in the previous chapter. The SP-RR is a simple sphere with a radius of a. It is implemented with careful attention to refraction and nonlinearity. Three materials, N-BK7, N-LASF9, and S-LAH79, are considered. Each has a distinct refractive index, n, and nonlinear coefficient, n2. (This variable, n2, differs from the directional cosine component in the y direction, also called n2, but the context of the variable will make its usage clear.) Each also has a broad and roughly constant transparency across visible to near-infrared wavelengths—being approximately 90% transparency above a wavelength of 450 nm, as shown in Figure 3.2. The breath of these wavelengths spans the operational wavelengths of typical indoor visible light communication systems [81] as well as outdoor free-space optical communication systems [89]. Uniform and collimated optical beams10 are incident on the SP-PC transceiver along an optical axis (OA) that is oriented with the azimuthal angle, φ, and polar angle, θ, shown on the xyz-coordinate system in Figure 3.1(a). The PC gaps are arranged to have their geometrical centres form an equilateral triangle with a geometrical centre that coincides with the geometrical centre of the substrate (as well as with that of the SP-RR). The distance from the geometrical centre of each PC gap to the geometrical centre of the SP-RR is defined as aΔ. This arrangement is shown Figure 3.1(b). The three PC switches are activated with bias voltages that are applied to the electrodes on the periphery of the substrate. This will have incident optical beams encode data onto photocurrents, which are summed on the common inner electrode. The photodetection characteristics of the output photocurrent, iout(t), are investigated in the following subsection, for OWC operations in active downlinks.                                                    10 In this chapter, the incident optical beams are the combination of two optical beams: one optical beam with a wavelength of 780 nm is used for photodetection in the active downlink; the other optical beam with a wavelength of 1550 nm is used for retro-modulation in the passive uplink.  82   Figure 3.1 Schematics are shown as (a) an oblique view and (b) a top view of the SP-PC transceiver (not to scale).  The SP-PC transceiver consists of three radial and equally-spaced PC switches, a SP-RR, and a substrate, which also acts as an aperture. Each PC switch is activated with a bias voltage, and each has a gap width of w and a gap length of l. The distance from the geometrical centre of each PC gap to the geometrical centre of the SP-RR is defined as a∆. The incident optical beams illuminate the SP-PC transceiver along azimuthal angle, φ, and polar angle, θ, as defined by the xyz-coordinate system in the figure.  83 Figure 3.2 Transmittance is shown as a function of wavelength, #, for N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00) materials (from left to right). The figure inset shows refractive indices as a function of wavelength, #, for N-BK7 (n = 1.51) [90], N-LASF9 (n = 1.85) [91], and S-LAH79 (n = 2.00) [92] materials.  3.2 Transceiver analyses: Photodetection The SP-PC transceiver's capabilities for photodetection are investigated in this subsection. The analyses are motivated by a desire to optimize the directionality and speed. Subsection 3.2.1presents the theoretical analyses on the directionality of the transceiver. Subsections 3.2.2 and 3.2.3 present the respective experimental analyses on its directionality characteristics and ultrafast transient characteristics.   3.2.1   Theoretical analyses      The photodetection process for the SP-PC transceiver will have a directional dependence to its operation. Unlike the CC-PC transceiver, however, the directional dependence of the SP-PC 00.250.50.7511.250.15 0.65 1.15 1.65 2.15Transmittance (a. u.)Wavelength, ! (µm) 84  transceiver will be straightforward given its planar arrangement of PC switches and lack of internal reflections. The directional dependence can be analyzed for a uniform intensity of I0 illuminating the SP-PC transceiver. Each PC gap captures a distinct incident power, characterized by the incident light rays' directional cosine components of n1 = cosφ⋅sinθ, n2 = sinφ⋅sinθ, and n3 = cosθ, in the respective x, y, and z direction. Thus, the light rays incident on PC1, PC2, and PC3, can be expressed by the vector  1 2 3ˆ ˆ ˆ ˆr n x n y n z= − − − , (51) and the normal vector for each PC gap's area will be equal to     ˆA wlz= . (52) Given uniform illumination of the three PC gaps, the incident power on each PC gap is found by simply projecting the component of the normal vector in (52) onto the light rays' vector in (51). The result,  0 3 0ˆP I r A wln I= − ⋅ = , (53) is the same for all the PC gaps. This incident power only depends on the polar angle, θ, and it is shown normalized with respective to wlI0, as a function of θ, in Figure 3.3. The incident power exhibits a monotonic decrease with respect to the polar angle, θ, ranging from 0° to 90°. This is understandable given that normal incidence, θ = 0°, produces the greatest light flux on the PC gap, while glancing incidence, θ = 90°, produces no light flux on the PC gap. If three equal DC bias voltages, Vb1 = Vb2 = Vb3, are applied to the three outer input electrodes, the PC switches produce photocurrents with the same amplitudes, and the summed output photocurrent at the common inner electrode will behave with the trend seen in Figure 3.3.  85   Figure 3.3 Theoretical incident power on each PC gap is shown as a function of the polar angle, θ, ranging from 0º to 90º. The results are normalized.  3.2.2   Experimental analyses of the directionality characteristics In this subsection, proof-of-principle tests are described for the SP-PC transceiver with DC voltage biasing to verify its photodetection characteristics at the optimal orientation, i.e., φ  = 0° and θ = 0°. The experimental setup is shown in Figure 3.4. A 100 mW, 780 nm laser diode is employed to provide above-bandgap photon absorption for the semi-insulating GaAs in the PC gap. The optical beam is collimated and expanded by a lens pair to illuminate the SP-PC transceiver with a uniform intensity and activate the PC switches. The SP-PC transceiver is mounted onto a gyroscope as shown in Figure 3.4 to allow for independent rotations of the azimuthal angle, φ, and polar angle, θ. Three power supplies are used to apply the voltage bias to the PC1, PC2, and PC3 switches. The photocurrents are summed at the common inner electrode of 86  the SP-PC transceiver to produce an output photocurrent, iout(t). To test the photodetection capability of the SP-PC transceiver, the laser diode is modulated at its highest modulation frequency of 1 MHz. Its uniform intensity on the SP-PC transceiver is 0.5 mW/cm2. The three PC switches are biased with the same DC voltage, i.e., Vb1 = Vb2 = Vb3 = 5 V The resulting output photocurrents are shown in Figure 3.5(a). The 1 MHz modulation on the laser beam is effectively photodetected by the SP-PC transceiver. The output photocurrents on the primary vertical axis of Figure 3.5(a) for the three PC switches are seen to have nearly identical waveforms, with individual peak-to-peak amplitudes of i1(t) ≈ 0.42 µA, i2(t) ≈ 0.41 µA, and i3(t) ≈ 0.40 µA. The 0.7% discrepancy between the peak-to-peak amplitudes is attributed to the slight imperfections of the GaAs PC gaps. This small discrepancy is ignored for the purposes of this study. The summed output photocurrent is displayed on the secondary vertical axis of Figure 3.5(a). It has a peak-to-peak amplitude of iout(t) ≈ i1(t) + i2(t) + i3(t) ≈ 1.23 µA.   Figure 3.4 A schematic of the experimental setup for photodetection is shown with the SP-PC transceiver. Three power supplies are connected to the three PC switches to provide voltage biasing. The output photocurrent, iout(t), is sampled by way of the common inner electrode through the substrate and processed by a DAQ system with an oscilloscope. 87    Figure 3.5 Proof-of-principle results for the SP-PC transceiver with DC voltage biasing are shown. Individual photocurrents and the summed output photocurrent, iout(t), are shown on the primary vertical axis and secondary vertical axis as a function of time, respectively. The figure inset shows the SP-PC transceiver (not to scale) as viewed from the source. -6.0-5.0-4.0-3.0-2.0-1.00.01.02.00.000.501.001.502.002.503.003.500.0 1.0 2.0 3.0 4.0 5.0Output photocurrent, iout (t) (µA)Individual photocurrents  (µA)Time (!s)i1(t)i2(t)i3(t)iout(t) PC1PC2PC3PC1PC2PC388  3.2.3   Experimental analyses of the ultrafast transient characteristics In this subsection, the ultrafast transient characteristics of the SP-PC transceiver are studied for photodetection in OWC active downlinks. The analyses of the ultrafast transient characteristics of the SP-PC transceiver are carried out in a similar manner to those of the CC-PC transceiver. The transient characteristics are analyzed by decomposing the operation into the two fundamental responses of a photoconductor: the material impulse response and the geometrical input response. Such an approach can accommodate the demands of OWC links, which often incorporate illumination that is broadband (potentially spanning the visible spectrum) and multi-directional (in terms of φ and θ). The material impulse response is dictated largely by the broadband illumination, which manifests itself as wavelength-dependent time delays in the transient photoconductivity of the semiconductor. The geometrical input response is dictated largely by the multi-directional illumination, which manifests itself as dimension-dependent transit time delays in the incident optical power. Further delay times associated with the subsequent electrical response, due to transmission lines, cables, and measurement equipment, are not considered in this work. The material impulse response and geometrical input response that contribute to the output photocurrent, iout(t), are analyzed in the following subsections.   3.2.3.1   Material impulse response The material impulse response is defined by the transient photoconductivity of GaAs in the PC gaps. The response is investigated by using the pump-probe differential transmission system presented in Section 2.2.3.1 of Chapter 2. The photoconductivity of the semi-insulating GaAs in a PC gap is sampled by the 1550 nm probe beam during photoexcitation by the pump beam. Measurements are made with pump beams having wavelengths of 390 nm (violet) and 780 nm (red), as this corresponds to the extreme ends of the visible spectrum. 89  The transient photoconductivity results are shown in Figure 2.19. The photoexcitation commences at 0 ps in both figures due to the simple planar arrangement of the GaAs PC gaps in the SP-PC transceiver. This zero-time, t0', coincides with the arrival of the incident laser pulse on the first PC gap. Note that there is a τd ≈ 3 ps time difference between the material impulse response for the 390 nm (violet) and 780 nm (red) photoexcitation, like that seen in section 2.2.3.1. This is due to the significant excess electron energy for the 390 nm (violet) wavelength photoexcitation, which leads to delays from intervalley (and intravalley) scattering, as shown in the inset of Figure 2.19 (a). In such a case, it becomes necessary for the hot electrons to undergo relaxation from high within the bandstructure down to the valence band edge before they can contribute appreciably to photoconduction (i.e., have a high mobility).  3.2.3.2   Geometrical input response The geometrical input response of the SP-PC transceiver is analyzed here. It is dictated by the dimensions of the structure and the directionality of the illumination—both of which result in transit time delays. In analogy to the analyses on the CC-PC transceiver, the geometrical input response is defined by the output photocurrent, iout(t), which is proportional to the summed optical power on the three PC gaps. Due to the planar arrangement of the SP-PC transceiver, the transient analyses of the incident optical power on the three PC gaps are far easier than those of the CC-PC transceiver. (There are no reflections to be considered for the SP-PC transceiver.) The incident optical power for the SP-PC transceiver is analyzed here for an orientation with φ = 0° and θ = 0°, being the optimal alignment, and an orientation with φ  = 45° and θ = acos(1/√3) ≈ 54.7°, for a comparison to the ultrafast transient response analyses of the CC-PC transceiver.  The incident optical intensity, I(t), is characterized by a laser pulse with a Gaussian envelope, 90  having a FWHM of τp ≈ 100 fs. The envelope is used to create the expression for the incident optical power, P(t), on the three PC gaps. The incident optical power is  ' ' '0 1 2( ) [ ( ) ( ) ( )] ( ) (3 )P t t t t I t wl dδ τ δ τ δ τ τ τ+∞−∞= − + − + − − ×∫ ,  (54) where, wl is the area of one PC gap, δ(⋅) is a delta function, and the zero-time, t0', is defined by the arrival of the incident optical pulse on the first PC gap. The integrand of Eqn. (54) reveals the contributions to the geometrical input response: the first delta function, δ(τ – t0'), in the bracket corresponds to the first illumination at a time delay of t0' = 0 on the first PC gap; the second delta function, δ(τ – t1'), in the bracket corresponds to the second illumination at a time delay of t1' on the second PC gap; and the third delta function, δ(τ – t2'), in the bracket corresponds to the third illumination at a time delay of t2' on the third PC gap. Note here that for the optimal illumination with φ = 0° and θ = 0°, i.e., normal incidence, the time delays are all clearly zero, i.e., t0' = t1' = t2' = 0. Thus, the corresponding incident optical power, P(t), can be simplified to        22 ln 2( ) 3exp ,ptP t Dτ⎧ ⎫⎡ ⎤⎛ ⎞⎪ ⎪⎢ ⎥= −⎜ ⎟⎨ ⎬⎜ ⎟⎢ ⎥⎪ ⎪⎝ ⎠⎣ ⎦⎩ ⎭  (55) where D = I0wl/31/2 is a constant. For orientations with any other azimuthal and polar angles, the time delays can be shown to be t0' = 0, t1' = [31/2a∆⋅cos(30°+φ)⋅sin(θ)]/c, and t2' = [31/2a∆⋅cos(30°–φ )⋅sin(θ)]/c, where c is the speed of light in free space, and a∆ is the distance from the geometrical centre of each PC gap to the geometrical centre of the SP-RR. Thus, for the orientation with φ = 45° and θ ≈ 54.7°, the resulting time delays are t0' = 0, t1' = (√3–1)a∆⋅/2c, and t2' = (√3+1)a∆⋅/2c. The corresponding incident optical power is 91      2'02 2' '1 22 ln 2( )( ) exp2 ln 2( ) 2 ln 2( )exp exp ,pp pt tP t Dt t t t!! !" # $% &'( ) *= ' ++ ,- + ,) *( . /0 123# $ # $% & % &' ' () * ) *' + '+ , + , 4+ , + ,) * ) *(. / . /0 1 0 15   (56) where D = I0wl/31/2 is a constant. Note that the incident optical power has timescales that are dominated by the device geometry, i.e., the distance from the geometrical centre of each PC gap to the geometrical centre of the SP-RR, a!, and it has the same amplitude for the contributions of the PC gaps.      (a)                                           (b) Figure 3.6 The material impulse response is shown as the normalized transient photoconductivity, "(t), for (a) 390 nm (violet) and (b) 780 nm (red) pump photoexcitation, with respective pump fluences of 20 µJ/cm2  and 40 µJ/cm2 on the GaAs PC gaps of SP-PC transceiver. The GaAs electronic bandstructure is shown in theinsets with the relevant photoexcitation transitions and intervalley scattering processes. -0.20.00.20.40.60.81.01.21.4-5 0 5 10 15Transient photoconductivity, !(t) (a. u.)Time (ps)-0.20.00.20.40.60.81.01.21.4-5 0 5 10 15Transient photoconductivity, !(t) (a. u.)Time (ps)92        (a)  (b)        (c) Figure 3.7 Responses are shown for the SP-PC transceiver, having any distance, a$, from the geometrical centre of each PC gap to the geometrical centre of the SP-RR, with illumination along "  = 0° and ! = 0°. The geometrical input response is shown in (a) as the incident optical power, P(t), on the PC gaps for both 390 nm (violet) and 780 nm (red) photoexcitation. The resulting overall response is shown as the output photocurrent, iout(t), for (b) 390 nm (violet) and (c) 780 nm (red) photoexcitation. The results are normalized. The figure inset shows the SP-PC transceiver (not to scale) as viewed from the source. 0.00.20.40.60.81.01.21.4-2.5 0.0 2.5 5.0 7.5Incident optical power, P(t) (a. u.)Time (ps)t0' = t1' = t2' 0 ps! = 0° & " = 0°PC1PC2PC30.00.20.40.60.81.01.21.4-5 0 5 10 15 20Output photocurrent, i out(t), (a. u.)                                                                                                                   Time (ps)! = 0° & " = 0°PC1PC2PC30.00.20.40.60.81.01.21.4-5 0 5 10 15 20Output photocurrent, i out(t), (a. u.)                                                                                                                   Time (ps)! = 0° & " = 0°PC1PC2PC393        (a)           (b)                (c) Figure 3.8 Responses are shown for the SP-PC transceiver, having a distance of a$ ! 4.33 mm from the geometrical centre of each PC gap to the geometrical centre of the SP-RR, with illumination along "  = 45° and ! ! 54.7°. The geometrical input response is shown in (a) as the incident optical power, P(t), on the PC gaps for both 390 nm (violet) and 780 nm (red) photoexcitation. The resulting overall response is shown as the output photocurrent, iout(t), for (b) 390 nm (violet) and (c) 780 nm (red) photoexcitation. The results are normalized. The figure inset shows the SP-PC transceiver (not to scale) as viewed from the source. 0.00.20.40.60.81.01.21.4-15.0 0.0 15.0 30.0 45.0 60.0Incident optical power, P(t) (a. u.)Time (ps)t1' = 5.28 pst2'= 19.71 ps! = 45° & " ! 54.7°PC1PC2PC3t0' = 0 ps0.00.20.40.60.81.01.21.4-5 5 15 25 35 45 55Output photocurrent, i out(t), (a. u.)                                                                                                                   Time (ps)! = 45° & " ! 54.7°PC1PC2PC30.00.20.40.60.81.01.21.4-5 10 25 40 55Output photocurrent, i out(t), (a. u.)                                                                                                                   Time (ps)! = 45° & " ! 54.7°PC1PC2PC394 (a)                (b)                        (c) Figure 3.9 Responses are shown for the SP-PC transceiver, having a distance of a$ ! 0.17 mm from the geometrical centre of each PC gap to the geometrical centre of the SP-RR, with illumination along "  = 45° and ! ! 54.7°. The geometrical input response is shown in (a) as the incident optical power, P(t), on the PC gap for both 390 nm (violet) and 780 nm (red) photoexcitation. The resulting overall response is shown as the output photocurrent, iout(t), for (b) 390 nm (violet) and (c) 780 nm (red) photoexcitation. The results are normalized. The figure inset shows the SP-PC transceiver (not to scale) as viewed from the source. 0.00.20.40.60.81.01.21.4-0.5 0.0 0.5 1.0 1.5 2.0 2.5Incident optical power, P(t) (a. u.)Time (ps)t0' = 0 pst2' = 0.79 ps! = 45° & " ! 54.7°PC1PC2PC3t1' = 0.21 ps0.00.20.40.60.81.01.21.4-5 0 5 10 15 20Output photocurrent, i out(t), (a. u.)                                                                                                                   Time (ps)! = 45° & " ! 54.7°PC1PC2PC30.00.20.40.60.81.01.21.4-5 0 5 10 15 20Output photocurrent, i out(t), (a. u.)                                                                                                                   Time (ps)! = 45° & " ! 54.7°PC1PC2PC395      The geometrical input response is shown first for the optimal orientation, with φ  = 0° and θ = 0°, by way of the normalized incident optical power in Figure 3.7(a) for 390 nm (violet) and 780 nm (red) photoexcitation. As one would expect, the geometrical input response of the SP-PC transceiver simply follows the optical pulse envelope, and it is independent of the wavelength and device dimensions. The geometrical input response for the orientation of φ  = 45° and θ ≈ 54.7° differs from that for φ  = 0° and θ = 0°. The SP-PC transceiver has a distance of a∆ ≈ 4.33 mm from the geometrical centre of each PC gap to the geometrical centre of the SP-RR. This new arrangement yields the multiple optical pulses seen in Figure 3.8(a). For both 390 nm (violet) and 780 nm (red) photoexcitation, the initial peak is at t0' = 0 ps, and it is defined by the first illumination on the PC3 gap. After a time delay of t1' = 5.28 ps, the optical pulse strikes the PC1 gap which is spatially close to the PC3 gap and it forms the second peak shown in the figure. A final peak is observed after a time delay of t2' = 19.71 ps, and it is attributed to illumination on the PC2 gap, which is the most distant from the PC3 gap.  3.2.3.3   Overall device response The overall response of the SP-PC transceiver is seen as a single output photocurrent, iout(t), on the common inner electrode, and it is defined by a convolution of the material impulse response and geometrical input response. Figures 3.7(b) and (c) show the overall response of the SP-PC transceiver, given illumination along the optimal orientation of φ  = 0° and θ = 0°, and the response is shown as output photocurrents for 390 nm (violet) and 780 nm (red) photoexcitation, respectively. Both output photocurrents can be achieved for a SP-PC transceiver having any distance a∆ from the 96  geometrical centre of each PC gap to the geometrical centre of the SP-RR, given the normal incidence of illumination. However, differing overall responses are apparent for the two wavelengths, with approximately 3 ps for 390 nm (violet) and approximately 200 fs for 780 nm (red) photoexcitation. This difference is mainly due to the distinct material impulse responses and their dominance in the convolution process with the geometrical input response, which is an impulse-like pulse of optical power with a duration of τp = 100 fs, as shown in Figure 3.7(a). This difference in material response time, τd, between the 390 nm (violet) and 780 nm (red) photoexcitation, will exist for multi-wavelength operation, and it must be considered for the design of future ultrafast OWC transceivers. For this investigation, with semi-insulating GaAs, a material response time of τd ≈ 3 ps is witnessed, but in general, this delay time will depend upon the relaxation rates, due to intervalley and intravalley scattering, in the selected semiconductor. Figures 3.8(b) and (c) show the overall response of the SP-PC transceiver, along the orientation of φ  = 45° and θ ≈ 54.7°, as output photocurrents for 390 nm (violet) and 780 nm (red) photoexcitation, respectively. Both output photocurrents are for a SP-PC transceiver having a distance of a∆ ≈ 4.33 mm from the geometrical centre of each PC gap to the geometrical centre of the SP-RR. The oblique incidence here introduces time delays during illumination of the PC gaps, which forms the complex geometrical input response seen for the incident optical power in Figure 3.8(a). The time delays of t1' = 5.28 ps and t2' = 19.71 ps seen for this study of the incident optical power lead to overall response times of 20.04 ps for 390 nm (violet) and 19.84 ps for 780 nm (red) photoexcitation for the output photocurrents in Figures 3.8(b) and (c), respectively. (The overall response time is defined here as the risetime from 10% to 90% of the maximum.) Step-like contributions from the PC gaps are seen in both figures—as one would expect from pulses being incident on the multiple PC gaps from an oblique angle. Ultimately, the relatively 97  large dimensions of this SP-PC transceiver diminish the importance of the material impulse responses, as the geometrical input response dominates the overall device response.   To distinguish the role of the material impulse response from the geometrical input response, a SP-PC transceiver is formed with a distance of a∆ ≈ 0.17 mm from the geometrical centre of each PC gap to the geometrical centre of the SP-RR. It is analyzed for illumination along φ  = 45° and θ ≈ 54.7°. Its geometrical input response is shown as the incident optical power in Figure 3.9(a) for 390 nm (violet) and 780 nm (red) photoexcitation. Small time delays of t1' = 0.21 ps and t2' = 0.79 ps are seen for illumination of the second and third PC gaps (following incidence on the first PC gap). The output photocurrents for this structure are shown in Figures 3.9(b) and (c) for 390 nm (violet) and 780 nm (red) photoexcitation, respectively. The overall response times are 3.78 ps for 390 nm (violet) and 0.93 ps for 780 nm (red) photoexcitation. The output photocurrent profiles are virtually identical to those of the respective material impulse responses in Figure 2.19. Clearly, the smaller device dimensions here diminish the importance of the geometry input response, and this leads to the overall response being dominated by the material impulse response, with its delay of τd ≈ 3 ps. To facilitate future design processes with SP-PC transceivers, the overall response times are investigated for a series of SP-PC transceivers having distances from the geometrical centre of each PC gap to the geometrical centre of the SP-RR, a∆, ranging from 0.17 mm to 4.33 mm. The overall response times of the spherical PC transceivers are shown in Figure 3.10 for 390 nm (violet) and 780 nm (red) photoexcitations. The optical illumination is incident along φ  = 45° and θ ≈ 54.7°. The trend that is seen here is similar to that of the CC-PC transceiver, in section 2.2.3.3, in that there are two distinct dimensional regimes. In the small-dimensional regime, below a∆ ≈ 1.15 mm, the overall response is dominated by 98  the material impulse response while the geometrical input response plays a negeligible role. This effect can be seen as two distinct trendlines in the overall response times. The slower overall response time (upper trendline) corresponds to 390 nm (violet) photoexcitation, while the faster overall response time (lower trendline) corresponds to 780 nm (red) photoexcitation. Both of these trendlines are roughly linear, showing a slope of 1.97 ps/mm and an R-squared fitting coefficient of 0.983 for the upper trendline, and a slope of 4.41 ps/mm and an R-squared fitting coefficient of 0.999 for the lower trendline. The slope of the lower trendline is two times larger than that of the upperline trendline, and this is attributed to the faster material impulse response for 780 nm (red) photoexcitation, over that of 390 nm (violet) photoexcitation. The vertical separation between the trendlines at a∆ ≈ 0.17 mm is equal to the difference in the material impulse response times, τd ≈ 3 ps, and this observation is logical given that the overall response here would be due solely to the material response. In the large-dimensional regime, beyond a∆ ≈ 1.15 mm, the overall response is dominated by the geometrical input response while the material impulse response plays a negeligible role. Basically, the large device dimensions here contribute to a slow geometrical input response, with long time delays between the optical pulses striking the individual PC gaps. This can be realized by looking at Figures 3.8(b) and (c). In both figures, the first contribution to the output photocurrent is produced by illumination on the PC3 gap, and before this contribution disappears, due to charge-carrier recombination, the second contribution to the output photocurrent is produced by illumination on the PC1 gap. This second contribution adds to the first contribution at a time delay of t1' = 5.28 ps. At a time delay of t2' = 19.71 ps, the third contribution, from the PC2 gap, is added to the overall response. Ultimately, the consecutive addition of contributions seen here from the PC gaps is a result of the geometrical delay times being much shorter than the 99material response time. In such a situation, the overall response time scales linearly with the dimensions of the SP-PC transceiver.      Some fundamental design principles can be established from this investigation of the SP-PC transceiver. In general, the broadband operation of a transceiver must be carefully considered in terms of its differing material response times for short and long wavelengths—as denoted by (din these analyses. This difference in material response times must then be contrasted to the geometrical transit time delays. To this end, larger device geometries lead to overall response times that are dictated by geometrical (i.e., dimensional) constraints, while smaller device geometries lead to overall response times that are dictated by material (i.e., wavelength) constraints. This conclusion is in agreement with that concluded for the CC-PC transceiver.   Figure 3.10 The overall response time of the SP-PC transceiver is shown for a SP-PC transceiver having a distance from the geometrical centre of each PC gap to the geometrical centre of the SP-RR, a$, ranging from 0.17 mm to 4.33 mm, for 390 nm (violet) and 780 nm (red) photoexcitation. The trendlines are shown as the dashed lines, and the figure inset shows the SP-PC transceiver (not to scale) as viewed from the source. 0.05.010.015.020.025.030.035.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5Overall response time (ps)Distance, a! (mm)PC2PC1PC3! = 45° & " " 54.7°100  3.3 Transceiver analyses: Retro-modulation  In the previous subsection, the photodetection capabilities of the SP-PC transceiver were investigated for OWC active downlinks in terms of directional characteristics and ultrafast transient characteristics. It was shown that the photodetection speed of the SP-PC transceiver is dictated to a large extent by the distance, a∆, from the geometrical centre of each PC gap to the geometrical centre of the SP-RR. The analyses were carried out for polar angles ranging from 0° to 90°, corresponding to operation over 2π steradians, i.e., half of a sphere, but the introduction of the SP-RR in this section will impact this directionality. The protrusion of the SP-RR above the substrate has the potential to block the incident optical beam if the incident rays come in at a glancing angle (i.e., θ is too large) and/or the PC gaps are too close to the SP-RR (i.e., a∆ is too small). To mitigate such blocking and ensure that all three PC gaps are fully illuminated, the SP-RR developed in this section is introduced with a radius, a, that conforms to a∆ and the desired angular FOV. To this end, the SP-RR's radius of a and the angular FOV must be defined according to     cos(FOV/2)a aΔ≤ .   (57) This inequality shows that there is a balancing of constraints between photodetection and retro-modulation. Photodetection can facilitate high-speed operation with a wide angular FOV when aΔ is made small. However, this has repercussions on the retro-modulation process, as a must also be made small. This leads to diminished retroreflected powers, which scale in proportion to a2. To balance the desire for high-speed operation, a wide angular FOV, and a sufficiently large retroreflected power, an angular FOV of 120° is deemed to be acceptable. This yields a SP-RR with a radius of a = 2.5 mm and a radial separation of the PC gaps of a∆ ≈ 4.33 mm. This SP-PC transceiver will facilitate photodetection with an overall response time of approximately 20 ps, as 101  seen by Figure 3.10, over a solid angle of approximately 2π/3 steradians. At the same time, the transceiver will enable retro-modulation over a solid angle of 2π steradians, with a speed that is determined within this subsection. The capabilities for spherical retroreflection and all-optical modulation are integrated within the SP-PC transceiver shown in Figures 3.11(a) and (b). A uniform and collimated incident signal beam illuminates the top of the structure. This beam is focused by the entrance interface, reflected by the rear interface, and re-collimated by the entrance interface, for return to the source. At the same time, a local control beam illuminates the rear interface of the structure. This control beam is used to enable all-optical modulation of the incident signal beam while it is reflecting off the rear interface. Thus, nonlinear beam interaction at the rear interface is exploited to have local optical data (on the local control beam) be encoded for return to the source (on the retroreflected signal beam). The overall retro-modulation process is characterized by the material characteristics of the SP-RRs. It is necessary to carefully define the appropriate refractive index, n, and nonlinear coefficient, n2, for retroreflection and modulation. Three glass materials are investigated for implementation of this retro-modulation: N-BK7 is tested as a benchmark because it exhibits a low refraction index of n = 1.51 and a low nonlinear coefficient of n2 = 3.2 × 10-16 cm2/W; N-LASF9 is tested because it exhibits a moderate refractive index of n = 1.85 and a moderate nonlinear coefficient of n2 = 1.7 × 10-15 cm2/W; S-LAH79 is tested because it exhibits a large refractive index of n = 2.00 and a high nonlinear coefficient of n2 = 2.8 × 10-15 cm2/W. The refractive indices, n, are defined by Schott glass data, and the nonlinear coefficients, n2, are defined from calculations with the Boling-Glass-Owyoung (BGO) model [93]. The uniform and collimated incident signal beam, at a wavelength of 1550 nm, illuminates the 102  SP-RR along an OA that is oriented at an azimuthal angle of φ and polar angle of θ with respect to the xyz-coordinate system in Figure 3.11(a). The intensive local control beam, at a wavelength of 780 nm, illuminates the rear surface of the SP-RR and generates an appreciable change of the refractive index, Δn, which only occurs on the rear interface of SP-RR. Isolation of the beams is achieved in the system with a 1550-nm-bandpass dichroic filter (not shown), which passes the 1550 nm signal beam and blocks the 780 nm local control beam. The substrate within which the SP-RR is mounted acts as an aperture. The characteristics of spherical retroreflection are optimized by way of theoretical analyses in the following subsection.             (a)                                            (b) Figure 3.11 Schematics are shown of the SP-PC transceiver, as (a) an oblique view and (b) a cross-sectional view. A collimated incident signal beam illuminates the SP-RR, at an azimuthal angle, φ, and polar angle, θ, with respect to the xyz-coordinate system. This forms a retroreflected signal beam that returns to the source. A local control beam illuminates the SP-RR's rear interface to apply all-optical modulation to the signal beam. A bandpass dichroic filter (not shown) passes the 1550 nm signal beam and blocks the 780 nm local control beam. In this design, the substrate in the xy-plane acts as an aperture. 103  3.3.1 Theoretical analyses  To establish the desired level of retroreflection for retro-modulation, it is necessary to characterize refraction in the SP-RR and define an optimal refractive index. An analogous characterization and optimization of nonlinearity for the glass material of the SP-RRs is deemed to be unnecessary. (This is because it is understood that a large nonlinear coefficient, n2, yields improved uplink performance—given that the modulation depth on the retroreflected beam is linearly proportional to n2 [94].) To characterize the refraction, a ray-tracing model is developed. The SP-RR has a refractive index of n and a radius of a. It is shown in Figure 3.12. The SP-RR is illuminated by an incident light ray running parallel to the OA, at a separation of y0 from the OA.11 The intersection of the light ray and the entrance interface of the SP-RR is defined as (z0, y0), and the incident angle is defined as   0 0i0arcsin arctany ya zθ⎛ ⎞⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠.  (58) The light ray is refracted at this intersection point to form a transmitted angle of  0 00t 2 2 20arcsin arctany yan a n yθ⎛ ⎞⎛ ⎞ ⎜ ⎟= =⎜ ⎟ ⎜ ⎟⎝ ⎠ −⎝ ⎠.     (59) The beam is focused to the point (z1, y1) on the rear interface of the SP-RR, where  2 2 20 01 22 ( 1),1Dy D a yzD− + − −=+  (60)  2 21 1y a z= − , (61)                                                   11 Note that spherical retroreflection occurs mainly with the paraxial region of the spherical RR being close to the OA, i.e., y0 << a. 104  and  2 2 2 2 20 0 0 02 2 2 2 2 20 0 0.y a n y y a yDa n y a y y− − −=− − +  (62)     After the light ray is focused, it propagates with an angle of θ01 = arctan(D) off of the OA and subsequently strikes the rear interface of the SP-RR. A portion of the light ray's power refracts through the interface at the transmitted angle of θ1t = θi and exits the SP-RR. (This portion of the beam is not of interest to this theoretical analysis.) The remaining portion of the light ray's power reflects at the intersection point of (z1, y1), on the rear interface of the SP-RR, with a reflected angle of θ1i = θ0t. The light ray returns through the SP-RR and strikes the intersection point of (z2, y2), where  2 2 21 12 2( 1) 2,1E z E a zzE− + −=+  (63)  2 22 2 ,y a z= − −   (64) and   ,1F DED F−=+ ⋅ (65)  2 2 20 02 2 202.2y a n yFa n y−=− (66) The beam refracts at this intersection point and exits the SP-RR at a retroreflected angle of θt off the OA. This retroreflected angle is  2t i2arcsin yzθ θ⎛ ⎞= +⎜ ⎟⎝ ⎠.  (67) For ideal retroreflection, the incident angle, θi, should be equal to the retroreflected angle, θt. 105  This would have the retroreflected light ray return to the source in a direction that is anti-parallel to the incident light ray. However, in practice, there will exist an angular offset between these angles—even within the paraxial region, i.e., y0 << a. For this study, the desired level of retroreflection is deemed to have |θt – θi | ≤ 0.03°,12 and the beam intensities are analyzed at two key points within the system, being at the intersection of the OA and rear interface and after propagation a distance of L by the retroreflected beam. The characteristics of the SP-RR are investigated first by way of the intensity at the intersection  Figure 3.12 The ray-tracing model is shown for the characterization of the SP-RR with respect to the refractive index, n. An incident light ray runs parallel to the OA, and it is focused by the entrance interface, reflected by the rear interface, and re-collimated by the entrance interface for return to the source (being anti-parallel to the incident light ray).                                                    12 This condition will achieve a sufficient level of retroreflection according to the details in Section 3.3.2. 106  of the OA and rear interface, Is(z = –a). This intensity is plotted as a function of the SP-RR's refractive index, n, in Figure 3.13(a). It is clear that refractive indices close to n = 2.00 form an intense focus at the rear interface of SP-RR. Such results agree with the limiting case of the thick-lens formula for a lens with a thickness of 2a and radii of curvature having equal magnitudes of a,   21 1 1 2 ( 1)( 1) a nnf a a na−⎡ ⎤= − + −⎢ ⎥⎣ ⎦.  (68) Here, we see that a sphere with a refractive index of n = 2.00 focuses at the rear interface, i.e., yields a focal length of f = a. For our materials, S-LAH79 (n = 2.00) meets this condition. This observation is illustrated by ray-tracing results13 in the inset of Figure 3.13(a), which show that a SP-RR having n = 2.00 forms a high-intensity point focus at the intersection of the OA and rear interface. In contrast, the SP-RR having n = 1.85 focuses the beam slightly outside the rear interface, and the SP-RR having n = 1.51 focuses the beam far beyond the rear interface. The characteristics of the SP-RR are also investigated by way of the intensity on the OA following propagation of the retroreflected beam back toward the source over a distance of z = L = 3 m. This intensity, Is(z = L), is shown as a function of the SP-RR's refractive index, n, in Figure 3.13(b). It is apparent from the figure that the S-LAH79 (n = 2.00) SP-RR best achieves retroreflection, as its retroreflected signal intensity is 9 × 105 times larger than that of the N-LASF9 (n = 1.85) SP-RR and 4 × 106 times larger than that of the N-BK7 (n = 1.51) SP-RR. The observation that S-LAH79 best achieves retroreflection agrees with the prior observation that S-LAH79 also achieves focusing at the rear interface, as the focusing at the rear interface is necessary to have the retroreflected beam be anti-parallel to the incident beam.                                                   13 The ray-tracing simulations are shown for rays within the paraxial region, i.e., y0 << a, of the spherical RRs.  107  3.3.2 Experimental analyses  The theoretical assertions from the prior subsection agree (albeit qualitatively) with experimental tests of retroreflection for the three SP-RRs. For these tests, a 1 mW, 650 nm CW laser diode is employed for the tests. The SP-RRs are fully illuminated with a uniform laser beam having an intensity of 2.26 mW/cm2. A beamsplitter is used to sample the beam being retroreflected from the SP-RR, and a silicon photodetector (DET 36A/M, Thorlabs, USA) is used to measure the power of the sampled beam. A propagation distance of L = 3 m is used. The retroreflected signal intensity of the S-LAH79 (n = 2.00) SP-RR is measured to be approximately 35 µW/cm2. This intensity is 7 × 105 times larger than the 50 pW/cm2 retroreflected signal intensity of the N-LASF9 (n = 1.85) SP-RR. The retroreflected signal intensity of the N-BK7 (n = 1.51) SP-RR is far lower and is below the noise floor of the testing system. These assertions agree qualitatively with the prior theoretical results. The observations of increasing intensities for the increasing refractive indices of the SP-RRs result from an enhancement of collimation on the retroreflected beams. The optimal SP-RR, comprised of S-LAH79 (n = 2.00), forms a retroreflected beam spot that is approximately 1.8 mm in diameter following the 3 m propagation. This corresponds to a divergence angle of approximately arctan(1.8 / 3000) 0.03≈ ° . The power in this beam is mainly due to the fraction of the incident beam illuminating the paraxial area of the SP-RR. This paraxial area is estimated to be the central 3% of the SP-RR's cross-sectional area. The power associated with the non-paraxial area is subject to spherical aberration—and thus it does not focus on the rear surface of the SP-RR and it does not form a collimated retroreflected beam. Such observations are in agreement with the ray-tracing results in the Figure 3.13(b) insets. The SP-RR having n = 2.00 readily achieves retroreflection over its paraxial area, with minimal divergence. The SP-RR 108  having n = 1.85 shows moderate retroreflection over its paraxial area, with a divergence angle of approximately 2°. The SP-RR having n = 1.51 exhibits poor retroreflection, with a divergence angle of approximately 8°.  To characterize the all-optical modulation of the SP-PC transceivers, a series of time-resolved impulsive-excitation studies are carried out. The experimental schematic is shown in Figure 3.14. Local control pulses14 with a 100 fs duration and 780 nm wavelength illuminate the rear interface of the SP-RR, with an intensity ranging from 0.52 to 2.10 GW/cm2. Incident signal pulses, with a 100 fs duration and 1550 nm wavelength, illuminate the entrance interface of the SP-RR. With such an arrangement, the control beam modulates the signal beam at the rear interface and the modulated signal beam is retroreflected for its return to the source. For these time-resolved tests, the local control pulses are delayed by a motorized stage and the retroreflected beam's intensity (being proportional to its power) is recorded as a function of the time delay. Phase-sensitive lock-in detection is used for noise rejection.     Results of the impulsive excitation tests are shown in Figure 3.15 as the retroreflected signal intensity, Is(t), as a function of time, t, for SP-PC transceivers comprised of N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00), displayed bottom to top. The retroreflected signal intensities are all normalized with respect to the S-LAH79 (n = 2.00) results. It is readily apparent that the local control beam can modulate the signal beam on an ultrashort timescale. The retroreflected signal intensities are characterized by pulses with a FWHM of approximately 120 fs. The time-domain characteristics of the retro-modulated signals in Figure 3.15 give insight into the mechanism for this all-optical modulation. All three signals are seen to                                                   14 Given the 100 mW average power for our FemtoFiber Laser system (Toptica Photonics, 100fs, 90 MHz), an unfocused local control beam cannot provide a high enough intensity to support nonlinear mixing with the signal beam across the full rear interface of the spherical RR. Thus, the local control beam is focused onto the OA by a 40× microscope objective to create a sufficiently high intensity. 109        (a)         (b) Figure 3.13 The (a) incident signal intensity, Is(z = –a), at the rear interface of the SP-RR, and (b) retroreflected signal intensity, Is(z = L), following propagation back toward the source, are shown versus the SP-RR refractive index, n. Ray-tracing model simulations are shown as figure insets for N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00) SP-RRs.  110   Figure 3.14 A schematic of the time-resolved impulsive excitation setup is shown (not to scale). The retroreflected signal intensity, Is(t), is recorded as a function of the time delay, t, between pulses in the signal beam (yellow) and control beam (red). The figure shows the 1550/780 nm pulsed laser source, delay stage, neutral-density variable filter, photodetector, dichroic filter, beamsplitter, and SP-PC transceiver.   be symmetric with respect to the zero-time, and each has a FWHM that is comparable to the control and signal beams' pulse duration. Thus, the nonlinear mixing between the local control pulses and signal pulses is deemed to be nonresonant in nature, i.e., it is due to nonlinear electronic polarization of the glass rather than resonant charge-carrier photogeneration and recombination. Moreover, the retroreflected signal intensities increase upon application of the local control beam. This positive polarity indicates that the nonlinear coefficient, n2, is positive and that the local control beam creates a transient increase in the refractive index (and a corresponding increase in the retroreflected signal intensity). The small negative sidelobes in the figure are attributed to the control-beam-induced increase to the signal beam's absorption, within 111the bulk of the SP-RR, in accordance with the Kramers-Kronig relations [95]. (The negative sidelobes occur slightly after and before the zero-time because the bulk absorption will appear with slightly shorter and longer path lengths, respectively.) The modulation on the retroreflected signal power, %Ps, is shown in Figure 3.16, as a function of the (peak) local control beam intensity, for the N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00) SP-RRs. Linear trends are readily apparent in the figure, and the slopes are used to extract nonlinear coefficients for the materials. For the N-BK7 (n = 1.51) SP-RR, the signal levels are especially low and are seen only for the highest local control beam intensity of 2.1 GW/cm2. This leads to a nonlinear coefficient of n2 = (3 ± 1) " 10-16 cm2/W. This value is in rough agreement with the experimental value of 3.5 " 10-16 cm2/W measured in a prior study [96], Figure 3.15 Retroreflected signal intensity, Is(t), versus time, t, is shown for retro-modulation with the N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00) SP-RRs, listed here from the weakest signal intensity (bottom) to the strongest (top).  -0.250.000.250.500.751.001.25-900 -700 -500 -300 -100 100 300 500 700 900Retroreflected signal intensity, Is(t)(a. u.)Time, t (fs)SP-RRsn = 2.00, S-LAH79 (black)n = 1.85, N-LASF9 (red)n = 1.51, N-BK7     (blue)~ 120 fsSP-PC transceiverPC3PC2 PC1112Figure 3.16 Modulation on the retroreflected signal power, %Ps, is shown in a function of the (peak) local control beam intensity, Ic, with squares, triangles, and diamonds denoting N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00) SP-RRs, respectively.   and it is on the same order as the value of 3.2 " 10-16 cm2/W calculated from the BGO model [93]. For the N-LASF9 (n = 1.85) SP-RR, a nonlinear coefficient of n2 = (1.3 ± 0.1) " 10-15cm2/W is found. This value is comparable to the experimental value of 9.6 " 10-16 cm2/W measured in a prior study [97], and it is on the same order as the value of 1.7 " 10-15 cm2/W calculated from the BGO model [93]. For the S-LAH79 (n = 2.00) SP-RR, a nonlinear coefficient of n2 = (1.8 ± 0.1) " 10-15 cm2/W is found. To author's best knowledge, this value has not been measured in prior experimental studies, but it is on the same order as the value of 2.8 " 10-15 cm2/W calculated from the BGO model [93]. Note that the observed linear trends in Figure 3.16 suggest that the local control beam intensity can be further increased to establish a greater 0.000.250.500.751.001.251.500.00 0.50 1.00 1.50 2.00Retroreflected signal power,  !Ps(nW)Local control beam intensity, Ic (GW/cm2)SP-PC tranceiverS-LAH79 n = 2.00N-LASF9 n = 1.85N-BK7 n = 1.51PC1PC2PC3113  modulation depth on the retroreflected signal power. Higher order nonlinearities and/or damage are not observed for the local control beam intensities used here.  3.4 Summary In this chapter, an SP-PC transceiver was introduced with integrated PC switches and a SP-RR for the needs of OWC systems. The PC switches facilitated photodetection for uni-directional OWC operation in active downlinks. The SP-RR facilitated retro-modulation for bi-directional OWC operation in passive uplinks.   The photodetection capabilities of the SP-PC transceiver were investigated first. The directional-dependence of the photodetection was studied theoretically, and proof-of-principle experimental tests were carried out at the optimal orientation. It was seen that the SP-PC transceiver can effectively photodetect modulated data from a remote source. The transient characteristics of the photodetection for the SP-PC transceiver were investigated in terms of the material impulse response and geometrical input response. The findings were similar to those for the CC-PC transceivers, in that these two responses must be considered together for ultrafast OWC operation in active downlinks seeking broad spectral and directional characteristics. The retro-modulation capabilities of the SP-PC transceiver were investigated next, for SP-RRs being comprised of N-BK7 (n = 1.51), N-LASF9 (n = 1.85), and S-LAH79 (n = 2.00). It was concluded from theoretical and experimental analyses that the SP-PC transceiver comprised of S-LAH79 (n = 2.00) is best-suited for operation as an OWC transceiver. It provides optimal retroreflection with broad directionality (2π steradians) and all-optical modulation on ultrafast timescales (120 fs). The near-instantaneous nature of the observed impulse responses suggests that the SP-PC transceiver can be applied for all-optical modulation with data rates well into the terabit-per-second regime.  114  Chapter 4: Conclusion     Concluding remarks are given within this chapter. The remarks include a summary of the contributions of my work and suggestions for future work with ultrafast OWC transceivers.  4.1 Summary of contributions Emerging OWC systems have two fundamental operational modes, being active downlink and passive uplink, and these operational modes demand effective photodetection, retroreflection, and modulation. With this in mind, two new architectures were introduced within this dissertation to meet the demands of OWC transceivers, and both transceivers can facilitate high-speed operation for bandwidths up to approximately 5 GHz15. This bandwidth is calculated by convolving the measured 160 ps material response time and 4 ps estimated electrical response time, according to the measured kiloOhm PC gap resistance and estimated femtofarad PC capacitance. The sensitivity of the transceivers is also quantified by way of noise equivalent power (NEP) estimations. Given the measured 10 nA dark current and the above calculated 5 GHz bandwidth, the NEP value is estimated to be 0.2 pW/√Hz (corresponding to a minimal detectable optical power being 14 nW. It is in the same order of magnitude as the values reported from other researchers [17, 54, 79]. Furthermore, for a standard optical wireless environment, with a typical 2 m height between the proposed transceiver and the optical transmitter on the ceiling, a minimum power of 100 mW is required on the optical transmitter with a solid 60º radiation angle. This is a reasonable value for the typical optical transmitter. In Chapter 2, the CC-PC transceiver was introduced as an OWC multi-directional transceiver.                                                   15 The measured operation bandwidth of the transceiver is about 100 MHz, and this measurement is limited by the available measuring equipment. However, both transceiver can potentially operate up to 50 GHz according to the 20 ps overall response time investigated in sections 2.2.3 and 3.2.3.      115  Theoretical and experimental analyses of the transceiver showed that it was able to provide effective active downlink operation at a gigahertz bandwidth, which is in the same order of magnitude as the values reported from other researchers [11, 20, 25] and the state-of-the-art implementation for RGB-based visible light communications [98]. The analyses also showed that the transceiver could provide passive uplink operation at a 100 Hz bandwidth, which is much lower than the reported kilohertz bandwidth (achieved via mechanical modulation [49, 69]) and megahertz bandwidth (achieved via electrical modulation [79–81]). The major conclusions of this work are given here: i. For point-to-point laser-based OWC systems, a multitone frequency biasing technique is recommended for use with the CC-PC transceiver. This is because the CC-PC transceiver can enable effective photodetection of incoming signals from transmitters at a gigahertz data rate, and at the same time, the multitone photocurrents can be separately extracted and used for optimization of the optical link alignment. Such an optimization maximizes the signals for photodetection and retroreflection.  ii. For well-separated indoor LED-based OWC systems, a DC-shifted AC3φ biasing technique is recommended for use with the CC-PC transceiver. This architecture can effectively enable photodetection at a gigahertz data rate and create an overall transceiver responsivity that is largely independent of the incident beam's AOA, i.e., it has a wide FOV (spanning 60° × 40°). This uniform responsivity supports strong SNR performance for the multi-directional nature of indoor LED-based OWC systems.  iii. For OWC active downlinks, care should be taken to consider both the structural dimensions and the material characteristics of the CC-PC transceiver. This is because the wavelength-dependent material response is found to dominate the overall response of the 116  device when the structural dimensions are small, i.e., the transit times within the device are short. In contrast, the dimensional-dependent geometrical input response is found to dominate the overall response of the device when the structural dimensions are large, i.e., the transit times within the device are long. Future ultrafast OWC devices should carefully balance these constraints.  iv. For bi-directional OWC passive uplinks, an external LC modulator can be used with the CC-PC transceiver. The modulation depth of this modulator can be made appreciable. However, its modulation speed, operating on a millisecond timescale, is far too slow for future OWC applications seeking broadband data transmission.     In Chapter 3, a SP-PC transceiver was introduced as an OWC multi-directional transceiver. Theoretical and experimental analyses of the device showed that it could also provide effective active downlink operation at a gigahertz bandwidth, which is in the same order of magnitude as the values reported from other researchers [11, 20, 25] and the state-of-the-art implementation for RGB-based visible light communications [98]. The analyses also showed that the transceiver could provide effective passive uplink operation at a terahertz bandwidth, which is beyond the reported megahertz bandwidth from the start-of-the-art implementation for bi-directional OWC links [81]. The major conclusions of this work are given here: i. For laser-based or indoor LED-based OWC systems, a DC bias voltage can be applied with the SP-PC transceiver to facilitate photodetection at gigahertz data rates. At the same time, given the planar configuration of the PC switches, the device can operate with an appreciable angular FOV, being 120°. ii. For ultrafast OWC active downlinks, the SP-PC transceiver has a similar conclusion to that of the CC-PC transceiver, in that care should be taken to consider both the structural 117  dimensions and the material characteristics. The wavelength-dependent material response dominates the overall response of devices for small dimensions, and the dimensional-dependent geometrical input response dominates the overall response of the devices for large dimensions. These characteristics should be balanced in implementations of future ultrafast OWC devices.  iii. For OWC passive uplinks, all-optical modulation is recommended for the SP-PC transceiver. The ultrafast switching speed of all-optical modulation is on a femtosecond timescale, and the overall device enables broad retroflection over a solid angle of 2π steradians. Such characteristics are advantageous for future ultrafast OWC systems. Overall, throughout the theoretical and experimental investigations in this dissertation, the SP-PC transceiver offers the similar photodetection performance to that of the CC-PC transceiver for OWC active downlinks. On the other hand, the SP-PC transceiver offers significantly improved retro-modulation performance over that of the CC-PC transceiver for OWC passive downlinks. Thus, the SP-PC transceiver is recommended, from the author's standpoint, for future implementations of bi-/multi-directional OWC networks that seek multi-wavelength and multi-directional operations.  4.2 Future work It is worth noting that the two compact OWC transceivers introduced in this dissertation are prototypes. With this in mind, the presented work corresponds to technology readiness levels 4 (component and/or breadboard validation in laboratory environment) and 5 (component and/or breadboard validation in relevant environment) in the National Aeronautics and Space Administration. The process of developing the OWC transceivers in this dissertation has also led to some recommendations for future work (and improvements) in this field. 118  The first improvement, corresponding to the CC-PC transceiver, pertains to its communication speed in OWC passive uplinks. The use of the external LC modulator limits the transceiver's use to kilohertz data rates, and this should be improved upon. An alternative way to carry out such improvements is to implement a high-speed electrical modulator. A MQW absorber, for example, can be installed at the entrance interface of the CC-PC transceiver to modulate the retroreflected beam at a speed up to gigabit-per-second. To further carry out such improvements, modulation can be implemented by way of micro-scale semiconductor retro-structures. By selecting the correct semiconductor crystallographic orientations and etchants, CC micro-structural arrays can be etched directly onto a semiconductor surface (without the need for planar fabrication techniques) [99–103]. Such a retro-structure provides the required retroreflection and a means by which the incident signal beam can be modulated. All-optical modulation can be carried out by a local control beam, which photoinjects charge-carriers and modulates the incident signal beam. Such an implementation can facilitate ultrafast (subpicosecond) switching times for ultrafast OWC passive uplinks.  The second improvement, corresponding to the SP-PC transceiver, corresponds to the need to reduce the intensity of the local control beam during operation in OWC passive uplinks. (Such a need is directly related to the need for increasing the modulation depth on the signal beam.) The presented SP-PC transceiver uses nonlinear beam interaction in the applied glass, and this makes it necessary to have the control beam apply intensities on the order of GW/cm2. This is a high intensity. With this in mind, alternative materials can be considered to be coated on the rear interface of the SP-RR. The materials would be selected to increase the modulation depth with their appreciable nonlinearities and increase the reflection at the rear interface with their high refractive index. One ideal candidate of those alternative materials is semiconductor 119  nanoparticles [104]. Semiconductor nanoparticles typically have an appreciable nonlinear coefficient, n2, in the order of 10-12 cm2/W, which is about a thousand times bigger than the applied glass used in this dissertation. 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Such a system established a bi-directional OWC link, as shown in Figure A.1(a). Moreover, the collected three photocurrents were used in differential combinations for active control and optimization of the optical alignment. The theory and methodology for the optical retroreflection, photodetection, and real-time control characteristics were presented, and the technique was verified experimentally with a silicon PD retro-detection prototype. The work is seen in two refereed journal articles [J14, J15], one refereed conference proceeding [C15] and one invited book chapter [B2].      As an extension of my Master's work, I collaborated with researchers in the Positioning and Navigation Signal Processing Laboratory, under the supervision of Dr. Richard Klukas at the University of British Columbia's Okanagan campus. We employed this CC-based photosensor for indoor optical wireless location (OWL) systems, as shown in Figure A.1(b). This indoor OWL technology measures the three photocurrents and uses them to estimate the AOA of the optical source. (The photocurrent amplitudes are a function of the AOA's azimuthal angle and polar angle.) The work is seen in one refereed journal article [J11], two refereed conference proceedings [C9, C13], and one invited book chapter [B1]. 135       (a) (b) Figure A.1 A bi-directional OWC system is shown in (a) with an LED as the light source. The CC-based photosensor is shown in the inset. The OWL system is shown in (b) with two optical sources.   136  Appendix B  Microlenses with Tuned Focal Characteristics for Optical Wireless Imaging In Chapter 3, a SP-PC transceiver was developed and investigated, but the basic idea of using a SP-RR was arrived at following investigations of polymer microlenses. Details of the initial investigations on polymer microlenses are presented in this Appendix.  B.1   Background     Microlenses are key elements for optoelectronic devices. These sub-millimeter lenses can be applied in individual or arrayed implementations to enable coupling on microscopic scales [105–107] and support numerous applications—particularly optical wireless technologies [16, 48, 108]. Microlenses are most effective when their physical form is tailored to the desired imaging application. Micro-optical elements can be adapted in real-time, by way of thermal [3], electrical [109–111], or pneumatic [112] control, for use as microlenses with tunable focal characteristics. Or, micro-optical elements can be adapted during their fabrication to create customized (permanent) microlenses [113, 114]. It is often desirable to have these microlenses exhibit short focal lengths, to support compact device integration [115, 116], as well as sufficiently large numerical apertures (NAs), to support broad FOV characteristics [117, 118]. These needs are especially true for the optical wireless devices, as commented upon in the literature [48, 117], as compact device integration and broad FOV characteristics can support small device form factors and broad imaging reception from optical transmitters distributed across large overhead areas. A user-controlled microlens fabrication technique can be applied to meet these needs. In this Appendix, a user-controlled microlens fabrication technique, electro-dispensing, is implemented to create polymer microlenses. Microlenses are fabricated and ultimately studied to gauge their abilities for compact device integration (i.e., short focal lengths) and broad FOV imaging (i.e., large NAs). Numerous microlenses are formed, and complete theoretical and 137  experimental analyses are presented for three limiting-cases of the microlens forms. The microlenses are ultimately integrated into optical wireless imaging receivers to test their significant communication performances.  B.2   Microlenses fabrication The desired microlens characteristics for short focal lengths and large NAs can be met through fabrication with well-controlled microlens volumes and shapes. The electro-dispensing technique, being based on the principle of electrowetting-on-dielectric, provides this through in situ dispensing, tuning, and curing of ultraviolet (UV)-curable polymer droplets. The system schematic is shown in Figure B.1(a). The UV-curable polymer NOA 68 is used. NOA 68 gives broad spectral transmission across 400 nm to 1400 nm, with a refractive index, n ≈ 1.58, being similar to that of silica. The polymer droplets are dispensed on a silica substrate, through a metal micro-needle tip having a 110 µm inner diameter and 240 µm outer diameter. The metal micro-needle tip is 450 µm above the silica substrate, and it is immersed within an appropriate filler solution, ranging from air (for low microlens contact angles with narrow FOVs) to glycerol (for high microlens contact angles with broad FOVs). A copper ground plane exists below the silica substrate. The silica substrate has a thickness of 130 µm and dielectric constant of 3.8. A pneumatic control system (Nordson EFD UltimusTM V High Precision Dispenser) is employed to apply the precise dispensing pressure and time to deposit the desired polymer volume for the microlens. A voltage, V, is then applied to the metal micro-needle tip, to tune the droplet shape according to the Lippmann-Young law, cosα = cosα0 + CV2/(2γmf), where α and α0 are the respective microlens contact angles with and without applied voltage, C is the specific capacitance, i.e., capacitance per unit area of the microlens-substrate interface, and γmf is the microlens-filler surface tension [119, 120]. This process allows the voltage on the metal micro- 138 Figure B.1 Schematics of the (a) electro-dispensing system and (b) microlens configuration above the CMOS image sensor. SEM images are shown in (b) of the acute-angle (! = 30°), right-angle (! = 90°), and obtuse-angle (! = 120°) microlenses, left to right, and the CMOS image sensor array, with a pixel size of 6 % 6 &m2and a representative 25 &m diameter focal spot. 139  needle tip to tune the microlens contact angle and thus the overall shape [121]. (For microlens tuning with lower voltages, the substrate can be made to dominate the specific capacitance, C, by increasing its dielectric constant and decreasing its thickness.) When the desired droplet shape is obtained, UV-curing is applied to solidify the droplet into the microlens. The complete electro-dispensing technique, with its in situ direct-dispensing and user-controlled voltage-tuning, enables the reproducible formation of individual/arrayed microlenses of various sizes and shapes. Three microlens forms are investigated, with differing contact angles, α, and diameters, 2r. The lenses are integrated above a complementary metal–oxide–semiconductor (CMOS) image sensor as shown in Figure B.1(b). An acute-angle microlens with α = 30° and 2r = 800 µm is electro-dispensed in an air filler solution with 0 V applied to the metal micro-needle tip. A right-angle microlens with α = 90° and 2r = 500 µm is electro-dispensed in a glycerol filler solution with 200 V applied to the metal micro-needle tip. An obtuse-angle microlens with α = 120° and 2r = 500 µm is electro-dispensed in a glycerol filler solution with 100 V applied to the metal micro-needle tip. Scanning electron microscope (SEM) images of the acute-, right-, and obtuse-angle microlenses are shown as insets in Figure B.1(b), along with an SEM image of the CMOS image sensor array (Omnivision, OV7720).   B.3   Theoretical analysis The cross-sectional profile of a general spherical microlens is shown in Figure B.2. The microlens is mounted face-down above the CMOS image sensor, with the silica substrate acting as a superstrate. The microlens has a radius r along the microlens-superstrate interface, a radius of curvature R, and a microlens-superstrate contact angle α. A two-dimensional Cartesian coordinate system (x, y) is defined, with its x-axis along the microlens-superstrate interface and 140  its y-axis along the OA. An optical beam illuminates the microlens at an incident angle, θ, off the OA. Focusing is defined by the axial focal length, f(θ), being the vertical distance from the superstrate to the focal point, and the off-axial focal deflection, ρ(θ), being the horizontal distance from the OA to the focal point. The image sensor and superstrate are parallel, with a separation, f(θ=0°), that is the axial focal length for incidence along the OA. For incidence off the OA, the vertical separation between the focal point and image sensor plane is defined as the axial focal contraction, ∆f(θ), and the image size on the image sensor is defined as the off-axial focal spot size, ∆ρ(θ). Theoretical ray-tracing analyses are carried out first for focal characteristics parallel to the OA. Results are collected for the acute-, right-, and obtuse-angle microlenses with their respective contact angles of α = 30°, α = 90°, and α = 120°. The microlens axial focal length, f(θ), and axial focal contraction, ∆f(θ), are shown in Figure B.3(a) and (b), respectively, normalized with respect to the microlens radius, r, for incident angle, θ, spanning from 0° to 60°. The theoretical axial focal length, f(θ), results of Figure B.3(a) show that the right-angle microlens exhibits especially short focal lengths, compared to that of the acute- and obtuse-angle microlenses. This suggests that the right-angle microlens can best support the pursuit of compact device integration. It can also be seen from Figure B.3(a) that both the right- and obtuse-angle microlenses exhibit reduced dependence between the axial focal length, f(θ), and incident angle, θ, compared to that of the acute-angle microlens. This suggests that both the right- and obtuse-angle microlenses are able to maintain a sharp focus on the image sensor across a wide range of θ values. The exact dependence between this axial focal contraction, ∆f(θ), and the incident angle, θ, is shown in Figure B.3(b) for the three microlenses. It is seen that the right- and obtuse-angle microlenses exhibit smaller ∆f(θ) values, by approximately a factor of two, when 141  compared to the acute-angle microlens. Theoretical ray-tracing analyses are carried out next for focal characteristics perpendicular to the OA. Results for the three microlenses are quantified in terms of the off-axial focal deflection, ρ(θ), and off-axial focal spot size, ∆ρ(θ), in Figure B.4(a) and (b), respectively, normalized with respect to the microlens radius, r.   Figure B.2 Cross-sectional profile of the spherical microlens. Optical rays are incident at an angle, θ, off the OA. The focal point of the rays is defined by an axial focal length, f(θ), and off-axial focal deflection, ρ(θ). The image on the image sensor is defined by an axial focal contraction, ∆f(θ), and off-axial focal spot size, ∆ρ(θ).  142    Figure B.3 Theoretical ray-tracing results, versus incident angle, θ, for the (a) axial focal length, f(θ), and (b) axial focal contraction, ∆f(θ). Experimental axial focal length results are shown in (a) as a discrete cross, circle and star at θ = 0°for the acute-, right-, and obtuse-angle microlenses, respectively. All results are normalized with respect to the microlens radius, r. 143    Figure B.4 Theoretical ray-tracing results, versus incident angles, θ, for the (a) off-axial focal deflection, ρ(θ), and (b) off-axial focal spot size, ∆ρ(θ). Experimental off-axial focal deflection results are shown in (a) as discrete crosses, circles and stars for the acute-, right-, and obtuse-angle microlenses, respectively. All results are normalized with respect to the microlens radius, r. 144  The results for off-axial focal deflection, ρ(θ), in Figure B.4(a) show that the acute-angle microlens exhibits the large off-axial focal deflection, while right- and obtuse-angle microlenses exhibit similar small off-axial focal deflection. This suggests that right- and obtuse-angle microlenses can equally support the pursuit of compact device integration. To define an operational FOV, a maximum off-axial focal deflection of 2r is deemed to be acceptable, as it would allow microlens arrays to be formed with a centre-to-centre pitch of twice the diameter. The right- and obtuse-angle microlenses can then be used for imaging with θ up to 60°, for an equivalent FOV of 120°, while the acute-angle microlens can only be used for imaging with θ up to 30°, for an equivalent FOV of 60°. This suggests that the right- and obtuse-angle microlenses can equally support the pursuit of large NAs for broad FOV characteristics. The results for off-axial focal spot size, ∆ρ(θ), shown in Figure B.4(b), exhibit similar responses for the acute-, right-, and obtuse-angle microlenses. The ∆ρ(θ) values are all sufficiently small, below 3% of the radius, to ensure that well-defined focal spots are formed on the CMOS image sensor by the paraxial region of the incident beam. The overall ∆ρ(θ) curves for the three microlenses exhibit minimal observable difference across the range of θ values. The right- and obtuse-angle microlenses show similar ∆ρ(θ) curves because of their similar axial focal contraction curves in Figure B.3(b). At the same time, the acute-angle microlens shows a ∆ρ(θ) curve that is similar to that of  the right- and obtuse-angle microlenses because its pronounced axial focal contraction in Figure B.3(b) is counterbalanced by its lower beam divergence (compared to that of the right- and obtuse-angle microlenses).   B.4   Experimental analysis  The validity of the theoretical results is confirmed through experimental tests of the acute-, 145  right-, and obtuse-angle microlenses. The microlenses are mounted above a CMOS sensor, as shown in Figure B.2, and images are captured by the optical emitter array with LEDs positioned at varying incident angles. The summary in Table B.1 compares the theoretical and experimental axial focal lengths and NAs for θ = 0°. The experimental axial focal length results at θ = 0° are shown in Figure B.3(a) as crosses, circles, and stars for the respective acute-, right-, and obtuse-angle microlenses. Good agreement (less than 5% error) is seen between the theory and experiment. The experimental off-axial focal deflection results for increasing θ are shown in Figure B.4(a) as crosses, circles, and stars for the respective acute-, right-, and obtuse-angle microlenses. Good agreement (less than 6% error) is witnessed between theory and experiment. The theoretical and experimental results exhibit strong linearity, with an R-squared of 0.999, which allows each microlens to resolve widely distributed optical emitters with minimal distortion. Little or no comatic aberration is observed for any microlenses, within their FOVs. The overall optical characteristics suggest that the right-angle microlens with α = 90° is best-suited for the imaging demands of optical wireless applications. In terms of compact device integration, its respective axial focal length (700 µm) and off-axial focal deflection (435 µm) are only 2.788 and 1.736 times the microlens radius, r. In terms of FOV characteristics, its large NA (0.533) leads to an extraordinarily broad FOV (120°).  Table B.1 Theoretical vs. experimental comparison of focal length and NA for the acute-angle microlens, α = 30°, right-angle microlens, α = 90°, and obtuse-angle microlens, α = 120°, normalized by r. α φ(θ=0°) (theory) φ(θ=0°) (exp.) Error ΝΑ (theory) ΝΑ (exp.) Error 30° 3.714 (1485 µm ) 3.764 (1510  µm ) 1.4% 0.411 0.406 1.2% 90° 2.724 (680  µm  ) 2.788 (700  µm  ) 2.4% 0.545 0.533 2.2% 120° 3.222 (805  µm  ) 3.064 (770  µm  ) 4.9% 0.468 0.490 4.7%  146  B.5   Optical wireless imaging characterization      Proof-of-principle tests are carried out with the three microlenses integrated within optical wireless imaging receivers. The receivers are tested in an optical wireless testbed, having an equally-spaced 3 × 3 LED optical transmitter grid. The LEDs can be made to support wavelength discrimination by way of independent modulation of their red (λR = 625 nm), green (λG = 565 nm), and blue (λB = 470 nm) wavelength inputs. The LEDs can be made to support frequency discrimination by applying three modulation frequencies, with each of the nine LEDs having a distinct wavelength-frequency combination. Such a system enables wavelength and frequency filtering, for noise rejection, and it allows each LED to be differentiated from its neighbours during multiplexing [11, 48] or diversity reception [15, 17]. The imaging receivers are tested below the LED optical transmitter grid, in terms of SNRs and imaging resolutions.      In terms of SNR, the dominant noise source is found to be ambient light, similar to other works [48], so the SNR is defined here by a ratio of the signal to ambient light levels, at the specified LED's wavelength and frequency. (The image sensors use spatial filtering to localize LEDs in the images, then wavelength and frequency filtering for further noise rejection.) The three image sensors are positioned the same distance below the centre of the LED optical transmitter grid, with the outermost LEDs being at the edge of the FOV for the acute-angle microlens. In this configuration, the imaging receiver with the acute-angle microlens yields an SNR of 20 dB, while the imaging receivers with right- and obtuse-angle microlenses both yield an SNR of 30 dB. The 10 dB improvement in SNR for the right- and obtuse-angle microlenses over the acute-angle microlens is attributed to their broad FOV imaging capabilities—which support acquisition of intense signal peaks that dominate well over the surrounding ambient light levels. 147  In terms of imaging resolutions, the imaging receivers should be capable of isolating individual LEDs, for practical LED separations in the LED optical transmitter grid. For the ongoing study, the imaging resolution is limited by the 6 × 6 µm2 pixel size on the imaging sensor. The angular imaging resolution of the imaging receiver with the acute-angle microlens is estimated to be 0.2 degrees/pixel, while the angular imaging resolutions of the imaging receivers with right- and obtuse-angle microlenses are both estimated to be 0.6 degrees/pixel. For a standard optical wireless environment, with a typical 2 m height between the imaging receiver and the LED optical transmitter grid, all three imaging receivers can provide effective resolving of distributed LEDs, defined across three pixels, given 2, 6, and 6 cm minimum separations between LEDs for the respective acute-, right-, and obtuse-angle microlenses.  B.6   Summary In this study, customized microlenses were fabricated and investigated for integrated imaging applications, given demands for compact device integration and broad FOV imaging. Theoretical and experimental analyses of electro-dispensed microlenses were carried out for acute-, right-, and obtuse-angle microlenses, with good agreement seen between theory and experiment. The right-angle microlens demonstrated superior overall imaging characteristics, with a small focal length and large NA. Its 120° FOV is the broadest ever demonstrated for integrated microlenses. The microlenses were integrated within optical wireless imaging receivers for performance testing. Ultimately, it was found that the electro-dispensed microlenses could be tailored for effective operation in optical wireless environments.     148  Appendix C  Ray-tracing Model for a Spherical Microlens  In this Appendix, the ray-tracing model for a spherical microlens is presented. The relevant parameters are defined in Figure C.1 and listed in Table C.1.  Figure C.1 Cross-sectional profile of a spherical microlens is shown with the ray-tracing model solutions. Optical rays are incident at a polar angle, θ, off the OA, and contact angle, α, of a spherical microlens is defined from 30° to 120° in this model.  149  Table C.1 Parameters defined for the ray-tracing model of a general spherical microlens are listed. r           radius of the microlens δ          beam width of incident beam (<< r) θ           incident angle off the OA R          a radius of curvature nair        refractive index of air nlens        refractive index of the microlens (x0, y0)  origin of the microlens yF          focal plane when θ = 0° (x1, y1)  intersection of the centre beam line (red)                with the bound of the microlens (x2, y2)  intersection of the upper beam line (blue)                with the bound of the microlens (x3, y3)  focal point of the three beam line (red,               blue and green) (x4, y4)  intersection of the lower beam line (green)                with the bound of the microlens (θU, θL)  incident angles of the upper and lower                 beam lines at the bound of the microlens (γU, γL)   refractive angles of the upper and lower                 beam lines at the bound of the microlens (βU, βL)  normal angles of the upper and lower                 beam lines at the bound of the microlens (ξU, ξL)  normal angles of the upper and lower                 beam lines at the focal point. (xL, yF)  left bound of the focal spot at the focal                plane attributed to lower beam line  (xR, yF)  right bound of the focal spot at the focal                plane attributed to lower beam line (xA, yF)  true centre of the focal spot at the focal                plane attributed to centre beam line (xV, yF)  calculated centre of the focal spot at the                focal plane by averaging xR and xL (yupp ycen ylow) Upper/Centre/Lower incident beam   The parameters introduced in Table C.1 are then derived and summarized as follows:   upptan( * sec )*cot ,tany x r θ δ θ θα= + +  (69)  cen *cot ,tanry x θα= +  (70)  lowtan( * sec )*cot ,tany x r θ δ θ θα= + −  (71) 150   0 0,x =  (72)  0 ,tanryα=     (73)  1 sin ,x R θ= −  (74)  1 cos ,tanry R θα= − +  (75)  2 cos sin ,x Rθ δ θ= − ∗ −  (76)  2 21 2 ,tanry R xα= − − +  (77)  4 cos sin ,x Rθ δ θ= ∗ −  (78)  2 24 4 ,tanry R xα= − − +   (79)  2 0U2 0arctan( ),y yx xβ −=−   (80)  4 0L4 0arctan( ),y yx xβ −=− (81)  U ,2 Uπθ θ β= − −  (82)  L L ,2πθ β θ= − +  (83)  U lens Uarcsin( *sin ),nγ θ=  (84)  L lens Larcsin( *sin ),nγ θ=  (85)  U U U,ξ γ β= +  (86) 151   L L L,ξ γ β= +  (87)  2 U 23Utantan ,cot tanry xxξαθ ξ− ∗ −=− (88)  2 U U 23Utan tan tantan ,1 tan tanry xyθ ξ ξαθ ξ− ∗ ∗ − ∗=− ∗ (89)  R 3 F 3 U( ) cot ,x x y y ξ= + − ∗  (90)  A F( ) tan ,tanrx y θα= − ∗  (91)  L 3 F 3 L( ) cot ,x x y y ξ= + − ∗  (92)  R LV .2x xx +=   (93)     The characterization of focusing is carried out as follows. The axial focal length is   f(α,θ) = y3(α,θ).       (94)     The axial focal contraction is  ∆f(α,θ) = y3(α,θ = 0°) – y3(α,θ).      (95)     The off-axial focal deflection is   ρ(α,θ) = xA(α,θ) ≈ xV(α,θ).      (96)     The off-axial focal spot size is   ∆ρ(α,θ) = xR(α,θ) – xL(α,θ).      (97) Note that Eqns. (94) and (95) are used for plotting Figure B.3, and Eqns. (96) and (97) are used for plotting Figure B.4.  152  Appendix D  Three-phase AC Circuit Design In this Appendix, an AC3φ circuit is designed. It is shown as a schematic in Figure D.1. The values of the resistors (R5 to R11) and capacitors (C1 to C3, C6, C9 and C10) used in the circuit are determined according to the derived phase shift and amplitude attenuation equations, 2 1arctan( )3 6RCfRCfπϕπ= − −  and 2 22 11/ 3 ( )3 6RCfARCfππ= + − , respectively, where f is the input AC voltage frequency, and R and C are the resistance and capacitance. The designed AC3φ circuit is built in LTspice (Figure D.2) and tested in an experiment (Figure D.3). Simulated and experimental results are shown in Figure D.4 and Figure D.5, respectively.   Figure D.1 AC3φ circuit is designed. The generated AC3φ voltages are delivered to individual PC switches via respective op-amps.  153Figure D.2 The LTspice schematic of the AC3" circuit is shown with the calculated values for resistors and capacitors. (Op-amps are not shown.)    Figure D.3 Photograph of the AC3" circuit. (Op-amps are not shown.)    154   Figure D.4 The LTspice simulation results of the designed AC3φ circuit.     Figure D.5 Photograph of the oscilloscope display of the output of the built AC3φ circuit. All three outputs are seen to have the identical frequency and amplitude.  155  Appendix E  Photoconductive Device Microfabrication Processes In this Appendix, the metal sputtering and UV photolithography processes employed to fabricate PC switches are given.   Metallization Process: Metal:                         Cr Sputter system:  Armstrong Engineering Corp. Nexdep Deposition System Process gas:   Argon Process gas pressure:  3.0 mTorr Gas flow rate:   8.06 sccm Deposition rate:  1 Å per second Final thickness:  50 nm Deposition time:  Approximately 10 minutes  Metal:                         Au Sputter system:  Armstrong Engineering Corp. Nexdep Deposition System Process gas:   Argon Process gas pressure:  3.0 mTorr Gas flow rate:   8.06 sccm Deposition rate:  2 Å per second Final thickness:  150 nm Deposition time:  Approximately 20 minutes  156  UV Photolithographic Process16: (valid for creating features down to 10 µm) Metal:           50/150 nm Cr/Au Mount:          Crystalbond onto a microslide (CrystalbondTM 509 at 140 °C)  Photoresist:   MICROPOSIT® S1813 Positive  Spinning:      Spread at 250 rpm for 30 seconds (Laurell Technol. Corp. WS-650 Spin Processor)                       Spread at 500 rpm for 30 seconds (Laurell Technol. Corp. WS-650 Spin Processor)             Spread at 2000 rpm for 60 seconds (approximately 2 µm thickness)  Soft Bake:     Bake at 110 °C for 10 minutes (Fisher Isotemp 500 Economy Vacuum Lab Oven) UV Expose:  30 seconds at 11.5W/cm2 (OAI Model 200 Mask aligner) Develop:       Develop for approximately 60 seconds (MICROPOSIT®MF-319) Hard Bake17:   Bake at 120°C for 60 minutes (Fisher Isotemp 500 Economy Vacuum Lab Oven) Etch:            Dip in Au etchant for 58 seconds (Transene Gold Etchant TYPE TFA)           Dip in Cr etchant for 15 seconds (Transene Chromium Etchant TYPE 1020)           Dip in photoresist remover for 10 seconds (MICROPOSIT®Remover 1165)                                                           16 Note that the fabrication time suggested in this process is based on the use of fresh chemical solutions in each step. It may vary with the degradation of the chemical solution.   17 This process is optional. It is not necessary for creating features larger than 100 μm.  157  Appendix F  Time-resolved Pump-probe Reflectivity Measurement In ultrafast measurements, time-resolved spectroscopy is commonly used to study the dynamic processes that lead to changing material properties18. Of relevance to my experimental work is the time-resolved pump-probe reflectivity setup, as it is used to test my semiconductor material response. In general, a strong pump laser pulse illuminates the semiconductor surface to change its intrinsic lattice properties, by way of the carrier density, refractive index and material reflectivity, and modulate the intensity of a co-propagating probe laser pulse. Depending on the wavelength (i.e., photon energy) of the probe laser pulse, the reflectivity can be analyzed with either a Drude conductivity model (if the probe photon energy is below the material’s bandgap) or the Kramers-Kronig relationships (if the probe photon energy is above the material’s bandgap).      The 780 nm, 120 fs pulsed laser time-resolved pump-probe experiment setup is shown in Figure F.1. The 120 mW pulse laser is first split by a 10/90 beamsplitter: the weaker probe laser beam is focused by a 40× micro-objective onto the semi-insulating GaAs wafer and subsequently reflected back onto a biased silicon photodetector; the stronger pump beam is chopped at an audio frequency (1 kHz) and is delayed by a motorized delay line, then focused by a lens onto the probe focal spot. The ultrafast phenomena at the focal spot is brought about by the strong pump laser pulse photoexcitation and is mapped onto the back reflected probe power (to be monitored via Labview software). The semi-insulating GaAs material response is then seen to be approximately 160 ps within the Labview control interface in Figure F.2 (the Labview core block diagram is shown in Figure F.3).                                                   18 With pulsed lasers, it is possible to study processes that occur on time scales as short as 10−15 seconds. 158   Figure F.1 A time-resolved pump-probe reflectivity setup is shown for probing the ultrafast carrier dynamics in a GaAs wafer.   Figure F.2 The Labview user interface is shown for the time-resolved pump-probe reflectivity experiment. The semi-insulating GaAs material response is shown in the top Channel 1 window.  159    Figure F.3 The A block diagram of the Labview program is shown for the time-resolved pump-probe reflectivity measurement.               160  Appendix G  Mathematical Expressions of Incident Optical Power for Individual PCs  In Chapter 2, we investigated the theoretical normalized incident optical power for PC1, PC2 and PC3 gaps, given by various directional cosine component inequality permutations. Here, the complete mathematical expressions of incident optical power for the individual PC gap are summarized in this Appendix based on Table 2.1.      The mathematical incident optical power expression for the PC1 gap is  P1-total = n1+ R*n1*((2*n2) ≥ (n1 + n3))   + R*n1*((2*n3) ≥ (n1 + n2))   + R*n1*n2/( n1 + n3 – n2)*((2*n2) < (n1 + n3))   + R*n1*n3/( n1 + n2 – n3)*((2*n3) < (n1 + n2))   + R2*n1*n2/( n2 + n3)*((2*n3) ≥ (n1 + n2))   + R2*n1*n3/( n2 + n3)*((2*n2) ≥ (n1 + n3))   + R2*n1*(n2/( n2 + n3) – (n1 + n2 – 2*n3)/(n1 + n2 + n3))*((n1 – 2*n2) ≤ (2*n3) < (n1 + n2))   + R2*n1*(n3/( n2 + n3) – (n1 + n3 – 2*n2)/(n1 + n2 + n3))*((n1 – 2*n3) ≤ (2*n2) < (n1 + n3))              161      The mathematical incident optical power expression for the PC2 gap is P2-total = n2   + R*n2*((2*n1) ≥ (n2 + n3))   + R*n2*((2*n3) ≥ (n1 + n2))   + R*n2*n1/( n2 + n3 – n1)*((2*n1) < (n2 + n3))   + R*n2*n3/( n1 + n2 – n3)*((2*n3) < (n1 + n2))   + R2*n2*n1/( n1 + n3)*((2*n3) ≥ (n1 + n2))   + R2*n2*n3/( n1 + n3)*((2*n1) ≥ (n2 + n3))   + R2*n2*(n1/( n1 + n3) – (n1 + n2 – 2*n3)/(n1 + n2 + n3))*((n2 – 2*n1) ≤ (2*n3) < (n1 + n2))   + R2*n2*(n3/( n1 + n3) – (n2 + n3 – 2*n1)/(n1 + n2 + n3))*((n2 – 2*n3) ≤ (2*n1) < (n2 + n3))      The mathematical incident optical power expression for the PC3 gap is I3-total = n3   + R*n3*((2*n1) ≥ (n2 + n3))   + R*n3*((2*n2) ≥ (n1 + n3))   + R*n3*n1/( n3 + n2 – n1)*((2*n1) < (n2 + n3))   + R*n3*n2/( n1 + n3 – n2)*((2*n2) < (n1 + n3))   + R2*n3*n1/( n1 + n2)*((2*n2) ≥ (n1 + n3))   + R2*n3*n2/( n1 + n2)*((2*n1) ≥ (n2 + n3))   + R2*n3*(n1/( n1 + n2) – (n1 + n3 – 2*n2)/(n1 + n2 + n3))*((n3 – 2*n1) ≤ (2*n2) < (n1 + n3))   + R2*n3*(n2/( n1 + n2) – (n2 + n3 – 2*n1)/(n1 + n2 + n3))*((n3 – 2*n2) ≤ (2*n1) < (n2 + n3)) 162  Appendix H  Matlab Ray-tracing Code for Retroreflected Power of a CC-PC Transceiver Theoretical retroreflected power of the right-angled CC-PC transceiver is modeled with a ray-tracing approach, whereby it is illuminated from a sufficiently large optical beam with a uniform intensity grid at various φ and θ  directions, both ranging from 0° to 90°. The complete Matlab program is attached here.  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Here define CCR visible structure a=linspace(0,1,2);                             % Define the dimension of the CCR  b=linspace(0,1,2); c=linspace(0,1,2); [x1,y1]=meshgrid(a,b);                      % x-y plane z1=zeros(length(x1),length(y1)); [x2,z2]=meshgrid(a,c);                      % x-z plane y2=zeros(length(x2),length(z2)); [y3,z3]=meshgrid(b,c);                       % y-z plane x3=zeros(length(y3),length(z3));  % plot the CCR structure in figure h1=surf(x1,y1,z1,'FaceColor','r');hold on                % plot x-y plane h2=surf(x2,y2,z2,'FaceColor','y');hold on                           % plot x-z plane h3=surf(x3,y3,z3,'FaceColor','b');hold on                % plot y-z plane xlabel('X-axis'); ylabel('Y-axis'); zlabel('Z-axis'); axis([-5,5,-5,5,-5,5]); grid on 163  % Here make incident source (surface) for CCR structure phi=0:1:90; Phi=phi*pi/180;          % define horizontal angles                      theta=0:1:90; Theta=theta*pi/180;             % define vertical angles x=zeros(length(Phi),length(Theta));  y=zeros(length(Phi),length(Theta)); z=zeros(length(Phi),length(Theta)); for m=1:length(Phi)      for n=1:length(Theta)            [x(m,n),y(m,n),z(m,n)]=sph2cart(Phi(m),Theta(n),3);      end     end surf(x,y,z,'FaceColor','g')  % Ray tracing part – generate ray traces from source plane to CCR structure Power_Difference=zeros(length(Phi),length(Theta)); Retropoint=zeros(length(Phi),length(Theta));  y4=linspace(-3,3,1000);           % Create initial incident plane in y and z y5=meshgrid(y4,z4); z5=meshgrid(z4,y4); z5=z5'; x5=zeros(length(y4),length(z4))+3;          % Create initial incident plane in x x6=zeros(length(x5),length(y5)); y6=zeros(length(x5),length(y5));            % Create rotated plane z6=zeros(length(x5),length(y5));                    Samp_point=length(z4)*length(y4);                   % count the number of incident light rays  164  for m1=1:length(Phi)             for n1=1:length(Theta)                   m1/size(Phi,2)*100                               % Running percentage x6=cos(Phi(m1))*cos(Theta(n1)).*x5-sin(Phi(m1))*cos(Theta(n1)).*y5-sin(Theta(n1)).*z5; y6=sin(Phi(m1)).*x5+cos(Phi(m1)).*y5; z6=cos(Phi(m1))*sin(Theta(n1)).*x5-sin(Phi(m1))*sin(Theta(n1)).*y5+cos(Theta(n1)).*z5;      x=cos(Phi(m1))*cos(Theta(n1)); y=sin(Phi(m1)); z=cos(Phi(m1))*sin(Theta(n1)); Retro_point=zeros(length(x6),length(y6));        % count the number of retroreflected light rays    % Create Ray tracing --time (ps), position (cm) and velocity (cm/ps)    for m11=1:length(x5)        for n11=1:length(y5) bit=12; pos0=[x6(m11,n11),y6(m11,n11),z6(m11,n11)];                    % Initial ray position vel0=[-x/bit -y/bit -z/bit];                                            % Initial velocity  % Propagating ray: time (ps), position (cm) and velocity (cm/ps) dt=0.5; time=0:dt:500; pos=zeros(size(time,2),size(pos0,2)); pos(1,:)=pos0; vel=zeros(size(time,2),size(pos0,2)); vel(1,:)=vel0; Mirror1=0; Mirror2=0; Mirror3=0;                              % PC flag index 165  for i=1:size(time,2)   vel(i+1,:) = vel(i,:);   pos(i+1,:) = pos(i,:) + vel(i,:)*dt;  if((abs(pos(i+1,1))<=(x/bit))&&(Mirror1==0)&&(pos(i+1,2)<=1)&&(pos(i+1,3)<=1)&&(pos  (i+1,2)>=0)&&(pos(i+1,3)>=0)&&((pos(i+1,2)+pos(i+3))<=1)&&((pos(i+1,2)+pos(i+3))>=0)),   vel(i+1,1) = - vel(i+1,1);  Mirror1=Mirror1+1; end  if((abs(pos(i+1,2))<=(y/bit))&&(Mirror2==0)&&(pos(i+1,1)<=1)&&(pos(i+1,3)<=1)&&(pos(i+1,1)>=0)&&(pos(i+1,3)>=0)&&((pos(i+1,1)+pos(i+3))<=1)&&((pos(i+1,1)+pos(i+3))>=0)),   vel(i+1,2) = - vel(i+1,2);  Mirror2=Mirror2+1;     end  if((abs(pos(i+1,3))<=(z/bit))&&(Mirror3==0)&&(pos(i+1,1)<=1)&&(pos(i+1,2)<=1)&&(pos(i+1,1)>=0)&&(pos(i+1,2)>=0)&&((pos(i+1,2)+pos(i+1))<=1)&&((pos(i+1,2)+pos(i+1))>=0)),    vel(i+1,3) = - vel(i+1,3);  Mirror3=Mirror3+1;     end    if ((Mirror1==1)&&(Mirror2==1)&&(Mirror3==1))                      % Retroreflection happens       Retro_point(m11,n11)=1;   end end 166  plot3(pos(:,1),pos(:,2),pos(:,3),'k'); hold on                % plot Ray trace end end  % Calculate how many lights get retroreflection. for parameter3=1:length(x6)             for parameter4=1:length(y6)                 Retropoint(m1,n1)=Retropoint(m1,n1)+Retro_point(parameter3,parameter4);             end end  Retropoint(m1,n1)= Retropoint(m1,n1)/Samp_point;     % Calculate retroreflection percentage  surf(x6,y6,z6,'FaceColor','m') ;                % plot the visible plane        end   end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   167  Appendix I  Derivation of Transient Optical Power of the CC-PC Transceiver In Section 2.2.3, the geometrical input response of a CC-PC transceiver was characterized in terms of the dimensions of the structure and the directionality of the illumination—as these attributes lead to varying transit time delays on the output photocurrent, iout(t). The incident optical power, P(t, λ), on the PC gaps consisted of three distinct illumination contributions:  direct illumination by the incident optical pulse, single-reflection illumination from reflections off its neighbouring PC surfaces, and double-reflection illumination from reflections off two neighbouring PC surfaces. All direct, single-reflection, and double-reflection illumination contributions must be considered for both clockwise and counter-clockwise reflective permutations around the structure.  Theoretical analyses of the incident optical power on the PC2 gap19, is presented in this Appendix with the incident optical intensity being along the central axis of symmetry (ϕ = 45° & θ ≈ 54.7°) for optimal photodetection and retro-modulation. Similar analyses can be applied for any other optical alignment.  The incident optical intensity is characterized by a laser pulse that has the Gaussian envelope  24ln 22p0( )tI t I e τ−= , (98) where, τp = 100 fs is the FWHM of the Gaussian envelope and I0 is the intensity amplitude. The zero-time is defined by the arrival of the incident optical pulse at the entrance interface of (a, a, a) of the CC-PC transceiver. All three above-mentioned distinct illumination contributions on the PC2 gap are analyzed in the following subsections.                                                     19 The PC gap of the CC-PC transceiver is considered to be a dimensionless line during the theoretical analyses, as the PC gap width, w = 200 μm, is much smaller than the PC gap length, l ≈ 3.54 mm and side-length, a = 5 mm.  168  I.1 Direct illumination contribution  Figure I.1 A schematic is shown for the direct illumination on PC2 gap. The optical beams are incident along the central axis of symmetry and passing through the entrance interface along the line B1B2 (shown as a blue dashed triangular) to strike the entire PC2 gap. The illuminated PC2 gap is shown in green.  Direct illumination contribution on the PC2 gap is first analyzed, and the schematic is shown in Figure I.1. The optical beams, from a sufficiently large plane with a uniform intensity of I(t), are incident parallel to the central axis of symmetry towards the CC-PC transceiver. Note that, the PC2 gap is fully illuminated by the optical beams passing the entrance interface through line A1A2, which contributes to the direct incident optical power, Pdirect(t). Here, line A1A2, with the points A1 of2( , , )3 3 3a b a b a b− − +and A2 of2( , , )3 3 3a b a b a b+ − −, is the projection of the PC2 gap (represented by line C1C2, with the points C1 of (0, 0, b) and C2 of (b, 0, 0)) onto the entrance interface along the central axis of symmetry. Line B1B2 is, therefore, the vertical distance in between line A1A2 and line C1C2, and its length, 3a b− , is used to determine the time delay, t0, defined as the transit time from the optical beam passing the entrance interface to striking the 169  PC2 gap. The direct incident optical power, Pdirect(t), is then  direct 024ln 2( )02024ln 2( )320( ) ( ) ( )( ).t tpa btcpP t I t t d wlI e d wlwlI eττ−−−−−= −==∫∫ , (99) where, 0 3a btc−=  is the time delay and 2l b=  is the length of the PC gap.   I.2 Single-reflection illumination contribution The single-reflection illumination contribution on the PC2 gap is analyzed next, and the schematics are shown in Figure I.2 as a two-step illustration. The optical beams are incident along the central axis of symmetry towards the CC-PC transceiver. A portion of the optical beams passes the entrance interface through line A1A3, with the point A3 of (0, b, b). It then follows the dashed line B3B4, to strike the PC1 Au surface on line A3C1 as shown in Figure I.2 (a). The point B3,2 2( , , )3 3 3a b x a b x a b x− − − + + −, is on the line A1A3 and the point B4, (0, x, b), is on the line C1A3 with 0 ( )x a b≤ ≤ − . This portion of the optical beam ultimately contributes to the single-reflection illumination onto the PC2 gap in the next step as shown in Figure I.2 (b). The optical beams reflect off the PC1 Au surface and illuminate the PC2 gap (represented by line C1C2), following the dashed line B4B5. The point B5, ( ,0, )x b x− , is on the line C1C2.  Similarly, the total length, d1, of the dashed lines B3B4 and B4B5 is used to determine the time delay, defined as the transit time from the optical beam passing the entrance interface to the striking of the PC2 gap. It is calculated as 170   1 12 2 ,33 3 3x a b a bd l− −= + = +  (100) where, 1 2l x= is defined as the length of the illuminated PC2 gap. Note that this case is more complicated than the analysis carried out for direct illumination. The optical beams, striking on the PC2 gap from the reflection-off the PC1 surface, are not hitting the PC2 gap at the same time: the optical beams passing through the point of A1 will first strike the PC2 gap directly at the point of C1, which represents the turn-on time for photoexcitation on the PC2 gap; the optical beams passing through the point of A3 will strike the PC1 surface and experience the longest propagation time to reflect onto PC2 gap at the point of C2, which represents the turn-off time for photoexcitation on the PC2 gap. The single-reflection incident optical power, Psingle-reflection(t, λ), is thus calculated to be  212p212p1single-reflection 14ln 2( )0 124ln 2[ ( )]3 32( )0 10( , ) 2 ( ) ( ) ( )2 ( ) ( )2 ( ) ,dtcl a btc ca bdP t R I t d wlcR I e d wlR w I e dlττλ λλλ−−−− +−−= −==∫∫∫ (101) where, R(λ) is the wavelength-dependent Au surface reflectivity, and a factor of 2 is included in this expression to account for clockwise and counter-clockwise internal reflections. To solve the Eqn. (101), we first let 1p p2 ln 2( 2 )2 ln 23l a bttcτ τ+ −′ = − , and its range is determined as 1 1p p p p2 3ln 2( 2 ) 2 ln 2( 2 )2 ln 2 2 ln 2,3l a b l a bt tc cτ τ τ τ⎡ ⎤+ − + −⎢ ⎥− −⎢ ⎥⎣ ⎦ for the integral of Eqn. (101) with 1p2 2ln 23dt dlcτ′ = .  171                (a)                                                                       (b) Figure I.2 Schematics are shown for the single-reflection illumination on PC2 gap as a two- step illustration. The incident optical beams, along the central axis of symmetry, first strike the PC1 Au surface along the line B3B4 (shown in (a)) and then reflect off the PC1 Au surface to strike the PC2 gap along B4B5 (shown in (b)). The illuminated PC2 gap is shown in green.  Eqn. (101) is then solved for the single-reflection incident optical power, Psingle-reflection(t, λ), as 2 2p pp p2 2pp p psingle-reflection2 ln 2 2 ln 2( )0 3p0 02 ln 2 2 ln 2 3( )2 ln 2 2 ln 2( )2 ln 2 2 ln 2 3( )3p0 0 0( , )32 ( ) ( )[ ]2 2ln 23( ) [ ].2 ln 2t a bct tt a bct a bt a bc ct tP tcR wI e dt e dtcR wI e dt e dtτ ττ τττ τ τλτλτλ−−′ ′− −−−−− −−′ ′− −′ ′= +′ ′= − +∫ ∫∫ ∫ (102) Given the error function definition of20erf ( )2x te dt xπ− =∫ , Eqn. (101) can be simplified as single-reflectionp0p p( , )( ) 3( )2 ln 2( ) 2 ln 2( )3 3( ) [erf ( ) erf ( )].2 2ln 2P ta b a bt tc c cR wIλτ πλτ τ− −− −= − (103) 172    Figure I.3 Schematics are shown for the double-reflection illumination on PC2 gap as a three-step illustration. The incident optical beams, along the central axis of symmetry, first strike the PC3 surface along the line B6B7   (shown in (a)), reflected onto PC1 surface along the line B7B8 (shown in (b)), and ultimately partially illuminate the PC2 gap along the line B8B9 (shown in (c)). The illuminated PC2 gap is shown in green, and the unilluminated PC2 gap is shown in grey.   I.3 Double-reflection illumination contribution The double-reflection illumination contribution on the PC2 gap is analyzed here. The schematics are shown in Figure I.3 as a three-step illustration. The optical beams are incident 173  parallel to the central axis of symmetry towards the CC-PC transceiver. A portion of the optical beams passes the entrance interface through the line A4A5, with the points A4 of 2 2( , , )6 3 6a b a b a b− + −and A5 of (b, b, 0). It then follows the dashed line B6B7 to strike the PC3 Au surface on the line A5A6, with the point A6 of (0, b/2, 0), as shown in Figure I.3 (a). The point B6, 1 13 2 3( , , )3 3 3a b x a b xa b+ − − ++ is on the line A4A5, and the point B7, 1 1( 2 , ,0)b x b x− − is on the line A5A6 with the range of 1( )02a bx −≤ ≤ . The optical beams then get reflected off the PC3 Au surface following the dashed line B7B8 to strike the PC1 Au surface on the line C1A6 as shown in Figure I.3 (b). The point B8, 1 1(0, , 2 )x b x− , is on the line C1A6. This portion of the optical beam ultimately contributes to the double-reflection illumination onto the PC2 gap in the next step as shown in Figure I.3(c). The optical beams reflect off the PC1 Au surface, following the dashed line B8B9 to partially illuminate the PC2 gap, represented by the line C1C3 with the point C3 of (b/2, 0, b/2). The point B9, 1 1( ,0, )x b x− , is on the line C1C3.   The total optical beam propagation length, represented by the summed length of the dashed lines B6B7, B7B8, and B8B9, is used to determine the time delay, and it is calculated as  23( 2 ) 3 .3a bd b−= +  (104) It is interesting to note that this total optical beam propagation length, from passing the entrance interface to illuminating the PC2 gap, is a constant, and it is only related to the device dimensions when the condition of b ≤ a/2 is satisfied. Thus, a discrete pulse is created for double-reflection illumination at this the optimal orientation.  The double-reflection incident optical power, Pdouble-reflection(t, λ), is calculated to be  174   2 2double-reflection224ln 2( )22 p03( 2 ) 3 24ln 2[ ( )]322 p0( , ) 2 ( ) ( ) ( )2 ( ) ( )( ) ,dtca b btc cdP t R I t d wlcR I e d wlR wlI eττλ λλλ−−−− +−= −==∫∫  (105) where R(λ) is the wavelength-dependent Au surface reflectivity. A factor of 2 is included to account for clockwise and counter-clockwise internal reflections.  I.4 Summary The total incident optical power onto the PC2 gap, P(t, λ), is then obtained by summing Eqns. (99), (103),and (105), and the final expression is ( )22 23p0pp p3( 2 ) 3 24ln 2[ ( )]322 p0,( ) 3( )2 ln 2( ) 2 ln 2( )3 3( ) [erf ( ) erf ( )]2 2ln 2( ) .a bln tcoa b btc cP t wlI ea b a bt tc c cR wIR wlI eττλτ πλτ τλ⎛ ⎞−⎛ ⎞−⎜ ⎟⎜ ⎟⎝ ⎠⎜ ⎟−⎜ ⎟⎜ ⎟⎝ ⎠−− +−=− −− −+ −+ (106) Note that an assumption of  π ≈ 2  is made in the final expression of Eqn. (50) in Section 2.2.3.2.     

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