Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Microfluidic and terahertz technologies for integrated spectroscopic systems Collier, Christopher Michael 2016

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2016_september_collier_christopher.pdf [ 14.25MB ]
Metadata
JSON: 24-1.0305861.json
JSON-LD: 24-1.0305861-ld.json
RDF/XML (Pretty): 24-1.0305861-rdf.xml
RDF/JSON: 24-1.0305861-rdf.json
Turtle: 24-1.0305861-turtle.txt
N-Triples: 24-1.0305861-rdf-ntriples.txt
Original Record: 24-1.0305861-source.json
Full Text
24-1.0305861-fulltext.txt
Citation
24-1.0305861.ris

Full Text

  i    MICROFLUIDIC AND TERAHERTZ TECHNOLOGIES FOR INTEGRATED SPECTROSCOPIC SYSTEMS by Christopher Michael Collier  B.A.Sc., The University of British Columbia, 2011 B.Mus., The University of Toronto, 2007  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)  July 2016 © Christopher Michael Collier, 2016  ii         The undersigned certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis entitled:    Microfluidic and terahertz technologies for integrated spectroscopic systems  Submitted by            Christopher Michael Collier          in partial fulfillment of the requirements of   The degree of                        Doctor of Philosophy                                                                  Dr. Jonathan 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. Thomas Johnson, School of Engineering, The University of British Columbia Supervisory Committee Member, Professor (please print name and faculty/school in the line above)  Dr. Murray Newman, Physics, The University of British Columbia University Examiner, Professor (please print name and faculty/school in the line above)  Dr. Matthew Reid, Physics, The University of Northern British Columbia External Examiner, Professor (please print name and university in the line above)   July 13, 2016 (Date submitted to Grad Studies)       iii  Abstract The terahertz (THz) spectrum, being approximately 0.1-10 THz, is the region of the electromagnetic spectrum that lies beyond the reach of electronic and optical devices. Because of this unique spectral region, THz radiation has found its place in many contemporary applications. In particular, THz radiation has been used in biochemical analyses, via THz spectroscopy. Terahertz spectroscopy is sensitive to vibrational and rotational modes of organic species, and this functionality can be enhanced by integrating THz spectroscopy within lab-on-a-chip platforms. Such platforms can enable high-sensitivity and rapid interrogation of biochemical species via THz spectroscopy. However, the integration of THz spectroscopy in lab-on-a-chip platforms has not yet been achieved. This is due to unresolved (and fundamental) challenges on the underlying structures and materials being used for microfluidic actuation and THz emission. This thesis addresses these challenges through enhancements towards a digital-microfluidic- (DMF)-based THz-time-domain-spectroscopy (TDS) system. For microfluidic actuation, this work focuses on the development of DMF structures having practical addressability and microfluidic actuation with independent two-dimensional control. Three such structures, the square electrode, cross-referenced, and multiplexer grid, are explored. It is found that the multiplexer grid is the only DMF structure that provides practical addressability and independent two-dimensional control. For THz emission, a variety of photoconductive materials are investigated to realize effective THz emission with minimal Joule heating flux. This is a key point for the integration of THz spectroscopy within lab-on-a-chip platforms, as it becomes necessary to avoid evaporation of the biochemical species. Materials exhibiting transient mobility (such as GaP) and surface-enhanced recombination Abstract  iv  (such as semiconductor nanocomposites and textured InP) are explored. It is found that photoconductive THz emitters made with textured InP materials provide similar THz emission characteristics to their bulk counterparts but have an order of magnitude lower Joule heating flux. Terahertz spectroscopy is ultimately performed on a variety of vapour, liquid, and solid samples to develop and test the THz spectroscopy analysis method, to propose dimensions and THz-compatible-materials for the DMF-based THz-TDS system, and to demonstrate THz-TDS on biochemical species. The findings of this work lay the groundwork for the development of future DMF-based THz-TDS systems.           v  Preface A publication list is presented below. The body of this thesis is based on [B1], [J1], [J5], [J10], [J12], and [J15]. A description of author contributions is given for these works.  Book Chapters [B1, related to Chapter 2 of this thesis] C. M. Collier, J. Nichols, and J. F. Holzman, "Digital microfluidics technologies for biomedical devices," in Microfluidics Devices for Biomedical Applications, 1st ed. Sawston, UK: Woodhead Publishing, 2013, ch. 4, pp. 139-164. C. M. Collier performed the experiments and analysis and wrote the manuscript. J. Nichols contributed to a section of this work not included in this thesis. J. F. Holzman provided guidance and faculty supervision for this project.  Journal Articles [J1, related to Chapter 3 of this thesis] C. M. Collier, T. J. Sterling, I. R. Hristovski, J. D. A. Krupa, and J. F. Holzman, "Photoconductive terahertz generation from textured semiconductor materials," Scientific Reports, vol. 6, 23185(1-10), 2016. C. M. Collier performed the experiments and analysis, wrote the manuscript, and revised the manuscript based on reviewer feedback. T. J. Stirling, I. R. Hristovski, and J. D. A. Krupa assisted with experiments and manuscript preparation under the supervision of C. M. Collier. J. F. Holzman provided guidance and faculty supervision for this project and contributed to the writing of the manuscript. Preface  vi  [J2] B. Born, S. Geoffroy-Gagnon, J. D. A. Krupa, I. R. Hristovski, C. M Collier, and J. F. Holzman, "Ultrafast all-optical switching via subdiffractional photonic nanojets and select semiconductor nanoparticles," ACS Photonics, vol. 3, pp. 1095-1101, 2016. [J3] 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," Optics Letters, vol. 40, pp. 1583-1586, 2015. [J4] C. M. Collier, K. A. Hill, M. A. DeWachter, A. M. Huizing, and J. F. Holzman, "Nanophotonic implementation of optoelectrowetting for microdroplet actuation," Journal of Biomedical Optics, vol. 20, 025004(1-5), 2015. [J5, related to Chapter 3 of this thesis] C. M. Collier, M. H. Bergen, T. J. Stirling, M. A. DeWachter, and J. F. Holzman, "Optimization processes for pulsed terahertz systems," Applied Optics, vol. 54, pp. 535-545, 2015. C. M. Collier performed the experiments and analysis, wrote the manuscript and revised the manuscript based on reviewer feedback. M. H. Bergen, T. J. Stirling, M. A. DeWachter assisted with experiments under the supervision of C. M. Collier. J. F. Holzman provided guidance and faculty supervision for this project and contributed to the writing of the manuscript. [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," Applied Optics, vol. 53, pp. 3647-3655, 2014. Preface  vii  [J7] C. M. Collier and J. F. Holzman, "Ultrafast photoconductivity of crystalline, polycrystalline and nanocomposite ZnSe material systems for terahertz applications," Applied Physics Letters, vol. 104, 042101(1-5), 2014. [J8] C. M. Collier, K. A. Hill, and J. F. Holzman, "Dielectrophoresis microjet for on-chip technologies," RSC Advances, vol. 3, pp. 23309-23316, 2013. [J9] C. M. Collier, B. Born, X. Jin, and J. F. Holzman, "Ultrafast charge-carrier and phonon dynamics in GaP," Applied Physics Letters, vol. 103, 072106(1-4), 2013. [J10, related to Chapter 3 of this thesis] 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 Journal of Quantum Electronics, vol. 49, pp. 691-696, 2013. C. M. Collier performed the experiments and analysis, wrote the manuscript and revised the manuscript based on reviewer feedback. B. Born, M. Bethune-Waddell, and X. Jin assisted with experiments under the supervision of C. M. Collier. J. F. Holzman provided guidance and faculty supervision for this project and contributed to the writing of the manuscript. [J11] X. Jin, C. M. Collier, J. J. A. Garbowski, B. Born, and J. F. Holzman, "Ultrafast transient responses of optical wireless communication detectors," Applied Optics, vol. 52, pp. 5042-5049, 2013. [J12, related to Chapter 3 of this thesis] C. M. Collier, B. Born, and J. F. Holzman, "Ultrafast response of SiC and Si nanocomposite material systems," Electronics Letters, vol. 48, pp. 1618-1619, 2012. Preface  viii  C. M. Collier supervised the experiments, performed the analysis, and wrote the manuscript. B. Born assisted with experiments under the supervision of C. M. Collier. J. F. Holzman provided guidance and faculty supervision for this project and contributed to the writing of the manuscript.  [J13] J. Nichols, C. M. Collier, E. L. Landry, M. Wiltshire, B. Born, and J. F. Holzman, "Optoelectronic control of digital lab-on-a-chip systems," Journal of Biomedical Optics, vol. 17, 067005(1-7), 2012. [J14] C. M. Collier, X. Jin, and J. F. Holzman, "Ultrafast refractometry for characterization of nanocomposite material systems," IEEE Photonics Technology Letters, vol. 24, pp. 590-592, 2012. [J15, related to Chapter 2 of this thesis] C. M. Collier, M. Wiltshire, J. Nichols, B. Born, E. L. Landry, and J. F. Holzman, "Nonlinear dual-phase multiplexing in digital microfluidic architectures," Micromachines, vol. 2, pp. 369-384, 2011. C. M. Collier performed the experiments and analysis, wrote the manuscript, and revised the manuscript based on reviewer feedback. M. Wiltshire assisted with experiments, J. Nichols and B. Born assisted with preparation of manuscript figures, and E. L. Landry provided simulation data. J. F. Holzman provided guidance and faculty supervision for this project and contributed to the writing of the manuscript. [J16] C. M. Collier, X. Jin, J. F. Holzman, and J. Cheng, "Omni-directional characteristics of composite retroreflectors," Journal of Optics A: Pure and Applied Optics, vol. 11, 085404(1-10), 2009. Preface  ix  Conference Proceedings and Presentations [C1] C. M. Collier, J. D. A. Krupa, I. R. Hristovski, T. J. Stirling, M. H. Bergen, and J. F. Holzman, "Textured semiconductors for enhanced photoconductive terahertz emission," Proceedings of SPIE Photonics West, San Francisco, USA, February, 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," Proceedings of SPIE Photonics West, San Francisco, USA, February, 2016.  [C3] C. M. Collier, K. A. Hill, M. A. DeWatcher, A. M. Huizing, and J. F. Holzman, "Optoelectrowetting for continuous microdroplet actuation," Proceedings of SPIE Photonics Europe, Brussels, Belgium, April, 2014. [C4] K. A. Hill, C. M. Collier, and J. F. Holzman, "Dielectrophoresis microjets: A merging of electromagnetics and microfluidics for on-chip technologies," Proceedings of SPIE Photonics Europe, Brussels, Belgium, April, 2014. [C5] M. H. Bergen, J. Nichols, C. M. Collier, X. Jin, and J. F. Holzman, "Retroreflective imaging systems for enhanced optical biosensing," Proceedings of SPIE Photonics Europe, Brussels, Belgium, April, 2014. [C6] C. M. Collier, B. Born, X. Jin, and J. F. Holzman, "Ultrafast spectroscopy of hot electron and hole dynamics in GaP," Proceedings of SPIE Optics and Photonics, San Diego, USA, August, 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," Proceedings of SPIE Optics and Photonics, San Diego, USA, August, 2013. Preface  x  [C8] B. Born, C. M. Collier, and J. F. Holzman, "Practical nanophotonic architectures for ultrafast all-optical switching," Proceedings of SPIE Optics and Photonics, San Diego, USA, August, 2013. [C9] 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," Proceedings of SPIE Optics and Photonics, San Diego, USA, August, 2013. [C10] X. Jin, C. M. Collier, B. W. D. Veerman, and J. F. Holzman, "Enhanced reception field of view and speed characteristics for optical wireless devices," Proceedings of the IEEE Photonics Society Summer Topical Meeting, Seattle, USA, July, 2012. [C11] C. M. Collier, X. Jin, B. Born, and J. F. Holzman, "Ultrafast optical analyses and characteristics of nanocomposite media," Proceedings of SPIE Photonics West, San Francisco, USA, January, 2012. [C12] J. Nichols, E. L. Landry, B. Born, M. Wiltshire, C. M. Collier, and J. F. Holzman, "Optical sensing for on-chip digital microfluidics," Proceedings of SPIE Photonics West, San Francisco, USA, January, 2012. [C13] C. M. Collier, J. Nichols, M. Wiltshire, B. Born, E. L. Landry, A. Ahmadi, and J. F. Holzman, "Optoelectronic elements for digital lab-on-a-chip systems," Presentation at Canadian Society for Chemistry Canadian Chemistry Conference and Exhibition, Montréal, Canada, June, 2011. [C14] C. M. Collier, B. Born, and J. F. Holzman, "Voltage phase control for enhanced addressability in highly-parallel digital microfluidic architectures," Proceedings of the Preface  xi  ASME International Conference on Nanochannels, Microchannels and Minichannels, Edmonton, Canada, June, 2011. [C15] X. Jin, C. M. Collier, J. Cheng, and J. F. Holzman, "Modulation and directionality characteristics of free-space optical transmission links," Proceedings of the IEEE Electro/Information Technology Conference, Windsor, Canada, June, 2009.   xii  Table of Contents Abstract .................................................................................................................................. iii Preface ......................................................................................................................................v Table of Contents .................................................................................................................. xii List of Tables ..........................................................................................................................xv List of Figures ...................................................................................................................... xvi Acknowledgements ............................................................................................................ xxvi Dedication ......................................................................................................................... xxviii Chapter 1: Introduction ..........................................................................................................1 1.1 Terahertz Spectroscopy in Lab-on-a-Chip Platforms ............................................... 1 1.2 Thesis Scope ............................................................................................................. 8 Chapter 2: Microfluidic Actuation.......................................................................................11 2.1 Background ............................................................................................................. 11 2.2 Potential Structures for Digital Microfluidic Devices ............................................ 11 2.2.1 Square Electrode Grid......................................................................................... 11 2.2.2 Cross-Referenced Grid ....................................................................................... 14 2.2.3 Multiplexer Grid ................................................................................................. 16 2.3 Multiplexer Grid Theory and Results ..................................................................... 19 Chapter 3: Terahertz Emission ............................................................................................32 3.1 Background ............................................................................................................. 32 3.1.1 Continuous Wave Terahertz Emitters ................................................................. 32 3.1.2 Pulsed Terahertz Emitters ................................................................................... 33 Table of Contents  xiii  3.2 Experimental Setups for Investigating Ultrafast Material and Terahertz  Responses………………………………………………………………………………… 39 3.2.1 Pump-Probe Setup for the Ultrafast Material Response ..................................... 40 3.2.2 Terahertz Setup for the Terahertz Response ....................................................... 43 3.2.2.1 Terahertz Setup Design............................................................................... 44 3.2.2.1.1 Collineation Process .............................................................................. 47 3.2.2.1.2 Autocorrelation Process ........................................................................ 49 3.2.2.1.3 Electro-Optic Process ............................................................................ 53 3.2.2.2 Operation of the Terhertz Setup ................................................................. 58 3.3 Photoconductive Terahertz Emitters with Transient Mobility ............................... 61 3.4 Photoconductive Terahertz Emitters with Enhanced Surface Recombination ....... 73 3.4.1 Nanocomposite Materials ................................................................................... 73 3.4.2 Textured Materials .............................................................................................. 82 Chapter 4: Terahertz Spectroscopy .....................................................................................96 4.1 Background ............................................................................................................. 96 4.2 Terahertz Spectroscopy Analysis Method .............................................................. 97 4.3 Terahertz-Time-Domain-Spectroscopy for Vapour ............................................. 103 4.4 Terahertz-Time-Domain-Spectroscopy for Liquid ............................................... 106 4.5 Terahertz-Time-Domain-Spectroscopy for Solids ............................................... 111 4.5.1 Terahertz-Time-Somain-Spectroscopy for a Glass Solid Sample .................... 111 4.5.2 Terahertz-Time-Domain-Spectroscopy for a Plastic Solid Sample.................. 113 4.5.3 Terahertz-Time-Domain-Spectroscopy for a Quartz Solid Sample ................. 113 Table of Contents  xiv  4.5.4 Terahertz Time-Domain-Spectroscopy of a Polydimethylsiloxane Solid Sample………………………………………………………………………………... 116 Chapter 5: Conclusions .......................................................................................................119 5.1 Conclusions .......................................................................................................... 119 5.2 Summary of Contributions ................................................................................... 119 5.3 Future Work .......................................................................................................... 123 References .............................................................................................................................126 Appendices ...........................................................................................................................143 Appendix A Photolithography and Microfabrication for Multiplexer Grid ..................... 143 Appendix B Photoconductive Terahertz Emitter as Hertzian Dipole Antenna ................ 146 Appendix C Circuit for Measuring Current from Photoconductive Terahertz Emitters .. 151 Appendix D Circuit for Creating 100 V Peak-to-Peak Squarewave ................................ 152 Appendix E Electro-Optic Detection Derivation .............................................................. 153 Appendix F MATLAB Script for Nanoparticle Analysis ................................................ 158 Appendix G Photoconductive Terahertz Detection .......................................................... 163 Appendix H MATLAB Script for Terahertz Spectroscopy Analysis Method ................. 164    xv  List of Tables Table 2.2.3.1 A comparison of structures for the DMF device is presented. The square              electrode, cross-referenced, and multiplexer grids are evaluated in terms of              independent 2-D control and practical addressability. ............................................... 19 Table 3.4.2.1 The charge-carrier lifetimes are shown for non-, fine-, coarse-texture InP              materials. The standard error for the charge-carrier lifetime for each material is              also shown. The charge-carrier lifetime decreases as the materials progress from              non-textured InP through to coarse-textured InP........................................................ 87 Table 3.4.2.2 The power dissipation per area is shown in non-, fine-, and coarse-textured              InP PC THz emitters and in the multiplexer grid DMF device. The power              dissipation per area (i.e., Joule heating flux) in the PC THz emitters is              significantly higher than in the multiplexer grid DMF device. The power              dissipation per area in the coarse-textured InP PC THz emitter is an order of              magnitude lower than that of the non-textured InP PC THz emitter. ......................... 94 Table 4.3.1 A comparison of frequencies of experimental and theoretical absorption              peaks for the water vapour sample and the corresponding rotational transition are              shown. The largest error between the frequencies of experimental and theoretical              absorption peaks is 0.1%. ......................................................................................... 105    xvi  List of Figures Figure 1.2.1 A conceptual schematic is shown of a DMF-based THz-TDS system (in the              red box). The system implements microfluidic technology by way of a DMF              device (in the blue box). The DMF device uses upper and lower electrodes for              microfluidic actuation. The system also implements THz technology by way of              PC THz emission and detection (in the green boxes). The PC THz emission and              detection is carried out by way of respective upper and lower electrodes. ................ 10 Figure 2.2.1.1 The structure of the DMF square electrode grid is shown. An actuating              voltage amplitude is applied to the left of microdroplet 1 (i = 60 electrode), and              microdroplet 1 is actuated while microdroplet 2 remains stationary. ......................... 13 Figure 2.2.2.1 The structure of the DMF cross-referenced gridis shown. An above-             threshold actuating voltage amplitude (V0 ≫ Vth) is applied to the left of              microdroplets 1 and 2, and both microdroplets actuate to the left.............................. 15 Figure 2.2.3.1 The structure of the multiplexer grid is shown. The multiplexer grid uses              an actuating voltage amplitude that is both smaller than the actuation threshold              voltage and larger than half the actuation threshold voltage (Vth/2 < V0 < Vth), so              that only microdroplet 1 actuates to the left. .............................................................. 18 Figure 2.3.1 The DMF device using the multiplexer grid is shown. The centre-tapped              transformer has Vin coupled to its input. The outputs of the transformer, V0(0°) and              V0(180°), are applied to the electrodes of the multiplexer grid. The inset shows the              orthogonal and overlapped upper row and lower column electrode plates. ............... 25 Figure 2.3.2 The configuration for determining the minimum required actuation  List of Figures  xvii              threshold voltage Vth is shown. The (a) initial and (b) final locations of a tested              2.06 μL microdroplet are displayed. This actuation threshold voltage is found by              slowly increasing the applied voltage amplitude up to the point of microdroplet              motion. The electrode pair of i = 11 and 12 is activated with V0(180°) while the              j = 13 and 14 electrode pair is activated with V0(0°). ................................................. 27 Figure 2.3.3 The independent actuation abilities of the multiplexer grid are shown.  The              microdroplets are 2.14 μL in volume and the (a) initial and (b) final locations are              displayed. The device input is Vin = 10.0 Vrms. The waveforms V0(180°) = 375              Vrms and V0(0°) = 375 Vrms are directed to the i = 4, i = 5 electrodes and j = 11,              j = 12 electrodes, respectively. Microdroplet 2 is moved from i = 9, j = 11.3 to a              new position of i = 4.8, j = 12.3 and microdroplet 2 is stationary. ............................. 29 Figure 2.3.4 Shown here is the complex motion and merging process for two              microdroplets in the multiplexer grid. Two microdroplets are moved in sequence              and ultimately mixed. The microdroplets are (a) initially at rest, (b) separated              from each other, (c) moved towards each other, and (d) finally merged together. .... 30 Figure 3.1.2.1  Photoconductivity and THz electric field for PC THz emitters with (a)              long duration photoconductivity and (b) short duration photoconductivity. The              results of (a) show a large amount of Joule heating flux while the results of (b)              show a small amount of Joule heating flux for similar emission of THz electric              field. ............................................................................................................................ 38 Figure 3.2.1.1  An isometric view of the pump-probe setup is shown. The pump-probe              setup consists of a dichroic beamsplitter that overlaps the (780 nm) pump and  List of Figures  xviii               (1550 nm) probe beams, a 40× microscope objective that focuses the beams              onto the semiconductor sample, an xyz translation stage for adjustments and              optimization, and an InGaAs photodiode for measuring the differential              transmission of the probe beam that passes through the semiconductor sample. ....... 41 Figure 3.2.1.2  A top view of the pump-probe setup is shown. The components are              labeled as follows: BSdichroic is a dichroic beamsplitter; MO40× is a 40× microscope              objective; SS is a semiconductor sample; TS is an xyz translation stage; PDInGaAs              is an InGaAs photodiode. ........................................................................................... 42 Figure 3.2.2.1.1  An isometric view of the THz setup is shown. The THz setup consists              of a 10× microscope objective that focuses the pump beam onto the PC THz              emitter, two parabolic mirrors that collect and focus the THz beam, a pellicle              beamsplitter that overlaps the THz beam with the probe beam, an EO ZnTe              crystal and a quarter waveplate that alter the polarity of the probe beam, a              polarizing beamsplitter that splits the probe beam into vertical and horizontal              polarizations, and a balanced Si photodiode that measures the difference between              the power of the horizontally and vertically polarized probe beam components. ...... 45 Figure 3.2.2.1.2  Top views of the THz setup are shown for the (a) collineation process,               (b) autocorrelation process, (c) EO process, and (d) full THz setup operation.              Components are labeled as follows: BB is a beam block; TS is an xyz translation              stage; MO is a microscope objective; PE is a PC THz emitter; PM is a parabolic              mirror; IA is an iris aperture; BSpel is a pellicle beamsplitter; FM is a flip mount;              BE is a bias electrode; EO is an EO crystal; QW is a quarter waveplate; BSpol  List of Figures  xix              is a polarizing beamsplitter; VA is a variable attenuator; PDSi is a pair of Si              photodiodes (linear, differential); PDGaP is a GaP photodiode (nonlinear). ............... 46 Figure 3.2.2.1.3  A photograph is shown of the THz setup with labeled components: TS              is an xyz translation stage; MO is a microscope objective; PE is a PC THz              emitter; PM is a parabolic mirror; IA is an iris aperture; BSpel is a pellicle              beamsplitter; EO is an EO crystal; QW is a quarter waveplate; BSpol is a              polarizing beamsplitter; VA is a variable attenuator; PDSi is a pair of Si              photodiodes (linear, differential). ............................................................................... 48 Figure 3.2.2.1.2.1  Results from the autocorrelation process, showing nonlinear              photocurrents from the GaP photodiode versus time, t, and corresponding delay              stage distance, x, over time-domain scans of (a) 200 ps (60 mm length) and (b)              1 ps (300 µm length). .................................................................................................. 51 Figure 3.2.2.1.3.1  Results from the EO process, showing experimental data points               (circles) and theoretical curves (solid lines) versus azimuthal rotation angular, ϕ.              The upper blue curve and data points, corresponding to the left axis, are acquired              from the use of parallel plate bias electrodes during the EO process. The lower              red curve and data points, corresponding to the right axis, are acquired from the              use of the complete THz setup.................................................................................... 56 Figure 3.2.2.2.1  Results from the complete THz setup operation, showing the THz              electric field in the (a) time-domain and (b) frequency-domain. The inset of (a)              shows the noise level for the THz setup, during the first 0.25 ps. .............................. 59 Figure 3.3.1  Measured differential spectral transmission, ΔT(λ)/T, versus wavelength, λ,  List of Figures  xx              for (a) GaP and (b) GaAs. The GaP bandstructure in the inset of (a) shows its              high central Γ valley energy, EΓ = 2.8 eV, and neighbouring L and X sidevalleys.              The X sidevalley of GaP has upper X7 and lower X6 valleys. The GaAs              bandstructure in the inset of (b) shows its low central Γ valley energy, EΓ = 1.4              eV, and higher L and X sidevalleys. ........................................................................... 65 Figure 3.3.2  Measured probe differential transmission, ΔT(t)/T, in time for (a) GaP with              390 nm (3.2 eV) pump photoexcitation and 780 nm (1.6 eV) probe sampling and               (b) GaAs with 780 nm (1.6 eV) pump photoexcitation and 1550 nm (0.8 eV)              probe sampling. The initial 10 ps of these time-resolved measurements are shown              in the respective insets. ............................................................................................... 68 Figure 3.3.3  The transient mobility, μ(t), responses are shown as a function of time for              GaP. Responses are shown for low 18 µJ/cm2 (upper curve), moderate 36 µJ/cm2               (middle curve), and high 72 µJ/cm2 (lower curve) pump fluences. .......................... 71 Figure 3.4.1.1 The theoretical charge-carrier density is shown for a hypothetical              nanoparticle with a diameter of 2a = 40 nm and a surface recombination velocity              of S = 100,000 cm/s. The x and y dimensions are Cartesian coordinates for an              equatorial plane through the nanoparticle................................................................... 77 Figure 3.4.1.2 Si (a) theoretical and (b) experimental nanoparticle differential              transmission results are shown versus time. Experimental differential              transmission results of bulk Si are also shown in (b). An SEM image of the Si              nanoparticles is shown in the inset of (b). .................................................................. 78 Figure 3.4.1.3 SiC (a) theoretical and (b) experimental nanoparticle differential  List of Figures  xxi              transmission results are shown versus time. Experimental differential              transmission results of bulk SiC are also shown in (b). An SEM image of the              SiC nanoparticles is shown in the inset of (b). ........................................................... 79 Figure 3.4.1.4 InP (a) theoretical and (b) experimental nanoparticle differential              transmission results are shown versus time. Experimental differential              transmission results of bulk InP are also shown in (b). An SEM image of the InP              nanoparticles is shown in the inset of (b). .................................................................. 81 Figure 3.4.2.1 The top view SEM topographies for non-, fine-, and coarse-textured InP              materials are shown in (a), (c), and (e), respectively. The isometric view SEM              topographies for respective non-, fine-, and coarse-textured InP materials are              shown in (b), (d), and (f), respectively, with images of the corresponding PC              THz emitters shown in the insets. The relative surface areas of the non-, fine-,              and coarse-textured InP materials are 1.0 ± 0.1, 2.9 ± 0.4, and 4.3 ± 0.6,              respectively. ................................................................................................................ 85 Figure 3.4.2.2 Differential transmission signals are shown for non-, fine-, and coarse-             textured InP materials with 780 nm pump and 1550 nm probe wavelengths. The               (normalized) differential transmission pump-probe signals are plotted as a              function of time and are curve-fit to decaying exponential functions to define the              charge-carrier lifetime of each measurement. The results are shifted vertically for              illustration purposes. ................................................................................................... 87 Figure 3.4.2.3. The THz responses of the non-, fine-, and coarse-textured InP PC THz              emitters are shown. In (a), THz electric field measurements are shown as a  List of Figures  xxii              function of applied voltage amplitude while each PC THz emitter is set to produce              a similar THz electric field amplitude. The THz electric field amplitude values are              normalized with respect to the non-textured InP emitter's response at an applied              voltage amplitude of 50 V. In (b), the corresponding photocurrent is measured as              a function of applied voltage amplitude. In (c), the ratio of the normalized THz              electric field amplitude over photocurrent is plotted as a function of bias voltage              amplitude. The error bars represent the standard error of the ratio of normalized              THz electric field amplitude over the photocurrent. ................................................... 89 Figure 3.4.2.4. The THz electric field responses of the non-, fine-, and coarse-textured              InP PC THz emitters are shown in the (a) time-domain and (b) frequency-domain.              The results of (a) are shifted vertically for illustration purposes. Similar time-             domain and frequency-domain responses are observed for the PC THz emitters.              An approximate 3.5 THz spectral bandwidth is observed for each of the non-,              fine-, and coarse-textured InP PC THz emitters. ........................................................ 92 Figure 4.2.1 An image of the THz spectroscopy is shown with a sample with thickness              of d0, absorption coefficient of α(f), and refractive index of n(f). The reference              THz electric field pulse (prior to passing through the sample) in the respective              time- and frequency-domain is Eref(t) and Eref(f) and the sample THz electric              field pulse (after passing through the sample) in the respective time- and              frequency-domain is Esam(t) and Esam(f). Fresnel coefficients at the initial (left)              and final (right) interface are t1 and t2, respectively. ................................................ 100 Figure 4.2.2 A reference THz electric field pulse is shown in the (a) time- and (b)  List of Figures  xxiii              frequency-domain (normalized to the noise floor, i.e., presented as the DR). The               (c) maximum measurable absorption coefficient is shown for exemplary samples              with thicknesses of d0 = 60, 120, 180, and 240 μm. ................................................. 101 Figure 4.3.1 The THz spectroscopy analysis method applied through THz-TDS of a              water vapour sample with (a) time-domain scans for reference (dry nitrogen)              and sample (water vapour) THz electric field pulses, (b) absorption coefficient              and maximum measurable absorption coefficient for the water vapour sample              over the THz spectrum, and (c) absorption coefficient for the water vapour              sample over 0.5 to 3 THz. ......................................................................................... 104 Figure 4.4.1 An image is shown of the THz spectroscopy for a liquid sample with              thickness of d0, absorption coefficient of α(f), and refractive index of n(f). The              incident THz electric field pulse passes through (a) the sample its two transparent              sample holding plates with thickness of dhp, absorption coefficient of αhp, and              refractive index of nhp, and (b) only the transparent holding plates, creating the              sample and reference THz electric field pulses. The incident THz electric field              pulse in the respective time- and frequency-domain is Ei(t) and Ei(f). The sample              THz electric field pulse in the respective time- and frequency-domain is Esam(t)              and Esam(f). The reference THz electric field pulse in the respective time- and              frequency-domain is Eref(t) and Eref(f). The Fresnel coefficients at the interfaces              are t1, t2, t3, t4, t5, and t6. ............................................................................................ 109 Figure 4.4.2 The absorption coefficient is shown over the THz spectrum for a water              liquid sample (black solid line), egg white protein liquid sample (red dashed  List of Figures  xxiv              line), and water liquid sample (violet circled line) as measured by Wang et al.               [131]. Also shown is the maximum measurable absorption coefficient (black              dashed line) over the THz spectrum for water and egg white protein liquid              samples with thickness of d0 = 160 μm. ................................................................... 110 Figure 4.5.1.1 The absorption coefficient (black solid line) over the THz spectrum is              shown for a glass solid sample with thickness d0 = 1.02 mm. The maximum              measurable absorption coefficient (black dashed line) is also shown. ..................... 112 Figure 4.5.2.1 The absorption coefficient (black solid line) over the THz spectrum is              shown for a plastic solid sample with thickness d0 = 180 μm. The maximum              measurable absorption coefficient (black dashed line) is also shown. ..................... 114 Figure 4.5.3.1 The absorption coefficient over the THz spectrum is shown for quartz              solid samples with thicknesses d0 = 1.06 mm (black solid line) and 2.12 mm (red              dotted line). The maximum measurable absorption coefficient is also shown for              thicknesses d0 = 1.06 mm (black long-dashed line) and 2.12 mm (red short-             dashed line). .............................................................................................................. 115 Figure 4.5.4.1 The absorption coefficient (black solid line) of a PDMS solid sample              over the THz spectrum is shown. The maximum measurable absorption              coefficient (black dashed line) is also shown. .......................................................... 118 Figure 5.3.1 A conceptual design schematic is shown for the full DMF-based THz-TDS              system. The DMF-based THz-TDS system should have a multiplex grid DMF              device with substrate layers made of quartz and dielectric layers made from              PDMS. The spacing between the top and bottom plates of the multiplexer grid  List of Figures  xxv              DMF device should be less than 100 μm. The THz emitter should be a textured              InP PC THz emitter and theTHz detector should be a textured InP PC THz              detector. The DMF-based THz-TDS system should make use of the THz              spectroscopy analysis method for the analysis of THz-TDS data. ........................... 125 Figure A.1 The general positive photolithography process with positive photoresist              is shown. ................................................................................................................... 145 Figure C.1 The transimpedance amplifier circuit is shown. ................................................. 151 Figure D.1 The squarewave amplifier circuit is shown. ....................................................... 152     xxvi  Acknowledgements I would like to express my gratitude to my supervisor, Dr. Jonathan Holzman. You provided tremendous support to my research and career and you are an excellent academic role model. I am fortunate to have had your guidance and friendship over these past years. I would also like to thank Dr. Kenneth Chau and Dr. Thomas Johnson for advice and guidance as Doctoral Committee Members. Thank you to Dr. Murray Newman for your willingness to serve as a University Examiner and thank you to Dr. Matthew Reid for your willingness to serve as an External Examiner. I would also like to acknowledge Dr. Spiro Yannacopoulos, who played a fundamental role in the development of the UBC School of Engineering.  I would like to thank David Arkinstall, Marc Nadeau, and Tim Giesbrecht for technical support and expertise.  I have been fortunate to have been surrounded with a very positive group of students in the UBC Integrated Optics Laboratory. In particular I would like to acknowledge several people. Xian Jin, thank you for being a great friend and colleague. I am very happy that our paths ran in parallel during our studies. Trevor Stirling, Ilija Hristovski, Kyle Hill, Mark Bergen, and Jeff Krupa, thank you for serving with such dedication in your roles as undergraduate research assistants on my many projects. Thank you also to the following UBC Integrated Optics Laboratory (past and present) students: Mike Wiltshire, Mitch Westgate, Blake Veerman, Jackie Nichols, Emily Landry, Alex Huizing, Blago Hristovski, Daniel Guerrero, Simon Acknowledgments  xxvii  Geoffroy-Gagnon, Jamieson Garbowski, Mark DeWachter, Shaylene Dekock-Kruger, Brandon Born, Max Bethune-Waddell, and Dr. Ali Ahmadi.  Thank you to my wife, Amanda. You have loved and supported me throughout this endeavor and in life. I am very blessed by our marriage. Your patience while I talk about science and engineering is appreciated. Thank you to my parents, Harry and Barbara, and my sister, Erin. You provided me with love and support throughout my whole life. I would like to thank Harry and Margaret Verwoerd for being great parents-in-law. Thank you to my uncle, Raymond Collier, for encouraging me in my engineering pursuits.  I would like to acknowledge financial support from the Natural Science and Engineering Research Council of Canada, the Finch family, the Killam family, the SPIE International Society for Optics and Photonics, and IODE Canada.    xxviii  Dedication   This thesis is dedicated to Amanda, Harry, Barbara, and Erin Collier.     1  Chapter 1: Introduction 1.1 Terahertz Spectroscopy in Lab-on-a-Chip Platforms The terahertz (THz) spectrum (sometimes known as the THz gap) is the portion of the electromagnetic spectrum that lies beyond the reach of contemporary electronic devices (which typically operate up to hundreds of GHz) and optical devices (which typically operate down to tens of THz) [1]. The limits of electronic and optical technologies have loosely defined the span of the THz spectrum to be 0.1-10 THz, corresponding to wavelengths of 30-3000 μm. This THz spectrum supports numerous applications. Terahertz radiation has been applied to wireless communications [2] to make use of the (unlicenced) THz spectrum. Tomography applications for THz radiation have also emerged [3]. Here, THz frequencies can be used to form three-dimensional plots of objects made from materials that are not compatible with other electromagnetic frequencies. Terahertz radiation has found applications in quality control for non-destructive testing of plastic weld joints [4]. Security applications have also benefitted from THz radiation for the detection of explosives, weapons, and illegal drugs [5]. Terahertz radiation has also found biomedical applications through imaging [6] and spectroscopy [7, 8] of biochemical species. In terms of imaging of biochemical species, the low photon energies of THz radiation provide an effective (non-ionizing) alternative to the high photon energies of X-ray radiation [9]. In terms of spectroscopy of biochemical species, the photon energies of THz radiation are well-suited to absorption via the vibrational and rotational modes of many organic materials [10]. In fact, spectroscopy of biochemical species is one of the foremost uses of THz radiation [7, 8, 11, 12]. Chapter 1: Introduction  2  Terahertz spectroscopy offers high-sensitivity characterizations for many of the vibrational and rotational modes of biochemical species, which result from intermolecular bonding. Other spectroscopic techniques have challenges in characterizing such modes [13, 14]. Consider, for example, Raman spectroscopy [15], which makes use of monochromatic pump radiation to induce inelastic scattering to lower photon energies (via Stokes shifts) or inelastic scattering to higher energies (via anti-Stokes shifts), and Fourier transform infrared (FTIR) spectroscopy [16], whereby broadband infrared radiation illuminates a sample and absorption is resolved by way of Fourier analyses. Raman spectroscopy has a difficult time in accessing the THz spectrum, as the applied notch filters cannot easily block the wavelength of the strong pump radiation while passing the subtly-shifted THz wavelengths [17]. At the same time, the extremely broadband nature of FTIR spectroscopy makes it detrimental to the sensitivity that is sought for the THz spectrum. In addition, FTIR spectroscopy requires complicated experimental setups to obtain the complete (complex) refractive index [18]. Additionally, a noted disagreement in the literature for DNA analyses calls into question the reliability of these techniques [19]. Terahertz spectroscopy can circumvent these challenges, but it also has challenges. In particular, the high sensitivities that are characteristic of THz spectroscopy make the technique highly susceptible to spectroscopic signatures arising from solids, liquids, and gases in the surrounding environment. It is for this reason that the biochemical interrogation process applied in THz spectroscopy is best implemented in a small device structure. To this end, a lab-on-a-chip platform is the ideal structure for handling and analysing biochemical species via THz spectroscopy, as the small device size will allow it to Chapter 1: Introduction  3  operate with low sample volumes and minimal contributions from the surrounding environment [20]. Despite the benefits of integrating THz spectroscopy within lab-on-a-chip platforms, the two systems have not been successfully integrated. The underlying microfluidic and THz  technologies have several key challenges that must first be resolved. That is the role of this thesis. In the remainder of this chapter, the relevant microfluidic and THz technologies are introduced, the challenges pertaining to their integration are identified, and the contributions of this thesis are proposed to resolve these challenges.  There have been notable efforts made through the past few decades to develop THz technologies. The efforts began in the mid-1980s, to a large extent, through the work of Auston. Auston introduced a biased semiconductor gap in the form of a photoconductive (PC) THz emitter. The PC THz emitter could be biased by an external electric field and triggered by an ultrafast (subpicosecond) laser pulse to generate free-space pulses of THz radiation [21]. This pioneering work enabled the modern field of THz science and technology. Terahertz technology is often implemented via pulsed THz radiation, generated either with biased PC THz switches, i.e., Auston switches, or through optical rectification in nonlinear crystals, i.e., electro-optic (EO) crystals. Such systems enable THz-time-domain-spectroscopy (TDS) with broad bandwidths, over several THz [17], for phase and absorption characterizations of dielectric constants. (The THz-TDS measurements explicitly define the dielectric constant, in a manner that is more straightforward than that of Raman spectroscopy or FTIR spectroscopy [10], which require complex data analyses after data acquisition.) It has been noted that THz-TDS has great merit for disease diagnostics. Jeong et al. found that THz-Chapter 1: Introduction  4  TDS can be used to detect changes in concentrations of red blood cells, which can be used to detect cancer [22]. Sun et al. found that THz-TDS could be used to detect the influenza A virus at lower concentrations than the standard enzyme-linked immunosorbent assay (ELISA) technique [23]. It has also been noted that THz-TDS has great merit for label-free proteomics analyses [19]. This is particularly beneficial for diagnostics of genetic diseases where labeling can lower the precision of gene detection [19]. Examples of proteometic laboratory analyses of biological THz-TDS include protein hydration studies by Laurette et al. [24], bovine serum albumin studies by George et al. [25], and DNA analyses by Globus et al. [26]. However, through these studies it has become apparent that THz-TDS has challenges that have prevented its widespread use. The THz-TDS systems are large, bulky, and expensive [27], and at the same time they are highly susceptible to spectroscopic signatures from trace chemicals in the environment as well as the overwhelming absorption from water within samples [25]. Such challenges can be addressed through the introduction of an appropriate microfluidic technology. Microfluidic technology emerged in the 1980s in response to many factors, including the success of microanalytical methods (e.g., gas-phase chromatography [28] and high-pressure liquid chromatography [29]), a need for portable biodetectors [30], the explosion of genomics [30], and many developments in microelectromechanical (MEMS) fabrication techniques [31]. A microfluidic device can function with especially small fluid volumes, so it can readily facilitate the interrogation of fluids with volumes on the order of microlitres and even picolitres [30]. The device does this by integrating capabilities for both microfluidic actuation and sensing. The systems typically achieve microfluidic actuation by way of Chapter 1: Introduction  5  continuous flow structures, with valves and pumps being used for pressure-based actuation of fluids in one-dimensional channels [32]. The small scale of these devices allows for minimal consumption of samples, increased automation, and reduced manufacturing cost [33]. For many analyses, however, there exists a desire for reconfigurability, and it is for this demand that digital microfluidic (DMF) devices have recently emerged [34, 35]. These DMF devices actuate individual microdroplets via applied voltages across the two-dimensional (2-D) plane of a chip [36]. Early DMF devices applied electrowetting, via dielectrophoresis, to actuate microdroplets [37, 38], but Joule heating became an issue, because of the resulting evaporation [39]. With this in mind, a promising alternative emerged in the form of electrowetting-on-dielectric (EWOD) devices. The EWOD-based DMF devices actuate microdroplets by way of electric fields acting on the solid/liquid interface [40, 41]. The Joule heating for such systems is especially low, as the dielectric layers block conduction current [42]. Microfluidic platforms have traditionally achieved sensing of fluids via visible light probing. The fluid properties are sensed using thin film photodetector integration [43], fluorescence [44], backreflection [45], and absorbance sensing [46]. Absorbance sensing is particularly desirable because it is relatively easy to implement, given that reactants do not require special preparation or tagging. Absorbance sensing is often performed with wavelengths in the visible and infrared spectral regions, and its use has supported both Raman and FTIR spectroscopy in microfluidic devices [47]. However, these techniques suffer from insensitivity to vibrational and rotational modes [10, 48]. Given the shortcomings of Raman and FTIR spectroscopy and the merits of microfluidic technologies, there is great interest in integrating microfluidic and THz Chapter 1: Introduction  6  technologies, to enable THz spectroscopy within lab-on-a-chip platforms. In fact, there exist explorations of rudimentary systems with combined microfluidic and THz technologies, consisting of off-chip THz radiation emission/detection and continuous flow microfluidic devices [12, 25]. However, there is much work left to be done to enhance the underlying technologies if they are to be integrated. In particular, the processes of microfluidic actuation and THz emission must implemented in a manner that accommodates small spatial constraints and low power consumption. A DMF-based THz-TDS system is a viable choice to achieve this, but such a system must first resolve the fundamental structural and material challenges for the microfluidic and THz technologies. This thesis addresses these structural and material challenges. It is envisioned that the proposed DMF-based THz-TDS system would have future applications in proteomics and diagnostics. The proposed DMF-based THz-TDS system would make use of a DMF device to realize microfluidic actuation, while recognizing that such architectures have long-standing challenges of a structural nature. The structure that is most commonly used is the square electrode grid [49]. The structure provides complete microfluidic actuation control, as microdroplets can be attracted to any desired square electrode by simply applying a voltage to the relevant electrode. However, these square electrode grids require complex routing of address lines (between the electrodes and the external bias pads) when they are implemented with large numbers of electrodes. Such systems are typically not implemented with square electrode grids beyond 5 × 5 [49], because the inner electrodes become too difficult to address using standard planar fabrication. As a response to the square electrode grid, the cross-referenced grid was developed [50]. This alternative structure has two plates of parallel and Chapter 1: Introduction  7  linear electrodes that are spatially separated and orthogonal to each other. The microdroplet of interest is actuated between these plates. One plate of electrodes provides motion in a horizontal (x) direction and the other plate of electrodes provides motion in the orthogonal horizontal (y) direction. This structure provides practical addressability, given that each electrode is both an address line and an electrode. However, if multiple microdroplets are situated on one electrode, all of the microdroplets will be actuated (whether or not this is desired). With this challenge in mind, this thesis proposes a multiplexer grid that makes use of a cross-referenced grid structure and threshold-based microfluidic actuation. It is shown that the multiplexer grid can provide full microfluidic actuation across the 2-D plane of a DMF device. The proposed DMF-based THz-TDS system benefits from the high throughput and high sensitivity of microfluidics. The proposed DMF-based THz-TDS system would also make use of a THz-TDS system. The key challenges for such a system are largely of a material nature. The basic challenges for such THz-TDS systems pertain to their integration within lab-on-a-chip platforms, as it becomes necessary to minimize Joule heating during the PC THz emission process. (Terahertz emission via optical rectification is not used given the complexity of implementing EO crystals and polarization-sensitive optics within a lab-on-a-chip platform.) Joule heating is avoided because it would promote rapid evaporation of microdroplets. Moreover, the bias voltage for the onset of thermal runaway decreases with increased Joule heating, which limits the emission power and ultimately decreases the dynamic range of the THz measurements [20]. Joule heating is often mitigated through large-area PC THz emitters [51], because the heat is spread over large areas, for minimal Joule heating flux (i.e., Joule Chapter 1: Introduction  8  heating per area), but this is not possible in small-scale lab-on-a-chip platforms. Other proposed solutions for minimizing Joule heating include intricate electrode designs [52, 53], patterning of the active area [54], heat sink integration [55], low-temperature substrate growth [56], water-cooling [57], substrate irradiation [58], and laser-ablation [59]. However, these solutions are often at odds with the structures and materials being implemented in a lab-on-a-chip platform. With this challenge in mind, this thesis proposes new materials for THz emission, based upon transient mobility (with GaP) and surface-enhanced recombination (with nanocomposites and textured InP). It is found that surface-enhanced materials provide similar THz emission characteristics to their bulk counterparts, but they have an order of magnitude lower Joule heating.  1.2 Thesis Scope This thesis considers the underlying structures and materials needed to implement a DMF-based THz-TDS system. The system integrates microfluidic technology and THz technology to provide the functionality of THz spectroscopy within a lab-on-a-chip platform. A conceptual schematic of such a DMF-based THz-TDS system is presented in Figure 1.2.1. The schematic shows microfluidic technology being used for microfluidic actuation and THz technology for THz emission. Chapter 2 considers the structures (mainly) and materials for the microfluidic technology, through the implementation of an appropriate DMF architecture. Chapter 3 considers the structures and materials (mainly) for THz technology, through the introduction of materials for PC THz emission with reduced Joule heating. Chapter 4 demonstrates THz spectroscopy, through THz-TDS operation, and gives design considerations for such operation Chapter 1: Introduction  9  in lab-on-a-chip platforms. Chapter 5 summarizes the contributions of this thesis towards the development of future DMF-based THz-TDS systems.     Chapter 1: Introduction  10     Figure 1.2.1 A conceptual schematic is shown of a DMF-based THz-TDS system (in the red box). The system implements microfluidic technology by way of a DMF device (in the blue box). The DMF device uses upper and lower electrodes for microfluidic actuation. The system also implements THz technology by way of PC THz emission and detection (in the green boxes). The PC THz emission and detection is carried out by way of respective upper and lower electrodes.    11  Chapter 2: Microfluidic Actuation 2.1 Background A lab-on-a-chip platform for the proposed digital-microfluidic- (DMF)- based terahertz (THz)-time-domain-spectroscopy (TDS) system requires microfluidic actuation. In DMF devices, the microfluidic actuation is brought about by applying voltages on electrodes, to form a nonuniform distribution of electric fields over a microdroplet. The fringing electric fields from the electrodes polarize the microdroplet and induce a net force. In this chapter, the necessary structures for microfluidic actuation in DMF devices are explored. Relevant DMF device structures are first reviewed and a multiplexer grid DMF device is introduced.  2.2 Potential Structures for Digital Microfluidic Devices This subsection explores several DMF device structures to establish the necessary microfluidic actuation. The structures are the square electrode grid, the cross-referenced grid, and the multiplexer grid.  2.2.1 Square Electrode Grid The greatest degree of freedom for microfluidic actuation can be achieved by implementing a two-dimensional (2-D) square electrode grid [49]. A voltage applied to an activated electrode in an M × N grid creates a localized electric field that attracts neighbouring microdroplets through dielectric polarization and energy minimization. The advantage of this 2-D square electrode grid is its simplicity in microfluidic actuation—the M × N grid electrodes are activated by M × N independent voltage inputs for complete microfluidic actuation of Chapter 2: Microfluidic Actuation  12  microdroplets across the 2-D plane. The use of independent inputs for each grid location can, however, become a practical addressability limitation. Large-scale M × N grids, beyond roughly a 5 × 5 grid [49], are difficult to implement in the 2-D plane of a chip, without resorting to complex via-holes for out-of-plane access points. Each square electrode requires an individual electrical address line to be patterned in the plane of the chip, without it crossing other electrodes or lines. The scalability challenges in such highly-parallel M × N grids, with increasingly small electrode dimensions, can become unwieldy or even impossible. The advantages and disadvantages of the square electrode grid can be seen by way of its schematic in Figure 2.2.1.1. The figure shows two microdroplets present on the 16 × 16 grid. If a user desires to move microdroplet 1, but not microdroplet 2, a sufficiently high voltage, V0, can be applied to the address line for the electrode adjacent to microdroplet 1. In Figure 2.2.1.1, this is shown with the darkened electrode. The voltage creates a strong electric field at this location that polarizes the fluid to create a net force towards the high-field region. By carrying out this voltage-activation process through a sequence of steps, multiple microdroplets can be moved to various locations across the chip without interfering with adjacent and stationary microdroplets. For the structure shown, however, 256 input signals must be routed via address lines to each of the square electrodes, in the gaps between the square electrodes, without crossing any address lines. This can be exceedingly challenging. Overall, it can be deemed that the square electrode grid can provide independent 2-D control for microdroplet actuation, but it does not facilitate practical addressability.   Chapter 2: Microfluidic Actuation  13      Figure 2.2.1.1 The structure of the DMF square electrode grid is shown. An actuating voltage amplitude is applied to the left of microdroplet 1 (i = 60 electrode), and microdroplet 1 is actuated while microdroplet 2 remains stationary.   Chapter 2: Microfluidic Actuation  14  2.2.2 Cross-Referenced Grid Given the above challenges for the 2-D square electrode grid, an interesting solution was introduced by way of the cross-referenced grid [50]. The cross-referenced grid uses a bi-layered structure with voltages applied to perpendicular upper row and lower column linear electrodes. The elegance of such an implementation lies in that each linear electrode acts as both the actuating electrode and its own address line. This dual purpose for electrodes allows the number of electrode inputs to be greatly reduced: Only M + N inputs are needed for actuating microdroplets across the M × N grid. Thus, the cross-referenced grid provides practical addressability. The cross-referenced grid does have a fundamental challenge, however, when used with multiple microdroplets. When the microdroplet that is targeted for actuation shares a row or column with neighbouring microdroplets, the application of a voltage to the row or column results in motion of all the microdroplets. This challenge, relating to independent 2-D control of microdroplet actuation, is known as microdroplet interference [50]. Xiao et al. [60] and Xu and Chakrabarty [50] have proposed optimization routines to solve this problem. However, such techniques offer only algorithmic solutions to avoid microdroplet interference, and these solutions become increasingly complex for the microdroplet actuation on large M × N grids with many microdroplets. The advantages and disadvantages of the cross-referenced grid can be seen by way of its schematic in Figure 2.2.2.1. Horizontal upper row electrodes are indexed with i, while vertical lower column electrodes are indexed with j. These electrodes are patterned onto the chip as upper and lower planes. In Figure 2.2.2.1, microdroplet 1 is situated at i = 4, j = 13, while microdroplet 2 is situated at i = 9, j = 13. Voltage activation is applied to the j = 12  Chapter 2: Microfluidic Actuation  15      Figure 2.2.2.1 The structure of the DMF cross-referenced gridis shown. An above-threshold actuating voltage amplitude (V0 ≫ Vth) is applied to the left of microdroplets 1 and 2, and both microdroplets actuate to the left.   Chapter 2: Microfluidic Actuation  16  column electrode, pulling both microdroplet 1 and microdroplet 2 to the left. It is not possible to actuate microdroplet 1 while keeping microdroplet 2 stationary because of microdroplet interference. It is clear that an alternative actuation structure is needed for systems operating with multiple microdroplets, so that individual microdroplets can be independently actuated. Overall, it can be deemed that the cross-referenced grid supports practical addressability, but it performs poorly in terms of independent 2-D control for microfluidic actuation.   2.2.3 Multiplexer Grid Given the successes and challenges of the aforementioned microdroplet actuation techniques, the following work investigates a multiplexer grid. The multiplexer grid can provide complete independent 2-D control across an M × N grid along with the reduced M + N input complexity of the cross-referenced structure [61, 62]. The multiplexer grid makes use of the nonlinear relationship between microdroplet actuation and applied voltage, by way of an actuation threshold voltage [63-65]. The desired microdroplet motion is brought about by the doubling of a differential voltage that appears between overlapped upper row and lower column electrodes having opposite voltage polarities. The system is biased such that only the doubled voltage in the overlapping region overcomes the actuation threshold voltage to initiate microdroplet motion. Neighbouring microdroplets experience voltages that are lower than the actuating threshold voltage and do not undergo actuation—thereby eliminating the microdroplet interference challenge.  The multiplexer grid uses the same physical structure as the cross-referenced grid, but there are two important design differences in its operation: i. the multiplexer grid operates in Chapter 2: Microfluidic Actuation  17  a nonlinear actuation regime biased about an actuation threshold voltage, and ii. the multiplexer grid is driven by a bipolar voltage AC waveform having both positive and negative polarities. Such a structure is shown in Figure 2.2.3.1. The microfluidic actuation is achieved using two voltage waveforms. A voltage of +V0 is applied on the i = 4 upper row electrode while -V0 is applied on the j = 12 lower column electrode. The positive value V0 is defined as the actuating voltage amplitude. A voltage difference of V0 is created between upper and lower plates in all regions along the row and column electrodes except for the overlapped region, where the voltage difference is 2V0. By noting the actuating threshold voltage, Vth, needed for microfluidic actuation, this localized 2V0 can be leveraged by selecting V0 to be within the range Vth/2 < V0 < Vth. Thus, microdroplet motion only occurs within the overlapped region. Figure 2.2.3.1 shows that only microdroplet 1 moves to the left while microdroplet 2 remains stationary. Overall, it can be deemed that the multiplexer grid supports both practical addressability (with M + N inputs) and independent-2-D control for microfluidic actuation (across the M × N crosspoints).  Table 2.2.3.1 summarizes the capabilities of the structures for the DMF device, in terms of independent 2-D control for microfluidic actuation and practical addressability.   Chapter 2: Microfluidic Actuation  18      Figure 2.2.3.1 The structure of the multiplexer grid is shown. The multiplexer grid uses an actuating voltage amplitude that is both smaller than the actuation threshold voltage and larger than half the actuation threshold voltage (Vth/2 < V0 < Vth), so that only microdroplet 1 actuates to the left. Chapter 2: Microfluidic Actuation  19  Table 2.2.3.1 A comparison of structures for the DMF device is presented. The square electrode, cross-referenced, and multiplexer grids are evaluated in terms of independent 2-D control and practical addressability.  Independent 2-D control Practical addressability Square electrode grid Yes No Cross-referenced grid No Yes Multiplexer grid Yes Yes   2.3 Multiplexer Grid Theory and Results To gain a thorough understanding on the multiplexer grid implementation, it is necessary to establish the relationship between row and column input applied voltages and the desired 2-D microdroplet motion. In this work, the ith upper row electrode receives an actuating voltage amplitude of V0 and the state is represented by the row voltage matrix [Vr,i]. The spatial voltage distribution (normalized to V0) is  [ ]=0..00000:..:::::0..000001..111110..000000..:::::0..000000,VV ir (1) Values of "1" along the ith row signify positive voltage activation. Similarly, the jth lower column electrode receives an actuating voltage amplitude of -V0 and its state is represented by the column voltage matrix [Vc,j]. The spatial voltage distribution (normalized to -V0) is Chapter 2: Microfluidic Actuation  20   [ ]=−0..010..0:..:::..:0..010..00..010..00..010..00..010..00..010..00,VV jc (2) Values of "1" along the jth column signify negative voltage activation. The motion that results from the input states of Equations (1) and (2) manifests itself through a surface tension change—denoted here as the matrix [Δγij]. There are two distinct forms for the surface tension change in relation to input voltages. The first form for the surface tension change and microdroplet motion corresponds to a linear system, without a microdroplet motion threshold. Surface tension changes result from the existence of a nonzero value for either [Vr,i/V0] or  [Vc,i/V0]. This "or" condition defines the device input-output characteristic and is represented here by the Boolean operator ˅ in the resulting surface tension change:  [ ] [ ] [ ] .0..010..0:..:::..:0..010..01..111..10..010..0:..:::..:0..010..00..010..0:..:::..:0..010..00..010..00..010..00..010..00..010..00..00000:..:::::0..000001..111110..000000..:::::0..000000,0,=∨=−∨=∆VVVV jcirijγ  (3) Unfortunately, such a system shows potential for surface tension changes over the full length of the i and j electrodes. This linear dependency and propensity for microdroplet interference is a manifestation of the large applied voltages (V0 ≫ Vth) that are typically used in cross-referenced grids. When multiple microdroplets are present, thoughtful path planning, routing, Chapter 2: Microfluidic Actuation  21  and scheduling [66] must be used to prevent inadvertent motion of neighbouring microdroplets and avoid microdroplet interference.  The second manifestation for surface tension changes and microdroplet motion uses a nonlinear relationship between actuation and applied inputs. In such a system, surface tension changes are initiated from the simultaneous existence of nonzero values for both [Vr,i/V0] and [Vc,i/V0]. This "and" condition defines the actuation characteristics and is represented here by the Boolean operator ˄. The resulting surface tension change for this nonlinear distribution is  [ ] [ ] [ ] .0..000..0:..:::..:0..000..00..010..00..000..0:..:::..:0..000..00..010..0:..:::..:0..010..00..010..00..010..00..010..00..010..00..00000:..:::::0..000001..111110..000000..:::::0..000000,0,=∧=−∧=∆VVVV jcirijγ (4) The response in Equation (4) signifies the operation of the multiplexer grid and its ability to offer full M × N actuation, localized to one grid position, with only M + N inputs.  The condition for localized motion only in the overlapped region requires adherence to the relation Vth/2 < V0 < Vth, which sets the actuating voltage amplitude, V0, between upper and lower limits defined by the actuating threshold voltage, Vth. This actuating threshold voltage is the minimum voltage that must be applied to commence actuation of a microdroplet, and it comes about from pinning of the microdroplet's contact line. The pinning leads to contact angle hysteresis, whereby the advancing and receding contact angles are different [65]. The value of this contact angle hysteresis, i.e., the difference between advancing and receding contact angles, is denoted here by α. Typical values for α are less than 10° [67]. An expression for the Chapter 2: Microfluidic Actuation  22  actuating threshold voltage can be found through the following derivation, which follows the work of Berthier [65], but with a mistake being corrected1. To begin the derivation, one can consider a microdroplet that is situated half on a grounded electrode and half on a charged electrode. There is a force that is horizontal and normal to an actuating electrode edge, which is expressed as  )cos()cos( 0θγθγ eeFx −= , (5) where e is the line integral along the microdroplet's perimeter on the electrode, γ is the liquid-vapour surface energy, θ is the actuated contact angle (i.e., the contact angle on the side of the charged electrode), and θ0 is the non-actuated contact angle (i.e., the contact angle on the side of the grounded electrode). This expression can be modified to include α as  )cos()cos( 0 αθγαθγ +−+= eeFx . (6) The first term on the right is the advancing capillary force,  )cos(,αθγ += eF ax , (7) and the second term on the right is the receding capillary force,  )cos( 0, αθγ +−= eF rx . (8) Given that α is much less than both θ and θ0, the respective advancing and receding capillary forces can be expressed as   )]sin()[cos(,θαθγ −= eF ax  (9)                                                  1 In Berthier's work, an incorrect trigonometric relationship is used. The correct trigonometric relationship,)sin()cos()cos( θαθαθ m≈± , is used here, and this leads to improved accuracy for the applicable case of θ ≫ α. Chapter 2: Microfluidic Actuation  23  and  )]sin()[cos( 00, θαθγ +−= eF rx , (10) due to small angle approximations. The total capillary force can then be represented as  )]sin()[sin()]cos()[cos( 00 θθγαθθγ −−−= eeFx . (11) Through the Lippmann-Young Equation [65],  )cos()cos(2 020 θθγ−=VC , (12) where C is the dielectric capacitance, the total capillary force can be represented as  0)]sin()[sin(2 020 >−−= θθγαeVeCFx , (13) which must be greater than zero for actuation. This criterion defines the actuating threshold voltage to be  )]sin()[sin(2 0θθγα−=CVth . (14) This expression is similar to other reported expressions for the actuating threshold voltage [67]. Equation (14) can be solved along with the Lippmann-Young Equation (12) to find Vth. With the actuating threshold voltage in mind, one can design a DMF device to have the appropriate range of operational voltages. If small actuation threshold/operating voltages are desired, it is advantageous to minimize static friction forces and maximize capacitance. If rapid microdroplet motion is desired, larger actuation threshold/operating voltages can be used by maximizing static friction forces and minimizing capacitance. Typical actuating threshold voltages range from tens to hundreds of volts [68] depending on the fluids and layered Chapter 2: Microfluidic Actuation  24  materials. It should be noted that a thin Teflon hydrophobic layer is often used in electrowetting-on-dielectric (EWOD) devices, as it provides a low α, which supports operation with low voltages [69]. The following section will elaborate on these practical issues through multiplexer grid design, fabrication, and implementation.  A waveform biasing scheme using bipolar AC voltage waveforms is ideal to facilitate operation of a DMF device using the multiplexer grid. A positive-polarity voltage waveform is applied to an upper row electrode with an negative-polarity voltage waveform applied to a lower column electrode. This AC operation lends itself to implementations with voltage transformers. It is therefore possible to have a sufficiently high V0 be applied on-chip, while the device input voltages can be made low, which is desirable. (This voltage conversion could also be achieved with a boost converter power electronic circuit for DC or squarewave voltages.) This voltage step-up advantage comes about from the highly-insulating dielectric layers on the chip that minimize current draw and power consumption, a property of EWOD DMF devices [42]. For the multiplexer grid, a centre-tapped transformer is selected because it gives a large voltage increase (having a voltage gain equal to the turns-ratio) with two opposite-polarity AC voltage waveform outputs (having equal amplitudes and a 180° phase difference).  A Hammond 117E4 centre-tapped transformer is chosen for testing and demonstration of the device. This transformer receives an AC voltage waveform input, Vin, at a frequency of 470 Hz (although higher frequencies could also be applied [70]). At this frequency, the transformer has a voltage gain of 75. Two AC voltage waveforms of opposite polarity are extracted at the three-output centre-tapped transformer and applied to the multiplexer grid with an electrode switching scheme. The DMF device setup is shown in Figure 2.3.1. The AC  Chapter 2: Microfluidic Actuation  25     Figure 2.3.1 The DMF device using the multiplexer grid is shown. The centre-tapped transformer has Vin coupled to its input. The outputs of the transformer, V0(0°) and V0(180°), are applied to the electrodes of the multiplexer grid. The inset shows the orthogonal and overlapped upper row and lower column electrode plates.    Chapter 2: Microfluidic Actuation  26  voltage waveform V0(0°) is applied by the j-phase electrode switch onto lower column electrodes, while the out-of-phase AC voltage waveform V0(180°) is applied by the i-phase electrode switch onto upper row electrodes. An overhead LEICA APOZ6 microscope and camera capture the on-chip microdroplet actuation.  Testing is performed on a 16 × 16 multiplexer grid with upper and lower plates separated by 1 mm. The plates have 50 nm thick copper films patterned as electrodes via UV photolithography. (The photolithography process is described in Appendix A.) The resulting multiplexer grid has electrodes with 600 μm centre-to-centre pitch and 550 μm width. The plates are then spin-coated at 5000 RPM with a 10 μm polydimethylsiloxane (PDMS) dielectric layer with a silicone elastomer curing-to-base ratio of 1:10. Finally, a thin Teflon hydrophobic layer is applied via a 2000 RPM spin-coat. The multiplexer grid is left with uniform and homogeneous PDMS and Teflon films. The Figure 2.3.1 inset shows the final orthogonally overlapped electrode plates.  To successfully operate the multiplexer grid, it is necessary to determine the actuation threshold voltage of the DMF device. To do this, a 1600 μm diameter microdroplet is placed at the i = 12.8, j = 13.4 point on the multiplexer grid, as shown in Figure 2.3.2(a). (Note that row i and column j fractions indicate intermediate locations between grid positions.) The microdroplet is tested for motion to the intermediate position between the i = 11 and 12 electrode pair and the j = 13 and 14 electrode pair. The voltage AC waveform V0(0°) is applied to the j = 13 and 14 electrode pair, while the out-of-phase voltage AC waveform V0(180°) is applied to the i = 11 and 12 electrode pair. The input AC voltage is initially set at Vin = 0 Vrms then increased. The microdroplet first moves at Vin = 8.3 Vrms, and this voltage is recorded to  Chapter 2: Microfluidic Actuation  27    Figure 2.3.2 The configuration for determining the minimum required actuation threshold voltage Vth is shown. The (a) initial and (b) final locations of a tested 2.06 μL microdroplet are displayed. This actuation threshold voltage is found by slowly increasing the applied voltage amplitude up to the point of microdroplet motion. The electrode pair of i = 11 and 12 is activated with V0(180°) while the j = 13 and 14 electrode pair is activated with V0(0°).  Chapter 2: Microfluidic Actuation  28  give the corresponding on-chip actuating threshold voltage of Vth = 620 Vrms. The post-actuation microdroplet position is shown in Figure 2.3.2(b). The established actuation threshold voltage range for multiplexing, Vth/2 < V0 <Vth, will therefore be 310 Vrms < V0 < 620 Vrms for this device, with a corresponding input range of 8.3 Vrms < Vin < 16.6 Vrms.  On a fundamental level, the multiplexer grid is able to move a single microdroplet without disturbing neighbouring microdroplets. This important aspect is tested with the two-microdroplet experiment shown in Figure 2.3.3. Two microdroplets of 1700 μm diameter are initially placed at i = 9, j = 6 and i = 9, j = 11.3, as shown in Figure 2.3.3(a). Note that both microdroplets share the same horizontal upper row electrode, i. The end result is shown in Figure 2.3.3(b). By applying an input voltage of Vin = 10.0 Vrms, one can successfully actuate microdroplet 2 with a velocity of 1.0 mm/s to a new position of i = 4.8 and j = 12.1, while microdroplet 1 is unperturbed.  In order to accommodate practical applications as a biofluidic device [71, 72], the multiplexer grid should be adapted to operate with a lower actuation threshold voltage. Thus, an effort is made to reduce the previous input voltage of 10 Vrms by redesigning the structure to have a thinner PDMS dielectric layer of 1 μm [73]. This will allow the same localized electric field to be formed across the insulating dielectric layers with a reduced voltage level. The revised multiplexer grid is tested and found to have Vth = 48 Vrms, corresponding to an input voltage within the range 0.64 Vrms < Vin < 1.28 Vrms. An input voltage of Vin = 0.64 Vrms is selected for use with this device.  The new low-voltage multiplexer grid operation is shown in Figure 2.3.4. Two microdroplets are used, with microdroplet 1 having a 1800 μm diameter and 2.54 μL volume Chapter 2: Microfluidic Actuation  29   Figure 2.3.3 The independent actuation abilities of the multiplexer grid are shown.  The microdroplets are 2.14 μL in volume and the (a) initial and (b) final locations are displayed. The device input is Vin = 10.0 Vrms. The waveforms V0(180°) = 375 Vrms and V0(0°) = 375 Vrms are directed to the i = 4, i = 5 electrodes and j = 11, j = 12 electrodes, respectively. Microdroplet 2 is moved from i = 9, j = 11.3 to a new position of i = 4.8, j = 12.3 and microdroplet 2 is stationary.   Chapter 2: Microfluidic Actuation  30      Figure 2.3.4 Shown here is the complex motion and merging process for two microdroplets in the multiplexer grid. Two microdroplets are moved in sequence and ultimately mixed. The microdroplets are (a) initially at rest, (b) separated from each other, (c) moved towards each other, and (d) finally merged together.     Chapter 2: Microfluidic Actuation  31  and microdroplet 2 having a 1600 μm diameter and 2.01 μL volume. As shown in Figure 2.3.4(a), the two microdroplets are initially at rest on the DMF device, with microdroplet 1 positioned at i = 7.5, j = 8 and microdroplet 2 positioned at i = 10.5, j = 12.5. The microdroplets are then moved in the sequence shown in Figure 2.3.4(b). Rows i = 4 and 13 and columns j = 12 and 13 are activated to move microdroplet 1 to the i = 4.5, j = 12.5 position and microdroplet 2 to the i = 12.5, j = 12.5 position. To facilitate microdroplet mixing, these microdroplets are moved into closer proximity as shown in Fig. 2.2.4(c). Rows i = 8, 9 and 12 and columns j = 11 and 12 are activated to move microdroplet 1 to the i = 8.5, j = 11.5 position and microdroplet 2 to the i = 12, j = 12 position. Finally, rows i = 9 and 10 and columns j = 9 and 10 are activated to merge the microdroplets at the i = 10, j = 12 position.   Overall, the multiplexer grid is shown to be a promising structure for DMF devices with independent 2-D control (across M × N crosspoints) for microdroplet actuation and practical addressability (with only M + N inputs).          32  Chapter 3: Terahertz Emission 3.1 Background The digital-microfluidic- (DMF)-based terahertz (THz)-time-domain-spectroscopy (TDS) system at the core of this thesis requires microfluidic actuation (relating to microfluidic technology) and THz emission (relating to THz technology), to ultimately enable THz spectroscopy in a lab-on-a-chip platform. The DMF device based on the multiplexer grid in the previous chapter meets the requirement for microfluidic actuation. This chapter will focus on the remaining requirement for THz emission, by considering the properties of the THz emitter.  Terahertz emission can be categorized according to two general types of THz emitters: continuous wave (CW) and pulsed. The following subsections describe these categories.  3.1.1 Continuous Wave Terahertz Emitters Continuous wave THz emitters fall into two general structures: electro-optic (EO) and photoconductive (PC). In EO CW THz emitters, two CW optical beams with different frequencies interact in an EO crystal and monochromatic radiation at the difference frequency is created. If the frequencies of the two CW optical beams are selected to have a difference that corresponds to a frequency that lies in the THz spectrum, then THz radiation can be emitted. Photoconductive CW THz emitters operate in a similar way. This technique is conventionally known as photomixing [74]. Here, photocurrents are induced in a semiconductor at the (THz) difference frequency between two incident optical waves. These photocurrents can be made to couple to patterned electrode antennas on the semiconductor Chapter 3: Terahertz Emission  33  surface for monochromatic THz emission. Unfortunately, these techniques require phase-locking and frequency tuning between the two laser sources for broadband THz spectroscopy studies, and are therefore undesirable for the proposed lab-on-a-chip platform.  3.1.2 Pulsed Terahertz Emitters To provide the required broadband THz radiation to be used in THz spectroscopy, pulsed THz emitters can be used. Similar to CW THz emitters, pulsed THz emitters fall into two general structures: EO and PC. Optical rectification is a pulsed EO THz emission technique that can produce broadband pulses of THz radiation. Originally introduced by Bass et al. [75], optical rectification is based on the Pockels effect [76] according to the relationship  )())(())(( 0 tEtEtEP ⋅= χε  (15) where P(E) is the polarization of the material, ε0 is the permittivity of free-space, χ(E(t)) is the electric susceptibility, and E(t) is the applied (often optical) electric field. The electric susceptibility can be expanded to include higher-order susceptibility coefficients,  .)()())(( 2321 L+++= tEtEtE χχχχ  (16) This expansion provides the general electric polarization of  ).(])()([))(( 23210 tEtEtEtEP ⋅+++= Lχχχε  (17) The Pockels effect is seen in Equation (17) when χ2 is non-zero and dominant over its higher-order susceptibility coefficients. The nonlinear component of the electric polarization Pnl2(t) is then proportional to the square of the electric field and is denoted by Chapter 3: Terahertz Emission  34   )].2cos(1[2)()(20202202 tEtEtPnl ωχεχε +== (18) for an applied electric field, E(t) = E0cos(ωt), where E0 and ω are the respective magnitude and angular frequency of the applied electric field. The DC component of this polarization is the optical rectification of the applied electric field and is of interest for EO pulsed THz emitters. When the applied electric field is an ultrafast pulsed laser, this DC nonlinear polarization will become an electromagnetic pulse with a duration that is similar to the pulse duration of the ultrafast pulsed laser. (The second harmonic term, cos(2ωt), does not contribute to optical rectification but is useful for second harmonic generation applications [77, 78].) Optical rectification has the potential for large THz electric field amplitudes [79] and is an effective emission method for generation of pulsed THz radiation, but it typically requires long THz/optical phase-matched propagation lengths and is therefore unsuitable for integration in the lab-on-a-chip platform. An alternative technique for generating pulsed THz radiation is the PC pulsed THz emitter (or Auston THz switch [21]). In this thesis, PC pulsed THz emitters will simply be referred to as PC THz emitters. A PC THz emitter consists of a semiconductor material with two metal bias voltage electrodes on the surface being separated by a gap. The semiconductor material is photoexcited with a pulse from an ultrafast pulsed laser having above-bandgap-energy photons. The photogenerated charge-carriers accelerate because of the bias electric field from the bias voltage electrodes. A fast transient photocurrent (i.e., transient dipole) is formed. The electric field in the far-field that radiates from this transient photocurrent/dipole is proportional to the derivative of the photocurrent, thus ultrafast laser pulses (100 fs or shorter Chapter 3: Terahertz Emission  35  duration) can be used to produce very broadband (several THz) electromagnetic pulses. Photoconductive THz emitters are of particular interest for the THz-TDS lab-on-a-chip applications as they are broadband [80], compact [53], scalable with both bias voltage amplitude and optical fluence excitation [81], and make use of the bias voltage electrodes that are already present in the DMF devices [61].  Photoconductive THz emitters have well known structures—and equally well known challenges pertaining to their materials. Photoconductive THz emitters based on conventional materials suffer from Joule heating [58], which is exaggerated in small-scale applications, such as lab-on-a-chip systems, where heating cannot be dissipated through increasing the active area of the emitter, as is done in large-area PC THz emitters. The Joule heating prevents the THz electric field from being scaled up by simply increasing the bias voltage amplitude or pump fluence [58]. This is because the onset of thermal runaway (for which the photocurrent grows nonlinearly with the bias voltage amplitude) is inversely proportional to the pump fluence [82]. Likewise, the average power of the THz radiation is prevented from being scaled up by simply increasing the repetition rate of the incident pump pulses [83], as Joule heating increases proportionally to the repetition rate of the incident pump pulses. Beyond these power limitations for THz emission, Joule heating in integrated PC THz emitters is also undesirable because it encourages evaporation of the biochemical species. This is a noted problem with lab-on-a-chip platforms [39]. Integrated components on the lab-on-a-chip platform must not significantly change the temperature of the biochemical species. The THz electric field emitted by a PC THz emitter is proportional to the time-rate-of-change of the photoconductivity through Chapter 3: Terahertz Emission  36  [ ]bTHz EdttntqdtE )()()( µ∝         (19) where q is the elementary charge constant, μ(t) is the mobility, n(t) is the charge-carrier density, and Eb is the bias electric field. This time-rate-of-change relationship can be seen by approximating a PC THz emitter as a Hertzian dipole antenna, as shown in Appendix B. Terahertz electric field pulses are created in the first few picoseconds after optical excitation as this corresponds to the greatest time-rate-of-change in photoconductivity. However, residual photocurrent consumption will continue for as long as the photoconductivity remains at a large value, as dictated by either the mobility or charge-carrier lifetime of the semiconductor material. The prolonged photoconductivity causes Joule heating flux (being Joule heating per area) according to [84]  ∫=000)(TH dttTKσφ , (20) where T0 is the laser pulse repetition period and K is a proportionality constant. The Joule heating flux expression can be quantified further as  ,1)(1220/0 2200000dEqKVTdtedEqKVTdtdwtiVT optFLbtToptFLbT bHµτµφ τ Φ≈Φ== −∫∫   (21) where Vb is the bias voltage amplitude, Φ is the pump fluence, d is the spacing between electrodes, w is the electrode width, and Eopt is the photon energy of (780 nm) probe beam, and KFL is a constant representing fluence loss from the mismatch between the optical spot size and the active area of the PC THz emitter and Fresnel reflection of the pump beam at the semiconductor/air interface. The photocurrent is i(t) = I0e-t/τ where I0 = KFLΦqμwVb/d. To illustrate residual photocurrent consumption, Figure 3.1.2.1(a) shows photoconductivity and Chapter 3: Terahertz Emission  37  THz electric field versus time for a PC THz emitter with a long duration photoconductivity. The THz electric field pulse is created when the photoconductivity quickly rises. However, the photoconductivity remains at a large value for the duration of the long photoconductivity lifetime, creating considerable Joule heating flux while contributing little to generation of the THz electric field. In contrast, Figure 3.1.2.1(b) shows photoconductivity and THz electric field versus time for a PC THz emitter with a short duration photoconductivity. Again, the THz electric field is created in the first picosecond after optical excitation, showing a similar THz electric field response. The photoconductivity, however, reduces its value very quickly for significantly reduced Joule heating flux.   As mentioned, a common solution to Joule heating is to use a large-area PC THz emitter, however, this solution is unsuited to the small-scale dimensions of the DMF-based THz-TDS system. To illustrate this, the emitted THz power, Pemitted, and the Joule heating, PH, can be considered. It can be shown that the emitted THz power from a PC THz emitter is  202222222024)(optrtFLbittedem ETcKVwqPτpiµη Φ=  (22) for a photoconductivity rise-time of τrt. The derivation is shown in Appendix B. The ratio between the Joule heating and the emitted THz power, Pemitted, can be shown to be  dwKqEcPdwPPFLoptrtemittedHemittedHΦ==µηττpiφ02224. (23) For a required emitted THz power, the Joule heating can be made small by increasing the width of the PC THz emitter (as in large-area PC THz emitters). However, the width (and area) of Chapter 3: Terahertz Emission  38   Figure 3.1.2.1  Photoconductivity and THz electric field for PC THz emitters with (a) long duration photoconductivity and (b) short duration photoconductivity. The results of (a) show a large amount of Joule heating flux while the results of (b) show a small amount of Joule heating flux for similar emission of THz electric field.  Chapter 3: Terahertz Emission  39  the PC THz emitter is restricted in the small-scale DMF-based THz-TDS system. Therefore, the Joule heating must be lowered in other ways. Other proposed solutions to Joule heating can be complicated. The proposed solutions include intricate electrode designs [53, 78], patterning of the active area [54], heat sink integration [55], low-temperature substrate growth [56], water-cooling [57], substrate irradiation [58], and laser-ablation [59].  To minimize Joule heating, this chapter proposes a reduction to the photoconductivity, σ(t) = qμ(t)n(t), following the generation of the picosecond-duration THz electric field pulse. Two techniques are proposed: i. introducing a transient mobility (whereby the value of μ(t) is reduced after optical excitation) through a GaP material and ii. reducing the charge-carrier lifetime (whereby the value of n(t) is reduced after optical excitation) through enhanced surface recombination materials (i.e., nanocomposite and textured materials). These techniques are explored in sections 3.3 and 3.4, respectively. The investigations start with a description of the experimental setups used to measure the ultrafast material response, characterizing the transient mobility and charge-carrier lifetime, and the THz response, characterizing the emitted THz electric field amplitude and the corresponding photocurrent consumption. These experimental setups are the pump-probe and THz setups, respectively.  3.2 Experimental Setups for Investigating Ultrafast Material and Terahertz Responses In this section, the applicable experimental setups are investigated. To measure the ultrafast material response, for characterizing the transient mobility and charge-carrier lifetime, a pump-Chapter 3: Terahertz Emission  40  probe setup is used. To measure the THz response, for characterizing the emitted THz electric field amplitude and the corresponding photocurrent consumption, a THz setup is used.  3.2.1 Pump-Probe Setup for the Ultrafast Material Response The transient mobility and charge-carrier lifetime of various semiconductor materials can be characterized by analysing their ultrafast material responses using a pump-probe setup. The pump-probe setup is shown in Figure 3.2.1.1 and Figure 3.2.1.2 with isometric and top views, respectively. The pump and probe beams have a 100 fs pulse duration [85] and 780 and 1550 nm wavelengths, respectively. The pump beam wavelength of 780 nm has a corresponding photon energy of 1.6 eV which can photoexcite charge-carriers from the valence to the conduction band for semiconductors with bandgap energy being less than 1.6 eV. A second harmonic crystal can be added into the pump line to create a 390 nm (3.2 eV) pump wavelength for wide bandgap semiconductors. The 1550 nm probe wavelength is chosen as its 0.8 eV photon energy is below the bandgap of the investigated semiconductors (although a 780 nm probe wavelength can be used for wide bandgap semiconductors). The pump and probe beams are overlapped with a dichroic beamsplitter (labeled BSdichroic), and then focused onto the sample semiconductor (labeled SS) with a 40× microscope objective (labeled MO40×), the position of which can be adjusted by an xyz translation stage (labeled TS). As the photons of the pump beam induce photoconductivity changes to the semiconductor sample, there is a measurable differential probe transmission on the InGaAs photodiode (labeled PCInGaAs). Chapter 3: Terahertz Emission  41      Figure 3.2.1.1  An isometric view of the pump-probe setup is shown. The pump-probe setup consists of a dichroic beamsplitter that overlaps the (780 nm) pump and (1550 nm) probe beams, a 40× microscope objective that focuses the beams onto the semiconductor sample, an xyz translation stage for adjustments and optimization, and an InGaAs photodiode for measuring the differential transmission of the probe beam that passes through the semiconductor sample.     Chapter 3: Terahertz Emission  42       Figure 3.2.1.2  A top view of the pump-probe setup is shown. The components are labeled as follows: BSdichroic is a dichroic beamsplitter; MO40× is a 40× microscope objective; SS is a semiconductor sample; TS is an xyz translation stage; PDInGaAs is an InGaAs photodiode.    Chapter 3: Terahertz Emission  43  3.2.2 Terahertz Setup for the Terahertz Response The THz response, relating to the radiated THz electric field and photocurrent consumption of PC THz emitters, is characterized with a THz setup, which is investigated in this section of the thesis. The transimpedance amplifier circuit that is used to measure the photocurrent consumption of the PC THz emitter is shown in Appendix C. There are practical challenges that must be considered when implementing THz setups for measuring pulsed THz electric fields. These challenges have been noted in the literature [86-88], as pulsed THz setups require careful alignment with consideration to both space and time. Spatial alignment of the THz beam has sub-wavelength tolerances, which demands precision in the transverse and axial dimensions, and such alignment is further complicated by the fact that the THz beam is invisible to the naked eye. Temporal alignment of the THz beam has subpicosecond tolerances, which demands precision in defining the THz-probe optical path difference in the overall time-resolved THz setup. Meeting these spatial and temporal alignment constraints simultaneously can be challenging. The above challenges are addressed in this section. Three design processes are introduced for effective implementation of the THz setup. A collineation process is applied to enable precise spatial overlap of the THz and probe beams—and thereby address the challenge of aligning invisible and visible beams in the collinear geometry of the parabolic mirrors. An autocorrelation process is applied to enable precise temporal overlap of the THz and probe pulses—and thereby address the challenge of balancing the optical path differences during the (unoptimized and typically noisy) initial scans. An EO process is applied to optimize and Chapter 3: Terahertz Emission  44  calibrate the polarization-sensitive optics—and thereby address the challenge of maximizing and quantifying the THz-electric-field-induced modulation of the probe polarization. The remainder of this section is laid out as follows. Section 3.2.2.1 describes the THz setup design processes, with subsections introducing the collineation, autocorrelation, and EO processes. Section 3.2.2.2 illustrates the complete THz setup operation.  3.2.2.1 Terahertz Setup Design The THz setup is shown in the schematic of Figure 3.2.2.1.1 with a SolidWorks isometric view shown to scale. The THz setup consists of a 10× microscope objective that focuses the (780 nm) pump beam onto the PC THz emitter, two parabolic mirrors that collect and focus the THz beam, a pellicle beamsplitter that overlaps the THz beam with the (780 nm) probe beam, an EO ZnTe crystal and a quarter waveplate that alter the polarity of the probe beam, a polarizing beamsplitter that splits the probe beam into vertical and horizontal polarizations, and a balanced Si photodiode that measures the difference between the power of the horizontally and vertically polarized probe beam components.  This THz setup can be implemented systematically by the addition of a few components and by following the collineation, autocorrelation, and EO processes. Top-view experimental configurations for these processes are shown to scale in Figure 3.2.2.1.2. The collineation process is shown in Figure 3.2.2.1.2(a). The autocorrelation process is shown in Figure 3.2.2.1.2(b). The EO process is shown in Figure 3.2.2.1.2(c). The complete THz setup is shown in Figure 3.2.2.1.2(d). The components are as follows: a beam block is labeled BB; the xyz translation stages are labeled TS; the 10× microscope objective is labeled MO10×; the  Chapter 3: Terahertz Emission  45     Figure 3.2.2.1.1  An isometric view of the THz setup is shown. The THz setup consists of a 10× microscope objective that focuses the pump beam onto the PC THz emitter, two parabolic mirrors that collect and focus the THz beam, a pellicle beamsplitter that overlaps the THz beam with the probe beam, an EO ZnTe crystal and a quarter waveplate that alter the polarity of the probe beam, a polarizing beamsplitter that splits the probe beam into vertical and horizontal polarizations, and a balanced Si photodiode that measures the difference between the power of the horizontally and vertically polarized probe beam components.   Chapter 3: Terahertz Emission  46   Figure 3.2.2.1.2  Top views of the THz setup are shown for the (a) collineation process, (b) autocorrelation process, (c) EO process, and (d) full THz setup operation. Components are labeled as follows: BB is a beam block; TS is an xyz translation stage; MO is a microscope objective; PE is a PC THz emitter; PM is a parabolic mirror; IA is an iris aperture; BSpel is a pellicle beamsplitter; FM is a flip mount; BE is a bias electrode; EO is an EO crystal; QW is a quarter waveplate; BSpol is a polarizing beamsplitter; VA is a variable attenuator; PDSi is a pair of Si photodiodes (linear, differential); PDGaP is a GaP photodiode (nonlinear).  Chapter 3: Terahertz Emission  47  PC THz emitter is labeled PE; the parabolic mirrors, with gold coating, a 90° off-axis reflection, 76.2 mm diameter, and 50.8 mm effective focal length, are labeled PM; the iris aperture is labeled IA; the pellicle beamsplitter, with a 76.2 mm diameter and 2 μm thickness, is labeled BSpel; the flip mount is labeled FM; the parallel plate bias electrodes are labeled BE; the EO crystal, being ZnTe with a <110> orientation and 500 μm thickness, is labeled EO; the quarter waveplate is labeled QW; the polarizing beamsplitter is labeled BSpol; the variable attenuator is labeled VA; the pair of (linear and balanced) Si photodiodes are labeled PDSi; the (nonlinear) GaP photodiode is labeled PDGaP. A translation stage (not shown) varies the optical path difference between the 780 nm pump and 780 nm probe pulse trains, which originate from an Erbium-doped fibre laser with a 100 fs pulse duration and 90 MHz repetition frequency. A second variable attenuator (not shown) is placed in the pump beam to adjust its power. Figure 3.2.2.1.3 shows a photograph of the THz setup as used in the UBC Integrated Optics Laboratory. (The flip mount and GaP photodiode are removed for this image.) The labels are the same as those in Figure 3.2.2.1.2.  3.2.2.1.1 Collineation Process The THz setup alignment commences with a collineation process that has the pump beam and probe beam achieve propagation that is overlapped and parallel, i.e., collinear. In this way, the propagation of the visible pump beam can be made to mimic the subsequent propagation of the invisible THz beam. This collineation process facilitates the transverse and axial spatial alignment of the THz setup.  Chapter 3: Terahertz Emission  48         Figure 3.2.2.1.3  A photograph is shown of the THz setup with labeled components: TS is an xyz translation stage; MO is a microscope objective; PE is a PC THz emitter; PM is a parabolic mirror; IA is an iris aperture; BSpel is a pellicle beamsplitter; EO is an EO crystal; QW is a quarter waveplate; BSpol is a polarizing beamsplitter; VA is a variable attenuator; PDSi is a pair of Si photodiodes (linear, differential).   Chapter 3: Terahertz Emission  49  The collineation process is shown in Figure 3.2.2.1.2(a). The THz setup is configured without the PC THz emitter, to allow the incident pump beam to be focused by the microscope objective and re-collimated by the primary parabolic mirror. To reduce the divergence angle from the first parabolic mirror, the numerical aperture (NA) of the microscope objective, NA ≈ 0.25, is chosen to be sufficiently close to that of the parabolic mirror, NA ≈ 0.4. The THz setup is configured with its flip mount deflected out of the beam path to allow the pump and probe beams to be overlapped and collimated, prior to their being focused by the secondary parabolic mirror. An iris aperture is introduced into the pump beam, and it is adjusted in diameter to form comparable pump and probe beam sizes for ease of alignment. A pickoff mirror (not shown) is inserted into the THz setup before the secondary parabolic mirror to deflect the pump and probe beams out of the THz setup. The primary parabolic mirror and pellicle beamsplitter are adjusted to establish near-perfect overlap and collimation between the pump and probe beams, with approximately 1 mm of beam separation over a 4 m propagation distance. (Note that the probe beam and apertured pump beam are observed with the aid of an infrared sensor card.) The pickoff mirror is then removed, and the collinear pump and probe beams are focused by the secondary parabolic mirror to a common focus in the EO crystal. In terms of the formal design processes, the procedures continue through temporal alignments in the autocorrelation process.  3.2.2.1.2 Autocorrelation Process The THz setup alignment applies an autocorrelation process to define the zero-time between the 780 nm pump pulses and 780 nm probe pulses as they propagate through the THz setup. Chapter 3: Terahertz Emission  50  This zero-time is used in the completed THz setup, as an estimate of the state in which the THz pulses and probe pulses have equal optical path differences. The autocorrelation process is shown in Figure 3.2.2.1.2.1(b). The PC THz emitter remains outside of the pump beam path, to allow the pump beam to pass through the THz setup, and the pump beam power is adjusted to be equal to that of the probe beam. An optical chopper is inserted into the main beam path of the laser to modulate both the pump and probe beams. The flip mount in the THz setup is deflected into the pump and probe beam paths to reflect the collinear pump and probe beams onto the GaP photodiode. A GaP photodiode is chosen because its 2.3 eV bandgap is larger than the 1.6 eV photon energy of the pump and probe beams. This leads to two-photon photoexcitation and highly-sensitive nonlinear mixing between the pump and probe beams [85]. The photocurrent from the GaP photodiode is filtered and amplified by a transimpedance preamplifier, and the resulting voltages are filtered and recorded by a lock-in amplifier that is referenced to the optical chopper frequency. The voltage signal is recorded as a function of the pump-probe time delay, during scanning of the pump-probe transmission stage, and this forms the desired autocorrelation. A representative autocorrelation is shown in Figure 3.2.2.1.2.1. Figure 3.2.2.1.2.1(a) shows a coarse scan of the GaP photodiode photocurrent for a 60 mm scan length of the pump-probe translation stage—corresponding to 200 ps of pump-probe time delay. This coarse scan shows the zero-time of interest for the system. Figure 3.2.2.1.2.1(b) shows a subsequent fine scan of the GaP photodiode photocurrent for a 300 µm scan length of the pump-probe translation stage—corresponding to a 1 ps pump-probe time delay. The observed zero-time of the pump-probe autocorrelation signal can be used to estimate the zero-time of the final THz- Chapter 3: Terahertz Emission  51   Figure 3.2.2.1.2.1  Results from the autocorrelation process, showing nonlinear photocurrents from the GaP photodiode versus time, t, and corresponding delay stage distance, x, over time-domain scans of (a) 200 ps (60 mm length) and (b) 1 ps (300 µm length). Chapter 3: Terahertz Emission  52  probe system in the ultimate THz setup, but it will be necessary to compensate for the added optical path length introduced by the PC THz emitter. The time delay associated with the additional optical path length can be approximated as tSM(nSM - 1)/c, where tSM is the thickness of the semiconductor material of the PC THz emitter, nSM is the refractive index of the semiconductor material of the PC THz emitter, and c is the speed of light in free-space. The variation of group indices over the typical range 3.59 to 3.61 (for a broadband of THz frequencies) results in changes to the path length of less than 1 μm, and these small changes to the translation distance are negligible to the zero-time measured by the autocorrelation process. For the initial system alignment, with a tSM = 350 µm thick GaAs PC THz emitter having a group index of nSM = 3.6, the pump delay line must be shortened by 0.9 mm, corresponding to a 3 ps time delay, to compensate for the PC THz emitter. Experimental tests of the autocorrelation process and the final THz setup, with a PC THz emitter, suggest that the autocorrelation process can reliably define the zero-time path length (delay time) to within an error of 0.7 mm (2 ps). The sub-millimetre length scale of this error is far lower than that achieved by ruler measurements of the optical path differences, which in statistical tests of the standard deviation yields a 14 mm (50 ps) error. Moreover, the sub-millimetre length scale autocorrelation process error is well within the scanning range of commercial THz rapid scanning systems that can scan, for example, over 9 mm (30 ps) [89]. It is worth noting that the autocorrelation process can also be used to find the approximate zero-time path length for THz setups that achieve generation of THz radiation via optical rectification—but only by compensating for the optical path length of the introduced EO crystal (and filters). Chapter 3: Terahertz Emission  53  The completion of the autocorrelation process leaves the system in a state of precise spatial and temporal alignment, and the remaining optimization steps are implemented as part of the EO process.  3.2.2.1.3 Electro-Optic Process The remaining challenge for implementing the THz setup relates to the mapping of the THz electric field onto the probe beam's polarization. The THz electric field must effectively modulate the probe's polarization state, within the EO crystal, and this can only be done if the THz setup is configured with the proper EO crystal orientation and the proper balancing of the polarization-sensitive optics. These challenges are addressed by the EO process, which involves the application of a static bias electric field, from parallel plate bias electrodes, to facilitate both optimization of the EO crystal orientation (for effective THz detection) and calibration of the THz setup (to quantify the absolute THz electric field amplitude). The configuration uses sufficiently large parallel plate bias electrodes to ensure homogeneity of the static bias electric field lines within the EO crystal. The implemented THz setup makes use of EO sampling with the Pockels effect in an EO crystal [90], through the EO process shown in Figure 3.2.2.1.2(c). The pump beam is blocked for this process. A 500-μm-thick <110> ZnTe EO crystal is introduced into the THz setup, with an initially unknown crystallographic orientation, and a quarter waveplate is introduced after the EO crystal to bias the probe with a circular polarization state. The horizontally-polarized probe beam is focused by the secondary parabolic mirror, within the EO crystal, and passes through the quarter waveplate. (The probe beam is now either Chapter 3: Terahertz Emission  54  circularly-polarized or elliptically-polarized.) The probe beam then propagates through a polarizing beamsplitter, to split it into orthogonal polarizations (vertical and horizontal), and the orthogonally-polarized beams are detected by the pair of Si photodiodes. The differential photocurrent from the two Si photodiodes is filtered and amplified by a transimpedance preamplifier, and the resulting voltages are filtered and recorded by a lock-in amplifier. With the above configuration, the absence of a THz electric field in the EO crystal is seen as a negligible change in the probe's polarization state, with its circular polarization leading to a negligible differential photocurrent. In contrast, a finite THz electric field, with a horizontal linear polarization, interacts with the probe pulse in the EO crystal. The THz electric field induces birefringence in the EO crystal—to change the polarization of the probe pulse from its original balanced circular polarization state (coming about from the use of a quarter waveplate) to an unbalanced elliptical polarization state (coming about from THz-induced changes to the probe polarization state). The THz-induced ellipticity on the probe polarization state, compared to the circular polarization state, is proportional to the THz electric field, and the level of polarization ellipticity is measured by passing the probe beam through a polarizing beamsplitter cube, with the two orthogonally-polarized output beams being directed onto two Si photodiodes. The Si photodiode currents are differenced. In this way, the EO sampling system has the THz electric field in the EO crystal be proportional to the difference in the photodiode currents. This differencing allows the THz setup to double the THz-induced signal change to the probe beam, while simultaneously rejecting common noise in the two orthogonal probe beam polarizations. Chapter 3: Terahertz Emission  55  For the above operation to be successful, the EO crystal should be oriented for maximal THz-induced changes to the probe's polarization state, and the polarization-sensitive components should be appropriately balanced. These conditions can be met by introducing an applied static electric field within the EO crystal to mimic the role of the THz beam. The THz setup can then be optimized. To carry out optimization for the EO process, a set of parallel plate bias electrodes are introduced into the THz setup. The parallel plate bias electrodes are positioned as two parallel metal planes on either side of the EO crystal. The electrodes are much larger than the transverse cross-section of the EO crystal to have their field lines penetrate the crystal with a homogeneous distribution, with a direction that matches that of the THz polarization. For the THz setup, the THz and probe beams have horizontal polarizations, so the field from the parallel plate bias electrodes is made to have a horizontal direction. An AC bias voltage of 100 Vp-p at 45 kHz is applied to the parallel plate bias electrodes, facilitating lock-in detection. The circuit to create the 100 Vp-p 45 kHz signal, used in the both EO process and the full THz setup operation, is described in Appendix D. The EO crystal orientation and the polarization-sensitive components are then optimized to achieve a maximal electric-field-induced change to the probe's polarization state and resulting differential photocurrent. The normalized response for this EO process can be seen in the blue (upper) curve of Figure 3.2.2.1.3.1, shown as a function of the EO crystal's azimuthal rotation angle, ϕ. The bias electrodes <110> ZnTe experimental results (circles) are plotted on top of the corresponding bias electrodes <110> ZnTe theoretical curve (solid line). The theoretical curve for this <110>-oriented crystal follows the trend cos(ϕ)cos(2ϕ) – sin(ϕ)sin(2ϕ)/2, the derivation and details of which are given  Chapter 3: Terahertz Emission  56    Figure 3.2.2.1.3.1  Results from the EO process, showing experimental data points (circles) and theoretical curves (solid lines) versus azimuthal rotation angular, ϕ. The upper blue curve and data points, corresponding to the left axis, are acquired from the use of parallel plate bias electrodes during the EO process. The lower red curve and data points, corresponding to the right axis, are acquired from the use of the complete THz setup.  Chapter 3: Terahertz Emission  57  in Appendix E or Planken et al. [91]. It is readily apparent from this figure that the maximal THz electric field signal will be achieved for an EO crystal orientation at ϕ = 0° or ϕ = 180°. The present THz setup is configured for operation with the EO crystal oriented at ϕ = 0°. Trial-and-error to identify this optimal angle would be more difficult—particularly if the initial THz electric field signal is not yet measured and the zero-time is unknown. It is important to note that the EO process provides a means to measure absolute THz electric fields with the THz setup. This ability arises by defining a calibration ratio for the THz setup—linking a known static electric field amplitude, in the EO crystal when a voltage is applied to the parallel plate bias electrodes, to its measured differential photocurrent value. The static electric field in the EO crystal is approximated as Vbe/dbe, where Vbe is the applied voltage amplitude on the bias electrodes and dbe is the spacing between bias electrodes (corresponding to the width of the EO crystal). A value of dbe = 5 mm is used given the 5 mm width of the electric-optic crystal. The complete THz setup uses this calibration ratio to define absolute THz electric fields for measured THz waveforms. Note that THz setups typically operate with an EO crystal having a (110) surface orientation, so it is advantageous to have the sides of the crystal be cut along the (110) and (001) planes. This allows the parallel plate electrodes to be brought up against (and parallel to) the edges of the EO crystal—yielding a strong and homogenous horizontal electric field along the global maximum of the angular EO response (seen in Figure 3.2.2.1.3.1).  Chapter 3: Terahertz Emission  58  3.2.2.2 Operation of the Terhertz Setup The previously-introduced collineation, autocorrelation, and EO processes have configured the THz setup for optimal generation and detection of THz radiation. The complete THz setup is shown in Figure 3.2.2.1.2(d). The complete THz setup is implemented by introducing the PC THz emitter. For this initial system alignment, the PC THz emitter is comprised of two bias electrodes, separated by a 70 μm gap, on a 350-μm-thick double-sided-polished semi-insulating (SI)-GaAs wafer. The unattenuated pump beam, at a power of up to 50 mW, is focused by the microscope objective. The PC THz emitter is translated into the focus of the pump beam. A multimeter may be used at this stage to aid the PC THz emitter positioning—by optimizing its position to establish the least resistance across the gap. The PC THz emitter is then activated by biasing it with a 45 kHz 100 Vp-p square-wave. This applied bias voltage provides an electric field of approximately 6 kV/cm, which is below the breakdown electric field of GaAs [92]. The lock-in amplifier is referenced to the 45 kHz waveform. This high-frequency is used to minimize the effects of laser noise (which scales as the inverse of the frequency) and reduce effects from acoustic vibrations (for which the pellicle beamsplitter is especially sensitive). The complete THz setup can be operated at this stage, and minor adjustments can be made throughout the THz setup, by way of the xyz translation stages. A representative result for the complete THz setup is shown in Figure 3.2.2.2.1. The time-domain THz electric field waveform is shown normalized in Figure 3.2.2.2.1, with its inset showing a scan of the noise level (with a peak amplitude of 1.1 × 10-3, calculated as √2 times the root-mean-squared noise value). These results are achieved for a lock-in integration  Chapter 3: Terahertz Emission  59   Figure 3.2.2.2.1  Results from the complete THz setup operation, showing the THz electric field in the (a) time-domain and (b) frequency-domain. The inset of (a) shows the noise level for the THz setup, during the first 0.25 ps. Chapter 3: Terahertz Emission  60  time constant of 300 ms. The normalized signal-to-noise (SNR) ratio for these results is 1,700 Hz1/2, where this normalized SNR is defined as the ratio of THz electric field peak amplitude to noise peak amplitude (i.e., the non-normalized SNR) divided by the square root of the lock-in integration time constant. Note that the SNR is defined with peak electric field ratios, as opposed to power ratios, as this is the norm for analyses of THz radiation, and the SNR is stated as a normalized quantity, with respect to the integration time constant, to factor out SNR improvements from the integration of random noise and quantify only the THz setup characteristics. According to the calibration ratio from the EO process in Section 3.2.2.1.3, the absolute THz electric field peak amplitude is found to be (7 ± 1) V/cm. This THz electric field peak amplitude can be compared to the idealized results from the equation, ETHz,0 = (2πν)-1n-3r41-1L-1cΔP<110>/Pprobe, [91, 93] where ETHz,0 is the THz electric field peak amplitude, n is the ZnTe refractive index, υ is the 780 nm frequency, c is the speed of light in a vacuum, r41 is the ZnTe EO coefficient, L is the length of the ZnTe EO crystal, and ΔP<110>/Pprobe = 2 × 10-4 is the differenced Si powers divided by the probe power. This equation, which is a simplified form of Equation (86) in Appendix E, gives a THz peak electric field of 7 V/cm, which agrees with that found by the EO process. The dependencies of the THz electric field amplitudes with the EO crystal's azimuthal rotation angle that correspond to the measured THz electric field results are shown as the red (lower) curve of Figure 3.2.2.1.3.1, where good agreement with theory is again seen. The frequency-domain THz response is shown in Figure 3.2.2.2.1(b). The THz radiation shows emission up to a frequency of approximately 3.5 THz, with strong water vapour absorption Chapter 3: Terahertz Emission  61  peaks [94]. Note that the total time-domain scan length is 16 ps, although the scan is only displayed for 11 ps, giving a frequency resolution just under 0.1 THz. These water vapour absorption resonances produce the oscillations in Figure 3.2.2.2.1(a) that follow the THz electric field time-domain waveform at times beyond 2 ps. The observations of spectroscopic features, such as these resonances, are characteristic of a high operational sensitivity—which is ultimately indicative of success for this THz setup. The pump-probe and THz setups will now be used to characterize the ultrafast material response and the THz response of PC THz emitters with transient mobility (GaP) and reduced charge-carrier lifetime (nanocomposites and textured InP) characteristics.  3.3 Photoconductive Terahertz Emitters with Transient Mobility As mentioned previously, PC THz emitters are of particular interest as the strength of the emitted THz electric field is scalable with bias voltage amplitudes and pump fluences [81] and the required bias electrodes can be piggybacked onto those of the DMF devices. Photoconductive THz emitters radiate a THz electric field pulse by way of accelerating charge-carriers within the first few picoseconds of optical excitation. However, these charge-carriers often have lifetimes that are much longer than the THz pulse durations, creating residual photocurrents which lead to unnecessarily large Joule heating, which is undesirable in the lab-on-a-chip platform. In PC THz emitters, semiconductor materials are typically excited in such a way as to produce a mobility that is constant. This is usually achieved by choosing an optical excitation with photon energy similar to a direct bandgap, as this excites charge-carriers to the bottom of the central Γ valley. Classic examples of this are GaAs or InP PC THz emitters being Chapter 3: Terahertz Emission  62  illuminated by a 780 nm ultrafast pulsed laser. However, the residual photoconductivity can be limited if the mobility is limited in the first few picoseconds following optical excitation and THz emission. Ideally, a semiconductor would be excited to a state of high mobility in the first few picoseconds after optical excitation and then quickly transition to a state of low mobility with low residual photoconductivity. Cavichhia and Alfano [95] suggested that such a process is possible for GaP when illuminated at a wavelength of 390 nm. This section of the thesis analyses the GaP transient mobility (under 390 nm illumination) and compares it to the GaAs static mobility (under 780 nm illumination), as GaAs is a common material for PC THz emitters. In general, wide-bandgap semiconductors are appealing for optoelectronics [96/90-malik]. Especially high dielectric breakdown fields can be achieved with these materials, offering significant benefits for high-power PC THz technology. Ultrafast laser pulse photoexcitation of ZnSe [97], GaN [98], and diamond [99] have been applied for high-power THz emission with large PC bias fields, as the dielectric breakdown field strengths of these wide-bandgap semiconductors, being 0.125 [97], 3.3 [98] and 10 [100] MV/cm, respectively, are especially high. (Note that low input voltages are still desired, but the high bias fields can be created by amplifying the input voltage with a transformer or boost converter.) While PC THz emitters with wide-bandgap semiconductors can resist dielectric breakdown, it is important to note the associated susceptibility of these PC THz emitters to failure from Joule heating [58]. Wide-bandgap semiconductors typically have long charge-carrier lifetimes [101-103] following laser pulse photoexcitation, being 9 [101], 40 [102], and 34 ns [103] for the aforementioned ZnSe, GaN, and diamond, respectively. Long charge-Chapter 3: Terahertz Emission  63  carrier lifetimes lead to prolonged residual photocurrents, and this is undesirable in terms of Joule heating. With the above limitations in mind, GaP is investigated as a transient mobility material for the PC THz emitter. GaP has received significant attention for non-resonant THz emission [104, 105] because of its excellent phase-matching capabilities [104] and high optical phonon resonances [106]. There is a scarcity of literature on PC THz emission with GaP, however, and this is due mainly to its atypical bandstructure. GaP has a high central Γ valley that is well above its neighbouring L and X sidevalleys. Thus, the typical low-energy PC photoexcitation, with photon energies below the Γ valley energy, EΓ = 2.8 eV, would need indirect phonon-assisted electron transitions to the lower sidevalleys. Such indirect transitions have a low quantum efficiency, due to the need for coupling to phonons, and this is undesirable. In this section, it is shown that high-energy PC photoexcitation, with photon energies above the Γ valley energy, EΓ = 2.8 eV, initiates direct electron transitions into the central Γ valley and subsequent relaxation through a cascaded scattering sequence. Photoexcited electrons scatter rapidly from the high-mobility Γ valley into neighbouring low-mobility sidevalleys, and this establishes the desired transient mobility response for PC THz emission. Transient mobility has been observed in other semiconductors, such as GaAs [107] and InSb [108], and it is considered here for use in PC THz emitters. The ultrafast charge-carrier dynamics associated with photogeneration and transient mobility are studied for GaP via a series of pump-probe differential transmission experiments. The inherent relaxation mechanisms are identified, and ultrafast transient mobility is observed. The transient mobility response is then investigated for PC THz emitters. Chapter 3: Terahertz Emission  64  The transient mobility response of GaP can be revealed by linking its transient photoconductivity to the ultrafast charge-carrier dynamics following photoexcitation by an ultrafast above-bandgap laser pulse. The transient photoconductivity, σ(t) = qn(t)μ(t), is dominated by electron dynamics and is formed as the product of the electron charge, q, time-varying charge-carrier density, n(t), and time-varying mobility, μ(t). The time-rate-of-change of the transient photoconductivity radiates a THz electric field, ETHz(t). For a standard PC THz emitter, with a static mobility of μ, the emitted THz electric field forms from a subpicosecond rise of n(t). The slow fall in photoconductivity due to charge-carrier recombination contributes little to generation of THz radiation—but does have the material remain in a prolonged state of high photoconductivity with increased residual photocurrent. For the proposed PC THz emitter, with transient mobility of μ(t), the transient photoconductivity undergoes an initial rapid increase due to the photoexcitation of n(t) then a rapid decrease due to the reduction of μ(t). The rapid rise and fall of transient photoconductivity both contribute to the THz electric field—and the material is left in a state of low photoconductivity with minimal residual photocurrent. The initial photoexcitation response of GaP can be characterized by spectral analysis. The spectral differential transmission, ΔT(λ)/T, and GaP bandstructure are shown in Figure 3.3.1(a). The GaP conduction band has a high central Γ valley energy, EΓ = 2.8 eV, with lower L and X sidevalley energies, EL = 2.6 eV and EX = 2.3 eV, respectively [109]. The X sidevalley is the dominant relaxation pathway [95], as photoexcited electrons in the Γ valley rapidly scatter into and amongst the upper X7 and lower X6 valleys [110] of the X sidevalley. The  Chapter 3: Terahertz Emission  65   Figure 3.3.1  Measured differential spectral transmission, ΔT(λ)/T, versus wavelength, λ, for (a) GaP and (b) GaAs. The GaP bandstructure in the inset of (a) shows its high central Γ valley energy, EΓ = 2.8 eV, and neighbouring L and X sidevalleys. The X sidevalley of GaP has upper X7 and lower X6 valleys. The GaAs bandstructure in the inset of (b) shows its low central Γ valley energy, EΓ = 1.4 eV, and higher L and X sidevalleys.  Chapter 3: Terahertz Emission  66  presence of the lowest X sidevalley is clearly seen in the Figure 3.3.1(a) spectral differential transmission results, which rise at 550 nm from the EX = 2.3 eV energy of GaP. The remainder of this section of the thesis compares GaP photoexcitation to that of GaAs, whose well-established 1.4 eV direct bandgap spectral response and bandstructure are shown in Figure 3.3.1(b). The transient mobility of GaP that follows the initial photoexcitation can be observed by a time-resolved pump-probe investigation. Such an investigation is carried out here with the pump-probe setup. Pump beam laser pulses are focused on the GaP sample. The pump-probe results for GaP are measured by way of 390 nm (3.2 eV) pump photoexcitation at a fluence of Φ. The results are recorded as the probe differential transmission, ΔT(t)/T. The 780 nm (1.6 eV) probe photon energy is sufficiently far below the GaP conduction band to allow the probe differential transmission, ΔT(t)/T, to be susceptible mainly to pump-induced free-carrier absorption [95]. The GaP probe differential transmission, ΔT(t)/T, is shown in Figure 3.3.2(a) for 390 nm (3.2 eV) pump photoexcitation at Φ = 72 μJ/cm2. As a comparison, the GaAs ΔT(t)/T results are shown in Figure 3.3.2(b) for 780 nm (1.6 eV) pump photoexcitation at Φ = 18 μJ/cm2. Within the first picosecond, both semiconductors exhibit rapid decreases in ΔT(t)/T. After the first picosecond, however, dramatically different relaxation responses are observed. The GaP relaxation response is subject to charge-carrier scattering and thermalization throughout the bandstructure, while the GaAs relaxation response is subject to negligible scattering and minimal energy relaxation (due to the slight 0.12 eV excess energy of the hot electron population). Chapter 3: Terahertz Emission  67   A Drude free-carrier absorption model is applied to interpret the probe differential transmission, ΔT(t)/T, of GaP in terms of ultrafast charge-carrier dynamics and isolate the transient mobility. The pump-induced free-carrier absorption maps itself onto ΔT(t)/T by way of the time-varying charge-carrier density, n(t), and transient mobility, μ(t) = q/[Γs(t)m(t)]. The charge-carrier density, n(t), is set by the pump fluence, Φ, and penetration depth, δ = 100 nm. The time-varying scattering rate, Γs(t), evolves according to intervalley scattering and remains well below the probe angular frequency, ω. The time-varying electron effective mass, m(t), is proportional to the free-electron mass, me, and it transitions between effective masses of mΓ = 0.09me, mX7 = 0.72me, and mX6 = 1.33me as the electrons populate the respective Γ, X7 and X6 valleys [95]. Likewise, the transient mobility, μ(t), transitions between distinct values, determined in this study, as the electrons populate the Γ, X7 and X6 valleys. The underlying pump-induced charge-carrier dynamics are mapped onto the probe differential transmission, ΔT(t)/T, by way of changes to surface reflection and bulk transmission. The respective surface reflection and bulk transmission of the probe beam are subject to pump-induced changes to the surface refractive index, according to [111]  2202)(1)(2)()(ttmnetntnsss Γ+−=∆ωε (24) and bulk absorption coefficient, according to  22203)(1)()()()()(tttmncetnttss Γ+=∆=ωµεαα (25) Here, ω = 2π c / (780 nm) is the probe angular frequency, c is the free-space speed of light, ε0 is the permittivity of free-space, ns = εr1/2 = 3.66 is the surface refractive index that is equal to  Chapter 3: Terahertz Emission  68   Figure 3.3.2  Measured probe differential transmission, ΔT(t)/T, in time for (a) GaP with 390 nm (3.2 eV) pump photoexcitation and 780 nm (1.6 eV) probe sampling and (b) GaAs with 780 nm (1.6 eV) pump photoexcitation and 1550 nm (0.8 eV) probe sampling. The initial 10 ps of these time-resolved measurements are shown in the respective insets.  Chapter 3: Terahertz Emission  69  the square root of the dielectric constant, εr, and α(t) is the bulk absorption coefficient for the probe. (The change in the bulk absorption coefficient, Δα(t), is equal to absorption coefficient, α(t), as there is minimal absorption prior to optical excitation.) The probe angular frequency, ω, dominates over the time-varying scattering rate, Γs(t), according to ω2 ≫ Γs(t)2, as the scattering time constant is much larger than the probe period. The surface refractive index change, Δns(t), and bulk absorption coefficient change, Δα(t), contribute to the overall probe differential transmission, ΔT(t)/T, by way of  bbssTtTTtTTtT )()()( ∆+∆≈∆ (26) where Ts = 4ns/(ns+1)2 is the probe transmission at the surface, and Tb = e-α(t)δ is the probe transmission through the bulk pump-induced plasma with a depth of δ. The probe differential transmission at the surface, ΔTs(t)/Ts, is subject to Δns(t), and the probe differential transmission through the bulk, ΔTb(t)/Tb, is subject to Δα(t). Thus, the overall probe differential transmission in Equation (26) can be expressed as  22222)()()()()1(2)1()(ωωµδωω tttmcnqtnnnTtT pspsss−+−≈∆. (27) where  )()()(022tmqtntp εω = , (28) is the squared plasma frequency. The desired transient mobility μ(t) can then be expressed in terms of the measured ΔT(t)/T as Chapter 3: Terahertz Emission  70   1222)()()1(2)1()()(− ∆−+−=TtTtnnntmcnqtpssss ωωδµ . (29) The transient mobility, μ(t), of GaP is shown in Figure 3.3.3 for pump photoexcitation at 390 nm (3.2 eV) with fluences of Φ = 18, 36, and 72 µJ/cm2. These fluences correspond to charge-carrier densities of 3.5 × 1018, 7.0 × 1018, and 14 × 1018 cm-3, respectively. The transient mobility responses of all three fluences exhibit a rapid decrease to absolute minima followed by a slight increase to quasi-static levels. With higher fluence/carrier-density, the mobility lowers. The Figure 3.3.3 GaP transient mobility results are in close agreement with those of Cavicchia and Alfano. (See Figure 4 in [95].) The initial rapid decrease from the known Γ valley mobility of μΓ = 120 cm2/V∙s is associated with electron scattering from the central Γ valley to the neighbouring X sidevalley [95] over approximately 1 ps [110]. The electrons scattering to the X sidevalley populate both the upper X7 and lower X6 valleys. This results in especially low mobility minima of 4.16, 3.93, and 3.91 cm2/V∙s for the respective pump fluences of Φ = 18, 36, and 72 µJ/cm2. The electrons in the upper X7 valley then undergo scattering into the lower X6 valley, and this is seen as mobility increases to quasi-static values of 7.39, 7.24, and 6.98 cm2/V∙s for the respective pump fluences of Φ =  18, 36, and 72 µJ/cm2. This X7-to-X6 scattering occurs over approximately 4 ps, in good agreement with a prior measurement of 4.5 ps for the X7-to-X6 scattering transition [95]. It is important to note that the transient mobility following photoexcitation drops from its initial high mobility of μΓ = 120 cm2/V∙s to values that are an order of magnitude lower. The system is left in a final low-mobility state with a smaller residual photocurrent than if the mobility had stayed large. Whether or not this lowering of the mobility is enough to reduce the  Chapter 3: Terahertz Emission  71          Figure 3.3.3  The transient mobility, μ(t), responses are shown as a function of time for GaP. Responses are shown for low 18 µJ/cm2 (upper curve), moderate 36 µJ/cm2 (middle curve), and high 72 µJ/cm2 (lower curve) pump fluences.   Chapter 3: Terahertz Emission  72  Joule heating of a GaP PC THz emitter below that of an equivalent GaAs PC THz emitter will be investigated below.  The susceptibility to Joule heating for the GaP and GaAs PC THz emitters can be seen by using Equation (21) with the quasi-static mobility to calculate the Joule heating flux. It is found that a GaP PC THz emitter produces lower Joule heating flux than a GaAs PC THz emitter with the same bias voltage and 100 μm electrode gap spacing, under 50 mW optical pump illumination. However, this is at the expense of a lower emitted THz power due to the lower Γ valley mobility of GaP. When the GaP and GaAs PC THz emitters are biased just below their breakdown electric field biases, the GaP PC THz emitter is found to produce higher Joule heating flux than the GaAs PC THz emitter with comparable emitted THz power (calculated with Equation (22)). These predictions suggest that the GaP transient mobility is not predicted to have significantly improved performance for GaP PC THz emitters, compared to standard GaAs PC THz emitters, in terms of Joule heating.  Experimental data on the performance of GaP PC THz emitters is omitted from this thesis. This omission is because measuring the emission of THz radiation from GaP PC THz emitters is beyond our experimental capabilities. In order to collect experimental data on GaP PC THz emitters, and raise the THz signal level above the noise floor, a moderate 390 nm pump power and higher bias voltage (at a kHz frequency for lock-in and noise minimization) are required, which are not available. The 780 nm pump beam, at 50 mW power, when passed through the available second harmonic crystal, showed a conversion to 390 nm of only 0.3%. When compared to the (non-normalized) SNR that was achieved for a GaAs PC THz emitter, defined as the THz electric field amplitude divided by √2 times the root-mean-squared noise Chapter 3: Terahertz Emission  73  value, this low conversion efficiency and the relatively low peak mobility of GaP (approximately 120 cm2/V/s) lowered the SNR of the GaP PC THz emitter below a value of 1. This prevented the measurement of the THz electric field for the GaP PC THz emitter. It is envisioned that GaP PC THz emitters measurements would be effective if more powerful 390 nm pump illumination and higher bias voltage amplitudes are employed.  3.4 Photoconductive Terahertz Emitters with Enhanced Surface Recombination To continue the exploration of materials for reducing the Joule heating in PC THz emitters, the concept of transient photoconductivity is explored through reductions to the charge-carrier lifetime. Semiconductor samples with enhanced surface recombination are considered. The enhanced surface recombination contributes to a lowering of the charge-carrier lifetime. This section analyses nanocomposite and textured materials in terms of ultrafast material and THz responses, using the respective pump-probe and THz setups. To begin this analysis, nanocomposite materials with semiconductor nanoparticles embedded within a polymer host, are studied.   3.4.1 Nanocomposite Materials Semiconductor nanoparticles have been applied in many contemporary photonic systems [112, 113] as their large surface-area-to-volume ratios and small diameters (typically at or below the semiconductor diffusion length) provide increased surface effects and reduced charge-carrier lifetimes [77, 78]. At the same time, semiconductor nanoparticles can be embedded in a polymer host to form a nanocomposite material enabling easy device integration. This section Chapter 3: Terahertz Emission  74  considers nanocomposite materials as candidates for use in the PC THz emitter for the ultimate DMF-based THz-TDS system. The ultrafast material responses and THz responses of various nanocomposite materials are investigated. The nanocomposite materials are made with Si, SiC, and InP nanoparticles embedded in a Norland Optical Adhesive polymer host material2. Si, SiC, and InP are chosen as they have been used for THz emission [114-116] and are commercially available in nanoparticle form from the supplier American Elements. The response of a nanocomposite material under transient photoexcitation can differ significantly from that of a bulk semiconductor. Therefore, a mathematical model is used to understand the ultrafast dynamics of the nanocomposite material, where a complex interplay is formed between charge-carrier diffusion and recombination. Increased recombination contributions are observed from surface states as the semiconductor nanoparticle size is reduced below the diffusion length [117-119]. This interplay can be seen with a transient solution of the charge-carrier density, n(r, t), according to  ( )rappliedtrntrnqDnEqnqtnttrnτµδ ),(),(1)(),( 0 −∇+⋅∇+=∂∂ (30) The first term on the right quantifies the near-instantaneous charge-carrier photogeneration of an initially uniform charge-carrier density of n0. The second term quantifies drift and diffusion with a mobility of μ, applied electric field of appliedE , and diffusion coefficient of D. The third term quantifies recombination with a charge-carrier recombination time of τr. The variable r is                                                  2 The fabrication of the nanocomposite materials involves mixing the semiconductor nanoparticles into the Norland Optical Adhesive polymer through a mechanical mixing/stirring process. The nanocomposite materials have less than 10% semiconductor nanoparticles and greater than 90% Norland Optical Adhesive polymer by weight. Chapter 3: Terahertz Emission  75  the radial dimension defined off the centre of the nanoparticle. The variable t is time. The presented analysis assumes that bulk recombination effects are negligible due to the long recombination lifetimes (i.e., τr ≈ ∞). The analysis is performed for the case of no applied electric field (i.e., appliedE  = 0) in order to highlight diffusion effects. Surface recombination is introduced into the model through a boundary condition at the nanoparticle radius of a [118],   arartrSnrtrnD===∂∂− ),(),( (31) where S is the surface recombination velocity for the semiconductor being studied. Equation (30) can be solved with respect to the boundary condition in Equation (31) for a result of  tDmmmmerrAtrn20)sin(),( λλ −∞=∑= (32) which is subject to  −−=)cos()sin()cos()sin(2 20aaaaaanAmmmmmmmm λλλλλλλ       (33) and 0)sin()1/()cos( =−+ aDSaaa mmm λλλ        (34) where λm is the eigenvalue from the partial differential equation. This equation is solved according to the assumption D ≈ Sa which provides eigenvalues of piλamm 212 += .        (35) In actuality, the nanoparticles adhere to the property D ≫ Sa, however, the assumption used in this thesis yields results that are within 20% of the exact numerical results. Equation (32) Chapter 3: Terahertz Emission  76  can be solved with a MATLAB script, presented in Appendix F. Figure 3.4.1.1 shows the charge-carrier density solution for a hypothetical nanoparticle with a diameter of 2a = 40 nm and surface recombination velocity of S = 100,000 cm/s for time instances of 0, 5, 10, and 15 ps. The charge-carrier density clearly diminishes as charge-carriers diffuse towards the outer surface and undergo surface recombination.  The net result of the above diffusion and surface recombination is a diminishing overall charge-carrier population in the nanoparticle. Figure 3.4.1.2 shows the differential transmission through Si nanoparticles (being a volumetric average of the charge-carrier density) with diameter 2a = 20 nm. Figure 3.4.1.2(a) shows the Si nanoparticle theoretical differential transmission solution (differential transmission is proportional to the integral of n(r, t) from Equation (32) over the sphere) and Figure 3.4.1.2(b) shows the experimental differential transmission results for Si nanoparticle and Si bulk materials collected with the pump-probe setup. A scanning electron microscope (SEM) image of the nanoparticles is shown in Figure 3.4.1.2(b). The theoretical differential transmission solution is in close agreement with the experimental differential transmission results for a surface recombination velocity of S = 5 × 104 cm/s (which agrees with the 4.4 × 104 cm/s value of Baek et al. [120]). Curve fitting the Si nanoparticle results to a decaying exponential shows a charge-carrier lifetime of 10 ps which is much faster than the charge-carrier lifetime of the Si bulk differential transmission results. An SEM image of the Si nanoparticles in shown in Figure 3.4.1.2(b). Figure 3.4.1.3 shows the differential transmission through a SiC nanoparticle with diameter 2a = 50 nm. Figure 3.4.1.3(a) shows the SiC nanoparticle theoretical differential transmission solution and Figure 3.4.1.3(b) shows the experimental differential transmission results for SiC  Chapter 3: Terahertz Emission  77      Figure 3.4.1.1 The theoretical charge-carrier density is shown for a hypothetical nanoparticle with a diameter of 2a = 40 nm and a surface recombination velocity of S = 100,000 cm/s. The x and y dimensions are Cartesian coordinates for an equatorial plane through the nanoparticle.    Chapter 3: Terahertz Emission  78   Figure 3.4.1.2 Si (a) theoretical and (b) experimental nanoparticle differential transmission results are shown versus time. Experimental differential transmission results of bulk Si are also shown in (b). An SEM image of the Si nanoparticles is shown in the inset of (b). Chapter 3: Terahertz Emission  79   Figure 3.4.1.3 SiC (a) theoretical and (b) experimental nanoparticle differential transmission results are shown versus time. Experimental differential transmission results of bulk SiC are also shown in (b). An SEM image of the SiC nanoparticles is shown in the inset of (b). Chapter 3: Terahertz Emission  80  nanoparticle and SiC bulk materials collected with the pump-probe setup. An SEM image of the SiC nanoparticles is shown in Figure 3.4.1.3(b). The theoretical differential transmission solution is in close agreement with the experimental differential transmission results for a surface recombination velocity of S = 4 × 105 cm/s (which agrees with the 105-106 values of Thomas et al. [121]). Curve fitting the SiC nanoparticle differential transmission solution to a decaying exponential shows a charge-carrier lifetime of 4 ps which is much faster than the charge-carrier lifetime of the SiC bulk differential transmission results. Figure 3.4.1.4 shows the differential transmission through InP nanoparticles with diameter 2a = 200 nm. Figure 3.4.1.4(a) shows the InP nanoparticle theoretical differential transmission solution and Figure 3.4.1.4(b) shows experimental differential transmission results for InP nanoparticle and InP bulk materials collected with the pump-probe setup. An SEM image of the InP nanoparticles is shown in Figure 3.4.1.4(b). The theoretical differential transmission results are in close agreement with the experimental differential transmission results for a surface recombination velocity of S = 1 × 106 cm/s (which agrees with the 1 × 106 cm/s value of Bothra et al. [122]). Curve fitting the InP nanoparticle differential transmission results to a decaying exponential shows a charge-carrier lifetime of 5 ps which is much faster than the charge-carrier lifetime of the InP bulk differential transmission results.  The measured InP surface recombination velocity of S = 1 × 106 cm/s is very high. Additionally, InP has a high mobility and has a 1.3 eV bandgap that is well suited to illumination with 780 nm pulsed lasers, e.g., titanium-sapphire and Erbium-doped fibre laser sources (with second harmonic generation). For these reasons, the following work will focus on the application of InP as a material for PC THz emission.  Chapter 3: Terahertz Emission  81   Figure 3.4.1.4 InP (a) theoretical and (b) experimental nanoparticle differential transmission results are shown versus time. Experimental differential transmission results of bulk InP are also shown in (b). An SEM image of the InP nanoparticles is shown in the inset of (b). Chapter 3: Terahertz Emission  82  An exhaustive number of tests were carried out to measure the THz emission from a PC THz emitter being comprised of an InP nanocomposite material. No measurable THz electric field could be found. This is most likely due to the partially conductive nature of the non-SI-InP nanoparticles. To test this hypothesis, experimental tests were carried out on a SI-InP microcomposite material. The SI-InP microparticles were fabricated to have a diameter of approximately 35 μm. Terahertz emission (albeit weak) was observed. With this in mind, the enhanced surface recombination being used for the proposed PC THz emitters must be introduced through another implementation. Textured semiconductor materials are considered for this.  3.4.2 Textured Materials As previously mentioned, materials used in PC THz emitters often have charge-carrier lifetimes that are much longer than the THz pulse durations, creating residual photocurrents which lead to unnecessary Joule heating. The prior section showed that surface recombination can be effective in reducing the charge-carrier lifetime. However, it is also desirable to have a SI material. Both of these pursuits can be met with textured semiconductor materials. The effectiveness of this approach is investigated in this section. The texturing increases the optically-excited surface area of the PC THz emitters and decreases the charge-carrier lifetime through increased contributions from surface recombination [77, 78]. This work continues with investigations of the ultrafast material response and the THz response of non-, fine-, and coarse-textured InP materials. The relative surface areas (quantifying roughness) are measured by way of SEM images, the ultrafast material responses (in terms of charge-carrier lifetimes) Chapter 3: Terahertz Emission  83  are measured by way of the pump-probe setup, and the THz responses (in terms of radiated THz electric field and photocurrent consumption) are measured by way of the THz setup. The temporal and spectral characteristics are found for PC THz emitters based on the three InP materials.  The Joule heating flux, ϕH, in a PC THz emitter can be quantified by integrating the electrical power over the charge-carrier lifetime and dividing the result by the laser pulse repetition period pulses and the active area of the PC THz emitter as in the previously introduced Equation (21). The linear proportionality that forms here between ϕH and τ makes it apparent that a short charge-carrier lifetime is desirable to reduce the effects of Joule heating. Surface recombination reduces the charge-carrier lifetime according to [119, 123]  SRSRb≈+=ττ11 (36) where R is the surface-area-to-volume ratio, and τb is the (exceedingly long) bulk charge-carrier lifetime of the material. For this work, pertaining to InP material, it is desired to have the charge-carrier lifetime be as short as possible, to reduce the steady-state photocurrent, and this is accomplished by photoinjecting charge-carriers into regions of the material with high densities of surface states. The presented approach for reducing the charge-carrier lifetime uses textured semiconductor materials. Texturing of a planar semiconductor surface can increase the presence of surface states, which ultimately increases R according to Equation (36) and decreases τ. This investigation uses non-, fine-, and coarse-textured InP materials to define three distinct regimes for the texturing—each with a characteristic length-scale of the Chapter 3: Terahertz Emission  84  texturing, l, that is compared to the L ≈ 2 µm diffusion length of the charge-carriers. The non-textured InP material has a negligible characteristic length-scale of the texturing, i.e., l ≈ 0 µm << L. The fine-textured InP material has an intermediate characteristic length-scale of the texturing, i.e., l ≈ 1 µm < L. The coarse-textured InP material has a large characteristic length-scale of the texturing, i.e., l ≈ 2 µm ≈ L. To fabricate the non-, fine-, and coarse-textured InP materials, a polished SI-InP sample is used as the non-textured InP material, and varying grit-sizes of optical polishing films are used to transform the InP non-textured material into fine- and coarse-textured InP materials. The InP sample is mechanically polished with a 6 μm grit diamond polishing film (Thorlabs LF6D) and a 30 μm grit diamond polishing film (Thorlabs LF30D) to produce the fine-textured and coarse-textured InP materials, respectively. Note that texturing was also pursued by way of anisotropic etching, but it was found that the mechanically-polished materials could more easily be divided into the three distinct regimes of texturing. Relative surface areas are used to define the materials, as the unit-less ratio of surface areas between the material of interest and the non-textured InP material. The relative surface area for each material is found through analyses of SEM images of numerous imaging sites. The SEM images are analysed with MountainsMap software that formulates three-dimensional greyscale topographies of the SEM images, and surface areas are extracted from these topographies. Representative images of non-, fine-, and coarse-textured InP materials are shown in Figure 3.4.2.1. Top view SEM topographies are shown in Figure 3.4.2.1(a), (c), and (e), and isometric view SEM topographies are shown in Figure 3.4.2.1(b), (d), and (f) for representative SEM topographies of non-, fine-, and coarse-textured InP materials,  Chapter 3: Terahertz Emission  85    Figure 3.4.2.1 The top view SEM topographies for non-, fine-, and coarse-textured InP materials are shown in (a), (c), and (e), respectively. The isometric view SEM topographies for respective non-, fine-, and coarse-textured InP materials are shown in (b), (d), and (f), respectively, with images of the corresponding PC THz emitters shown in the insets. The relative surface areas of the non-, fine-, and coarse-textured InP materials are 1.0 ± 0.1, 2.9 ± 0.4, and 4.3 ± 0.6, respectively.  Chapter 3: Terahertz Emission  86  respectively, with corresponding PC THz emitters shown in the insets. The relative surface areas of the non-, fine-, and coarse-textured InP materials are found to be 1.0 ± 0.1, 2.9 ± 0.4, and 4.3 ± 0.6, respectively, based on ten sites per material. The ultrafast material response of the non-, fine-, and coarse-textured InP materials are analysed with the pump-probe setup to determine the corresponding charge-carrier lifetimes. Representative (normalized) differential transmission, ΔT(t)/T, curves are shown as a function of time, t, in Figure 3.4.2.2 for the non-, fine-, and coarse-textured InP materials as black, red, and blue solid lines, respectively. The results are shifted vertically for illustration purposes. Note that the differential transmission results shown in this figure exhibit positive polarity, and this positive polarity agrees with theoretical calculations for (Drude) free-carrier absorption and dispersion in which the decreasing refractive index of free-carrier dispersion dominates. The ΔT(t)/T curves are curve-fit with decaying exponential functions to define the charge-carrier lifetimes. The charge-carrier lifetimes are found to be 200 ± 6, 100 ± 10, and 20 ± 3 ps, for the non-, fine-, and coarse-textured InP materials, respectively, and are shown in Table 3.4.2.1. The charge-carrier lifetimes are defined here as the charge-carrier lifetime mean plus or minus the charge-carrier lifetime standard error—based on six measurement sites per material. Standard error is defined as the standard deviation divided by the square root of the number of trials. Now that the ultrafast material responses (relating to the charge-carrier lifetimes) of the non-, fine-, and coarse-textured InP materials are measured, the THz responses (being the radiated THz electric field and corresponding photocurrent consumption) of the non-, fine-, and coarse-textured InP PC THz emitters can be determined with a THz setup. Initially,  Chapter 3: Terahertz Emission  87   Figure 3.4.2.2 Differential transmission signals are shown for non-, fine-, and coarse-textured InP materials with 780 nm pump and 1550 nm probe wavelengths. The (normalized) differential transmission pump-probe signals are plotted as a function of time and are curve-fit to decaying exponential functions to define the charge-carrier lifetime of each measurement. The results are shifted vertically for illustration purposes.   Table 3.4.2.1 The charge-carrier lifetimes are shown for non-, fine-, coarse-texture InP materials. The standard error for the charge-carrier lifetime for each material is also shown. The charge-carrier lifetime decreases as the materials progress from non-textured InP through to coarse-textured InP. Material Charge-carrier lifetime (ps) Charge-carrier lifetime standard error (ps) Non-textured InP 200 6 Fine-textured InP 100 10 Coarse-textured InP 20 3  Chapter 3: Terahertz Emission  88  measurements are taken with each PC THz emitter set to produce a similar THz electric field amplitude (normalized to the non-textured InP PC emitter's THz electric field amplitude at a bias voltage amplitude of 50 V), with amplitude standard errors of 0.26, 0.04, and 0.38 for the non-, fine-, and coarse-textured InP PC THz emitters, respectively, based on six measurement sites per material. This is shown in Figure 3.4.2.3(a) with normalized THz electric field amplitude, ETHz,0(Vb), plotted as a function of the bias voltage amplitude, Vb, for non-, fine-, and coarse-textured InP PC THz emitters, shown respectively as black crosses, red squares, and blue circles. Each emitter has a consistent 100 μm electrode gap size3. Simultaneously with the THz electric field measurements, the photocurrent, Iph(Vb), is measured as a function of bias voltage amplitude, Vb, and is plotted in Figure 3.4.2.3(b) for non-, fine-, and coarse-textured InP PC THz emitters, shown respectively as black crosses, red squares, and blue circles. The non-textured InP PC THz emitter has a very large photocurrent while the InP fine-textured PC THz emitter has a marginal photocurrent, and the InP coarse-textured PC THz emitter has a very small photocurrent. The dark resistance of the non-, fine-, and coarse-textured InP PC THz emitters is estimated to be 400 GΩ. The property of most interest is the ratio of normalized THz electric field amplitude over photocurrent, ETHz,0(Vb)/Iph(Vb), as this quantifies the level of Joule heating during operation. It is important to note that this ratio has a direct proportionality to, and can be interpreted as, the resistance across the PC THz emitter, given that ETHz,0(Vb) is linearly proportional to Vb. The ratio of the normalized THz electric                                                   3 The fabrication of the electrodes involves mixing equal parts MC Chemicals Pure Silver Conductive Epoxy Part A (09287) and Part B (09259) and applying to the semiconductor substrate with a fine-tipped tool. The gap size between electrodes is measured with stereoscope images of the PC THz emitters. Chapter 3: Terahertz Emission  89   Figure 3.4.2.3. The THz responses of the non-, fine-, and coarse-textured InP PC THz emitters are shown. In (a), THz electric field measurements are shown as a function of applied voltage amplitude while each Chapter 3: Terahertz Emission  90  PC THz emitter is set to produce a similar THz electric field amplitude. The THz electric field amplitude values are normalized with respect to the non-textured InP emitter's response at an applied voltage amplitude of 50 V. In (b), the corresponding photocurrent is measured as a function of applied voltage amplitude. In (c), the ratio of the normalized THz electric field amplitude over photocurrent is plotted as a function of bias voltage amplitude. The error bars represent the standard error of the ratio of normalized THz electric field amplitude over the photocurrent.  field amplitude over photocurrent is plotted as a function of bias voltage amplitude, Vb, and is plotted in Figure 3.4.2.3(c) for non-, fine-, and coarse-textured InP PC THz emitters, shown respectively as black crosses, red squares, and blue circles. The measurements are the mean values for tests performed at six locations on each PC THz emitter. The error bars represent the standard error of the ratio of normalized THz electric field amplitude over the photocurrent. It is seen here that the ratio, ETHz,0(Vb)/Iph(Vb), increases with the degree of texturing, while ETHz,0(Vb) remains constant, indicating that texturing decreases Iph(Vb) and thus increases the resistance in the PC THz emitter. This suggests that there is a corresponding decrease in the Joule heating as the degree of texturing increases for the PC THz emitter. If desired, Vb or the laser fluence can be increased for the textured PC THz emitter(s) to scale up the THz electric field amplitude. It is clear from Figure 3.4.2.3(c) that the conversion between THz electric field and photocurrent increases dramatically as the PC THz emitters progress through non-, fine-, and coarse-texturing. It should be noted that non-, fine-, and coarse-textured InP PC THz emitters show an approximately linear relationship between normalized THz electric field amplitude and bias voltage amplitude right up to breakdown of the PC THz emitters. Chapter 3: Terahertz Emission  91  It is also important to test the time-domain and frequency-domain THz responses of the non-, fine-, and coarse-textured InP PC THz emitters. The THz response, ETHz(t) (time-domain) and ETHz(f) (frequency-domain), of the non-, fine-, and coarse-textured InP PC THz emitters are shown in Figure 3.4.2.4 in the (a) time-domain as a function of time, t, as respective black, red, and blue solid lines, and (b) frequency-domain as a function of frequency, f, as respective black solid, red long-dashed, and blue short-dashed lines. The displayed results of Figure 3.4.2.4(a) are shifted vertically for illustration purposes. Each scan is normalized with respect to its THz electric field amplitude. Similar time- and frequency-domain responses are observed for each PC THz emitter. The non-, fine-, and coarse-textured InP PC THz emitters each have a spectral bandwidth of approximately 3.5 THz. Thus, it can be concluded that residual photocurrents can be minimized in textured PC THz emitters, for reduced Joule heating, without sacrificing the temporal and spectral characteristics of the generated THz waveforms. The results of this chapter lead to some general comments and comparisons. To this end, standard materials for PC THz emitters, based on SI-GaAs [124], low-temperature-grown (LT-) GaAs [56], and SI-ZnSe [125], are compared to the non-, fine-, and coarse-textured SI-InP emitters of this work. The comparisons are made in terms of THz electric field emission (both in terms of spectral bandwidth and THz electric field amplitude), and power dissipation (relating to Joule heating), while biased just below the point of dielectric breakdown. The comparison of THz electric field emission for the PC THz emitters is considered here in terms of spectral bandwidth and power dissipation. The spectral bandwidths of non-, fine-, and coarse-textured InP PC THz emitters are measured to be roughly constant at 3.5  Chapter 3: Terahertz Emission  92   Figure 3.4.2.4. The THz electric field responses of the non-, fine-, and coarse-textured InP PC THz emitters are shown in the (a) time-domain and (b) frequency-domain. The results of (a) are shifted vertically for illustration purposes. Similar time-domain and frequency-domain responses are observed for the PC THz emitters. An approximate 3.5 THz spectral bandwidth is observed for each of the non-, fine-, and coarse-textured InP PC THz emitters. Chapter 3: Terahertz Emission  93  THz. This observation is shown in the results of Figure 3.4.2.4(b). The corresponding spectral bandwidths of SI-GaAs, LT-GaAs, and SI-ZnSe are found from the literature to be 3 [124], 4 [56], and 3 THz [125], respectively. These spectral bandwidths are comparable to the values measured for the InP PC THz emitters. The emitted THz power follows according to Equation (22). This analysis estimates the emitted THz power for the non-, fine-, and coarse-textured InP, SI-GaAs, and SI-ZnSe PC THz emitters to be similar and the LT-GaAs PC THz emitters to more than an order of magnitude lower when the PC THz emitters are biased near their breakdown electric field values. The comparison of power dissipation for the PC THz emitters is considered here. The Joule heating flux in a PC THz emitter is estimated according to Equation (21), which shows that Joule heating flux is proportional to charge-carrier lifetime and to mobility. The level of Joule heating flux in the non-textured SI-InP PC THz emitter is on the order of 104 W/cm2 while the level of Joule heating flux in the coarse-textured SI-InP PC THz emitter is on the order of 103 W/cm2, offering an order of magnitude improvement. (The estimated Joule heating in the fine-textured PC THz emitter is intermediate between these estimated values.) It is estimated that a corresponding SI-GaAs PC THz emitter would have Joule heating flux on the order of 104 W/cm2, a LT-GaAs PC THz emitter would have Joule heating on the order of 101 W/cm2, and a SI-ZnSe PC THz emitter would have Joule heating on the order of 106 W/cm2 (due to the very long ZnSe charge-carrier lifetime [78]). The InP PC THz emitters can also be compared to the multiplexer grid for the DMF device from Chapter 2 in terms of power dissipation per area, as shown in Table 3.4.2.2. The multiplexer grid has far lower power   Chapter 3: Terahertz Emission  94  Table 3.4.2.2 The power dissipation per area is shown in non-, fine-, and coarse-textured InP PC THz emitters and in the multiplexer grid DMF device. The power dissipation per area (i.e., Joule heating flux) in the PC THz emitters is significantly higher than in the multiplexer grid DMF device. The power dissipation per area in the coarse-textured InP PC THz emitter is an order of magnitude lower than that of the non-textured InP PC THz emitter. Device Power dissipation per area (W/cm2) Non-textured InP PC THz emitter 7400 Fine-textured InP PC THz emitter 3700 Coarse-textured InP PC THz emitter 740 Multiplexer grid DMF device Negligible (< 10-12)  dissipation per area, therefore, the main source of power dissipation in a DMF-based THz-TDS system is the PC THz emitter. This power dissipation per area (i.e., Joule heating flux) puts microfluidic samples at risk of evaporation. It is estimated that a lab-on-a-chip platform with an integrated non-textured InP PC THz emitter would experience temperatures changes during operation on the order of tens of degrees Celsius. In comparison, a lab-on-a-chip platform with an integrated coarse-textured InP PC THz emitter would experience temperature changes during operation on the order of single digits of degrees Celsius4. It is therefore a large                                                  4 These estimates are based on a thermal resistance calculation using )1(25)( / thermalteTCtT τ−−∆+°=  where T(t) is time-varying temperature of the PC THz emitter, ΔT = QthermalRthermal is the temperature change from the initial temperature (i.e., unilluminated) to the steady-state temperature (i.e., illuminated) of the PC THz emitter, Qthermal ≈ 200 mW or 20 mW (for the respective non- or coarse-textured InP PC THz emitters) is the heat dissipation, Rthermal ≈ 500 K/W is the thermal resistance of the PC THz emitter, t is time, and τthermal is the thermal time constant. Assuming some small lowering of the temperature through the substrate and dielectric layers of the DMF device, the change in temperature from room temperature to the steady-state temperature on the microdroplet is on the order of tens and single digits of degrees Celsius for lab-on-a-chip platforms with respective non- and coarse-textured InP PC THz emitters. Chapter 3: Terahertz Emission  95  benefit to the DMF-based THz-TDS system to use a textured PC THz emitter with lower Joule heating flux. It can be concluded from these comparisons that the proposed texturing treatment would not benefit all materials being used for PC THz emitters. It is the PC THz emitters being implemented with materials having long charge-carrier lifetimes, such as PC THz emitters using SI semiconductors, that will witness the greatest benefits of the proposed texturing treatment. These SI semiconductors are desirable due to their relatively low cost (when compared to epitaxially-grown semiconductors).  It should also be noted that the structure used for textured PC THz emission can be used for PC THz detection. The THz electric field provides the bias over the PC THz detector and a photocurrent is generated when an ultrafast probe pulse strikes the PC THz detector. This generated photocurrent is proportional to the charge-carrier density convolved with the THz electric field. The THz electric field can be extracted as the derivative of the photocurrent, as the PC THz detector is an integrating detector. Such PC THz detection is well-suited to on-chip integration as it avoids the complexity of EO THz detection. Further details are given in Appendix G. In the next chapter, considerations for THz spectroscopy and material selection for the DMF device in the DMF-based THz-TDS system are investigated.       96  Chapter 4: Terahertz Spectroscopy 4.1 Background To develop the digital-microfluidic- (DMF)-based terahertz (THz)-time-domain-spectroscopy (TDS) system, the THz spectroscopy analysis method for THz-TDS data must be investigated. Additionally, for compatibility with THz spectroscopy, the multiplexer grid DMF device must be carefully designed in terms of its plate separation (the separation distance between top and bottom plates of the multiplexer grid) and the materials used for the dielectric and substrate layers (as THz radiation must pass through the plates of the multiplexer grid with minimal absorption). This chapter investigates the THz spectroscopy analysis method and performs THz-TDS on vapour, liquid, and solid samples to investigate the above considerations. This chapter follows several steps to investigate the above considerations. First, an investigation is provided of the THz spectroscopy analysis method for analysing THz-TDS data (to develop the appropriate algorithm for quantifying the absorption of broadband THz radiation). This chapter then performs THz-TDS with this developed THz spectroscopy analysis method. Terahertz-TDS is performed on a water vapour sample to confirm that the THz spectroscopy analysis method is accurately measuring absorption in terms of frequency (as water vapour has THz absorption peaks with well known frequencies [94]). Terahertz-TDS is then performed on water and egg white protein liquid samples for the following reasons: i. to verify that the THz spectroscopy analysis method is accurately measuring absorption in terms of absolute absorption (accomplished through THz spectroscopy of well-studied liquid water and comparing results to literature values), ii. to make recommendations on the plate separation needed for the multiplexer grid DMF device (to ensure that enough THz radiation Chapter 4: Terahertz Spectroscopy  97  passes through liquid samples to measure the absorption coefficient sufficiently across the THz spectrum), and iii. to demonstrate THz-TDS on a nominal biochemical fluid sample (accomplished through THz-TDS of an egg white protein fluid sample). Finally, THz-TDS is performed on solid samples to make recommendations about what materials should be used in the substrate and dielectric layers of the plates integrated in the future DMF-based THz-TDS system.  4.2 Terahertz Spectroscopy Analysis Method Recently, THz-TDS has been used to extract the absorption coefficient of many materials in vapour [126, 127], liquid [128], and solid [129] states of matter. However, determining the correct THz spectroscopy analysis method has been a controversial topic over the past many years. Jepsen and Fischer suggest that interpretation of THz-TDS data requires caution, particularly for the highest frequency regime for any THz radiation pulse [20]. For example, it has been suggested that Kojima et al. may have mistaken the high frequency roll-off of THz-TDS data for a material property [20, 130]. Naftaly and Miles further explore the THz spectroscopy analysis method of Jepsen and Fischer [129]. This section investigates the THz spectroscopy analysis method, because the applied methodology will have important ramifications for THz-TDS technology on lab-on-a-chip platforms. Fundamentally, the THz spectroscopy analysis method should measure the absorption coefficient, α(f), and refractive index, n(f), across the THz spectrum. The absorption coefficient can be found when a THz electric field pulse passes through a sample of known thickness, d0. The sample changes the THz electric field pulse and transforms it from its original reference Chapter 4: Terahertz Spectroscopy  98  THz electric field pulse into the sample THz electric field pulse. Differences (due to absorption and refraction) between the amplitude and phase spectra of the reference and sample THz electric field pulse can be used to find the respective absorption coefficient and refractive index, as described by Jepsen and Fischer [20] and Naftaly and Miles [129]. For the THz spectroscopy analysis method, the absorption coefficient is first considered. Figure 4.2.1 shows an image of the THz spectroscopy for a general sample with thickness of d0, absorption coefficient of α(f), and refractive index of n(f). The sample changes the reference THz electric field pulse, denoted by Eref(t) and Eref(f) in the respective time- and frequency-domain, into the sample THz electric field pulse, denoted by Esam(t) and Esam(f) in the respective time- and frequency-domain. Here, the magnitude of the sample THz electric field pulse in the frequency-domain, |Esam(f)|, is related to the magnitude of the reference THz electric field pulse in the frequency-domain, |Eref(f)|, through  0)(21 |)(||)(| dfrefsam efEttfE α−= , (37) where t1 = 2/(nsam + 1) is the Fresnel transmission coefficient of the left vacuum-sample interface, t2 = 2nsam /(nsam + 1) is the Fresnel transmission coefficient of the right sample-vacuum interface, and nsam is the approximate refractive index of the sample. These Fresnel transmission coefficients are for semi-infinite interfaces. Internal reflections have been omitted from the analysis as the round-trip time is larger than the duration of the THz electric field pulse. Solving for α(f) yields   +−= |)(||)(|4)1(ln1)(20 fEfEnndfrefsamsamsamα. (38) Chapter 4: Terahertz Spectroscopy  99  Equation (38) is extremely important in quantifying the absorption coefficient of the sample, however, it is only valid if the absorption in the sample does not attenuate the sample THz electric field pulse below the noise floor of the reference THz electric field pulse. This noise floor defines the dynamic range, DR, of the reference THz electric field pulse, where the DR is the amplitude spectrum of the reference THz electric field pulse normalized to its noise floor. Figure 4.2.1 shows a reference THz electric field pulse in the (a) time- and (b) frequency-domain (expressed as the DR). The cutoff frequency is shown at approximately 4 THz where the noise floor begins. The maximum measurable absorption coefficient, αmax(f), is defined by the DR of the reference THz electric field pulse through the limiting case of  0max )(24)1(1 dfsamsam ennDRα−+= . (39) Solving for αmax(f) yields  += 20max )1(4ln1)(samsamnnDRdfα. (40) Essentially, if the (true) absorption coefficient is actually larger than the maximum measurable absorption coefficient, the THz-TDS data will only show the maximum measurable absorption coefficient. Figure 4.2.2(c) shows the maximum measurable absorption coefficient multiplied by exemplary samples with thicknesses of d0 = 60 μm (black solid line), 120 μm (red long-dashed line), 180 μm (green medium-dashed line), and 240 μm (blue short-dashed line). It is clear that for a given DR, a thinner sample can be used to measure the absorption coefficient to a higher frequency. Additionally, a sample with a high absorption coefficient will need a Chapter 4: Terahertz Spectroscopy  100      Figure 4.2.1 An image of the THz spectroscopy is shown with a sample with thickness of d0, absorption coefficient of α(f), and refractive index of n(f). The reference THz electric field pulse (prior to passing through the sample) in the respective time- and frequency-domain is Eref(t) and Eref(f) and the sample THz electric field pulse (after passing through the sample) in the respective time- and frequency-domain is Esam(t) and Esam(f). Fresnel coefficients at the initial (left) and final (right) interface are t1 and t2, respectively.   Chapter 4: Terahertz Spectroscopy  101   Figure 4.2.2 A reference THz electric field pulse is shown in the (a) time- and (b) frequency-domain (normalized to the noise floor, i.e., presented as the DR). The (c) maximum measurable absorption coefficient is shown for exemplary samples with thicknesses of d0 = 60, 120, 180, and 240 μm. Chapter 4: Terahertz Spectroscopy  102  reduced thickness in order for the absorption coefficient to be measured over a large region of the THz spectrum.  To continue the THz spectroscopy analysis method, the refractive index is considered. As stated, n(f) can be found by analysing differences between the phase spectrum of the reference THz electric field pulse, ∠ Eref(f), and the phase spectrum of the sample THz electric field pulse, ∠ Esam(f), through  12)]()([)(0+∠−∠= fdfEfEcfn refsampi. (41)   This requires that the phase shift between the phase spectra of the reference and sample THz electric field pulse be less than one period (i.e., 2π radians) or that a phase shift of integer multiples of one period is included in the analysis as needed. To avoid this issue, the sample thickness should be very small. For example, a sample with a refractive index of nsam ≈ 3 measured up to a frequency of 2.5 THz would need the thickness to be less than 100 μm. The maximum acceptable thickness is quantified in general as  )1(max −⋅= samnfcd . (42) Given these limitations, n(f) measurements are omitted from much of this analysis, however, with the small device dimensions of DMF devices, refractive index measurements are possible, at least over certain frequency ranges. Chapter 4: Terahertz Spectroscopy  103  Using this THz spectroscopy analysis method, the absorption coefficients of applicable vapour, liquid, or solid samples are measured. Refractive index measurements are provided for liquid samples that have small thicknesses. The MATLAB script for performing the THz spectroscopy analysis method on THz-TDS data is presented in Appendix H.  4.3 Terahertz-Time-Domain-Spectroscopy for Vapour  The THz spectroscopy analysis method is first applied through THz-TDS of a water vapour sample. The water vapour sample is essentially the water-based humidity around the THz setup. It has an associated absorption coefficient that spans the THz spectrum. The reference THz electric field pulse is collected by adding a positive pressure enclosure around the THz setup with a dry nitrogen inflow purge and eliminating the water vapour sample. The sample THz electric field pulse is collected by removing the enclosure and dry nitrogen inflow purge. Figure 4.3.1(a) shows the reference and sample THz electric field pulses in the time-domain. Figure 4.3.1(b) shows the absorption coefficient and maximum measurable absorption coefficient for the sample thickness that is defined by the propagation distance of the THz setup (d0 ≈ 30 cm). Figure 4.3.1(c) shows the absorption coefficient from 0.5 to 3 THz with water vapour absorption peaks labeled. The theoretical frequencies of the water vapour absorption peaks can be found in the literature [94]. Table 4.3.1 presents the experimental and theoretical frequencies for these absorption peaks, and the corresponding rotational transition for water. The notation that is used describes the rotational transitions ascaKKJ , where J is the rotational quantum number and Ka and Kc are the projections of J onto the principle rotation  Chapter 4: Terahertz Spectroscopy  104   Figure 4.3.1 The THz spectroscopy analysis method applied through THz-TDS of a water vapour sample with (a) time-domain scans for reference (dry nitrogen) and sample (water vapour) THz electric field pulses, (b) absorption coefficient and maximum measurable absorption coefficient for the water vapour Chapter 4: Terahertz Spectroscopy  105  sample over the THz spectrum, and (c) absorption coefficient for the water vapour sample over 0.5 to 3 THz.  Table 4.3.1 A comparison of frequencies of experimental and theoretical absorption peaks for the water vapour sample and the corresponding rotational transition are shown. The largest error between the frequencies of experimental and theoretical absorption peaks is 0.1%. Frequency of experimental absorption peaks (THz) Frequency of theoretical absorption peaks (THz) Corresponding rotational transition 0.555 0.557 101 - 110 0.750 0.753 202 - 211 0.991 0.989 111 - 202 1.101 1.098 303 - 312 1.161 1.159 541 - 634 1.206 1.208 413 - 422 1.411 1.411 514 - 523 1.601 1.604 404 - 413 1.666 1.663 212 - 221 1.716 1.715 505 - 432 1.761 1.764 624 - 633 1.796 1.796 615 - 624 1.866 1.869 523 - 532 1.921 1.921 313 - 322 2.041 2.042 422 - 431 2.076 2.077 322 - 413 2.166 2.166 202 - 313 2.196 2.199 321 - 330 2.221 2.223 505 - 514 2.266 2.266 414 - 423 2.341 2.345 716 - 725 2.391 2.393 313 - 404 2.426 2.429 927 - 936 2.461 2.465 423 - 432 2.646 2.641 303 - 414 2.681 2.687 515 - 524 2.776 2.776 110 - 221 2.881 2.882 625 - 634 2.971 2.971 111 - 220  Chapter 4: Terahertz Spectroscopy  106  axes. The agreement for the experimental and theoretical frequencies of the absorption peaks is well within the 16 GHz resolution of the 60 ps THz-TDS measurements, verifying that the THz spectroscopy analysis method is accurately measuring absorption in terms of frequency. (As the absorption coefficient measurement provides sufficient information for this verification, refractive index measurements are not performed.)  4.4 Terahertz-Time-Domain-Spectroscopy for Liquid The THz spectroscopy analysis method is next applied through THz-TDS of liquid samples. As the liquid samples must be held in place by a containing structure, the THz spectroscopy analysis method can be modified appropriately. Figure 4.4.1 shows an image of the THz spectroscopy for a general sample with thickness of d0, held in place by two sample holding plates with thickness of dhp. In Figure 4.4.1(a), the incident THz electric field pulse, denoted Ei(t) and Ei(f) in the time- and frequency-domain, propagates through a sample holding plate with absorption coefficient of αhp and refractive index of nhp, through the liquid sample with absorption coefficient of αsam(f) and refractive index of nsam(f), and again through an identical sample holding plate. The sample THz electric field pulse, denoted Esam(t) and Esam(f) in the time-domain and frequency-domain, then exits the second sample holding plate. The Fresnel transmission coefficients at each interface from left to right are t1 = 2/(nhp + 1), t2 = 2 nhp/(nsam + nhp), t3 = 2 nsam/(nsam + nhp), and t4 = 2 nhp/(nhp + 1) where nsam is the approximate refractive index of the liquid sample. In Figure 4.4.1(b), the incident THz electric field pulse propagates through the sample holding plate, through free-space of thickness d0, and again through an identical sample holding plate. The reference THz electric field pulse, denoted Esam(t) and Chapter 4: Terahertz Spectroscopy  107  Esam(f) in the respective time- and frequency-domain, then exits the second sample holding plate. The Fresnel transmission coefficients at each interface from left to right are t1 = 2/(nhp + 1), t5 = 2 nhp /(nhp + 1), t6 = t1, and t4 = t5. The magnitude of the sample and reference THz electric field pulses can be written as  0)()(24321 |)(||)(| dfdfisam eefEttttfE hphp αα −−=  (43) and  hphp dfiref efEttttfE )(26541 |)(||)(| α−= . (44) Solving for the absorption coefficient of the liquid sample yields  ++−= |)(||)(|)()1(ln1)( 220 fEfEnnnndfrefsamhsamsamhα . (45) The maximum measurable absorption coefficient can be found to be  ++= 220max )1()(ln1)(samhhsamnnnnDRdfα . (46) In the same way as before, if the (true) absorption coefficient is actually larger than the maximum measurable absorption coefficient, the THz spectroscopy analysis method will only show the maximum measurable absorption coefficient. The modified THz spectroscopy analysis method is applied first to a liquid water sample (as liquid water is well-studied over the THz spectrum) and is used to confirm the operation of the THz spectroscopy analysis method in terms of absolute absorption. Figure 4.4.1 shows the absorption coefficient of a water liquid sample (black solid line) along with the corresponding maximum measurable absorption coefficient (black dashed line) given the Chapter 4: Terahertz Spectroscopy  108  DR of the system and sample thickness of d0 = 160 μm. The absorption coefficient is compared to that measured by Wang et al. [131] with data captured through an image-to-data conversion software, presented in Figure 4.4.2 (purple circled line). The data is in excellent agreement, verifying that the THz spectroscopy analysis method is accurately measuring absorption in terms of absolute absorption. The liquid water results of Figure 4.4.2 show the absorption coefficient up to approximately 2.5 THz. By examining the maximum measurable absorption coefficient for d0 = 240 μm (not shown) and d0 = 80 μm (not shown), it is estimated that these spacings would provide spectroscopic results for the absorption coefficient up to approximately 2 and 2.8 THz, respectively. The higher measurable frequency for the small spacing, of just less than 100 μm, is desirable. Given that the THz spectroscopy analysis method is accurately measuring absorption in terms of frequency and absolute absorption, demonstration of THz-TDS on a nominal biochemical liquid sample (egg white protein) is performed. Figure 4.4.2 shows the absorption coefficient for an egg white protein liquid sample of thickness d0 = 160 μm (red dashed line). The absorption coefficient is measured up to a frequency of approximately 2.5 THz, where the DR of the reference THz electric field pulse begins to limit the measurement capability. This THz spectroscopy analysis method can be applied through THz-TDS measurements of many biological fluids for applications such as proteomics and DNA analyses [132]. Given the relatively small thickness of the water and egg white protein liquid sample, it is possible to also measure the refractive index across the THz spectrum according to Equation (41) for these liquid samples. The refractive index of the water liquid sample is found to be roughly constant at n(f) ≈ 2.1 between 1.5 to 2.5 THz, in close agreement with the  Chapter 4: Terahertz Spectroscopy  109   Figure 4.4.1 An image is shown of the THz spectroscopy for a liquid sample with thickness of d0, absorption coefficient of α(f), and refractive index of n(f). The incident THz electric field pulse passes through (a) the sample its two transparent sample holding plates with thickness of dhp, absorption coefficient of αhp, and refractive index of nhp, and (b) only the transparent holding plates, creating the sample and reference THz electric field pulses. The incident THz electric field pulse in the respective time- and frequency-domain is Ei(t) and Ei(f). The sample THz electric field pulse in the respective time- and frequency-domain is Esam(t) and Esam(f). The reference THz electric field pulse in the respective time- and frequency-domain is Eref(t) and Eref(f). The Fresnel coefficients at the interfaces are t1, t2, t3, t4, t5, and t6. Chapter 4: Terahertz Spectroscopy  110   Figure 4.4.2 The absorption coefficient is shown over the THz spectrum for a water liquid sample (black solid line), egg white protein liquid sample (red dashed line), and water liquid sample (violet circled line) as measured by Wang et al. [131]. Also shown is the maximum measurable absorption coefficient (black dashed line) over the THz spectrum for water and egg white protein liquid samples with thickness of d0 = 160 μm. Chapter 4: Terahertz Spectroscopy  111  literature value of n(f) ≈ 2.1 over this range of the THz spectrum [133, 134]. The refractive index of the egg white protein liquid sample is found to be a similar value.  4.5 Terahertz-Time-Domain-Spectroscopy for Solids The THz spectroscopy analysis method can be applied through THz-TDS of solid samples. The materials for these solid samples are candidates for use in the multiplexer grid DMF device (and other electrowetting-on-a-dielectric DMF devices) for the substrate and dielectric layers. Ideally, these materials would be virtually transparent to both visible light, for monitoring microdroplet position and microfluidic actuation, and THz radiation (i.e., with a low absorption coefficient), to avoid interference with THz spectroscopy. The substrate layer is also required to have some level of rigidity for stability of the DMF device. Glass, plastic, and quartz solid samples are analysed for suitability as the substrate layer and a polydimethylsiloxane (PDMS) solid sample is analysed for suitability as the dielectric layer. Measurement of the refractive index over the THz spectrum is not performed as the solid samples have (mostly) large thicknesses.  4.5.1 Terahertz-Time-Somain-Spectroscopy for a Glass Solid Sample The THz spectroscopy analysis method is applied through THz-TDS of a glass solid sample. Figure 4.5.1.1 shows the absorption coefficient (black solid line) and maximum measurable absorption coefficient (black dashed line) for a glass solid sample (Fisherbrand Microscope Slides) of thickness d0 = 1.02 mm. The absorption coefficient is in excellent agreement with previously reported data [129]. The relatively large thickness of this sample along with the  Chapter 4: Terahertz Spectroscopy  112   Figure 4.5.1.1 The absorption coefficient (black solid line) over the THz spectrum is shown for a glass solid sample with thickness d0 = 1.02 mm. The maximum measurable absorption coefficient (black dashed line) is also shown. Chapter 4: Terahertz Spectroscopy  113  large absorption coefficient of glass (over the THz spectrum) shows accurate data only up to a frequency of 1 THz. After this point, the maximum measurable absorption coefficient is measured rather than the (true) absorption coefficient. At a nominal frequency of 1 THz the absorption coefficient has a value of 50 cm-1. Although glass has high rigidity, the observation that the absorption coefficient of glass over the THz spectrum is very large indicates that glass is unsuitable for use as the substrate layer in the DMF-based THz-TDS system.  4.5.2 Terahertz-Time-Domain-Spectroscopy for a Plastic Solid Sample The THz spectroscopy analysis method is applied through THz-TDS of plastic solid samples. Figure 4.5.2.1 shows the absorption coefficient (black solid line) and maximum measurable absorption coefficient (black dashed line) for a plastic solid sample of thickness d0 = 180 μm (cellulose acetate). The absorption coefficient is in excellent agreement with previously reported data [135]. The relatively small thickness of this sample along with the relatively small absorption of plastic allows this measurement of the absorption coefficient almost up to the 4 THz cutoff frequency. At a nominal frequency of 1 THz the absorption coefficient has a value of 9 cm-1. The plastic sample is found to have a fairly low absorption coefficient over the THz spectrum, however, the plastic material has minimal rigidity and therefore is not ideal for use as the substrate layer in the DMF-based THz-TDS system.  4.5.3 Terahertz-Time-Domain-Spectroscopy for a Quartz Solid Sample  The THz spectroscopy analysis method is applied through THz-TDS of a quartz solid sample. Figure 4.5.3.1 shows the absorption coefficient for quartz solid samples (Ted Pella, Inc. Quartz Chapter 4: Terahertz Spectroscopy  114   Figure 4.5.2.1 The absorption coefficient (black solid line) over the THz spectrum is shown for a plastic solid sample with thickness d0 = 180 μm. The maximum measurable absorption coefficient (black dashed line) is also shown.  Chapter 4: Terahertz Spectroscopy  115   Figure 4.5.3.1 The absorption coefficient over the THz spectrum is shown for quartz solid samples with thicknesses d0 = 1.06 mm (black solid line) and 2.12 mm (red dotted line). The maximum measurable absorption coefficient is also shown for thicknesses d0 = 1.06 mm (black long-dashed line) and 2.12 mm (red short-dashed line).   Chapter 4: Terahertz Spectroscopy  116  Slides) of thicknesses d0 = 1.06 mm (black solid line) and 2.12 mm (red dotted line) as well as the maximum measurable absorption coefficient (shown as respective black long- and red short-dashed lines). The absorption coefficient is in excellent agreement with previously reported data [136]. It should be noted that the absorption coefficients measured for quartz solid samples with both thicknesses are virtually identical, showing that the THz spectroscopy analysis method is independent of sample thickness. At a nominal frequency of 1 THz the absorption coefficient has a value of 2 cm-1. As the quartz sample has a low absorption coefficient and high rigidity, quartz is selected for use as the substrate layer in the DMF-based THz-TDS system.  4.5.4 Terahertz Time-Domain-Spectroscopy of a Polydimethylsiloxane Solid Sample The THz spectroscopy analysis method is applied through THz-TDS of a PDMS solid sample. As a dielectric layer material in electrowetting-on-a-dielectric devices, PDMS is overwhelmingly the most common dielectric material choice because of its dielectric coefficient of εr = 2-3 (at non-zero frequencies) [137], electric field breakdown of approximately 2 × 105 V/cm [138], spinning coating compatibility [42], low cost [139], and transparency to visible light [140]. Therefore, PDMS will be analysed here in terms of its absorption coefficient in the THz spectrum. Figure 4.5.4.1 shows the absorption coefficient (black solid line) and maximum measurable absorption coefficient (black dashed line) for a PDMS solid sample of thickness d0 = 2.78 mm (10:1 ratio of Sylgard 184 Silicone Elastomer to Base). The absorption coefficient is in excellent agreement with previous estimates of THz absorption coefficient values for PDMS [141]. At a nominal frequency of 1 THz the absorption Chapter 4: Terahertz Spectroscopy  117  coefficient has a value of 9 cm-1. The absorption coefficient of the PDMS solid sample is relatively low, indicating that PDMS is suitable for use in the DMF-based THz-TDS system.  Given the findings of this Chapter, the recommendations for the overall DMF-based THz-TDS system can be summarized. It is recommended that the DMF-based THz-TDS system make use of the THz spectroscopy analysis method as it accurately measures absorption in terms of frequency and absolute absorption. It is recommended that the multiplexer grid DMF device within the DMF-based THz-TDS system have a maximum spacing (between top and bottom layers of the multiplexer grid DMF device) of 100 μm or less in order to make accurate measurements of liquid samples over much of the THz spectrum. It is recommended that the multiplexer grid DMF device within the DMF-based THz-TDS system have a substrate layer made from quartz, for low absorption of THz radiation and high rigidity, and a dielectric layer made from PDMS, for low absorption of THz radiation and favourable lab-on-a-chip properties.    Chapter 4: Terahertz Spectroscopy  118   Figure 4.5.4.1 The absorption coefficient (black solid line) of a PDMS solid sample over the THz spectrum is shown. The maximum measurable absorption coefficient (black dashed line) is also shown.  119  Chapter 5: Conclusions 5.1 Conclusions This chapter provides concluding remarks, including a summary of the contributions of this thesis, and it provides recommendations for future work for digital-microfluidic- (DMF)-based terahertz (THz)-time-domain-spectroscopy (TDS) systems.  5.2 Summary of Contributions A lab-on-a-chip platform operating as a DMF-based THz-TDS system fundamentally requires structures and materials for microfluidic actuation and THz emission. With this in mind, new microfluidic actuation structures and THz emission materials were introduced within this thesis to meet the demands of a DMF-based THz-TDS system.  In Chapter 2, structures for DMF devices were evaluated. The major conclusions of Chapter 2 are given here: i. Structures for DMF devices were evaluated including square electrode, cross-referenced, and multiplexer grids. The multiplexer grid was the only structure found to provide the needed independent two-dimensional control for microfluidic actuation and practical addressability. ii. A prototype of the multiplexer grid was developed and analysed. As the multiplexer grid prototype was found to perform very well, it is recommended that the multiplexer grid be used as the DMF device in the DMF-based THz-TDS system. Chapter 5: Conclusions  120  In Chapter 3, materials for THz emission were evaluated. Materials exhibiting transient mobility (such as GaP) and surface-enhanced recombination (such as nanocomposite and textured materials) were explored. The major conclusions of Chapter 3 are given here: i. Transient mobility was explored through analyses of GaP. The GaP material was shown to have a transient mobility which was analysed through its ultrafast material response. It was found that a GaP photoconductive (PC) THz emitter will not outperform standard semi-insulating PC THz emitters in terms of Joule heating because the benefit of the transient mobility of GaP does not compensate for the drawback of the long charge-carrier lifetime of GaP. Therefore, GaP PC THz emitters are not recommended for use in the DMF-based THz-TDS system. ii. Surface-enhanced recombination was explored through analyses of nanocomposite materials. The nanocomposite materials based on Si, SiC, and InP were found to have charge-carrier lifetimes of 10, 4, and 5 ps, respectively. Photoconductive THz emitters based on nanocomposite materials were found to emit poor THz electric field levels and are therefore not recommended for use in the DMF-based THz-TDS system. iii. Surface-enhanced recombination was explored through analyses of textured InP. Photoconductive THz emitters based on fine- and coarse-textured InP are compared to a standard PC THz emitter Chapter 5: Conclusions  121  based on non-textured InP. The fine- and coarse-textured InP PC THz emitters were found to have similar THz electric field amplitudes to the non-textured InP PC THz emitter, however, they were found to have considerably lower Joule heating (an order of magnitude lower for the coarse-textured InP PC THz emitter) due to their reduced charge-carrier lifetime. Therefore, textured InP PC THz emitters are recommended for use in the DMF-based THz-TDS system. In Chapter 4, considerations for THz spectroscopy were considered. The THz spectroscopy analysis method was developed and then applied through THz-TDS of vapour, liquid, and solid samples. The major conclusions of Chapter 4 are given here: i. The theory associated with the THz spectroscopy analysis method was developed. The THz spectroscopy analysis method was found to be able to extract the absorption coefficient and refractive index over the THz spectrum (up to approximately 3 THz for many of the measurements). The THz spectroscopy analysis method was found to accurately measure absorption in terms of frequency through THz spectroscopy of a water vapour sample and comparing absorption peaks to literature values. The method was shown to accurately measure absorption in terms of absolute absorption through THz spectroscopy of a liquid water sample and comparing the results to literature values. Given these capabilities, the THz Chapter 5: Conclusions  122  spectroscopy analysis method is recommended for use in the DMF-based THz-TDS system. ii. Terahertz-TDS was also performed on a nominal egg white protein liquid sample. Based on these studies (and those of the liquid water sample), it is recommended that the plate separation of the multiplexer grid, used in the DMF-based THz-TDS system, should be less than 100 μm to ensure accurate measurements up to frequencies approaching 3 THz for the dynamic range of the THz setup used in this thesis. iii. Terahertz-TDS was performed on glass, plastic, and quartz solid samples to identify an effective material for the substrate layer of the multiplexer grid used in the DMF-based THz-TDS system. It is recommended that quartz be used as the substrate layer in the multiplexer grid as it provides high THz transmission (through a low absorption coefficient of 2 cm-1 at a frequency of 1 THz) and is a rigid material (for stability of the DMF device within the DMF-based THz-TDS system). iv. Terahertz-TDS was performed on a polydimethylsiloxane (PDMS) solid sample to identify an effective material for the dielectric layer of the multiplexer grid used in the DMF-based THz-TDS system. It is recommended that PDMS be used as the dielectric layer in the multiplexer grid as it provides high THz transmission (through a Chapter 5: Conclusions  123  low absorption coefficient of 9 cm-1 at a frequency of 1 THz), a high electric field breakdown (of approximately 2 × 105 V/cm), and practical benefits (such as compatibility with spinning coating, low cost, and transparency to visible light). The recommendations for the DMF-based THz-TDS system can be summarized through a conceptual design schematic of the lab-on-a-chip platform shown in Figure 5.3.1. The DMF-based THz-TDS system should have a multiplex grid DMF device with substrate layers made of quartz and dielectric layers made of PDMS. The spacing between the top and bottom plates of the multiplexer grid DMF device should be less than 100 μm. The DMF-based THz-TDS system should use a textured InP PC THz emitter as the THz emitter and a textured InP PC THz detector as the THz detector.  5.3 Future Work The work of this thesis has led to several recommendations for future work for the development of the DMF-based THz-TDS system.  The first recommendation pertains to integration of the complete DMF-based THz-TDS system. The DMF-based THz-TDS system should consist of a multiplexer grid with quartz as the substrate layer and PDMS as the dielectric layer and an integrated textured InP PC THz emitter and detector. The second recommendation pertains to integration of the DMF-based THz-TDS system proposed in this thesis with compact ultrafast pulsed lasers. The complete DMF-based THz-TDS system should be integrated with compact ultrafast pulsed lasers. These compact Chapter 5: Conclusions  124  (and ideally inexpensive) ultrafast pulsed lasers could be mode-locked laser diodes (MLLD), as are being developed at ETH Zurich [142] and the University of Cambridge [143]. These MLLD have been reported to achieve average powers greater than 10 mW [144], pulse durations less than 400 fs [144], and emission at wavelengths as short as 750 nm [145, 146] (corresponding to a photon energy of 1.7 eV which is above the 1.3 eV bandgap of InP). The third recommendation pertains to applying the DMF-based THz-TDS system for various biochemical analyses. The DMF-based THz-TDS system could be applied for testing pharmaceutical drugs for influenza treatment, where THz-TDS has been shown to provide and sensitive and label-free alternative to the standard enzyme-linked immunosorbent assay (ELISA) technique [23] and where the high-throughput nature of DMF devices is a great advantage. The DMF-based THz-TDS system could be applied for testing of blood samples for disease diagnostics. Terahertz-TDS has recently been shown to be capable of blood analyses showing relative concentrations of red blood cells [22]. The concentration of red blood cells is related to the presence or absence of anemia and blood cancer. The use of the THz spectroscopy is beneficial as chemical testing of the blood is avoided and the use of the DMF device is beneficial as small consumption of the blood is desirable (particularly for patients who are weakened from illness or suffer from trypanophobia).   Chapter 5: Conclusions  125       Figure 5.3.1 A conceptual design schematic is shown for the full DMF-based THz-TDS system. The DMF-based THz-TDS system should have a multiplex grid DMF device with substrate layers made of quartz and dielectric layers made from PDMS. The spacing between the top and bottom plates of the multiplexer grid DMF device should be less than 100 μm. The THz emitter should be a textured InP PC THz emitter and the THz detector should be a textured InP PC THz detector. The DMF-based THz-TDS system should make use of the THz spectroscopy analysis method for the analysis of THz-TDS data.  126  References [1] P. H. Siegel, "Terahertz technology," IEEE Trans. Microw. Theory Technol., vol. 50, no. 3, pp. 910-928, 2002. [2] T. Nagatsuma et al., "Terahertz wireless communications based on photonics technologies," Opt. Express, vol. 21, no. 20, pp. 23737-23747, 2013. [3] K. B. Ozanyan, P. Wright, M. R. Stringer, and R. E. Miles, "Hard-field THz tomography," IEEE Sens. J., vol. 11, no. 10, pp. 2507-2513, 2011. [4] S. Wietzke et al., "Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints," J. Eur. Opt. Soc.-Rapid, vol. 2, 07013(1-5), 2007. [5] J. F. Federici et al., "THz imaging and sensing for security applications—explosives, weapons and drugs," Semicond. Sci. Technol., vol. 20, pp. S266-S280, 2005. [6] B. St. Peter et al., "Development and testing of a single frequency terahertz imaging system for breast cancer detection," IEEE J. Transl. Eng. Health Med., vol. 17, no. 4, pp. 785-797, 2013. [7] A. G. Markelz, A. Roitberg, and E. J. Heilweil, "Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz," Chem. Phys. Lett., vol. 320, pp. 42-48, 2000. [8] K. Ajito, "Terahertz spectroscopy for pharmaceutical and biomedical applications," IEEE Trans. Terahertz Sci. Technol., vol. 5, no. 6, pp. 1140-1145, 2015. [9] W. R. Tribe, D. A. Newnham, P. F. Taday, and M. C. Kemp, "Hidden object detection: security applications of terahertz technology," Proc. SPIE, vol. 5354, pp. 168-176, 2004. References  127  [10] X.-C. Zhang, "Terahertz wave air photonics: bridging the gap and beyond," in Laser and photonics systems: design and integration, 1st ed. Boca Raton, USA: CRC Press, 2014, ch. 8, pp. 149-151. [11] G. M. Png et al., "The impact of hydration changes in fresh bio-tissue on THz spectroscopic measurements," Phys. Med. Biol., vol. 53, pp. 3501-3517, 2008. [12] Q. Tang et al., "Microfluidic devices for terahertz spectroscopy of live cells toward lab-on-a-chip applications," Sensors, vol. 16, 476(1-11), 2016. [13] Y. Kutuvantavida, G. V. M. Williams, E. M. Pogson, D. Bhuiyan, and K. Radhanpura, "Material characterization at low frequencies using THz and Raman spectroscopy," Proc. IEEE, 2162-2027(1-3), 2012. [14] X.-C. Zhang, "THz Technology in Security Checks," in Introduction to THz wave photonics, 1st ed. Troy, USA: Springer, 2010, ch. 9, pp. 202. [15] J. K. Sahoo et al., "Analysis of enzyme-responsive peptide surfaces by Raman spectroscopy," Chem. Comm., vol. 52, pp. 4698-4701, 2016. [16] F. Shi et al., "A catalytic path for electrolyte reduction in lithium-ion cells revealed by in situ attenuated total reflection-fourier transform infrared spectroscopy," J. Am. Chem. Soc., vol. 137, pp. 3181-3184, 2015. [17] E. P. J. Parrott and J. A. Zeitler, "Terahertz time-domain and low-frequency raman spectroscopy of organic materials," Appl. Spectrosc., vol. 69, no. 1, pp. 1-25, 2015. [18] A. A. Mankova et al., "Terahertz time-domain and FTIR spectroscopic study of interaction of α-chymotrypsin and protonated tris with 18-crown-6," Chem. Phys. Lett., vol. 560, pp. 55-59, 2013. References  128  [19] M. Brucherseifer et al., " Label-free probing of the binding state of DNA by time-domain terahertz sensing," Appl. Phys. Lett., vol. 77, no. 24, pp. 4049-4051, 2000. [20] P. U. Jepsen and B. M. Fischer, "Dynamic range in terahertz time-domain transmission and reflection spectroscopy," Opt. Lett., vol. 30, no. 1, pp. 29-31, 2005. [21] D. H. Auston, K. P. Cheung, and P. R. Smith, "Picosecond photoconducting Hertzian dipoles," Appl. Phys. Lett., vol. 45, no. 3, pp. 284-286, 1984. [22] K. Jeong et al., "Characterization of blood using terahertz waves," J. Biomed. Opt., vol. 18, no. 10, 107008(1-5), 2013. [23] Y. Sun, J. Zhong, C. Zhang, J. Zuo, and E. Pickwell-MacPherson, "Label-free detection and characterization of the binding of hemagglutinin protein and broadly neutralizing monoclonal antibodies using terahertz spectroscopy," J. Biomed. Opt., vol. 20, no. 3, 037006(1-6), 2015. [24] S. Laurette et al., "Highly sensitive terahertz spectroscopy in microsystem," RSC Adv., vol. 2, pp. 10064-10071, 2012. [25] P. A. George et al., "Microfluidic devices for terahertz spectroscopy of biomolecules," Opt. Express, vol. 16, no. 3, pp. 1577-1582, 2008. [26] T. Globus et al., "Terahertz Fourier transform characterization of biological materials in a liquid phase," J. Phys. D: Appl. Phys., vol. 39, pp. 3405-3413, 2006. [27] R. J. B. Dietz et al., "All fiber-coupled THz-TDS system with kHz measurement rate based on electronically controlled optical sampling," Opt. Lett., vol. 39, no. 22, pp. 6482-6485, 2014. References  129  [28] J. R. Lotz and C. B. Willingham, "Gas-phase chromatrography," J. Chem. Educ., vol. 33, no. 10, pp. 485-489, 1956. [29] M. I. Aveldano, M. VanRollins, and L. A. Horrocks, "Separation and quantitation of free fatty acids and fatty acid methyl esters by reverse phase high pressure liquid chromatography," J. Lipid Res., vol. 24, pp. 83-93, 1983. [30] G. M. Whitesides, "The origins and the future of microfluidics," Nature, vol. 442, pp. 368-373, 2006. [31] H. Fujita, "A decade of MEMS and its future," Proc. IEEE, vol. 442, pp. 368-373, 2006. [32] N. Pamme, "Continuous flow separations in microfluidic devices," Lab Chip, vol. 7, pp. 1644-1659, 2007. [33] B. Kuswandi, Nuriman, J. Huskens, and W. Verboom, "Optical sensing systems for microfluidic devices: a review," Anal. Chim. Acta, vol. 601, no. 2, pp. 141-155, 2007. [34] R. B. Fair, "Digital microfluidics: is a true lab-on-a-chip possible?," Microfluid. Nanofluid., vol. 3, pp. 245-281, 2007. [35] A. H. C. Ng et al., "Digital microfluidic platform for the detection of rubella infection and immunity: a proof of concept," Clin. Chem., vol. 62, no. 2, pp. 420-429, 2015. [36] N. Mei, B. Seale, A. H. C. Ng, A. R. Wheeler, and R. Oleschuk, "Digital Microfluidic Platform for Human Plasma Protein Depletion," Anal.  Chem., vol. 86, pp. 8466-8472, 2014. [37] T. B. Jones, M. Gunji, M. Washizu, and M. J. Feldman, "Dielectrophoretic liquid actuation and nanodroplet formation," J. Appl. Phys., vol. 89, no. 2, pp. 1441-1448, 2001. References  130  [38] M. Washizu, "Electrostatic actuation of liquid droplets for microreactor Applications," IEEE Trans. Ind. Appl., vol. 34, no. 4, pp. 732-737, 1998. [39] L. Davousta and J. Theisen, "Evaporation rate of drop arrays within a digital microfluidic system," Sens. Actuators B, vol. 189, pp. 157-164, 2013. [40] H. Moon, A. R. Wheeler, R. L. Garrell, J. A. Loo, and C.-J. Kim, "An integrated digital microfluidic chip for multiplexed proteomic sample preparation and analysis by MALDI-MS," Lab Chip, vol. 6, pp. 1213-1219, 2006. [41] J. lee and C.-J. Kim, "Surface-tension-driven microactuation based on continuous electrowetting," J. MEMS, vol. 9, no. 2, pp. 171-180, 2006. [42] A. Ahmadi, "Electrohydrodynamic modeling of microdroplet motion in digital microfluidic systems," Ph.D. thesis, School of Engineering, UBC, Kelowna, BC, Canada, 2011. [43] L. Luan, R. D. Evans, N. M. Jokerst, and R. B. Fair, "Integrated optical sensor in a digital microfluidic platform," IEEE Sens. J., vol. 8, no. 5, pp. 628-635, 2008. [44] L. Novak, P. Neuzil, J. Pipper, Y. Zhang, and S. Lee, "An integrated fluorescence detection system for lab-on-a-chip applications," Lab Chip, vol. 7, pp. 27-29, 2007. [45] J. Nichols et al., "On-chip digital microfluidic architectures for enhanced actuation and sensing," J. Biomed. Opt., vol. 17, no. 6, 067005(1-7), 2012. [46] V. Srinivasan, V. K. Pamula, M. C. Pollack, and R. B. Fair, "Clinical diagnostics on human whole blood, plasma, serum, urine, saliva, sweat, and tears," Proc. MicroTAS, pp. 1287-1290, 2003. References  131  [47] P. C. Ashok and K. Dholakia, "Microfluidic Raman spectroscopy for bio-chemical sensing and analysis," in Optical nano- and microsystems for bioanalytics, 1st ed. Troy, USA: Springer, 2012, ch. 8, pp. 247-270. [48] A. Rahman, "Dendrimer based terahertz time-domain spectroscopy and applications in molecular characterization," J. Mol. Struct., vol. 1006, pp. 59-65, 2011. [49] D. Davids, S. Datta, A. Mukherjee, B. Joshi, and A. Ravindran, "Multiple fault diagnosis in digital microfluidic biochips," ACM J. Emerg. Technol., vol. 2, no. 4, pp. 262–276, 2006. [50] T. Xu and K. Chakrabarty, "A cross-referencing-based droplet manipulation method for high-throughput and pin-constrained digital microfluidic arrays," Proc. DATE, pp. 552-557, 2007. [51] M. Xu et al., "Terahertz generation and detection with InGaAs-based large-area photoconductive devices excited at 1.55 μm," Appl. Phys. Lett., vol. 103, no. 25, 251114(1-4), 2013. [52] C. W. Berry et al., "Significant performance enhancement in photoconductive terahertz optoelectronics by incorporating plasmonic contact electrodes," Nat. Commun., vol. 4, 1622(1-10), 2013. [53] A. Singh, H. Surdi, V. V. Nikesh, S. S. Prabhu, and G. H. Döhler, "Improved efficiency of photoconductive THz emitters by increasing the effective contact length of electrodes," AIP Adv., vol. 3, 122106(1-5), 2013. [54] S. G. Park et al., "Enhancement of terahertz pulse emission by optical nanoantenna," ACS Nano, vol. 6, no. 3, pp. 2026-2031, 2012. References  132  [55] T. Ackemann et al., "Diamond heat sinking of terahertz antennas for continuous-wave photomixing," J. Appl. Phys., vol. 112, 123109(1-6), 2012. [56] Y. C. Shen, P. C. Upadhya, E. H. Linfield, H. E. Beere, and A. G. Davies, "Ultrabroadband terahertz radiation from low-temperature-grown GaAs photoconductive emitters," Appl. Phys. Lett., vol. 83, no. 15, pp. 3117-3119, 2003. [57] P. C. M. Planken, C. E. W. M. van Rijmenam, and R. N. Schouten, "Opto-electronic pulsed THz systems," Semicond. Sci. Technol., vol. 20, pp. S121-S127, 2005. [58] A. Singh, S. Pal, H. Surdi, S. S. Prabhu, V. Nanal, and R. G. Pillay, "Highly efficient and electrically robust carbon irradiated semi-insulating GaAs based photoconductive terahertz emitters," Appl. Phys. Lett., vol. 104, 063501(1-5), 2014. [59] J. Madéo et al., "Ultrafast properties of femtosecond-laser-ablated GaAs and its application to terahertz optoelectronics," Opt. Lett., vol. 40, no. 14, pp. 3388-3391, 2015. [60] Z. Xiao and E. F. Y. Young, "CrossRouter: a droplet router for cross-referencing digital microfluidic biochips," Proc. Asia South Pacific Design Automation Conference, pp. 269-274., 2010. [61] C. M. Collier et al., "Nonlinear dual-phase multiplexing in digital microfluidic architectures," Micromachines, vol. 2, pp. 369-384, 2011. [62] C. M Collier, J. Nichols, and J. F. Holzman, "Digital microfluidics technologies for biomedical devices," in Microfluidic Devices for Biomedical Applications, 1st ed. Sawston, England: Woodhead Publishing, 2013, ch. 4, pp. 139-164. [63] R. Renaudot et al., "Optimization of liquid dielectrophoresis (LDEP) digital microfluidic transduction for biomedical applications," Micromachines, vol. 2, pp. 258-273, 2011. References  133  [64] S.-K. Fan, T.-H. Hsieh, and D.-Y. Lin, "General digital microfluidic platform manipulating dielectric and conductive droplets by dielectrophoresis and electrowetting," Lab Chip, vol. 9, pp. 1236-1242, 2009. [65] J. Berthier et al., "Actuation potentials and capillary forces in electrowetting based microsystems," Sens. Actuators A, vol. 134, pp. 471-479, 2007. [66] P.-H. Yuh and C.-L. Yang, "BioRoute: a network-flow-based routing algorithm for the synthesis of digital microfluidic biochips," IEEE Trans. Computer-Aided Design Integr. Circuits Syst., vol. 27, pp. 1928-1941, 2008. [67] R. Gupta, D. M. Sheth, T. K. Boone, A. B. Sevilla, and J. Fréchette, "Impact of pinning of the triple contact line on electrowetting performance," Langmuir, vol. 27, pp. 14923-14929, 2011. [68] M. G. Pollack, "Electrowetting-based microactuation of droplets for digital microfluidics," Ph.D. thesis, Dep. ECE, Duke University, Durham, NC, USA, 2001. [69] M. A. Nilsson, R. J. Daniello, and J. P. Rothstein, "A novel and inexpensive technique for creating superhydrophobic surfaces using Teflon and sandpaper," J. Phys. D: Appl. Phys., vol. 43, 045301(1-5), 2010. [70] S. H. Au, R. Fobel, S. P. Desai, J. Voldman, and A. R. Wheeler, "Cellular bias on the microscale: probing the effects of digital microfluidic actuation on mammalian cell health, fitness and phenotype," Integr. Biol., vol. 5, pp. 1014-1025, 2013. [71] C.-T. Ho, R.-Z. Lin, H.-Y. Chang, and C.-H. Liu, "Micromachined electrochemical T-switches for cell sorting applications," Lab Chip, vol. 5, pp. 1248-1258, 2005. References  134  [72] J. Chandrappan, L. Ruiqi, N. Su, G. H. Y. Yi, and K. Vaidyanathan, "Thermo-mechanical actuator-based miniature tagging module for localization in capsule endoscopy," J. Micromech. Microeng., vol. 21, pp. 247-274, 2010. [73] R. Renaudot et al., "Optimization of liquid dielectrophoresis (LDEP) digital microfluidic transduction for biomedical applications," Micromachines, vol. 2, pp. 258-273, 2011. [74] C. W. Berry et al., "High power terahertz generation using 1550 nm plasmonic photomixers," Appl. Phys. Lett., vol. 105, 011121(1-4), 2014. [75] M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, "Optical rectification," Phys. Rev. Lett., vol. 9, no. 11, pp. 446-448, 1962. [76] Z. Chen et al., "Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals," Appl. Phys. Lett., vol. 92, no. 25, 251111(1-3), 2008. [77] C. M. Collier, B. Born, and J. F. Holzman, "Ultrafast response of SiC and Si nanocomposite material systems," Electron. Lett., vol. 48, no. 25, pp. 1618-1619, 2012. [78] C. M. Collier and J. F. Holzman, "Ultrafast photoconductivity of crystalline, polycrystalline, and nanocomposite ZnSe material systems for terahertz applications," Appl. Phys. Lett., vol. 104, no. 4, 042101(1-5), 2013. [79] J. A. Fülöp, L. Pálfalvi, M. C. Hoffmann, and J. Hebling, "Towards generation of mJ level ultrashort THz pulses by optical rectification," Opt. Express, vol. 19, pp. 15090-15097, 2011. [80] P. J. Hale et al., "20 THz broadband generation using semiinsulating GaAs interdigitated photoconductive antennas," Opt. Express, vol. 22, no. 21, pp. 26358-26364, 2014. References  135  [81] M. Beck et al., "Impulsive terahertz radiation with high electric fields from an amplifier-driven large-area photoconductive antenna," Opt. Express, vol. 18, no. 9, pp. 9251-9257, 2010. [82] M. R. Stone, M. Naftaly, R. E. Miles, J. R. Fletcher, and D. Paul Steenson," IEEE Trans. Microw. Theory Tech., vol. 52, no. 10, pp. 2420-2429, 2004. [83] F. Buccheri and X.-C. Zhang, "Terahertz emission from laser-induced microplasma in ambient air," Optica, vol. 2, no. 4, pp. 366-369, 2015. [84] A. Guillet and F. Delamarre, "Adiabatic joule heating of copper from 4 K to the melting temperature," arxiv.org preprint, pp. 1-14, 2015. [85] C. M. Collier, X. Jin, and J. F. Holzman, "Ultrafast refractometry for characterization of nanocomposite material systems," IEEE Photon. Technol. Lett., vol. 24, pp. 590-592, 2012. [86] R. Chakkittakandy, J. A. W. M. Corver, and P. C. M. Planken, "Quasi-near field terahertz generation and detection," Opt. Express, vol. 17, no. 17, pp. 12794-12805, 2008. [87] H. Pahlevaninezhad, B. Heshmat, and T. E. Darcie, "Advances in terahertz waveguides and sources," IEEE Photon. J., vol. 3, no. 2, pp. 307-310, 2011. [88] N. K. Grady et al., "Terahertz metamaterials for linear polarization conversion and anomalous refraction," Science, vol. 340, pp. 1304-1307, 2013. [89] D. Zimdars, J. V. Rudd, and M. Warmuth, "A compact, fiberpigtailed, terahertz time domain spectroscopy system," Proc. International Symposium on Space Terahertz Technology, 2000, pp. 414–423. References  136  [90] Q. Wu and X.-C. Zhang, "Free-space electro-optic sampling of terahertz beams," Appl. Phys. Lett., vol. 67, no. 24, pp. 3523-3525, 1995. [91] P. C. M. Planken, H.-K. Nienhuys, H. J. Bakkerl, and T. Wenckebach, "Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe," J. Opt. Soc. Am. B, vol. 18, pp. 313–317, 2001. [92] X. Ropagnol, R. Morandotti, T. Ozaki, and M. Reid, "Toward high-power terahertz emitters using large aperture ZnSe photoconductive antennas," IEEE Photon. J., vol. 3, pp. 174-186, 2011. [93] G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum., vol. 73, pp. 1715-1719, 2002. [94] R. T. Hall, D. Vrabec, and J. M. Dowling, "A high-resolution, far infrared double-beam lamellar grating interferometer," Appl. Opt., vol. 5, pp. 1147-1158, 1966. [95] M. A. Cavicchia and R. R. Alfano, "Time-resolved IR-absorption spectroscopy of hot-electron dynamics in satellite and upper conduction bands in GaP," Phys. Rev. B, vol. 51, no. 15, pp. 9629-9633, 1995. [96] A. K. Malik and H. K. Malik, "Tuning and focusing of terahertz radiation by DC magnetic field in a laser beating process," IEEE J. Quantum Electron., vol. 49, no. 2, pp. 232-237, 2013. [97] J. F. Holzman and A. Y. Elezzabi, "Two-photon photoconductive terahertz generation in ZnSe," Appl. Phys. Lett., vol. 83, no. 14, pp. 2967-2969, 2003. References  137  [98] O. Imafuji, B. P. Singh, Y. Hirose, Y. Fukushima, and S. Takigawa, "High power subterahertz electromagnetic wave radiation from GaN photoconductive switch," Appl. Phys. Lett., vol. 91, 071112(1-3), 2007. [99] H. Yoneda, K. Tokuyama, K.-I. Ueda, H. Yamamoto, and K. Baba, "High-power terahertz radiation emitter with a diamond photoconductive switch array," Appl. Opt., vol. 40, no. 36, pp. 6733-6736, 2001. [100] J. Schein, K. M. Campbell, N. Qi, and A. Krishnan, "Ultra-fast UV triggered high voltage diamond switch,” Proc. IEEE Conf. Pulsed Power Plasma Sci. Record Abstracts, 2001, pp. 220-243. [101] T. Miyazawa, M. Ito, and H. Tsuchida, "Evaluation of long carrier lifetimes in thick 4H silicon carbide epitaxial layers," Appl. Phys. Lett., vol. 97, 202106(1-3), 2010. [102] J. R. Milward, W. Ji, A. K. Kar, C. R. Pidgeon, and B. S. Wherrett, "Photogenerated carrier recombination time in bulk ZnSe," J. Appl. Phys., vol. 69, no. 4, pp. 2708-2710, 1991. [103] H. Pernegger et al., "Charge-carrier properties in synthetic single-crystal diamond measured with the transient-current technique," J. Appl. Phys., vol. 97, pp. 073704(1-3), 2005. [104] D. Dietze, K. Unterrainer, and J. Darmo, "Dynamically phase-matched terahertz generation," Opt. Lett., vol. 37, no. 6, pp. 1047-1049, 2012. [105] K. Saito, T. Tanabe, and Y. Oyam, "Elliptically polarized THz wave generation from GaP-THz planar waveguide via collinear phasematched difference frequency mixing," Opt. Express, vol. 20, no. 23, pp. 26082-26088, 2012. References  138  [106] P. H. Borcherds, K. Kunc, G. F. Alfrey, and R. L. Hall, "The lattice dynamics of gallium phosphide," J. Phys. C, Solid State Phys., vol. 12, no. 22, pp. 4699-4706, 1979. [107] M. C. Nuss, D. H. Auston, and F. Capasso, "Direct subpicosecond measurement of carrier mobility of photoexcited electrons in gallium arsenide," Phys. Rev. Lett., vol. 58, no. 22, pp. 2355-2358, 1987. [108] P. Gu, M. Tani, S. Kono, K. Sakai, and X.-C. Zhang, "Study of terahertz radiation from InAs and InSb," J. Appl. Phys., vol. 91, no. 9, pp. 5533-5537, 2002. [109] Y. A. Goldberg, "Gallium phosphide (GaP)," in Handbook Series on Semiconductor Parameters, 1st ed. London, UK: World Scientific, 1996, pp. 104. [110] J. Sjakste, N. Vast, and V. Tyuterev, "Ab initio method for calculating electron-phonon scattering times in semiconductors: application to GaAs and GaP," Phys. Rev. Lett., vol. 99, no. 23, pp. 236405(1-)4, 2007. [111] J. Kim, "Effect of free-carrier absorption on the carrier dynamics of quantum-dot semiconductor optical amplifiers," J. Korean Phys. Soc., vol. 55, no. 2, pp. 512-516, 2009. [112] T. Sia et al., "Strong microwave absorption of hydrogenated wide bandgap semiconductor nanoparticles," ACS Appl. Mater. Interface, vol. 7, pp. 10407-10413, 2015. [113] X. Tang, L. Huang, W. Zhang, R. Jiang, and H. Zhong, "Photo-catalytic activities of plant hormones on semiconductor nanoparticles by laser-activated electron tunneling and emitting," Sci. Rep., vol. 5, 8893(1-9), 2015. References  139  [114] X.-C. Zhang and D. H. Auston, "Optoelectronic measurement of semiconductor surfaces and interfaces with femtosecond optics," J. Appl. Phys., vol. 71, no. 1, pp. 326-338, 1992. [115] X. Ropagnol, M. Bouvier, M. Reid, and T. Ozaki, "Improvement in thermal barriers to intense terahertz generation from photoconductive antennas," J. Appl. Phys., vol. 116, no. 4, 043107(1-7), 2014. [116] M. Reid, I. V. Cravetchi, R. Fedosejevsa, I. M. Tiginyanu, and L. Sirbu, "Enhanced terahertz emission from porous InP (111) membranes," Appl. Phys. Lett., vol. 86, 021904(1-3), 2005. [117] J. Barreto, T. Roger, and A. Kaplan, "Resolving the ultrafast dynamics of charge carriers in nanocomposites," Appl. Phys. Lett., vol. 100, 241906(1-4), 2012. [118] Q. X. Zhao, L. L. Yang, M. Willander, B. E. Sernelius, and P. O. Holtz, "Surface recombination in ZnO nanorods grown by chemical bath deposition," J. Appl. Phys., vol. 104,  073526(1-6), 2008. [119] J. F. Holzman et al., "Ultrafast carrier dynamics in InP photonic crystals," Nanotechnology, vol. 16, pp. 949-952, 2005. [120] D. Baek, S. Rouvimov, B. Kim, T.-C. Jo, and D. K. Schrodera, "Surface recombination velocity of silicon wafers by photoluminescence," Appl. Phys. Lett., vol. 86, 112110(1-3), 2005. [121] C. Thomas, S. Portnoff, and M. G. Spencer, "High efficiency 4H-SiC betavoltaic power sources using tritium radioisotopes," Appl. Phys. Lett., vol. 108, 013505(1-4), 2016. [122] S. Bothra, S. Tyagi, S. K. Ghandhi, and J. M. Borrego, "Surface recombination velocity and lifetime in InP," Solid-State Electron., vol. 34, pp. 47-50, 1991. References  140  [123] Joyce et al., "Ultralow surface recombination velocity in InP nanowires probed by terahertz spectroscopy," Nano Lett., vol. 12, pp. 5325-5330, 2012. [124] C. M. Collier et al., "Optimization processes for pulsed terahertz systems," Appl. Opt., vol. 54, pp. 535-545, 2015. [125] X. Ropagnol, F. Blanchard, T. Ozaki, and M. Reid, "Intense terahertz generation at low frequencies using an interdigitated ZnSe large aperture photoconductive antenna," Appl. Phys. Lett., vol. 103, 161108(1-4), 2013. [126] M. van Exter, C. Fattinger, and D. Grischkowsky, "Terahertz time-domain spectroscopy of water vapour," Opt. Lett., vol. 14, no. 20, pp. 1128-1130, 1989. [127] M. Naftaly and R. E. Miles, "Terahertz time-domain spectroscopy for material characterization," Proc. IEEE, vol. 95, no. 8, pp. 1658-1665, 2007. [128] M. Kondoh and M. Tsubouchi, "Liquid-sheet jets for terahertz spectroscopy," Opt. Express, vol. 22, no. 12, pp. 14135-14147, 2014. [129] M. Naftaly and R. E. Miles, "Terahertz time-domain spectroscopy of silicate glasses and the relationship to material properties," J. Appl. Phys., vol. 102, no. 4, 043517(1-6), 2007. [130] S. Kojima, M. Wada Takeda, and S. Nishizawac, "Terahertz time domain spectroscopy of complex dielectric constants of boson peaks," J. Mol. Struct., vol. 651, pp. 285-288, 2003. [131] T. Wang, P. Klarskov, and P. U. Jepsen, "Ultrabroadband THz Time-Domain Spectroscopy of a Free-Flowing Water Film," IEEE Trans. Terahertz Sci. Technol., vol. 4, no. 4, 2014. References  141  [132] L. Xie, Y. Yao, and Y. Ying, "The application of terahertz spectroscopy to protein detection: a review," Appl. Spectros. Rev., vol. 49, pp. 448-461, 2014. [133] G. M. Hale and M. R. Querry, "Optical constants of water in the 200-nm to 200-pm wavelength region," Appl. Opt., vol. 12, pp. 555-563, 1973. [134] M. L. Messenbrink, "Complex indices of refraction for water and ice from visible to long wavelengths," Ph.D. thesis, Dep. Air Force, Florida State University, Tallahassee, FL, 1996. [135] R. Piesiewicz et al., "Properties of building and plastic materials in the THz range," Int. J. Infrared Milli. Waves, vol. 28, no. 5, pp. 363-371, 2007. [136] M. Naftaly and R. E. Miles, "Terahertz time-domain spectroscopy: a new tool for the study of glasses in the far infrared," J. Non.-Cryst. Solids, vol. 351, pp. 3341-3346, 2005. [137] M. Molberg et al., "Frequency dependent dielectric and mechanical behavior of elastomers for actuator applications," J. Appl. Phys., vol. 106, 054112(1-7), 2009. [138] C.-P. Jen, T. G. Amstislavskaya, K.-F. Chen, and Y.-H. Chen, "Sample preconcentration utilizing nanofractures generated by junction gap breakdown assisted by self-assembled monolayer of gold nanoparticles," PLOS One, vol. 10, no. 5, 2015. [139] S. Sohail, D. Das, S. Das, and K. Biswas, "Study of PDMS as dielectric layer in electrowetting devices," in Physics of Semiconductor Devices, 1st ed. Troy, USA: Springer, 2014, pp. 487-490.  [140] D. K. Cai, A. Neyer, R. Kuckuk, and H. M. Heise, "Optical absorption in transparent PDMS materials applied for multimode waveguides fabrication," Opt. Mater., vol. 30, pp. 1157-1161, 2008. References  142  [141] I. E. Khodasevych et al., "Elastomeric silicone substrates for terahertz fishnet metamaterials," Appl. Phys. Lett., vol. 100, 061101(1-3) [142] R. Scollo et al., "Mode-locked laser diode with an ultrafast integrated uni-traveling carrier saturable absorber," Opt. Lett., vol. 30, no. 20, pp. 2808-2810, 2005. [143] X. Guo et al., "Monolithically integrated selectable repetition-rate laser diode source of picosecond optical pulses," Opt. Lett., vol. 39, no. 14, pp. 4144-4147, 2014. [144] M. G. Thompson, A. R. Rae, M. Xia, R. V. Penty, and I. H. White, "InGaAs quantum-dot mode-locked laser diodes," IEEE J. Sel. Top. Quantum Electron., vol. 15, no. 3, pp. 661-672, 2009. [145] L. Kong et al., "Semiconductor monolithic mode-locked laser for ultrashort pulse generation at 750 nm," Proc. 2014 International Semiconductor Laser Conference, pp. 137-138, 2014. [146] H. Wang et al., "760-nm Semiconductor Passively Mode-Locked Monolithic Laser for Picosecond Pulse Generation," Proc. CLEO: 2013, OSA Technical Digest, pp. 1-2, 2013. [147] E. Castro-Camus et al., "Photoconductive response correction for detectors of terahertz radiation," J. Appl. Phys., vol. 104, no. 5, 053113(1-7), 2008. [148] M. Tani, K. Sakai, and H. Mimura, "Ultrafast photoconductive detectors based on semi-insulating GaAs and InP," Jpn. J. Appl. Phys., vol. 36, pp. 1175-1178, 1997. [149] F. G. Sun, G. A. Wagoner, and X.-C. Zhang, "Measurement of free-space terahertz pulses via long-lifetime photoconductors," Appl. Phys. Lett., vol. 67, no. 12, pp. 1656-1658, 1995.   143  Appendices Appendix A  Photolithography and Microfabrication for Multiplexer Grid The photolithography process used in the multiplexer grid fabrication is described here. Figure A.1 shows a general photolithography process. To start with, electrode and adhesion metal layers are sputtered onto a substrate layer, as shown in Figure A.1(a). (The adhesion layer can be omitted if the electrode metal can adhere to the substrate layer.) A positive photoresist is applied to the electrode metal layer with a spincoating process, shown in Figure A.1(b). A mask is then fitted onto the positive photoresist layer with the opaque features facing down, shown in Figure A.1(c). The sample is then exposed to ultraviolet radiation from above, shown in Figure A.1(d). The positive photoresist remains unexposed in the regions protected by the opaque (patterned) sections of the mask and becomes exposed in the regions covered by the transparent sections of the mask. The sample can then by developed in a developing solution, dissolving the exposed positive photoresist, shown in Figure A.1(e). The pattern of the positive photoresist now exactly resembles that of the mask. The sample can then be submerged in an electrode metal etchant to remove the unwanted and unprotected electrode metal regions, shown in Figure A.1(f), and then submerged in an adhesion metal etchant to remove the unwanted and unprotected adhesion metal regions, shown in Figure A.1(g). Finally, the residual positive photoresist can be removed using a positive photoresist thinner, shown in Figure A.1(h). The substrate layer is now patterned with electrodes in the exact design as that of the mask. Note that this process can also be done with a negative mask and negative photoresist, whereby the mask features are the negative image of the design. Here, the Appendices  144  ultraviolet exposure results in the negative photoresist turning from soluble to insoluble in a developer solution. The recipe for the multiplexer grid digital microfluidic device is as follows: • Begin with Cu electrode metal sputtered onto a substrate of glass or quartz (adhesion layer is not needed for Cu electrode metal). • Spin coat the sample with a layer of positive photoresist (S1813) in three stages: i. 250 rpm for 30 seconds, ii. 500 rpm for 30 seconds, and iii. 2000 rpm for 60 seconds. • Soft bake the sample at 105°C for 10 minutes. • Using the mask aligner (OAI Model 204), align the mask with the ink side closest to the sample. • Expose to 365 nm (centrewavelength) 11 W/cm2 intensity radiation for 30 seconds. • Develop in developer solution (MF-319) for 60 seconds.  • Hard bake sample at 105°C for 60 minutes. • Etch the Cu electrode layer by quickly dipping sample into FeCl3 (MG Chemicals Ferric Chloride). Immediately rinse sample with deionized water. Repeat this process until the Cu has been etched off in the appropriate regions. • Swish sample in photoresist thinner (Microposit Remover 1165) for about 3 seconds to remove all residual positive photoresist. • This process can be used with Au as the electrode layer and Cr as the adhesion layer with Transene Chemicals Gold and Chrome Etchant, respectively.  Appendices  145       Figure A.1 The general positive photolithography process with positive photoresist is shown.    Appendices  146  Appendix B  Photoconductive Terahertz Emitter as Hertzian Dipole Antenna In this appendix, emission from a dipole antenna is considered and used to estimate the power of the emission from a photoconductive (PC) terahertz (THz) emitter. The analysis begins by considering a Hertzian dipole antenna set at the origin of a Cartesian coordinate axis with xaˆ ,yaˆ , and zaˆ unit vectors. Extending the Cartesian coordinate axis to a spherical coordinate system yields a vector, rr, with magnitude of r, and a direction defined by a polar angle of θ (on the x-y plane defined off of the x-axis) and an azimuthal angle of ϕ (defined off of the z-axis). The Hertzian dipole antenna is an infinitely thin wire with a small length of l (oriented length-wise in the zaˆ direction) and current of tjeItI ω0)( =  (the real part of which is)cos()( 0 tItI ω= ). The magnetic vector potential for such a Hertzian dipole antenna is  ∫−−=2/2/ 00ˆ4)( ll zjkradzreIrApiµrr, (47) where μ0 is the permeability of free-space and where k = ω/c for an angular frequency of ω and vacuum speed of light of c. (Note that the time-varying ejωt term has been dropped for simplicity.) This equation can be modified to a spherical coordinate vector through  θθθ aaa rz ˆsinˆcosˆ −= . (48) This yields a result of  θθ aAaArA rr ˆˆ)( −=rr (49) where  Appendices  147   θpiµ cos400 relIAjkrr−= (50) and  .sin400θpiµθrelIAjkr−−= (51) The magnetic field from the Hertzian dipole is  )(1)(0rArH rrrr×∇=µ  (52) and can be expressed as  θθφφ aHaHaHrH rr ˆˆˆ)( ++=rr (53) where  jkrejkrjkrlkIH −+−= 220)(11sin4θpiφ  (54) and  .0== θHHr  (55) The electric field from the Hertzian dipole is  )(1)(0rHjrErrrv×∇=ωε (56) and can be expressed as  θθφφ aEaEaErE rr ˆˆˆ)( ++=rv (57) where Appendices  148   jkrejkrjkrjkrlkIE −++−= 32020)(1)(11sin4θpiηφ  (58) and  jkrr ejkrjkrlkIE −+−= 32020)(1)(1cos24θpiη (59) and  0=θE  (60) where η0 = 1/ε0/c is the impedance of free-space. In the far-field (r > ωl2/π/c), the terms that scale with 1/r2 and 1/r3 are negligible, with the only electric field component being  .sin41sin400020 ωθpiηθpiηφ jerclIejkrlkIE jkrjkr −− =−= (61) The electric field can be expressed in the time domain by noting that multiplication by jω represents a derivative and by reintroducing the time-varying ejωt term, the real part of the ϕ-component of the electric field becomes  )./(sin4)]/(cos[sin4000 crtIdtdrclcrtIdtdrclE −=−= θpiηωθpiηφ  (62) This expression can be modified for a general current in a photoconductive (PC) THz emitter of IPC(t) to be  )./(sin40 crtIdtdrclE PC −= θpiηφ  (63) The current in a PC THz emitter over one laser pulse repetition period, T0, can be approximated as Appendices  149   .,,)/()( 0><=rtrtrtPC tKttItIτττ (64) where τrt is the rise-time of the current in the PC THz emitter and K is a slowly decaying exponential function which can be approximated as a constant (i.e., with a derivative of 0). The Poynting vector of the emission from the PC THz emitter is  .,0,sin16222222002><=rtrtrtttcrIlSττθτpiη (65) The emitted THz power collected by a parabolic mirror can be approximated as  .24sin16102220024/0 0 03222200200TcIlddtdcIlTPrtTrtissionem τpiηφθθτpiηpi pi== ∫ ∫ ∫  (66) This equation can be expressed in terms of the pump fluence, Φ, as  202222222024)(optrtFLbissionem ETcKVwqPτpiµη Φ= (67) where q is the elementary charge, μ is the mobility of the semiconductor, Vb is the applied bias voltage, Eopt is the photon energy of the 780 nm pump beam, and is a constant representing fluence loss from the mismatch between the optical spot size and the active area of the PC THz emitter and Fresnel reflection of the pump beam at the semiconductor/air interface. Here, the Hertzian dipole antenna length, l, is assumed to be equal to the electrode gap spacing, d. The ratio between the Joule heating, PH, as described in Chapter 3, and the emitted THz power, Pemitted, can be shown to be Appendices  150   dwKqEcPdwPPFLoptrtemittedHemittedHΦ==µηττpiφ02224 (68) where ϕH is the Joule heating flux, w is the electrode width, and τ is the charge-carrier lifetime.    Appendices  151  Appendix C  Circuit for Measuring Current from Photoconductive Terahertz Emitters The circuit shown below is a transimpedance amplifier circuit used to measure the current from a photoconductive (PC) terahertz (THz) emitter. The 100 Vp-p squarewavecircuit, PC THz emitter, variable capacitor, variable resistor, oscilloscope, OPA454 operational amplifier, enable/disable (E/D) pin, and enable/disable E/D common pin are labeled.  Figure C.1 The transimpedance amplifier circuit is shown.   Appendices  152  Appendix D  Circuit for Creating 100 V Peak-to-Peak Squarewave The circuit shown below amplifies a 10 Vp-p squarewave signal from a function generator to a 100 Vp-p squarewave signal operating with kHz frequencies. The function generator, oscilloscope and photoconductive (PC) terahertz (THz) emitter, OPA454 operational amplifier, enable/disable (E/D) pin, and E/D common pin are labeled.  Figure D.1 The squarewave amplifier circuit is shown.   Appendices  153  Appendix E  Electro-Optic Detection Derivation Electro-optic sampling with a <110> ZnTe crystal is investigated here. The probe and THz beams are polarized at the azimuthal rotation angle, ϕ, from the z0 basis vector of the primary coordinate system (x0,y0,z0) and enter the crystal along the [110] crystallographic direction. The incoming THz electric field,  00 ˆcosˆsin zEyEE THzTHzTHz φφ +=v, (69) is mapped onto the probe polarization with the field-dependent impermeability tensor  ( ) ( ) ∑+=kkTHzijkijTHzij ErE 0ηηv, (70) where ηij(0) is the static impermeability tensor, and rijk is the electro-optic tensor. Using the expression for the THz electric field in a crystallographic coordinate system (x1,y1,z1), where x0 = [101], y0 = [010], and z0 = [ 101], yields  111 ˆ2cosˆsinˆ2coszEyExEE THzTHzTHzTHzφφφ ++−=v . (71) The resulting index ellipsoid is  ,1cos2sin2cos2 114111411141221221221=++−++ yxErzxErzyErnznynxTHzTHzTHz φφφ  (72) where n is the refractive index of the electro-optic crystal. Equation (72) can be rewritten for probe beam propagation through the (110) plane by an axis transformation to the primary coordinate system, with x0 = 0. The resulting equation is   ( ) .1cos21sin1 410022041220 =−++− φφ THzTHz ErzynyErnz  (73) Appendices  154  In order to eliminate the Equation (73) y0z0 crossterm, and to subsequently find the principal axes for probe beam propagation, the coordinate system must be rotated by an angle α about the x0 axis to the (x2,y2,z2) coordinate system. Thus, the index ellipsoid is transformed into  ( ) .12coscos22sinsin2sincoscossin12sincossinsin14141224124122241241222=−−++−+−−αφαφαφαφαφαφTHzTHzTHzTHzTHzTHzErErzyErErnzErErny (74) With α = tan-1(-2 cotϕ)/2, Equation (74) can be rewritten as  .12cos312sin12cos312sin1 241222241222 = ++−++ +−−+φφφφTHzTHz ErnzErny  (75) A THz-induced phase retardation is produced from the corresponding principal refractive indices,    +++≅2cos312sin2)(24132φφφ THzyErnnn (76) and   +−+≅2cos312sin2)(24132φφφ THzzErnnn , (77) and the THz-induced phase retardation between the y2 and z2 electro-optic crystal axes is   cLErn THz φpiν 2413110cos31+=Γ >< . (78) Here, the probe beam frequency is denoted ν, the electro-optic crystal length is denoted L, and the free-space speed of light is denoted c. Appendices  155  The THz-induced birefringence, that is produced by the two different electro-optic crystal refractive indices, changes the polarization state of the probe beam as it propagates along with the THz beam. The probe beam passes through a quarter waveplate and a polarizing beamsplitter in order to measure this phase retardation. The quarter waveplate alignment has its slow axis and fast axis at an angle of 45° off of the polarization of the incident probe beam. A static π/2 phase retardation is applied to the electric field of the probe beam that exits the electro-optic crystal, yielding  ( )( )( ) 220220ˆ)])(2(exp[cosˆ)])(2(exp[sinzLnktiEyLnktiEtEzprobeyprobeprobeφpiνφαφpiνφα−++−+=v (79) and the electric field of the probe beam that exits the quarter waveplate becomes  ( )( ) ( )( ) ( )( ) ( )( ) ( ) ,ˆ)]}4/)(2(exp[4/sincos)]4/)(2(exp[4/cossin{ˆ)]}4/)(2(exp[4/coscos)]4/)(2(exp[4/sin{sin3202032020zLnktiLnktiEyLnktiLnktiEtEzyprobezyprobeprobepiφpiνpiφαφαpiφpiνpiφαφαpiφpiνpiφαφαpiφpiνpiφαφα−−++++−−+++−++−+++++−+++×=v (80) where the probe beam wavevector, k0 = 2πν/c, is defined for free-space and y3 and z3 are defined along the respective slow and fast axes. Upon transmission through the quarter waveplate, the propagating probe beam is divided into two orthogonal polarizations by the polarizing beamsplitter. The two transmission axes of the polarizing beamsplitter are aligned parallel and perpendicular to the polarization of the incident probe beam. The electric field for the first orthogonal polarization can be expressed as Appendices  156   ( ) {( ) ( )( ) ( )( ) ( )( ) ( ) }.)]4/)(2(exp[4/sincos)]4/)(2(exp[4/cossin)]4/)(2(exp[4/coscos)]4/)(2(exp[4/sinsin2202020201piφpiνpiφαφαpiφpiνpiφαφαpiφpiνpiφαφαpiφpiνpiφαφα−−++++−−+++−+−+++++−++++×=LnktiLnktiLnktiLnktiEtEzyzyprobeprobe (81) The electric field for the second orthogonal polarization can be expressed as  ( ) {( ) ( )( ) ( )( ) ( )( ) ( ) }.)]4/2(exp[4/sincos)]4/2(exp[4/cossin)]4/2(exp[4/coscos)]4/2(exp[4/sinsin2202020202pipiνpiφαφαpipiνpiφαφαpipiνpiφαφαpipiνpiφαφα−−++++−−+++−+−+++−+−+++−×=LnktiLnktiLnktiLnktiEtEzyzyprobeprobe (82) The electro-optic signal is ultimately determined by differencing the first polarization probe beam power,  ( ) ( ) ( )[ ] ( ) ,)()(2sin2sin22 22*111 −++=×= LnncPPtEtEAP zyprobeprobeprobeprobeoprobe φφpiνφαη (83) and the second polarization probe beam power,  ( ) ( ) ( )[ ] ( ) .)()(2sin2sin22 22*222 −+−=×= LnncPPtEtEAP zyprobeprobeprobeprobeoprobe φφpiνφαη (84) The resulting differenced electro-optic power signal is  ( )[ ] ( ) ,)()(2sin2sin 2221110 −+=−=∆ >< LnncPPPP zyprobeprobeprobe φφpiνφα  (85) where the total probe power is Pprobe = A/(2η0)Eprobe2, the probe beam area is A and the impedance of free-space is η0. Because of the small THz field-induced phase difference, an Appendices  157  expansion of the second sine term in Equation (85) is possible. With this expanded term the differential power can then be expressed as  ( ).2sinsin2coscos2413110 φφφφpiν−≅∆ ><cLErnPP THzprobe  (86) Similar analyses can be performed for <111> electro-optic crystals, yielding three-fold rotational symmetry in the response according to  .3sin238 413111 φpiνcLErnPP THzprobe≅∆ ><  (87) Similar analyses can be performed for <100> electro-optic crystals, yielding a negligible electro-optic response with  0100 =∆ ><P . (88)   Appendices  158  Appendix F  MATLAB Script for Nanoparticle Analysis %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This MATLAB script implements the  % nanoparticle analysis method %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Christopher Collier % Integrated Optics Laboratory % The University of British Columbia %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% close all clear clc  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Read in the nanoparticle analysis data from  % an excel plot with the following two columns: % time, t % differential transmission, dT(t)/T %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% nanoparticl_exp_data = xlsread('nanoparticle_exp_data.xlsx');   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Global variables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diameter = 50E-9; a = diameter/2;                 % Sphere radius [m] n0 = 1;                         % Initial charge-carrier density [m^3] S = 4*1E3;                      % Surface recombination velocity [m/s] D = S*a;                        % Diffusion coefficient [m^2/s] t_step = 0.01E-12;              % Time step size [s] t_end = 30E-12;                 % End time [s] t = 0:t_step:t_end;             % Time array [s] r = 0.0001E-9:0.1E-9:a;         % Radial dimension [m] n = zeros(size(t,2),size(r,2)); % charge-carrier density matrix [m^3] n2 = n;                         % charge-carrier density matrix without D = Sa [m^3]   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Setup eigenvalue analysis  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% lambda2 = 0; dlambda2 = 0.01/a; lambda2_max = 1000/a; Appendices  159  y_new = 0; k_const = 300;                  % Relationship between D2 and S2*a S2 = S;                         % Surface recombination velocity without D = Sa D2 = k_const*S2*a;              % Diffusion coefficient without D = Sa  i2 = 1; lambda_vector = lambda2:dlambda2:lambda2_max eqn = tan(lambda_vector.*a) - lambda_vector.*a/(1-S*a/D2); %figure, plot(lambda_vector, eqn); stop = 0;   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Find solution to get eigenvalues %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% while stop == 0 y_old = y_new; y_new = tan(lambda2*a) - lambda2*a/(1-S*a/D2); if y_old*y_new < 0 && abs(y_old - y_new) < 50     lambda_root(i2) = lambda2     i2 = i2 +1; end lambda2 = lambda2 + dlambda2; if i2 == 11      stop = 1; end end   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Solve for n for D = Sa and D ~= Sa %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for it = 1:size(t,2)   for ir = 1:size(r,2)      for m = 0:(i2-2)         %%%%%%%%%%%%%%%%%%%%%%%%         % analysis for D = Sa         %%%%%%%%%%%%%%%%%%%%%%%%         lambda = (2*m+1)*pi/2/a;         Am = 2*n0/lambda/lambda/a*(-lambda*a*cos(lambda*a)+sin(lambda*a));         n(it,ir)=n(it,ir)+Am/r(ir)*sin(lambda*r(ir))*exp(-D*lambda*lambda*t(it));                  %%%%%%%%%%%%%%%%%%%%%%%%         % analysis for D ~= Sa         %%%%%%%%%%%%%%%%%%%%%%%%         m2 = m + 1; Appendices  160          Am = 2*n0/(lambda_root(m2)*lambda_root(m2)*a - lambda_root(m2)*sin(lambda_root(m2)*a)*cos(lambda_root(m2)*a))*(-lambda_root(m2)*a*cos(lambda_root(m2)*a)+sin(lambda_root(m2)*a));         n2(it,ir)=n2(it,ir)+Am/r(ir)*sin(lambda_root(m2)*r(ir))*exp(-D2*lambda_root(m2)*lambda_root(m2)*t(it));     end   end end   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % plot n for D = Sa %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure subplot(2,3,1), plot(r*1E9,n(1,:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,2), plot(r*1E9,n(round(0.2*size(t,2)),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,3), plot(r*1E9,n(round(0.4*size(t,2)),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,4), plot(r*1E9,n(round(0.6*size(t,2)),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,5), plot(r*1E9,n(round(0.8*size(t,2)),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,6), plot(r*1E9,n(size(t,2),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1])   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % plot n for D ~= Sa %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure subplot(2,3,1), plot(r*1E9,n2(1,:)), xlabel('Radial dimension (nm)'), ylabel('Normalized carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,2), plot(r*1E9,n2(round(0.2*size(t,2)),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,3), plot(r*1E9,n2(round(0.4*size(t,2)),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,4), plot(r*1E9,n2(round(0.6*size(t,2)),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,5), plot(r*1E9,n2(round(0.8*size(t,2)),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1]) subplot(2,3,6), plot(r*1E9,n2(size(t,2),:)), xlabel('Radial dimension (nm)'), ylabel('Normalized charge-carrier density (unitless)'),axis([0 25 0 2.1])   Appendices  161  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Plot in n vs. r in 3-D plot %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% number_of_plots = 4; n_3d(1:size(r,2),1:size(r,2),1:number_of_plots) = 0; rr = -(a+0.1E-9):0.1E-9:(a+0.1E-9);         % Radial dimension in m xx = rr*1E9; yy = xx; [X,Y] = meshgrid(xx,yy);   count = [1 round(0.25*size(t,2)) (round(0.5*size(t,2))-1) (round(0.75*size(t,2))-1)]'; figure for k = 1:number_of_plots for x = 1:(2*size(r,2)+2)     for y = 1:(2*size(r,2)+2)         rr = round(sqrt((x-size(r,2))^2+(y-size(r,2))^2))+1;         if(rr <= size(r,2))             n_3d(x+1,y+1,k) = n(count(k),rr);         else             n_3d(x+1,y+1,k) = 0;         end     end end subplot(2,2,k) surf(X,Y,n_3d(:,:,k)) shading interp axis([-(a+0.1E-9)*1e9 (a+0.1E-9)*1e9 -(a+0.1E-9)*1e9 (a+0.1E-9)*1e9 0 1]) xlabel('\it{x} (nm)','fontname','Times New Roman','FontSize',18,'FontWeight','bold'),... ylabel('\it{y} (nm)','fontname','Times New Roman','FontSize',18,'FontWeight','bold'),... zlabel('normalized charge-carrier density (a.u.)','fontname','Times New Roman','FontSize',18,'FontWeight','bold'), end   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% averaging of n %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% n_absolute(1:length(t)) = 0; n2_absolute(1:length(t)) = 0; for itt = 1:length(t)     for irr = 2:length(r)         n_absolute(itt) = n_absolute(itt)+n(itt,irr)*4/3*pi*(r(irr)^3-r(irr-1)^3);         n2_absolute(itt) = n2_absolute(itt)+n2(itt,irr)*4/3*pi*(r(irr)^3-r(irr-1)^3);     end Appendices  162  end   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % plot theoretical data %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% n_absolute_normalized = n_absolute/max(n_absolute); n2_absolute_normalized = n2_absolute/max(n2_absolute); figure, plot(t*1E12,n_absolute_normalized) axis([0 t(length(t))*1E12 0 1]) xlabel('t (ps)'), ylabel('# of charge-carriers (a.u.)')   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % plot experimental data %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% hold on plot(nanoparticl_exp_data(:,1),nanoparticl_exp_data(:,2)) plot(t*1E12,n2_absolute_normalized, 'r') axis([0 t(length(t))*1E12 0 1]) xlabel('t (ps)'), ylabel('# of charge-carriers (a.u.)') hold off      Appendices  163  Appendix G  Photoconductive Terahertz Detection This appendix discusses photoconductive (PC) detection with PC THz detectors made from textured semiconductor materials. Photoconductive THz detectors operate with the THz electric field operating as an external bias. With the coincidence of an ultrafast probe pulse a photocurrent is created. The time-domain excitation response of the semiconductor material lifetime is convolved with the THz electric field pulse. The photocurrent, I(τd), as a function of the time delay, τd, from a PC THz detector follows  dttntEI dTHzd ∫∞∞−−∝ )()()( ττ (89) where ETHz(t) is the THz electric field pulse and n(t) is the charge-carrier density response. The PC THz detector falls into one of two categories [147]. The first category is direct sampling detectors where the charge-carrier lifetime is very short (< 1 ps). Here, n(t) acts like a delta function and the photocurrent is proportional to the THz electric field. The expensive and fabrication intensive low-temperature grown GaAs is often used for these direct sampling detectors [148]. The second category is integrating detectors where the charge-carrier lifetime is long (≫ 1 ps). Here, n(t) acts like a step function and the photocurrent is proportional to the integral of the THz electric field. In a reciprocal fashion, THz electric field is proportional to the time-rate-of-change of the photocurrent. Both semi-insulating GaAs and InP have been shown to be effective PC THz detectors [148, 149]. In such detectors, saturation effects can prevent operation at high probe gating fluences, however, the 20 ps charge-carrier lifetime of the textured InP material of this thesis should minimize this saturation effect.  Appendices  164  Appendix H  MATLAB Script for Terahertz Spectroscopy Analysis Method %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This MATLAB script implements the terahertz spectroscopy analysis method %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Christopher Collier % Integrated Optics Laboratory % The University of British Columbia %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% close all clear clc   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Read in the THz-TDS data from an excel plot with the following three columns: % time, t % reference THz electric field pulse, Eref(t) % sample THz electric field pulse, Esam(t) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% THz_data = xlsread('THz_TDS_exp_data.xlsx');    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Global variables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dt = THz_data(2,1)*1e-12;       % time step between data points [s] d0 = 160e-6;                    % thickness of liquid sample [m] c = 3e8;                        % speed of light in vacuum [m/s] n_hp = 2.1;                     % refractive index of sample holding plate n_sam = 2.1;                    % refractive index of liquid sample   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Fast Fourier Transform (FFT) variables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Tsamp = dt;                     % sampling period [s] Fsamp = 1/dt;                   % Sampling frequency [Hz] Lsamp = length(THz_data(:,1));  % Length of signal tsamp = (0:Lsamp-1)*Tsamp;      % Time vector [s]   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % The FFT is performed and the amplitude % and phase spectra and extracted for Eref(t) % and Esam(t) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Appendices  165  for k = 2:length(THz_data(1,:))   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % FFT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Ysamp(:,k-1) = fft(THz_data(:,k));  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Amplitude spectrum %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% amp2 = abs(Ysamp(:,k-1)/Lsamp); amp1(:,k-1) = amp2(1:Lsamp/2+1); amp1(2:end-1,k-1) = 2*amp1(2:end-1,k-1);   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Phase spectrum %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% phase2(:,k-1) = angle(Ysamp(:,k-1)); phase1(:,k-1) = phase2(1:Lsamp/2+1,k-1); phase1(2:end-1,k-1) = 2*phase1(2:end-1,k-1);   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Plot spectra  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% fsamp = Fsamp*(0:(Lsamp/2))/Lsamp;   figure, plot(fsamp*1e-12,amp1(:,k-1)') title('Single-Sided Amplitude Spectrum of E(t)') xlabel('f (THz)'), ylabel('|E(f)|') figure, plot(fsamp*1e-12,phase1(:,k-1)') title('Single-Sided Phase Spectrum of E(t)') xlabel('f (THz)'), ylabel('phase of E(f)')   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Phase and amplitude spectrum for Eref(t) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if k == 2 Eref_ampl = amp1(:,k-1); Eref_phase = phase1(:,k-1); end    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Phase and amplitude spectrum for Esam(t) Appendices  166  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if k == 3 Esam_ampl = amp1(:,k-1); Esam_phase = phase1(:,k-1); end end   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Dynamic range, DR, of Eref(f) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DR_ref_high = max(abs(Eref_ampl)); N_ref = length(fsamp); DR_ref_low = mean(abs(Eref_ampl(round(N_ref*1/10):round(N_ref*2/10)))); DR_ref_amp = DR_ref_high/DR_ref_low; DR_ref = DR_ref_amp.*abs(Eref_ampl)./max(abs(Eref_ampl)); figure, plot(fsamp*1e-12,DR_ref) title('DR vs. f'), xlabel('f (THz)'), ylabel('DR')   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Refractive index of liquid sample %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% phi_fft = Esam_phase - Eref_phase; n_f_fft = 1 + c.*phi_fft'./fsamp./(2*3.14*d0); figure, plot(fsamp*1e-12, n_f_fft) title('n(f) vs. f'), xlabel('f (THz)'), ylabel('n(f)')   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Absorption coefficient and maximum % measurable absorption coefficient of the  % liquid sample %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% A = abs(Esam_ampl)./abs(Eref_ampl); storage_vector_1 = log(A.*0.25.*(n_sam+n_hp).*(n_sam+n_hp)./n_sam./n_hp); alpha = -1/d0.*storage_vector_1; figure, plot(fsamp*1e-12,alpha/100) title('alpha(f) vs. f'), xlabel('f(THz)'), ylabel('alpha(f) (cm^-1)')   storage_vector_2 = DR_ref.*4.*n_sam.*n_hp./(n_sam+n_hp)./(n_sam+n_hp); alpha_max = 1/d0*log(storage_vector_2); hold on plot(fsamp*1e-12,alpha_max/100, 'r') axis([0 10 0 600]) hold off 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0305861/manifest

Comment

Related Items