Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Brodie, C. Harrison
Doctor of Philosophy - PhD
University of British Columbia
Assembly of free-space terahertz (THz) research instrumentation systems necessitate the use of application specific THz compatible optical components. The development, procurement, and expense of THz compatible optical components can be prohibitive for research stakeholders. Commercial three-dimensional (3D) printing (i.e., additive manufacturing) systems are investigated in this thesis, with regard to filament material selection and component fabrication, to address the accessibility of THz compatible optical components. The availability of emerging 3D printing filament materials increases year over year, prompting a need for literature to keep abreast with material characterisations of absorptive and refractive properties over the THz regime. This literature gap is rectified via a consolidative and comprehensive THz time-domain spectroscopy measurement study performed on twenty-four 3D printing filament materials. Optimal filament materials selected for use in THz compatible optical components are identified, being high impact polystyrene (HIPS) and cyclic olefin copolymer (COC), and are demonstrated as 3D printed THz Bragg structures (interference filters). The potential frequency-domain performance and tuneability of THz Bragg structures, fabricated with a commercial 3D printer, is demonstrated and characterised. The 3D printed THz Bragg structure characterisation is evaluated with finite-difference time-domain electromagnetic simulations and with a free-space THz experimental testbed. The absorptive effects of filament material selection are considered for THz Bragg structures with and without optical path equalization (i.e., responses of THz Bragg structures versus THz Bragg superstructures). The effect of commercial 3D printer Z-axis fabrication resolution is shown for the 3D printed THz Bragg structures. Frequency-domain stop-band metrics are analysed in terms of transmission loss, bandwidth, and frequency placement. Terahertz Bragg structures and superstructures fabricated from COC filament material demonstrate the potential for widespread rapid prototyping of THz compatible optical components.
TERAHERTZ CHARACTERISATIONS AND ANALYSES OF ADDITIVE MANUFACTURING MATERIALS AND STRUCTURES by C. Harrison Brodie B. Eng., University of Guelph, 2017 M.A.Sc., University of Guelph, 2019 A DISSERTATION 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) August 2024 © C. Harrison Brodie, 2024 ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a dissertation entitled: Terahertz Characterisations and Analyses of Additive Manufacturing Materials and Structures submitted by C. Harrison Brodie in partial fulfillment of the requirements of the degree of Doctor of Philosophy. Dr. Christopher Collier, School of Engineering, The University of British Columbia Supervisor Dr. Jonathan Holzman, School of Engineering, The University of British Columbia Supervisory Committee Member Dr. Ian Foulds, School of Engineering, The University of British Columbia Supervisory Committee Member Dr. Rudolf Seethaler, School of Engineering, The University of British Columbia University Examiner Dr. David Cooke, Department of Physics, McGill University External Examiner iii Abstract Assembly of free-space terahertz (THz) research instrumentation systems necessitate the use of application specific THz compatible optical components. The development, procurement, and expense of THz compatible optical components can be prohibitive for research stakeholders. Commercial three-dimensional (3D) printing (i.e., additive manufacturing) systems are investigated in this thesis, with regard to filament material selection and component fabrication, to address the accessibility of THz compatible optical components. The availability of emerging 3D printing filament materials increases year over year, prompting a need for literature to keep abreast with material characterisations of absorptive and refractive properties over the THz regime. This literature gap is rectified via a consolidative and comprehensive THz time-domain spectroscopy measurement study performed on twenty-four 3D printing filament materials. Optimal filament materials selected for use in THz compatible optical components are identified, being high impact polystyrene (HIPS) and cyclic olefin copolymer (COC), and are demonstrated as 3D printed THz Bragg structures (interference filters). The potential frequency-domain performance and tuneability of THz Bragg structures, fabricated with a commercial 3D printer, is demonstrated and characterised. The 3D printed THz Bragg structure characterisation is evaluated with finite-difference time-domain electromagnetic simulations and with a free-space THz experimental testbed. The absorptive effects of filament material selection are considered for THz Bragg structures with and without optical path equalization (i.e., responses of THz Bragg structures versus THz Bragg superstructures). The effect of commercial 3D printer Z-axis fabrication resolution is shown for the 3D printed THz Bragg structures. Frequency-domain stop-band metrics are analysed in terms of transmission loss, bandwidth, and frequency placement. Terahertz Bragg structures and superstructures fabricated from COC filament material demonstrate the potential for widespread rapid prototyping of THz compatible optical components. iv Lay Summary Optical systems frequently utilise custom optical components. Development of custom components that are compatible with (long) terahertz wavelengths can be prohibitive. To address this, the feasibility of three-dimensional printing technology is investigated for rapid prototyping of terahertz custom components. Three-dimensional printing technology has become readily available, with a variety of plastic filament materials, and is as capable of printing structures with feature sizes that appropriate for terahertz wavelengths. This thesis provides an update to the current literature by evaluating the myriad of available plastic filament materials for compatibility with terahertz wavelengths. Two ideal filament materials are identified for terahertz compatibility and are utilised in the fabrication of terahertz components, realised as terahertz Bragg structures. The performance of terahertz Bragg structures are evaluated in terms of three-dimensional printing fabrication resolution. Overall, the contributions of this work enable rapid scientific developments of terahertz technology. v Preface This thesis is based upon two published journal articles ([J5] and [J8] relating to Chapter 5 and Chapter 4, respectively), one accepted journal article ([J1] relating to Chapter 6), one invited conference proceeding ([C1] relating to Chapter 6), and two other conference proceedings ([C2] and [C4] relating to Chapter 5 and Chapter 4, respectively). A comprehensive publication list is included below, with author contribution details included for the publications directly related to the thesis chapters. Generative AI was not used for any aspects of this work. Journal Articles (Accepted and Published) [J1] C. H. Brodie, I. Spotts, and C. M. Collier, "Terahertz components by additive manufacturing: Material and fabrication characterizations realized through Bragg structures," IEEE Trans. Terahertz Sci. Technol. (2024), accepted. C. H. Brodie performed the experiments, analysis, and wrote the manuscript. C. H. Brodie revised the manuscript based on reviewer feedback. I. Spotts assisted with the experiments and manuscript preparation. C. M. Collier provided guidance, faculty supervision, and contributed to the writing of the manuscript. [J2] I. Spotts, C. H. Brodie, and C. M. Collier, "Integration of liquid crystal optical delay and mechanical stage optical delay for measurement of ultrafast autocorrelations and terahertz pulses," Meas. Sci. Technol. 35, 075208 (2024). [J3] S. Lepard, I. Spotts, C. H. Brodie, C. A. Leclerc, R. Eswar, H. Li, and C. M. Collier, "A digital microfluidic chip with programmable open system actuation and enhanced optical annealing with near‐infrared light," Eng. Reports 6, 1–12 (2024). [J4] R. Eswar, C. H. Brodie, H. Reguigui, and C. M. Collier, "An integrated and automated digital microfluidic device for dairy milk droplet actuation," Microsyst. Technol. 29, 1389–1398 (2023). vi [J5] C. H. Brodie, I. Spotts, and C. M. Collier, "THz Bragg structures fabricated with additive manufacturing," Appl. Opt. 62, 4465 (2023). C. H. Brodie performed the experiments, analysis, and wrote the manuscript. C. H. Brodie revised the manuscript based on reviewer feedback. I. Spotts assisted with the experiments and manuscript preparation. C. M. Collier provided guidance, faculty supervision, and contributed to the writing of the manuscript. [J6] I. Spotts, C. H. Brodie, D. Saeedkia, S. A. Gadsden, and C. M. Collier, "Improved Terahertz Time-Domain Spectroscopy via the Extended Kalman Filter," IEEE J. Sel. Top. Quantum Electron. 29, 1–12 (2023). [J7] R. Eswar, C. H. Brodie, and C. M. Collier, "Lock-In Amplified Fluorescence Spectroscopy in a Digital Microfluidic Configuration for Antibiotic Detection of Ciprofloxacin in Milk," J. Microelectromechanical Syst. 31, 927–934 (2022). [J8] C. H. Brodie, I. Spotts, H. Reguigui, C. A. Leclerc, M. E. Mitchell, J. F. Holzman, and C. M. Collier, "Comprehensive study of 3D printing materials over the terahertz regime: absorption coefficient and refractive index characterizations," Opt. Mater. Express 12, 3379 (2022). C. H. Brodie performed the experiments, analysis, and wrote the manuscript. C. H. Brodie revised the manuscript based on reviewer feedback. I. Spotts, H. reguigui, C. A. Leclerc, assisted with the experiments and manuscript preparation. M.E. Mitchell and J. F. Holzman assisted with the time-domain spectroscopy analysis and manuscript preparation. C. M. Collier provided guidance, faculty supervision, and contributed to the writing of the manuscript. [J9] I. Spotts, C. H. Brodie, C. A. Leclerc, S. A. Gadsden, M. Al-Shabi, and C. M. Collier, "Extended Kalman filter and extended sliding innovation filter in terahertz spectral acquisition," Opt. Contin. 1, 1003 (2022). vii [J10] C. H. Brodie and C. M. Collier, "Single-Point Detection Architecture via Liquid Crystal Modulation for Hyperspectral Imaging Systems," IEEE Access 8, 185012–185020 (2020). [J11] I. Spotts, C. H. Brodie, S. A. Gadsden, M. Al-Shabi, and C. M. Collier, "Comparison of nonlinear filtering techniques for photonic systems with blackbody radiation," Appl. Opt. 59, 9303 (2020). [J12] M. Del Rosso, C. H. Brodie, S. Ramalingam, D. M. Cabral, E. Pensini, A. Singh, and C. M. Collier, "Characterisation of graphene electrodes for microsystems and microfluidic devices," Sci. Rep. 9, 5773 (2019). [J13] C. H. Brodie, J. Devasagayam, and C. M. Collier, "A Hyperspectral Imaging Instrumentation Architecture Based on Accessible Optical Disc Technology and Frequency-Domain Analyses," IEEE Trans. Instrum. Meas. 68, 2531–2538 (2019). Conferences (Proceedings and Presentations) [C1] C. M. Collier, C. H. Brodie, and I. Spotts, "Terahertz components through additive manufacturing," Proceedings of Photonics North, Montreal, Canada, June, 2023. (Invited) C. H. Brodie performed the experiments, analysis, and wrote the manuscript. I. Spotts assisted with the experiments and manuscript preparation. C. M. Collier provided guidance, faculty supervision, and contributed to the writing of the manuscript. [C2] C. H. Brodie, I. Spotts, and C. M. Collier, "Far-infrared Bragg device," Proceedings of Photonics North, Montreal, Canada, June, 2023. C. H. Brodie performed the experiments, analysis, and wrote the manuscript. I. Spotts assisted with the experiments and manuscript preparation. C. M. Collier provided guidance, faculty supervision, and contributed to the writing of the manuscript. viii [C3] I. Spotts, C. H. Brodie, and C. M. Collier, "Liquid crystal assisted optical delay," Proceedings of Photonics North, Montreal, Canada, June, 2023. [C4] C. H. Brodie, I. Spotts, H. Reguigui, C. A. Leclerc, and C. M. Collier, "Terahertz time-domain spectroscopy of 3D printed materials," Proceedings of Photonics North, Niagara Falls, Canada, May, 2022. C. H. Brodie performed the experiments, analysis, and wrote the manuscript. I. Spotts, H. Reguigui, and C. A. Leclerc assisted with the experiments and manuscript preparation. C. M. Collier provided guidance, faculty supervision, and contributed to the writing of the manuscript. [C5] I. Spotts, C. H. Brodie, C. A. Leclerc, N. Jahed, D. Saeedkia, S. A. Gadsden, M. Al-Shabi, and C. M. Collier, " Terahertz extended Kalman filtering method," Proceedings of Photonics North, Niagara Falls, Canada, May, 2022. [C6] C. H. Brodie, and C. M. Collier, "Spatial light modulation and optical mixing for snapshot hyperspectral imaging architectures," Proceedings of SPIE Optics + Photonics, San Diego, USA, August, 2021. [C7] R. Eswar, C. H. Brodie, and C. M. Collier, "A scalable digital microfluidic platform for automation of onsite testing of dairy samples," Proceedings of SPIE Optics + Photonics, San Diego, USA, August, 2021. [C8] I. Spotts, C. H. Brodie, S. A. Gadsden, M. Al-Shabi, and C. M. Collier, "A comparison of nonlinear filtering methods for blackbody radiation applications in photonics," Proceedings of SPIE Optics + Photonics, San Diego, USA, August, 2021. [C9] C. H. Brodie, J. Devasagayam, and C. M. Collier, "Lock-in optical instrumentation for snapshot hyperspectral imaging," Proceedings of SPIE Photonics West, San Francisco, USA, February, 2020. ix [C10] M. Del Rosso, C. H. Brodie, and C. M. Collier, "Graphene material characterisation for optofluidic applications," Proceedings of SPIE Photonics West, San Francisco, USA, February, 2020. [C11] C. H. Brodie, J. Devasagayam, and C. M. Collier, "Snapshot hyperspectral imaging for food safety applications," Presentation at CSBE/SCGAB Annual General Meeting and Technical Conference, Guelph, Canada, July, 2018. [C12] C. H. Brodie, J. Devasagayam, and C. M. Collier, "Accessible snapshot hyperspectral imaging architectures," Presentation at Photonics North, Montreal, Canada, June, 2018. x Table of Contents Abstract ....................................................................................................................................................... iii Lay Summary ............................................................................................................................................. iv Preface .......................................................................................................................................................... v Table of Contents ........................................................................................................................................ x List of Tables ............................................................................................................................................ xiv List of Figures ............................................................................................................................................ xv Acknowledgements ................................................................................................................................ xxiv Chapter 1: Introduction ............................................................................................................................. 1 1.1 Terahertz Technologies ............................................................................................................. 1 1.2 Additive Manufacturing Technologies ...................................................................................... 3 1.3 Overview of Past Developments in Terahertz and Additive Manufacturing Technologies ...... 4 1.4 Thesis Scope .............................................................................................................................. 4 1.5 Thesis Outline............................................................................................................................ 7 Chapter 2: Literature Review .................................................................................................................... 8 2.1 Literature on Terahertz Characterisations of Additive Manufacturing based Fabrication Materials ............................................................................................................................................... 8 2.1.1 Terahertz Spectroscopy of Polylactic Acid Filament Materials ......................................... 8 2.1.2 Terahertz Spectroscopy of Alternatives to Polylactic Acid Filament Materials ............... 10 2.1.3 Terahertz Spectroscopy of Flexible Filament Materials ................................................... 10 2.1.4 Terahertz Spectroscopy of Dissolvable Support Filament Materials ................................ 10 2.1.5 Terahertz Spectroscopy of Nylon Filament Materials ...................................................... 11 2.1.6 Terahertz Spectroscopy of Packaging Thermoplastic Filament Materials ....................... 11 2.1.7 Terahertz Spectroscopy of Non-standard Filament Materials .......................................... 11 2.1.8 Thesis Contributions to Terahertz Spectroscopy of Additive Manufacturing Filament Materials ........................................................................................................................................ 12 xi 2.2 Literature on Terahertz Devices Fabricated with Additive Manufacturing............................. 13 2.2.1 Terahertz Lenses Fabricated with Additive Manufacturing ............................................. 14 2.2.2 Terahertz Polarisation Optics and Beam Splitters Fabricated with Additive Manufacturing ................................................................................................................................ 14 2.2.3 Terahertz Microfluidic Devices Fabricated with Additive Manufacturing ....................... 15 2.2.4 Terahertz Diffractive Devices Fabricated with Additive Manufacturing ......................... 15 2.2.5 Terahertz Solid Waveguides Fabricated with Additive Manufacturing ........................... 16 2.2.6 Terahertz Hollow Core Waveguides Fabricated with Additive Manufacturing ............... 16 2.2.7 Context and Relevance to Thesis ...................................................................................... 17 2.3 Literature on Bragg Structures Fabricated with Additive Manufacturing ............................... 17 2.3.1 Terahertz Hollow Core Waveguides with Bragg features Fabricated with Additive Manufacturing ................................................................................................................................ 19 2.3.2 Terahertz Photonic Crystal Devices .................................................................................. 20 2.3.3 Bragg Structures for Terahertz Waves Fabricated with Additive Manufacturing ............ 21 2.3.4 Applications of Terahertz Bragg Structure Fabricated with Additive Manufacturing ..... 22 2.3.5 Context and Relevance to Thesis ...................................................................................... 22 Chapter 3: Fundamental Concepts ......................................................................................................... 24 3.1 Relevant Electromagnetic Theory ........................................................................................... 24 3.2 Terahertz Operation ................................................................................................................. 25 3.3 Terahertz Emission .................................................................................................................. 27 3.3.1 Photoconductive Emission ................................................................................................ 27 3.3.2 Electro-Optic Emission ..................................................................................................... 30 3.4 Terahertz Detection ................................................................................................................. 32 3.4.1 Photoconductive Detection ............................................................................................... 33 3.4.2 Electro-Optic Detection .................................................................................................... 35 3.5 Terahertz Measurement and Terahertz Spectroscopy ............................................................. 38 xii 3.5.1 Terahertz Time-Domain Spectroscopy Measurements on Water Vapour ........................ 42 3.6 Finite-Difference Time-Domain Theory ................................................................................. 48 3.7 Chapter Conclusions ................................................................................................................ 52 Chapter 4: A Comprehensive Study of Three-Dimensional Printing Materials over the Terahertz Regime: Absorption Coefficient and Refractive Index Characterisations .......................................... 53 4.1 Background ............................................................................................................................. 53 4.2 Revisiting of Experimental Terahertz Method and Visualisation of Terahertz Time-Domain Spectroscopy System Configuration .................................................................................................. 55 4.3 The Terahertz Time-Domain Spectroscopy Method ............................................................... 57 4.4 Polylactic Acid Filament Materials ......................................................................................... 59 4.5 Common Alternatives to PLA Filament Materials .................................................................. 63 4.6 Flexible Filament Materials ..................................................................................................... 66 4.7 Dissolvable Support Filament Materials ................................................................................. 66 4.8 Nylon Filaments Materials ...................................................................................................... 68 4.9 Packaging Thermoplastic Filament Materials ......................................................................... 68 4.10 Non-Standard Filament Materials ........................................................................................... 70 4.11 Sample Images of Three-Dimensional Printed Materials........................................................ 76 4.12 Summary of Absorptive and Refractive Properties and Product Details on Three-Dimensional Printed Materials ................................................................................................................................ 78 4.13 Absorption Coefficient, Refractive Index, and Loss Tangent Analysis of Three-Dimensional Printed Materials ................................................................................................................................ 81 4.14 Chapter Conclusions ................................................................................................................ 86 Chapter 5: Terahertz Bragg Structures Fabricated with Additive Manufacturing ........................... 87 5.1 Background ............................................................................................................................. 87 5.2 Terahertz Time-Domain Spectroscopy of High Impact Polystyrene Filament Material ......... 88 5.3 Terahertz Bragg Structure Geometry ...................................................................................... 90 xiii 5.4 Operation of Finite-Difference Time-Domain Electromagnetic Simulation ........................... 92 5.5 Terahertz Experimental Testbed for Characterisation of Three-Dimensional Printed Bragg Structures ............................................................................................................................................ 95 5.6 Terahertz Bragg Structure Operation ...................................................................................... 95 5.7 Material Absorption Considerations...................................................................................... 104 5.8 Comparison to Other Techniques .......................................................................................... 106 5.9 Chapter Conclusions .............................................................................................................. 106 Chapter 6: Terahertz Components by Additive Manufacturing: Material and Fabrication Characterisations Realised Through Bragg Structures ...................................................................... 108 6.1 Background ........................................................................................................................... 108 6.2 Terahertz Time-Domain Spectroscopy of High Impact Polystyrene and Cyclic Olefin Copolymer Filament Materials ......................................................................................................... 111 6.3 Terahertz Bragg Superstructure Geometry ............................................................................ 114 6.4 Terahertz Bragg Superstructure Operation ........................................................................... 114 6.5 Theoretical Finite-Difference Time-Domain Simulation ..................................................... 118 6.6 High Impact Polystyrene Bragg Superstructure Experimental Results ................................. 120 6.7 Cyclic Olefin Copolymer Bragg Superstructure Experimental Results ................................ 123 6.8 Effect of Printing Resolution ................................................................................................. 124 6.9 Chapter Conclusions .............................................................................................................. 134 Chapter 7: Thesis Contributions and Future Work ............................................................................ 135 7.1 Summary of Thesis Contributions ......................................................................................... 135 7.2 Future Work .......................................................................................................................... 137 Bibliography ............................................................................................................................................ 138 Appendices ............................................................................................................................................... 160 Appendix A ...................................................................................................................................... 160 Appendix B ...................................................................................................................................... 165 xiv List of Tables Table 2.1.1 Terahertz Characterisation Parameters of Materials Used in Additive Manufacturing ............. 9 Table 3.5.1.1 Nominal Water Molecule Absorption Frequencies for HITRAN versus THz-TDS experimental data. ...................................................................................................................................... 47 Table 4.12.1 Summary of absorption coefficient, refractive index, maximum permissible frequency, minimum and maximum measured THz frequency, and measured THz bandwidth .................................. 79 Table 4.12.2 Summary of filament material information. .......................................................................... 80 Table 5.6.1 Dimensions and properties of the terahertz Bragg structures. ................................................. 97 Table 6.5.1 Terahertz Bragg superstructure; results and experimental parameters. ................................. 118 Table 6.8.1 Terahertz Bragg structure, fabricated with high impact polystyrene filament material; results and experimental parameters. ................................................................................................................... 128 Table 6.8.2 Terahertz Bragg structure, fabricated with cyclic olefin copolymer filament material; results and experimental parameters. ................................................................................................................... 130 xv List of Figures Figure 1.1.1 The electromagnetic spectrum showing the main frequency, f, and wavelength, λ, regimes, as defined in this thesis. The main regimes of electromagnetic radiation can be defined here as categorical regimes and are described in terms of wavelength and frequency. These regimes are as follows. Regime 1: Infrared (λ = 1-30 μm, f = 10-300 THz), Visible Light (λ = 0.4-1 μm, f = 300-750 THz), Ultraviolet (λ = 0.01-0.4 μm, f = 750-3×1016 Hz), X-ray (λ = 0.01-10 nm, f = 3×1016-3×1019 Hz), Gamma Radiation (λ < 0.01 nm, f > 3×1019 Hz). Regime 2: Microwave (λ = 3-300 mm, f = 1-100 GHz), Radio (λ > 300 mm, f < 1 GHz). Regime 3: Terahertz Radiation (λ = 30-3000 μm, f = 0.1-10 THz). Regime 3 is the focus of this thesis. ............................................................................................................................................................ 2 Figure 1.3.1 Publication records per year, accessed via the EngineeringVillage (Elsevier Inc.) search engine, with results aggregated from Compendex, GEOBASE, and GeoRef databases on September 10, 2023. The legend indicates the search terms used, with subfigure (b) showing an expanded view of subfigure (a). .... 5 Figure 3.3.1.1 The photoconductive emitter with a laser pulse generating a terahertz pulse. .................... 27 Figure 3.3.1.2 The (a) current density, (b) terahertz electric field vs. time, and (c) terahertz electric field magnitude vs. frequency are shown for a hypothetic photoconductive terahertz emitter based on a semiconductor with charge-carrier lifetime of approximately 20 ps. ........................................................ 29 Figure 3.3.2.1 Electro-optic terahertz emission has a laser pulse interacting with an electro-optic emitter to produce a terahertz pulse. .......................................................................................................................... 31 Figure 3.4.1.1 The photoconductive detector process is shown. The terahertz pulse is shown in grey and the optical probe pulse is shown in red. ........................................................................................................... 34 Figure 3.4.2.1 The electro-optic terahertz detection process. The terahertz pulse is shown in grey and the optical probe pulse is shown in red. ........................................................................................................... 36 Figure 3.5.1 A terahertz time-domain spectroscopy system. ..................................................................... 40 Figure 3.5.1.1 (a) a measured terahertz pulse vs. time and (b) the same terahertz pulse vs. frequency. This is for a vapour free environment. ............................................................................................................... 44 xvi Figure 3.5.1.2 (a) a measured terahertz pulse vs. time and (b) the same terahertz pulse vs. frequency. This is for a vapour-present environment. ......................................................................................................... 45 Figure 3.5.1.3 The dynamic range of the measurement is shown as a black curve and the noise floor is shown as a yellow-dashed line. .................................................................................................................. 46 Figure 3.5.1.4 The absorption coefficient of water vapour (α) is shown in blue and the maximum measurement (αmax) is shown in red. .......................................................................................................... 47 Figure 3.5.1.5 The absorption coefficient is shown for a water vapour sample. Characteristic absorption peaks are indicated with cardinal lettering A through G. ........................................................................... 48 Figure 3.6.1 A depiction of a Yee grid scheme for a one-dimensional finite-difference time-domain electromagnetic simulation. ........................................................................................................................ 50 Figure 4.2.1 (a) A three-dimensional model of the terahertz time-domain spectroscopy setup is shown upon an optical table. (b) A top-view of the three-dimensional model of the terahertz time-domain spectroscopy setup is shown. The abbreviation labels are as follows: pump laser beam (Pump), probe laser beam (Probe), microscope objective (MO), photoconductive emitter (PE), parabolic mirror (PM), THz beam path (THz), three-dimensional printed sample material (Sample), pellicle beam splitter (BSpel), electro-optic crystal (EO), lens (L), mirror (M), quarter wave plate (QW), polarisation beam splitter (BSpol), and balanced silicon photodiode (PDsi). ....................................................................................................................................... 56 Figure 4.3.1 The absorption coefficient (solid curves) and alpha max. (dotted curves) are each shown for polylactic acid (PLA) filament material with approximate sample thicknesses of 700 µm (blue) and 1400 µm (red). ..................................................................................................................................................... 59 Figure 4.4.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample materials: (a) polylactic acid (PLA) filament material, (b) PLA filament material with embedded copper (PLA Cu) particles, (c) PLA filament material with embedded iron (PLA Fe) particles, and (d) PLA filament material with embedded tungsten (PLA W) particles. ....................... 60 xvii Figure 4.4.2 The absorption coefficient and refractive index are shown for the approximate sample thicknesses of 300 µm, 700 µm, and 1400 µm for the following sample filament materials: (a) polylactic acid filament material embedded with pine wood particles (PLA Pine) and (b) PLA filament material embedded with conductive particles (PLA Cond.). .................................................................................... 62 Figure 4.5.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lightest respective colour), 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample materials: (a) polyethylene terephthalate glycol (PETG) filament material, (b) acrylonitrile styrene acrylate (ASA) filament material, (c) acrylonitrile butadiene styrene (ABS) filament material, and (d) polycarbonate co-polyester (PC CPE) filament material. ........................................................................................................................................ 64 Figure 4.6.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample materials: (a) thermoplastic elastomer filament material (TPE) and (b) thermoplastic polyurethane filament material (TPU). ................................................................................ 65 Figure 4.7.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample materials: (a) polyvinyl alcohol (PVA) filament material and (b) high impact polystyrene (HIPS) filament material. ............................................................................................ 67 Figure 4.8.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample materials: (a) Nylon 910 filament material and (b) Nylon 230 filament material. ...................................................................................................................................................... 69 Figure 4.9.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lightest respective colour), 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample filament materials: (a) polypropylene (PP) filament material and (b) high density polyethylene (HDPE) filament material. ....... 71 xviii Figure 4.10.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample filament materials: (a) low temperature polycaprolactone (LT PCL) filament material and (b) polyvinyl butyral (PVB) filament material. ....................................................... 72 Figure 4.10.2 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample materials: polymethylmethacrylate (PMMA) filament material. .................................................................................................................................................................... 74 Figure 4.10.3 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lightest respective colour), 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample materials: (a) photopolymer liquid resin for stereolithography printers (i.e., SLA) and (b) polyetherimide (PEI) filament material. .... 75 Figure 4.10.4 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample materials: cyclic olefin copolymer (COC) filament material. .................................................................................................................................................................... 76 Figure 4.11.1 Images of the three-dimensional printed material samples are shown. ................................ 77 Figure 4.13.1 Absorption coefficient versus loss tangent is shown ............................................................ 82 Figure 4.13.2 Refractive index versus loss tangent is shown. .................................................................... 83 Figure 4.13.3 Extinction coefficient versus loss tangent is shown. ............................................................ 84 Figure 5.2.1 The absorption coefficient (blue) and refractive index of (yellow) are shown for the high impact polystyrene (HIPS) filament material used in the three-dimensional printing of the experimental terahertz Bragg structure. The absorption coefficient (red) and refractive index (black) of acrylonitrile butadiene styrene (ABS) filament material is displayed. A trendline (not shown), approximating the absorption coefficient (blue) of high impact polystyrene filament material, over the 0.5 THz to 1.2 THz spectrum, is established with a slope of 4.5 cm-1/THz. ................................................................................................... 89 xix Figure 5.3.1 An overview of the terahertz Bragg structures are shown. (a) The N = 6 material layer terahertz Bragg structure is shown for a three-dimensional (left) and a top-view (right). (b) An enlarged top-view image of the terahertz Bragg structure is shown, with high impact polystyrene material layers and air gap thicknesses with refractive indices being d2, n2, and d1, n1, respectively. (c) The N = 18 material layer THz Bragg structure is shown for a three-dimensional view. ............................................................................ 91 Figure 5.4.1 A simplified example of the terahertz Bragg structure is theoretically investigated with a finite-difference time-domain simulation as shown for multiple time intervals. (a) A Gaussian electric field pulse (blue) is propagated through free-space toward three material layers of high impact polystyrene filament material (yellow) surrounding two air gap layers. (b-c) The Gaussian electric field pulse is propagating through the high impact polystyrene layers. (d) Sufficient time has elapsed for all transmitted and reflected electric field energy to be recorded. (e) The theoretical frequency-domain spectrum of the natural logarithm intensity ratio is shown having frequency rejection at four distinct frequency bands. ............................... 94 Figure 5.5.1 A graphical overview of the terahertz experimental testbed is shown with the following functional components: microscope objective (MO), photoconductive terahertz emitter (PE), parabolic mirror (PM), terahertz beam path (THz), pellicle beam splitter (BSpel), electro-optic crystal (EO), quarter wave plate (QW), polarisation beam splitter (BSpol), balanced silicon photodiode (PDsi), mirror (M), lens (L), pulsed laser pump beam (Pump), and pulsed laser probe beam (Probe). The terahertz Bragg structure is shown within the optical axis of the terahertz beam path (THz) and shown as an expanded inset image (outlined in blue). ........................................................................................................................................ 96 Figure 5.6.1 (a) The theoretical natural logarithm intensity ratio of the N = 6 layer terahertz Bragg structure is shown in red for the wide frequency-domain spacing. (b) The theoretical natural logarithm intensity ratio of the N = 18 layer terahertz Bragg structure is shown in red for the wide frequency-domain spacing. (c) The experimental characterisation of the terahertz Bragg structure with wide frequency-domain spacing is presented here for both N = 6 layer (yellow) and N = 18 layer (blue) variations. ...................................... 99 xx Figure 5.6.2 The incident electric field (red), Ei(t), and transmitted electric field (blue), Et(t), time-domain data is presented for the (a) N = 6 and (b) N = 18 layer terahertz Bragg structures corresponding to wide frequency-domain spacing, F = 0.20 THz. ............................................................................................. 100 Figure 5.6.3 (a) The theoretical natural logarithm intensity ratio of the N = 6 layer terahertz Bragg structure is shown in red for the narrow frequency-domain spacing. (b) The theoretical natural logarithm intensity ratio of the N = 18 layer terahertz Bragg structure is shown in red for the narrow frequency-domain spacing. (c) The experimental characterisation of the terahertz Bragg structure with narrow frequency-domain spacing is presented here for both N = 6 layer (yellow) and N = 18 layer (blue) variations. .................... 102 Figure 5.6.4 The incident electric field (red), Ei(t), and transmitted electric field (blue), Et(t), time-domain data is presented for the (a) N = 6 and (b) N = 18 layer terahertz Bragg structures corresponding to narrow frequency-domain spacing, F = 0.17 THz. ............................................................................................. 103 Figure 5.7.1 (a) The measured incident (red) and transmitted (blue) terahertz frequency spectra are shown, for the N = 18 layer terahertz Bragg structure, with alternating layer dimensions d1 = 750 µm and d2 = 500 µm. (b) The natural logarithm intensity ratio (blue), corresponding to the above-mentioned terahertz Bragg structure, is presented here. A linear trendline approximating the absorption of HIPS filament material, for a sum total material thickness equivalent to this terahertz Bragg structure, is indicated as a dashed line. The maximum detectable natural logarithm intensity ratio is displayed in red. .............................................. 105 Figure 6.2.1 The terahertz time-domain spectroscopy results for high impact polystyrene (HIPS) filament material (black) and cyclic olefin copolymer (COC) filament material (grey) are shown for (a) open air conditions and (b) nitrogen purge conditions. The corresponding absorption coefficient, α, and refractive index, n, are represented as, striated curves, and solid curves, respectively. ............................................ 112 Figure 6.2.2 A 3D view of the THz experimental testbed is shown with components: microscope objective (MO), photoconductive terahertz emitter (PE), parabolic mirror (PM), terahertz beam path (THz), pellicle beam splitter (BSpel), electro-optic crystal (EO), quarter wave plate (QW), polarisation beam splitter (BSpol), balanced silicon photodiode (PDsi), mirror (M), lens (L). The pump beam (Pump) and probe beam (Probe), shown in red, originate from a 780 nm 100 fs pulsed laser (not shown). The terahertz Bragg superstructure xxi (Bragg Device) is shown within the optical axis of the terahertz beam path (THz) and shown as an expanded inset image (outlined in green). The terahertz Bragg structure, which can replace the terahertz Bragg superstructure, is shown as an inset image (outlined in blue). .................................................................. 113 Figure 6.3.1 Overview images of the geometry and function of terahertz Bragg superstructure is presented. (a) The terahertz Bragg superstructure is represented as a three-dimensional view, with corresponding incident (blue) and transmitted (red) THz electric field pulses, being ETHz,INC, and ETHz,TRN, respectively. (b) A top-view representation of the terahertz Bragg superstructure geometry is shown for air, n1, and material, n2, interfaces having distances, d1, and d2, respectively. ........................................................................... 115 Figure 6.4.1 The experimental time-domain results of the terahertz Bragg superstructure, fabricated from cyclic olefin copolymer filament material, are shown for the design case corresponding to narrow Fmajor and narrow Fminor frequency periodicities in the terahertz spectrum. The time-domain experimental results are represented for both incident (blue), and transmitted (red), terahertz electric field pulses for: (a) 400 picosecond time scale, and (b) 100 picosecond timescale. Shown in (c) and (d) are FDTD time-domain results. ....................................................................................................................................................... 116 Figure 6.4.2 An illustrative depiction of the theoretical natural logarithm intensity ratio for the terahertz Bragg superstructure is shown as a function of frequency. The frequency-domain features of interest, being the wide and narrow frequency peak spacing's, are represented as ∆Fmajor and ∆Fminor, respectively. ...... 117 Figure 6.5.1 The theoretical results of the finite-difference time-domain electromagnetic simulation of an ideal (lossless) terahertz Bragg superstructure is shown for three frequency designs. The theoretical natural logarithm intensity ratio is displayed for a terahertz Bragg superstructure having (a) narrow ∆Fmajor and narrow ∆Fminor, (b) wide ∆Fmajor and narrow ∆Fminor, (c) and narrow ∆Fmajor and wide ∆Fminor. ............... 119 Figure 6.6.1 The experimental results of the terahertz Bragg superstructure, fabricated from lossy high impact polystyrene filament material, is shown for three frequency designs. The natural logarithm intensity ratio is displayed for a high impact polystyrene terahertz Bragg superstructure having (a) narrow ∆Fmajor and narrow ∆Fminor, (b) wide ∆Fmajor and narrow ∆Fminor, (c) and narrow ∆Fmajor and wide ∆Fminor. ......... 121 xxii Figure 6.7.1 The experimental results of the terahertz Bragg superstructure, fabricated from cyclic olefin copolymer filament material, is shown for three frequency designs. The natural logarithm intensity ratio is displayed for a cyclic olefin copolymer terahertz Bragg superstructure having (a) narrow ∆Fmajor and narrow ∆Fminor, (b) wide ∆Fmajor and narrow ∆Fminor, (c) and narrow ∆Fmajor and wide ∆Fminor. ............................ 122 Figure 6.8.1 The experimental results of the terahertz Bragg structure, fabricated with high impact polystyrene filament material, are shown. The terahertz response (blue) is displayed along with the maximum measurable value (red), for each corresponding fabrication pitch resolution, dres.: 50 µm, 100 µm, 150 µm, 200 µm, 250 µm, 300 µm, 350 µm, and 400 µm. A SEM image showing the terahertz Bragg structure fabrication pitch resolution is shown. Each inset image was taken at the same SEM magnification and each image is a 1,000 µm (vertical image height) by 1,000 µm (horizontal image width) for overall 1 mm2 area. The grey region of the terahertz spectrum indicates the frequency regime equal to and above the resolution frequency, Fres. ......................................................................................................................... 127 Figure 6.8.2 The experimental results of the terahertz Bragg structure, fabricated with cyclic olefin copolymer filament material, are shown. The terahertz response (blue) is displayed along with the maximum measurable value (red), for each corresponding fabrication pitch resolution, dres.: 50 µm, 100 µm, 150 µm, 200 µm, 250 µm, 300 µm, 350 µm, and 400 µm. A SEM image showing the maximum and minimum terahertz Bragg structure fabrication pitch resolution is shown. Each inset image was taken at the same SEM magnification and each image is a 1,000 µm (vertical image height) by 1,000 µm (horizontal image width) for overall 1 mm2 area. The grey region of the terahertz spectrum indicates the frequency regime equal to and above the resolution frequency, Fres. ........................................................................ 129 Figure 6.8.3 Three potential Bragg structures and Bragg superstructures, with N material layers, are evaluated for (a) the estimated print time versus printing resolution, and (b) the estimated print time versus the resolution frequency, Fres. .................................................................................................................. 132 Figure 6.8.4 Three potential Bragg structures and Bragg superstructures, with N material layers, are evaluated for (a) the estimated print time versus printing resolution, and (b) the estimated print time versus the resolution frequency, Fres. ....................................................................................................................133 xxiii Figure A.1 (a) The frequency-domain result of a 1D FDTD electromagnetic simulation modeling a Bragg superstructure comprised of HIPS material is shown. (b) The experimental frequency-domain result of a Bragg superstructure fabricated from HIPS filament material is shown. ....................................................161 Figure A.2 (a) The frequency-domain result of a 1D FDTD electromagnetic simulation modeling a Bragg superstructure comprised of COC material is shown. (b) The experimental frequency-domain result of a Bragg superstructure fabricated from COC filament material is shown. ....................................................162 Figure A.3 The frequency-domain result of a 1D FDTD electromagnetic simulation modeling a Bragg superstructure for an ideal case is shown in terms of (a) transmittance, (b) reflectance, and (c) loss. .......163 Figure A.4 The frequency-domain result of a 1D FDTD electromagnetic simulation modeling a Bragg superstructure comprised of HIPS material is shown in terms of (a) transmittance, (b) reflectance, and (c) loss. ............................................................................................................................................................164 Figure B.1 A front view representation of the THz Bragg superstructure is shown. ...................................165 xxiv Acknowledgements I would like to extend my sincere gratitude to my supervisor, Dr. Christopher Collier. Thank you for your excellent guidance and dedicated research support. You have made a significant impact on my education and I am truly thankful for your academic mentorship. Thank you to Dr. Jonathan Holzman and Dr. Ian Foulds for serving as the Doctoral Committee Members. Thank you to Dr. Rudolf Seethaler for your willingness to serve as the University Examiner. Thank you to Dr. David Cooke for your willingness to serve as the External Examiner. It’s been my great privilege to have worked alongside an exceptional group of students in the Collier Research Group at UBC. Thank you to the following students (past and present): Isaac Spotts, Camille Leclerc, Seth Lowry, Rahul Eswar, Michelle Del Rosso, Jasen Devasagayam, Shravani Prasad, Vikram Prasad, Abdulla AlSawalhi, Sean Worthington, Malley Richardson, James Flood, and Chris Ty. Thank you Isaac Spotts for being a great friend and research collaborator. Thank you to Dr. Holzman and the Integrated Optics Laboratory students for your research collaborations and friendships. Thank you: Michael Mitchell, Alexander MacGillivray, Ahmed Nasr, Alexis Guidi, Matthias Jenne, and Ayush Madhan-Sohini. Thank you to my loving parents, Donna and Keith. I am grateful for your support and encouragement throughout my academic journey. I would like to acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada, the SPIE International Society for Optics and Photonics, and the Walter C. Sumner Foundation.1 Chapter 1: Introduction This thesis provides an exploration of terahertz (THz) components that are fabricated with a three-dimensional (3D) printer. An introduction is provided here in Chapter 1. Relative literature is discussed in Chapter 2. The underlying fundamental knowledge is shown in Chapter 3. Three-dimensional printed materials are characterised in Chapter 4. Terahertz components, being THz Bragg structures, are made, tested, and compared to theoretical results in Chapter 5. The effects of 3D printing resolution and underlying material absorption are considered for such THz Bragg structures and superstructures in Chapter 6. Concluding remarks are made in Chapter 7. 1.1 Terahertz Technologies Terahertz radiation was traditionally an unreachable region on the electromagnetic spectrum. (The electromagnetic spectrum is shown in Figure 1.1.1.) However, since the mid-1980s, scientists and engineers have been able to produce and detect THz radiation. This technological advancement largely arose due to the development of ultrafast pulsed lasers. As THz radiation was traditionally difficult to generate with electronic or light wave technologies the THz regime has been called the 'THz gap' [1]. The generation of THz radiation has also been made possible from advancements in non-linear crystal optics [2] and photoconductor/semiconductor technologies [3]. Terahertz radiation, as utilised in THz based technologies, has advantages over traditional light based technologies. Specifically, THz radiation can pass through non-polar materials (due to a long penetration depth and low absorption) [4], as well as, exhibit high selectivity with polar materials (due to a short penetration depth and high absorption) [4]. The unique properties of THz radiation (e.g., non-ionizing and strong interaction with many molecules) are well-suited for the development of new applications of science and technology. The onset of THz technologies is promising and is being developed for applications in various scientific and industrial sectors [5]. The emergent scientific applications for THz radiation and THz 2 Figure 1.1.1 The electromagnetic spectrum showing the main frequency, f, and wavelength, λ, regimes, as defined in this thesis. The main regimes of electromagnetic radiation can be defined here as categorical regimes and are described in terms of wavelength and frequency. These regimes are as follows. Regime 1: Infrared (λ = 1-30 μm, f = 10-300 THz), Visible Light (λ = 0.4-1 μm, f = 300-750 THz), Ultraviolet (λ = 0.01-0.4 μm, f = 750-3×1016 Hz), X-ray (λ = 0.01-10 nm, f = 3×1016-3×1019 Hz), Gamma Radiation (λ < 0.01 nm, f > 3×1019 Hz). Regime 2: Microwave (λ = 3-300 mm, f = 1-100 GHz), Radio (λ > 300 mm, f < 1 GHz). Regime 3: Terahertz Radiation (λ = 30-3000 μm, f = 0.1-10 THz). Regime 3 is the focus of this thesis. technologies are numerous, comprising of but not limited to THz time-domain quantum optics [6], THz spintronics [7], THz time-domain polarimetry [8], THz time-domain spectroscopy (THz-TDS) [9], THz non-linear spectroscopy [10], THz sensing of biological effects [11], THz spectroscopy of materials [12], air phonics based THz generation and detection [13], THz intersubband devices [14], near field THz imaging [15], far field multi-pixel THz imaging [16], THz scanning tunneling microscopy [17], and THz sensing for astronomy [18]. Moreover, industry specific applications for THz technologies are currently being developed, such as THz devices for satellite communications [19], THz devices for wireless telecommunications [20], medical imaging and diagnostics [21], THz inspection for aerospace components [22], and THz inspection for security applications [23]. This development of THz technologies for industrial applications is ongoing. However, several THz technologies are currently established for application within industry. Such established industrial THz technologies are THz porosity measurement of pharmaceutical tablets [24], THz assessment of automotive paint layers [25], and THz failure assessment of manufactured integrated circuits [26]. Furthermore, there are ongoing instrumentation and device research efforts aimed at refining THz technologies for increasing THz signal-to-noise ratio [27], minimizing THz signal acquisition time [28], 3 reducing the size of THz systems [29], and reducing the cost of THz systems [30]. There is interest in realizing the full potential of THz radiation in scientific and industrial applications, as evidenced by the abovementioned contributions to the THz science and technology literature. However, developments of rapid prototyping for THz components have not been widely explored, motivating such exploration. 1.2 Additive Manufacturing Technologies Additive manufacturing (AM) is an emergent technology, developing in parallel to that of THz technologies. Additive manufacturing, that is, 3D printing, is successfully deployed for rapid prototyping of custom components via utilisation of computer added design [31], and has gained considerable interest and adoption by research, industrial, and enthusiast communities alike. Additive manufacturing can be described as the automated fabrication of components or structures using an additive or successive layer-by-layer material adhesion process [32]. The specific AM fabrication process is often categorized by the type of fabrication material used (e.g., solid, liquid resin, or powder) and the fabrication process needed to adhere the successive material layers into a solid structure [33]. The two AM fabrication processes relevant to this thesis are as follows. First, fused deposition modeling, i.e., fused filament fabrication (FFF), is a solid material AM fabrication process utilising various thermoplastic filament materials [31]. Second, the vat polymerization fabrication process, i.e., stereolithography apparatus, is a liquid material AM fabrication process. The vat polymerization process is often performed using the laser based stereolithography technique, or the digital photomask based stereolithography technique, i.e., digital light processing [34]. Digital light processing utilises a programmable liquid crystal photomask matrix coupled with light emitting diode illumination. There are additional AM fabrication processes, however, their consideration is outside the scope of this thesis. This thesis focuses primarily on FFF-made structures, as this is the most common 3D printing technology [35]. Substantial research on AM is ongoing aimed at leveraging this technology in various scientific and industrial applications. Such applications are AM of components for dentistry [36], AM for biomaterials research [37], AM component research towards medical implants [38], AM of building 4 materials for construction industry [39], AM for aerospace applications [40], and AM of lab-on-a-chip devices for biochemical and chemical analyses [41]. Moreover, AM applications in the field of optics and photonics are also being explored [34]. Additive manufacturing for optics and photonics applications relating to, lenses [42] [43], waveguides [44] [45], polarisation optics [46–48], fibre optics [49] [50] is demonstrated in the literature for visible wavelengths. Of particular relevance to this thesis is the use of AM in the field of THz optics and photonics [51] [52]. This is a focus of this thesis. 1.3 Overview of Past Developments in Terahertz and Additive Manufacturing Technologies The intersection of AM and THz technology is of recent interest to the research community and is currently being explored. The intense research interest for AM, THz, and the intersection of AM and THz as research topics is shown in Figure 1.3.1. The publications per year for each of the abovementioned research topics is searched using Boolean logic search terms and compiled from Compendex, GEOBASE, and GeoRef databases. Figure 1.3.1(a) shows the rise in publications for THz research (red line, blue dot) in the early 1990s with AM or 3D printing (blue line, yellow dot) garnering increased publications in the late 2000s. The initial rise in publications for THz and AM or 3D printing (green line, blue dot) research is noticeable around the late 2010s and early 2020s, as more clearly shown in the expanded view of Figure 1.3.1(b). This publication tracking is evidence that THz/AM is an emerging field of study of particular interest to the research community. This thesis aims to support these on-going efforts. 1.4 Thesis Scope Many publications for THz and AM are focused on the development of THz compatible optical devices and components [53] [54]. Research in this area is driven by the need to mitigate the documented prohibitive development, procurement, and expense of traditional THz compatible components [55] [56]. This thesis investigates the use of a commercial AM system, with consideration for filament material selection and component fabrication, to address the accessibility of THz compatible materials and structures, and demonstrate the feasibility and function of such THz structures fabricated with AM. 5 Figure 1.3.1 Publication records per year, accessed via the EngineeringVillage (Elsevier Inc.) search engine, with results aggregated from Compendex, GEOBASE, and GeoRef databases on September 10, 2023. The legend indicates the search terms used, with subfigure (b) showing an expanded view of subfigure (a). 6 This research is at the intersection of both THz and AM technologies. Specifically, this thesis provides a comprehensive study introduced for the THz characterisations of AM filament materials via THz-TDS. This comprehensive study fills the research gap and updates the current body of THz materials literature, keeping abreast of the ongoing development of commercially available AM filament materials. These THz material characterisations are supported for various sample thicknesses. The appropriate THz compatible filament materials are selected and leveraged for the development of THz compatible structures fabricated with AM. This comprehensive material study is presented in Chapter 4 of this thesis and is published in the journal Optical Materials Express [57]—with elements of this work disseminated in the 2022 Proceedings of Photonics North [58]. This provides a library of THz-TDS measurements for 3D printing materials. A second study is provided that investigates Bragg structures (i.e., interference filters) fabricated via AM operating within the THz spectrum. The THz Bragg structure is fabricated from high impact polystyrene (HIPS) filament material—a filament material which is thoroughly characterised here with THz-TDS. The geometry and theoretical operation of the THz Bragg structure is investigated with finite-difference time-domain (FDTD) electromagnetic simulations. The THz Bragg structure is evaluated using a THz experimental test bed. This investigation of 3D printed THz Bragg structures is presented in Chapter 5 of this thesis and published in the journal Applied Optics [59]—with elements of this work disseminated in the 2023 Proceedings of Photonics North [60]. This provides the methodology for analysis of 3D printed THz components. Furthermore, a third study explores THz Bragg structures and THz Bragg superstructures fabricated via AM, for two THz compatible filament materials, being HIPS and cyclic olefin copolymer (COC). The abovementioned THz Bragg superstructures are simulated with FDTD electromagnetic simulations and demonstrated with agreement using a THz experimental testbed. Moreover, the effect of AM Z-axis fabrication resolution over the 50 to 400 µm range is explored for the THz spectral response (i.e., transmission loss, bandwidth, and frequency placement of frequency-domain stop-band). Terahertz Bragg structures and superstructures made from COC filament material are shown great promise for rapid 7 prototyping of THz photonic elements. This comparison of HIPS and COC THz Bragg structures and superstructures is presented in Chapter 6 of this thesis and is accepted at IEEE Transactions on Terahertz Science and Technology—with elements of this work disseminated in the 2023 Proceedings of Photonics North [61]. This provides evidence of the enhanced performance of COC and the resolution limits for 3D printing of THz components. 1.5 Thesis Outline The content of this thesis is presented with the following framework. Chapter 2 provides a literature review of THz compatible additive manufacturing materials and structures, including THz Bragg structures. Chapter 3 provides an overview of the fundamental concepts and theories leveraged in the theoretical and experimental contributions of this thesis. Subtopics include relevant electromagnetic theory, THz emitters, THz detectors, THz-TDS operation and analysis, and fundamentals of FDTD analysis. Chapter 4 presents a published experimental work of an exhaustive THz characterisations on additive manufacturing materials [57]. Chapter 5 presents published experimental and theoretical work on THz compatible Bragg structures fabricated with additive manufacturing [59]. Chapter 6 presents an accepted (primarily) experimental work on THz compatible Bragg structures and superstructures with material and fabrication characterisations. Chapter 7 presents the thesis conclusions and makes suggestions for future work. 8 Chapter 2: Literature Review This chapter provides a thorough review of recent literature encompassing the following topics: Terahertz Characterisations of Additive Manufacturing Based Fabrication Materials (Chapter 2.1), Terahertz Devices Fabricated with Additive Manufacturing (Chapter 2.2), Bragg Structures Fabricated with Additive Manufacturing (Chapter 2.3). The literature covered in these Chapters were aggregated using Google Scholar, Engineering Village Compendex, and Connected Papers search tools. 2.1 Literature on Terahertz Characterisations of Additive Manufacturing based Fabrication Materials Many filament materials can be deployed for additive manufacturing via FFF. These materials are available in their filament material form (suitable for use in FFF additive manufacturing (i.e., AM sample)), or in their corresponding primary form (that is not suitable for FFF additive manufacturing (i.e., pure sample)). An assortment of such materials has been characterised in the THz regime with spectroscopic methods, for a variety of sample thickness and frequency ranges. This is presented in Table 2.1.1. 2.1.1 Terahertz Spectroscopy of Polylactic Acid Filament Materials Polylactic acid (PLA) filament material is commonly utilised for FFF based AM. Kaluza et al. characterised various PLA samples fabricated with FFF AM over the THz region from 0.1 to 1.0 THz [62]. Busch et al. presents absorption and refractive index characterisations for a 1 mm thick PLA sample fabricated with AM over 0.2 to 1.5 THz [63]. Additionally the work of Squires and Lewis show PLA absorption and refractive index characterisation of a 1 mm thick sample fabricated with AM for the 0.3 to 1.8 THz region [64]. Peng et al. explored mixing quartz powder, at differing ratios, to PLA to increase the refractive index and lower the absorption in the THz spectrum between 0.3 and 1.0 THz [65]. Conductive PLA (i.e., PLA Cond.) samples fabricated with AM, being 2.6 mm and 4.0 mm thick, were characterised by Hernandez-Serrano et al. for 0.3 to 3.0 THz [66]. 9 Table 2.1.1 Terahertz Characterisation Parameters of Materials Used in Additive Manufacturing Material Freq. Range [THz] Sample Thickness [mm] 3D Printed Ref. ABS 0.3–1.0 1.6–2.5 No [67] 0.3–1.8 1.0 Yes [64] 0.2–1.5 1.0 Yes [63] ABS Cond. 0.3–0.8 1.0 Yes [64] COC 0.3–20 0.132 No [71] 1.0–10 3.2 No [70] 0.3–2 0.3 Yes [73] 0.3–3 2.0 Yes [74] 2.0–14 0.25 No [72] HDPE 0.2–1.5 5.0 Yes [63] 1.0–10 0.1 No [70] HIPS 0.3–1.8 1.0 Yes [64] PETG 0.3–1.8 1.0 Yes [64] 0.2–2.5 0.25 Yes [68] PLA 0.3–1.8 1.0 Yes [64] 0.2–1.5 1.0 Yes [63] 0.1–1.0 n/a Yes [62] 0.3–1.0 2.6–4.0 No [65] PLA Cond. 0.3–3.0 0.22 Yes [66] PP 0.3–1.8 1.0 Yes [64] 0.2–1.5 5.0 Yes [63] 0.1–1.0 n/a Yes [62] PS 0.2–1.5 5.0 Yes [63] 0.2–1.8 0.65–0.86 No [69] 1.0–10 0.4 No [70] PMMA 1.0–10 0.3 No [70] PVA 0.3–1.8 1.0 Yes [64] TPE 0.3–1.8 1.0 Yes [64] Nylon 0.3–1.8 1.0 Yes [64] 0.2–1.5 1.0 Yes [63] Photopolymer Resin 0.2–1.4 1.0–3.0 Yes [75] 0.3–2.5 3.0 Yes [76] 10 2.1.2 Terahertz Spectroscopy of Alternatives to Polylactic Acid Filament Materials Fused filament fabrication can make use of alternative materials AM. Such filament materials are acrylonitrile butadiene styrene (ABS) and polyethylene terephthalate glycol (PETG). The abovementioned filament materials have been characterised in the THz spectrum in terms of refractive index and absorption coefficient. Peng et al. characterised ABS for THz frequencies (0.3 to 1.0 THz), as a pure sample, and at various ratios with rice husk ask to increase the refractive index [67]. Squires and Lewis demonstrate characterisations of ABS as an AM sample, being 1 mm thick, from 0.3 to 1.8 THz [64]. Likewise, Busch et al. investigated an AM sample of ABS for THz frequencies, being 1 mm in thickness form 0.2 to 1.5 THz [63]. The characterisation of PETG for AM samples was performed by Squires and Lewis, specifically a 1 mm thick sample, with absorption and refractive index evaluated over 0.3 to 1.8 THz [64]. Moreover, Naftaly et al. characterised an AM PETG sample of 0.25 mm thickness over 0.2 to 2.5 THz [68]. 2.1.3 Terahertz Spectroscopy of Flexible Filament Materials Additive manufacturing with the FFF method can be accomplished with a flexible filament material, such as, thermoplastic elastomer (TPE). The TPE filament material has been explored for absorption and refractive index over the THz regime by Squires and Lewis [64]. Specifically, a 1 mm AM sample of TPE was evaluated over 0.3 to 1.8 THz. 2.1.4 Terahertz Spectroscopy of Dissolvable Support Filament Materials Additive manufacturing can also incorporate the use of dissolvable support filament materials. These filament materials can be dissolved by a specific solvent and are often used in AM of components with complex geometries. The two most common dissolvable support filament materials are polyvinyl alcohol (PVA) and high impact polystyrene (HIPS). The aforementioned dissolvable support filament materials were characterised by Squires and Lewis as AM samples, 1 mm thick, from 0.3 to 1.8 THz [64]. 11 2.1.5 Terahertz Spectroscopy of Nylon Filament Materials Nylon filament material has been characterised for the THz spectrum. Squires and Lewis demonstrate characterisations of nylon filament material as an AM sample, being 1 mm thick, from 0.3 to 1.8 THz [64]. Likewise, Busch et al. investigated an AM sample of nylon filament material for THz frequencies, being 1 mm in thickness from 0.2 to 1.5 THz [63]. 2.1.6 Terahertz Spectroscopy of Packaging Thermoplastic Filament Materials Common thermoplastics used in packaging have been deployed as filament materials for AM. These packaging thermoplastic filament materials include polypropylene (PP), high density polyethylene (HDPE), and polystyrene (PS). Busch et al. characterised PP, HDPE, and PS, as AM samples over the THz regime (0.2 to 1.5 THz) for sample thickness between 1 mm and 5 mm [63]. Polystyrene is evaluated over the 0.2 to 1.8 THz, as a pure sample, by Farman et al. [69]. High density polyethylene and PS are investigated by Cunningham et al., with these samples characterised in the THz regime in their pure form, with sample thicknesses between 0.1 and 0.4 mm for 1 to 10 THz [70]. Polypropylene is characterised by Squires and Lewis for an AM sample of 1 mm thickness from 0.3 to 1.8 THz [64]. Additional characterisations on PP were performed by Kaluza et al. over 0.1 to 1.0 THz [62]. 2.1.7 Terahertz Spectroscopy of Non-standard Filament Materials Cyclic olefin copolymer is of considerable interest to far-infrared and THz research. The spectral response of COC over the THz spectrum was conducted by Wollack et al., such that, spectroscopy was performed for a 132 µm pure sample over 0.3 to 20 THz [71]. Cunningham et al. performed THz spectroscopy on COC for 1.0 to 10 THz using a 3.2 mm pure sample [70]. Additional characterisations of a pure sample of COC were performed by D'Angelo et al., for a 25 µm sample, over 2.0 to 14 THz [72]. Cyclic olefin copolymer is shown to have low absorption coefficient and sufficient refractive index, with this material being utilised in FFF AM as a filament material. The COC filament material was fabricated 12 into a sample of 300 µm and evaluated over 0.3 to 2 THz by Mavrona et al. [73]; additionally, a similar COC AM sample, 2.0 mm, was characterised by Busch et al. for 0.3 to 3 THz [74]. Polymethyl methacrylate (PMMA) is investigated in the THz regime by Cunningham et al. for a 300 µm thick pure sample over 1.0 to 10 THz [70]. Liquid photopolymer resins used in stereolithography based AM processes are investigated over the THz spectrum, by Duangrit et al., for there dielectric properties. A selection of stereolithography AM samples were evaluated from 0.2 to 1.4 THz for various sample thicknesses between 1.0 and 3.0 mm [75]. Stereolithography AM samples embedded with aluminum oxide were investigated for changes in absorption and refractive properties. Ornik et al. performed such characterisations on stereolithography AM samples, 3.0 mm thick with aluminum oxide, over 0.3 to 2.5 THz [76]. 2.1.8 Thesis Contributions to Terahertz Spectroscopy of Additive Manufacturing Filament Materials This thesis provides an updated material study of THz-TDS measurements on many standard and non-standard 3D printed materials. In particular, the results can be used to assess if the presented 3D printing materials lend themselves to use as THz compatible materials. Chapter 4 of this thesis presents measurements over an extended THz bandwidth with multiple sample thicknesses. This includes the methodologies, measurements, and results for various groups of 3D printing materials: PLA filament materials; common alternatives to PLA filament materials; flexible filament materials; dissolvable support filament materials; nylon filaments materials; packaging thermoplastic filament materials (i.e., PP filament material and HDPE filament material); and non-standard filament materials. Such work yields several contributions. First, it can provide a comprehensive and consolidative set of THz-TDS measurements, where previously THz-TDS measurements were spread across many studies for FFF filament materials [63], [64] and for stereolithography photopolymer resin materials [75]. Second, it offers a comparison of thick and thin sample THz-TDS measurements, for verification of measurement accuracy of thick and thin samples, particularly when approaching sample thicknesses above and/or below the dopt = 13 2/α(f) optimal sample thickness for free-space THz-TDS measurements. (In the previous in-line equation dopt is the optimal sample thickness and α(f) is the absorption coefficient as a function of frequency, f [77].) Third, it extends the measured bandwidth by up to 1.20 THz beyond prior studies, e.g., previous reports provide a maximum THz-TDS bandwidth of 1.80 THz for ABS filament material, HIPS filament material, and HDPE filament material [64]. In contrast, this thesis work shows extended bandwidth maximum values of 2.56 THz, 2.66 THz, and 3.00 THz for ABS filament material, HIPS filament material, and HDPE filament material, respectively. Fourth, it gives the first (to the author's knowledge) THz-TDS measurements of polyvinyl butyral (PVB) filament material, acrylonitrile styrene acrylate (ASA) filament material, low temperature polycaprolactone (LT PCL) filament material, and polyetherimide (PEI) filament material. This thesis work primarily focuses on FFF 3D printed materials, rather than stereolithography 3D printed materials. 2.2 Literature on Terahertz Devices Fabricated with Additive Manufacturing Terahertz compatible optical devices and components are being explored using AM. Additive manufacturing, utilising the FFF process, can make use of interchangeable filament materials. Selection of the appropriate filament material for FFF based AM enables creation of THz compatible optical devices with suitable absorption coefficient and refractive index properties. The AM of THz compatible optical devices and components has and is being explored by researchers for a variety of applications. The below subchapters (i.e., Chapters 2.2.1 to 2.2.7) provide a literature overview of AM of THz compatible optical components and devices. The AM of THz compatible optical components and devices to be discussed are as follows: 1. lenses, 2. polarisation optics and beam splitters, 3. THz microfluidic devices, 4. THz diffractive devices, 5. solid waveguides, and 6. hollow core waveguides. 14 2.2.1 Terahertz Lenses Fabricated with Additive Manufacturing Aspherical, elliptical-aspheric, and planar-hyperbolic lenses were fabricated using AM and evaluated for use in THz systems from 0.1 to 2.0 THz by Squires et al. [78]. Zhang et al. investigate a plano-convex THz lens fabricated with AM [79]. Additionally, the work of Price et al., showed a flat-top aspheric lens pair, designed and fabricated with AM, and evaluated for suitability of application with THz imaging [80]. Moreover, an adapted THz compatible flat-top lens, fabricated with AM, was explored by Bezziou et al. for different design parameters [81]. Gradient-refractive-index lenses, fabricated with AM, were explored by Hernandez-Serrano et al., for THz frequencies under 0.7 THz [82]. Likewise, Zhou et al. design and investigate a similar gradient-refractive-index lens design, fabricated with AM, for performance within the THz regime [83]. Furthermore, cylindrical, aspheric, and achromatic, THz lenses fabricated from COC filament material via FFF based AM were explored by Busch et al. [74]. These works all make efforts to use AM to manipulate the physical directionality of THz beams. 2.2.2 Terahertz Polarisation Optics and Beam Splitters Fabricated with Additive Manufacturing The capability to manipulate the polarisation of THz waves is studied for THz optical devices fabricated with AM. Hernandez-Serrano et al. has developed a grid polariser using conductive PLA filament material and has shown the performance of the TE and TM polarisation modes for 0.3 to 2.7 THz spectra [66]. Additional works, by Ryu et al. on a grid polariser fabricated with AM for THz frequencies, were undertaken for THz synchrotron applications [84]. A birefringent wave plate, following a q-plate design, was fabricated with AM and evaluated for THz radiation in the creation of cylindrical vector beams, as demonstrated in the work Hernandez-Serrano and Castro-Camus [85]. A beam splitter tunable by an applied compression force was fabricated with AM for the THz frequency range (i.e., 0.1 to 0.5 THz), as shown by the work of Busch et al. [86]. A frequency dependent polarisation beam splitter was developed with AM for the THz regime by Hernandez-Serrano and Castro-Camus for 0.1 to 0.4 THz [87]. Such efforts have produced manipulation for split-ratios and polarisation of THz beams. 15 2.2.3 Terahertz Microfluidic Devices Fabricated with Additive Manufacturing Additive manufacturing is being leveraged for microfluidic devices to be used within THz platforms. Spectroscopic THz measurements were performed on a microfluidic device made from COC filament material via AM, as shown from the work of Zwyssig et al. [88]. Cao et al. demonstrate a resonant fluidic sensor for THz wavelengths, fabricated with AM using a PLA filament material [89]. Rapid prototyping is ideal for development of microfluidic devices and this also applies for microfluidic-THz devices. 2.2.4 Terahertz Diffractive Devices Fabricated with Additive Manufacturing Additive manufacturing is capable of fabricating diffractive devices with feature sizes on the order of THz wavelengths. These THz compatible diffractive devices have been demonstrated experimentally by various research groups. A survey of such literature on diffractive devices fabricated with AM is presented here. Diffractive lenses fabricated from AM are demonstrated by Furlan et al. with periodic and aperiodic phase profiles [90]. The work of Liu et al. shows a diffractive lens fabricated from AM for a continuous THz Airy beam [91]. Multiple focal spots were explored using diffractive THz optics as shown by Komorowski et al. [92]. Diffractive flat optics were developed for linear THz scanners using AM for fabrication [93]. Diffractive lenses for duel plane THz holograms were devised and fabricated using AM by Jia et al. [94]. Multiple designs of diffraction optics for THz waves were investigated for method of coding phase and diffraction efficiency and fabricated via AM [95]. Wide band diffraction using meta-gratings were fabricated with AM as demonstrated by Dong et al. [96]. Diffractive focal plane arrays fabricated from AM for THz wavelengths have been investigated by Szkudlarek et al. [97]. Additionally, fan-out patterns for THz beams were shown using diffractive optics fabricated with AM [98]. Such efforts are aimed at manipulating the physical-spectral separation of THz beams. 16 2.2.5 Terahertz Solid Waveguides Fabricated with Additive Manufacturing The propagation of THz waves can be redirected to follow the contour of a solid core waveguide. The use of waveguides allows THz to be leveraged towards applications in communications [99]. The work of Weidenbach et al. investigates the fabrication of solid core waveguides using AM. Specifically, bending losses were evaluated for different diameters, optical path splitting waveguides, and a variable directional coupler waveguide [100]. The THz performance of similar waveguides has been evaluated for multiple filament materials, being PS and COC, as shown by Guo et al. [101]. Logic gates for THz frequencies have been fabricated with AM as structures derived from solid core waveguides. Ortiz-Martinez et al. demonstrate the logic gates of OR, AND, and XOR, for 0.13 THz operation [102]. Solid core waveguides fabricated from AM are leveraged in THz communications by demonstrating multiplex and de-multiplex capabilities, as shown by the work of Hernandez-Serrano et al. The multiplex operation is frequency dependent, i.e., having the propagation of THz waves in the solid core waveguides and redirecting for different THz frequencies [103]. 2.2.6 Terahertz Hollow Core Waveguides Fabricated with Additive Manufacturing Hollow core THz waveguides can be fabricated with FFF based AM. There have been multiple efforts to explore hollow core waveguides for THz wavelengths by leveraging AM. For example, Stefani et al. developed hollow core THz waveguides for multiple filament materials such as ABS and flexible and rigid stereolithography photopolymer resins. These hollow core THz waveguides were characterised over 0.2 to 0.6 THz [104]. Another work by Ma et al., investigates a hollow core THz waveguide fabricated with AM with an internal disordered reflector structure [105]. A polycarbonate filament material hollow core wave guide was fabricated with AM and characterised from 0.1 to 0.6 THz with anti-resonant frequency peaks [106]. Anti-resonant effects in the THz regime are further explored by Talataisong et al., for hollow core waveguides fabricated with AM and COC filament material [107]. Low loss PP filament material is considered for a hollow core waveguide fabricated with AM having an internal microstructure towards applications in THz communications [108]. Talataisong et al. provided additional investigations of THz 17 hollow core waveguides fabricated with AM and PETG filament materials. The aforementioned PETG hollow core waveguides were stretched to cause deformation in the waveguide structure and were characterised [109]. Hollow core waveguide were investigated for THz pulse propagation whilst being imbedded with metallic wire structures after fabrication from AM [110]. Additional works and comparisons of hollow core waveguides fabricated from AM for THz waves are described in a review by S. Islam et al. [111]. Such efforts are directed towards hollow core waveguides for propagating and coupling to THz beams. Several of the above-mentioned hollow core waveguides are fabricated with internal structures which manifest resonant features in the frequency-domain. Additional research on hollow core waveguides with internal structures having a periodic Bragg geometry have also been performed. Periodic Bragg structures are a focus point of this thesis, therefore, the literature surrounding this will be expanded upon in Chapter 2.3. 2.2.7 Context and Relevance to Thesis The above subchapters have described a variety of general 3D printed THz devices and concepts. One of the focuses of this thesis is periodic THz structures, which is described in the next subchapter. Therefore, this thesis will not be exploring spatial beam manipulations, or other more niche applications, e.g., microfluidics or waveguides. However, the material characterisations of this thesis complement the abovementioned ongoing efforts. Periodic Bragg structures fabricated with AM for THz wavelengths are another central theme for this thesis. Therefore, the literature surrounding Periodic Bragg structures will be expanded upon in Chapter 2.3. 2.3 Literature on Bragg Structures Fabricated with Additive Manufacturing This literature review subchapter provides an overview of previous efforts for THz Bragg components, fabricated with AM, be they THz Bragg structures (alternating refractive indices with optical 18 path equalization) or THz Bragg superstructures (alternating refractive indices with distinctly different optical path lengths). The implementation of THz Bragg structures, fabricated with AM, manifest in a variety of forms. These forms include the following: a periodic internal structure within a hollow core waveguide; photonic crystal structures with repeating patterns on one-dimensional, two-dimensional, or 3D planes. It should be noted that the one-dimensional photonic crystal is most similar to that of a Bragg grating, i.e., Bragg structure. Bragg structures for THz waves, being fabricated with AM or by other methods, will be covered in this literature review subchapter. The alternating refractive indices of periodic material structures affect the temporal propagation of incident pulsed THz waves (i.e., temporal manipulation), inducing resonant features in the frequency-domain. The relationship between periodic temporal manipulation of pulsed THz waves, via alternating spatial material periodicity, and the corresponding frequency-domain effects are described by a Fourier relationship. A fundamental Fourier transform relationship is that periodicity within the time-domain (often implemented through spatial periodicity) produces periodicity in the frequency-domain. The periodic impulse train Fourier transform pair provides insight into the duality of the time and frequency spacing. The periodic impulse train Fourier transform pair is ∑ 𝛿(𝑡 − 𝑛𝑇0) ↔ ∞𝑛=−∞1𝑇0∑ 𝛿 (𝑓 −𝑛𝑇0) .∞𝑛=−∞ (1) where t is time, f is frequency, n is integers of the period, T0 is the temporal (related to spatial) period, implying a frequency-domain periodicity of f0 = 1/T0. Thus manipulation of spatial periodicity will produce manipulations of frequency-domain periodicity. With this in mind, this subchapter will look at devices fabricated with AM producing frequency-domain periodic responses. 19 2.3.1 Terahertz Hollow Core Waveguides with Bragg features Fabricated with Additive Manufacturing Hollow core waveguides for THz waves can be fabricated with AM to have (periodic) Bragg internal structures. Pulsed THz beams confined to a hollow core Bragg waveguide will interact with the periodicity of the Bragg structure, resulting in resonant features in the frequency-domain. Ding et al. demonstrated a hollow core Bragg waveguide, fabricated with AM, for pulsed THz. The aforementioned waveguide is made of concentric rings within a greater hollow core waveguide structure. These concentric rings were connected to supporting structures, which deviate from the ideal Bragg geometry, causing transmission loss. The optimal design and placement of these internal supporting structures for the Bragg concentric rings was evaluated experimentally [112]. Terahertz hollow core waveguides with Bragg structures, fabricated with AM, were investigated further, with respect to the supporting structures of the concentric rings by Bai et al. The supporting structures were designed with cascaded discontinuities along the waveguide to minimize transmission loss. It was shown that the cascaded supporting structure design had comparable transmission loss to that of the ideal hollow core waveguide with Bragg structures [113]. Cruz et al., examined a THz hollow core waveguide with Bragg structures, fabricated with AM, for various physical dimensions through uniform scaling. It was shown that the resonant features in the frequency-domain (i.e., photonic band gap), are tunable corresponding to the dimensions of the hollow core waveguide. The results showed comparable transmission between waveguide designs over 0.1 to 1.0 THz [114]. Li et al., developed a THz hollow core waveguide, fabricated with AM, with internal Bragg structures. This waveguide combined the use of a defect layer to produce a known spectral feature, to be leveraged a as a sensor from 0.1 to 0.3 THz. The hollow core waveguide is capable of detecting the thickness of PMMA film samples inserted into the defect feature. The frequency value of the spectral feature, corresponding to the defect layer, varies constantly with a change in PMMA sample thickness. Furthermore, these authors showed that concentration of lactose powder can be measured with the waveguide, when the defect layer and corresponding frequency feature, interact with the absorption spectrum of lactose powder [115]. Li et al. further refine the sensing capability of the THz hollow core waveguide, fabricated 20 with AM, with internal Bragg structures. They develop the aforementioned waveguide sensor for multichannel sensing of samples in parallel via multiple defect layers for a single THz pulse cycle [116]. Additional experimental works of hollow core waveguides fabricated with AM for THz sensing applications with internal Bragg structures, or with alternative internal structures, are found in the literature [117–122]. 2.3.2 Terahertz Photonic Crystal Devices Terahertz photonic crystals devices, being structures fabricated with periodic patterns on the order of THz wavelengths. Here, one-dimensional and multidimensional efforts are summarized. Withayachumnankul et al. present a one-dimensional photonic crystal for THz frequencies (i.e., Bragg structure or interference filter). The one-dimensional photonic crystal was a multilayer interference structure with alternating dielectric materials with different refractive indices. Such a one-dimensional photonic crystal was fabricated by combining slabs of 50 µm thick silicon wafers and 170 air gap µm thick spacer rings into a completed assembly. This one-dimensional photonic crystal structure was evaluated for THz frequencies up to 1 THz. The temporal manipulation of a pulsed THz beam was acquired over a sufficiently long 550 ps optical path length THz spectrometer scan [123]. The one-dimensional photonic crystal structure was explored by Li et al., towards a multi-channel THz mirror and filter. The one-dimensional photonic crystal structure was fabricated from an indium antimonite (InSb) semiconductor material. The corresponding frequency-domain response of several material slab thicknesses and temperatures are examined for this structure for 2.5 to 6.0 THz bandwidth. This tunable THz filter is proposed for future applications in THz communication systems [124]. Similarly, multilayer mirror structures (i.e., one-dimensional photonic crystal) are evaluated by Schiwon et al., for the THz regime within a wavenumber of 100 to 700 cm-1 (corresponding to 3 to 21 THz). Such a multilayer mirror is constructed from 10 µm silicon wafers and 44 µm air gap layers. The corresponding frequency response of this mirror demonstrates multiple features of reflection and transmission [125]. Additional notable works on one-dimensional photonic crystals, operating within the THz regime, not fabricated with AM, are 21 available in the literature [126–132]. Multi-dimensional photonic crystal devices, not fabricated with AM, operating within the THz regime have also been demonstrated in the literature. These photonic crystal devices have periodic geometries repeating in multiple axial planes [133–137]. 2.3.3 Bragg Structures for Terahertz Waves Fabricated with Additive Manufacturing Among the principal themes of this thesis is the fabrication of THz compatible Bragg structures via AM. Bragg structures, consisting of alternating layers of dissimilar refractive indices, are capable of temporal modulation of incident pulsed beams. The literature encompassing THz Bragg structures fabricated with AM is described by several terms corresponding to the Bragg interference condition. Description of devices with similar operating principal to Bragg structures (somewhat interchangeably) use the following terms: anti-reflective layers, Fabry-Perot cavities, dielectric filters, interference filters, rugate filters, Bragg reflectors, and photonic crystal devices. Once such device was introduced by Revuri et al., whereby FFF based AM was utilised to fabricate PLA interface layers for the temporal manipulation of THz pulses. Multiple PLA interface layers, 116 µm thick, are assembled within a structure between air gap spacer rings, also 116 µm thick. This Fabry-Perot filter device was characterised over 0.3 to 0.7 THz. For multiple air gap thicknesses, first and second order interference peaks were examined for full-width-at-half-maximum, transmission, frequency, finesse. This structure was fabricated from individual components that were later assembled manually [138]. A similar work to the above-mentioned device, fabricated with quartz interface layers, 45 µm thick, and air gap layers via steel spacer rings, 100 µm thick, without AM is demonstrated by Balzerowski et al. [139]. An implementation of a Bragg reflector was fabricated with stereolithography based AM by Park et al., with a resonant feature is measured at 0.11 THz [140]. Bomba et al. established a similar effect in the THz spectrum with an anti-reflection structure fabricated with stereolithography based AM. This structure was a two-dimensional photonic crystal, or etalon plate, capable of temporally manipulating incident THz pulses, manifesting as resonant reflections in the frequency-domain from 0.1 to 1.0 THz [141]. The AM fabrication of a device consisting of many Fabry-Perot resonators was demonstrated by Kubiczek et al., 22 with COC filament material. This THz compatible device establishes resonant features in the frequency-domain from 0.1 to 2.5 THz. It was further shown that the frequency of these resonant features change corresponding to the angle of incidents for pulsed THz beams [142]. A chirped Bragg grating integrated waveguide for THz systems fabricated by AM was presented by Jahn et al., as a grating coupler to focus specific frequencies of THz radiation out of such a waveguide [143]. 2.3.4 Applications of Terahertz Bragg Structure Fabricated with Additive Manufacturing Another important point of reflection is the myriad of applications that THz Bragg components are leveraged to undergo. Several of these key applications are discussed here. A waveguide with Bragg structure geometries is leveraged for the sensing of gas with THz radiation [144]. The Bragg waveguide design contained a phase-shifted feature (i.e., similar to a defect feature), causing a distinct spectral response in the frequency-domain. The spectral response from the phase-shifted Bragg feature changes in amplitude and frequency placement as gas of differing refractive indices is introduced into the cavity of the waveguide. This work, by Cao et al., is undertook for a static empty waveguide cavity, a waveguide cavity with air flow, and with glycerol vapor flow showing a frequency shift from 141.11 THz to 141.06 THz of the resonant mode [144]. Microfluidic devices for THz sensing [88] [89] is an application for THz Bragg devices, as previously discussed in Chapter 2.2.3. Spectroscopic, refractive index sensing, and thickness assessment, of samples in situ with hollow core THz Bragg waveguides fabricated with AM are an additional application of merit (Chapter 2.3.1). 2.3.5 Context and Relevance to Thesis Given this reflection on the literature, an important contribution is to investigate 3D printing resolution of the THz compatible materials found from the materials study of Chapter 4. These questions are explored though Chapter 5 and Chapter 6. Chapter 5 lays out a thorough methodology for studying Bragg structures theoretically (realized through FDTD electromagnetic simulations of Maxwell's equations) 23 and experimentally (realized through 3D printed objects). Chapter 6 provides a thorough comparison of two top candidates for THz compatible filament materials (HIPS and COC), with explorations of printing resolution and underlying absorption effects. 24 Chapter 3: Fundamental Concepts This thesis chapter explores the underlying fundamental concepts of this thesis, being relevant electromagnetic theory, THz operation, THz emission, THz detection, THz measurement and spectroscopy, and FDTD theory. 3.1 Relevant Electromagnetic Theory Photonic technologies operate via the utilisation of light, which is an electromagnetic wave. Maxwell's equations are the cornerstone of all electromagnetic theory [145], and are described below in the differential form. Maxwell's first equation is Gauss's law for a fixed electric field and is described by ∇⃗ ∙ ?⃗? = 𝜌𝜀𝑟𝜀0 . (2) The quotient between the electric charge volume density, ρ, and the electric permittivity of free space, ε0, times the relative permittivity, εr, is equivalent to the divergence of the electric field vector, ?⃗? . That is to say, the net electric field from charges enclosed in a volume is equal to the electric field passing through the surface of the enclosed volume (i.e., point charges/electric monopoles exist). Maxwell's second equation is Gauss's law for a fixed magnetic field and is described by ∇⃗ ∙ ?⃗? = 0 . (3) The divergence of a magnetic field, ?⃗? , passing through a surface of an enclosed volume is equal to zero. Simply put, magnetic monopoles do not exist; only magnetic dipoles. Maxwell's third equation is Faraday's law for a transient magnetic field and is described by ∇⃗ ⨉ ?⃗? = −𝜇r𝜇0𝜕?⃗? 𝜕𝑡 . (4) The time rate of change for a vector of magnetic field, ?⃗? , is equal to the curl of the electric field vector, ?⃗? , with proportionality described by the relative magnetic permeability of a material, μr, and the magnetic permeability of a free-space medium, μ0. This expression denotes that a magnetic field vector changing in time begets an encircling and orthogonal electric field of opposing magnitude. Maxwell's fourth equation is the Ampere-Maxwell law for transient electric fields and is described as 25 ∇⃗ ⨉ ?⃗? = 𝜀r𝜀0𝜕?⃗? 𝜕𝑡+ 𝜎?⃗? . (5) The derivative of electric field, ?⃗? , multiplied with the associated relative electric permittivity of a material and the electric permittivity of free space is linearly related to the curl of the magnetic field. This is the displacement current. Also linearly related to the curl of the magnetic field is the drift current, being the current density vector, 𝐽 , where 𝐽 = 𝜎?⃗? , which includes the conductivity, 𝜎. The equation states that an electric field vector changing in time generates an encircling and orthogonal magnetic field vector. The electromagnetic wave equations for electric and magnetic fields were consolidated by Maxwell. Maxwell rectified discontinuities between the preceding Gauss-Faraday-Ampere electromagnetic laws of physics and unified them into the above four equations. This contribution permitted the conformation that light was an electromagnetic wave via the wave equations. The wave equations are derived by interpreting Maxwell's third or fourth equation for time varying magnetic and electric fields, in relation to each other. The result of this established proof is shown below. The wave equations are expressed as ∇⃗ 2?⃗? = 𝜇𝑟𝜇0𝜀𝑟𝜀0𝜕2?⃗? 𝜕𝑡2 , (6) and ∇⃗ 2?⃗? = 𝜇𝑟𝜇0𝜀𝑟𝜀0𝜕2?⃗? 𝜕𝑡2 . (7) Broadly speaking, these equations assert that the electric magnetic field components of light are in-phase and orthogonal. A time variation in the magnetic field is equivalent to a spatial variation in electric field, over time. This corresponds to a time variation in electric field being equivalent to a spatial variation in magnetic field, over time. Both of these two phenomenon occur in lockstep and describe the propagation of light through free-space. 3.2 Terahertz Operation Terahertz measurements are performed by using a sophisticated optical system that (typically) employs the use of mode-locked pulsed lasers [146] [147]. A laser pulse train (i.e., pump beam) excites the 26 THz emitter, which creates THz pulses. A THz pulse is measured with another laser pulse train (i.e., probe beam) on an optical delay line. Terahertz measurements are taken by applying multiple sets of two laser pulses (split from one initial beam through a beam splitter), synchronized in time, to both excite (i.e., pump beam) the THz emitter and measure (i.e., probe beam) the decay dynamics of sample excitation for many frequencies. Terahertz measurements can be used for THz spectroscopy, often referred to as THz-TDS [148]. In THz spectroscopy, the high peak power and short femtosecond duration of mode locked laser pulses used in THz measurements allow for capturing of absorptive and refractive properties of a sample over the THz regime. Terahertz time-domain spectroscopy carries the advantages of enhanced penetration depth of electromagnetic radiation into samples and THz wavelength dependant interaction of sample constituent structures (i.e., proteins, large molecules, etc.)—facilitating additional scientific revelations from formerly well characterised sample materials [149]. These measurements are performed by measuring a THz pulse without a sample and with a sample in the THz beam path and comparing amplitude (for absorption coefficient) and phase (for refractive index) of the Fourier transform of the (before and after sample) THz pulses. Terahertz spectroscopy systems (THz-TDS systems) based upon mode-locked lasers have emerged as an adaptation from conventional pump-probe spectroscopy systems. In pump-probe spectroscopy measurements, the (above bandgap) pump beam excites a semiconductor sample, and the transmission of the (below bandgap) probe beam through the semiconductor sample is affected by the charge-carrier dynamics caused by the pump beam. This can be useful for studying semiconductors for use in THz emitters [150]. Pulsed THz devices make use of photoconductive or electro-optic processes for generation or detection of THz. The physics of photoconductive and electro-optic processes can be manipulated in both forward and reverse directions. Thus, detection and generation of THz can both be performed for either photoconductive or electro-optic device architectures. 27 3.3 Terahertz Emission The generation of THz radiation for THz-TDS is achieved by utilising a THz emitter. Terahertz emitters are devices that generate THz radiation by leveraging the reverse processes of the photoconductive effect of semiconductors or the electro-optic effect of nonlinear optical crystals. The working principle of THz emission for both photoconductive and electro-optic emitters are examined below. 3.3.1 Photoconductive Emission The photoconductive THz emitter is comprised of a semiconductor wafer, e.g., a gallium arsenide, patterned with surface electrodes [151]. A diagram for the photoconductive THz emitter device is shown on Figure 3.3.1.1 The gallium arsenide wafer and surface electrodes are represented as a long rectangle, and two rectangles with dark colouring, respectively. The red and grey cones represent operation beam paths for the laser pulse (?⃗? opt(𝜔𝑡))and THz pulse (?⃗? THz), respectively. Figure 3.3.1.1 The photoconductive emitter with a laser pulse generating a terahertz pulse. The operation of the photoconductive THz emitter is as follows: A red laser pulse with wavelength being 780 nm and having a duration of approximately 100 fs (i.e., ?⃗? opt(𝜔𝑡)), is generated from a mode-locked laser. This laser pulse is transmitted and focused onto the photoconductive gallium arsenide wafer whilst the two surface electrodes are energized to a potential difference, Vb (i.e., the bias voltage). The bias 28 voltage creates an electric field, ?⃗? bias, between the surface electrodes. Before arrival of the ?⃗? opt(𝜔𝑡) onto the THz emitter, the current between the bias and ground electrodes is prevented due to the high resistance of the gallium arsenide wafer (and THz semiconductors are often selected to have high dark resistance). The conductivity of gallium arsenide is modulated by the laser pulse [152], which can be expressed as 𝜎 = 𝑞(𝑝h𝜇h + 𝑛e𝜇e) ≅ 𝑞𝑛e𝜇e . (8) Before the incidence of the laser pulse onto gallium arsenide, the associated semiconductor conductivity, σ, is approximately zero (i.e., the flow of current between electrodes is restricted). In this instance, the near-zero conductivity of the gallium arsenide, inversely described as high resistivity, is attributed to an insufficient density of free electron charge carriers, 𝑛e ≅ 0. For reference, 𝑞 represents the elemental charge constant of an electron. 𝑛e and 𝑝h represent the density of negative electrons and positive 'holes' type free charge carriers, respectively. 𝜇e and 𝜇h represent the mobility of these charge carriers types. Since 𝜇h ≪ 𝜇e of gallium arsenide and other common semiconductors, the mobility of holes is assumed negligible (i.e., 𝜇h ≅ 0) with respects to gallium arsenide conductivity, resulting in the following approximation: 𝜎 ≅ 𝑞𝑛e𝜇e . The arrival and interaction of the laser pulse within the gallium arsenide surface, between the electrode gap, mobilizes electron charge carriers within the semiconductor, that is, 𝑛e ≠ 0 . This mobilization of charge carriers induces a drift current between the bias and ground electrodes during the lifetime of the laser pulse width. The density of this drift current (i.e., current density) is expressed as a function of conductivity, 𝜎, and bias electric field, ?⃗? bias, in 𝐽 = 𝜎?⃗? bias (9) It is generally accepted that the generation of THz radiation by the photoconductive THz emitter is governed by well-known principles outlined in radio frequency engineering for antenna theory. Antenna theory stipulates that the mobilization of charge carriers within the gallium arsenide, cause the semiconductor to act like antenna and an electric field, ?⃗? THz, is emitted. The THz electric field magnitude 29 is proportional to the derivative of current density [153], 𝐽 , as described in 𝐸⃗⃗ ⃗THz ∝𝜕𝐽 𝜕𝑡. Thus, THz radiation, ?⃗? THz (i.e., the THz pulse represented as the grey conical emission on the right side of Figure 3.3.1.1), is ejected from the reverse facing surface of gallium arsenide photoconductive emitter as an expanding beam. (The THz radiation can later be directed onto a sample for operation of THz-TDS experiments.) An illustration of time- and frequency-domain photoconductive processes occurring within the gallium arsenide THz emitter is shown in Figure 3.3.1.2 Current density, THz electric field over time, and THz electric field over frequency are represented by subfigures (a), (b), and (c), respectively. Figure 3.3.1.2 The (a) current density, (b) terahertz electric field vs. time, and (c) terahertz electric field magnitude vs. frequency are shown for a hypothetic photoconductive terahertz emitter based on a semiconductor with charge-carrier lifetime of approximately 20 ps. Terahertz generation processes can be further described as such; the mobilization of free electron charge carriers within gallium arsenide induces a flow of electrons with current density, 𝐽(𝑡).The current density, shown as a green trace on Figure 3.3.1.2(a), increase from a zero value at time zero, to that of maximum amplitude for the short duration (approx. 100 fs) of the incident laser pulse, ?⃗? opt(𝜔𝑡). After the 30 lifetime of the laser pulse, the induced current density within the gallium arsenide then decreases to zero amplitude over a much longer time scale of approximately 20 picoseconds. The electric field of the THz emission, ?⃗? THz(𝑡), shown as a blue trace on Figure 3.3.1.2(b), is proportional to the time derivative of current density. The duration of the THz pulse is 2 picoseconds. The Fourier transform of ?⃗? THz(𝑡), being ?⃗? THz(𝑓), is shown as a purple trace on Figure 3.3.1.2(c). The Fourier domain representation of the THz electric field, ?⃗? THz(𝑓), identifies the amplitude of the component sinusoidal frequencies that makeup the pulse within the ?⃗? THz(𝑡) signal. The ?⃗? THz(𝑓) appears to have a bandwidth of approximately 2 THz (roughly the reciprocal of the duration of the THz pulse) before distortions are dominant at higher frequencies—seen as lobe-like oscillations. The THz bandwidth is important for THz-TDS as this will impact what range of frequencies can produce reliable spectroscopy measurements. The DC component shown in Figure 3.3.1.2(c) is non-physical and would not satisfy a wave equation. Its presence is related to the assumption of only emission based off a drift current. A more fulsome model would also include carrier density dependant screening of the bias field. 3.3.2 Electro-Optic Emission The electro-optic THz emitter is comprised of a nonlinear crystal. Zinc telluride or gallium phosphide are common nonlinear crystals used for electro-optic THz emission [146]. A diagram for the electro-optic THz emitter device is shown on Figure 3.3.2.1. The nonlinear zinc telluride crystal is represented as a long rectangle with orange shading. The red triangle on the left side of this figure represents operation beam path for the laser pulse, being ?⃗? opt(𝜔𝑡). The grey triangle and overlapping light red triangle, on the right side of this figure, represents the operation beam paths for the emitted THz pulse (?⃗? THz(𝑡)) and the generated second harmonic of laser pulse (?⃗? opt(2𝜔𝑡)), respectively. 31 Figure 3.3.2.1 Electro-optic terahertz emission has a laser pulse interacting with an electro-optic emitter to produce a terahertz pulse. The operation of the electro-optic THz emitter is as follows: A red laser pulse with wavelength being 780 nm and having a duration of 100 fs (i.e., ?⃗? opt(𝜔𝑡)), is generated from a mode locked laser. This laser pulse is to be transmitted and focused onto the electro-optic zinc telluride nonlinear crystal. The electro-optic crystal is optically excited by the ultra-fast optical pulse, ?⃗? opt(𝜔𝑡), such that, THz electric field, ?⃗? THz(𝑡), is generated via the optical rectification process. Second harmonic generation of the excitation optical pulse also occurs, for which an optical emission, ?⃗? opt(2𝜔𝑡), resides with twice the frequency, and half the wavelength (i.e., 390 nm), than that of the excitation pulse. The emission of THz electric field and second harmonic generation is formed by birefringence, being the Pockels effect [146]. The optical rectification process is defined to be ?⃗? = 𝜀r𝜀0?⃗? = (𝜒 + 1)𝜀0?⃗? = 𝜒𝜀0?⃗? + 𝜀0?⃗? = ?⃗? + 𝜀0?⃗? , (10) where the electric flux density, ?⃗? , is the product of electric field, ?⃗? , permittivity of free space 𝜀0, and the relative permittivity of the medium, 𝜀r. The relative permittivity of the medium can be delineated as the electric field susceptibility constant plus one, 𝜒 + 1. This leads to the expression of material polarisation, ?⃗? , such that, ?⃗? = 𝜒𝜀0?⃗? . The Pockels effect is included within the expression 32 𝑃(𝐸(𝑡)) = 𝜒𝜀0(𝐸(𝑡)) ⋅ 𝐸(𝑡), (11) where, 𝜒, is a geometric series expansion. The expanded form being 𝜒(𝐸(𝑡)) = 𝜒0 + 𝜒1𝐸(𝑡) + 𝜒2𝐸2(𝑡) + ⋯+ 𝜒n𝐸n(𝑡), (12) and 𝑃(𝐸(𝑡)) = 𝜀0(𝜒0 + 𝜒1𝐸(𝑡) + 𝜒2𝐸2(𝑡) + ⋯+ 𝜒n𝐸n(𝑡)) ⋅ 𝐸(𝑡). (13) The Pockels effect [154] arises when 𝜒1 is the prevailing order of electric field susceptibility, causing a second order nonlinear material polarisation, 𝑃𝑛𝑙(𝑡), within the electro-optic crystal 𝑃𝑛𝑙(𝑡) = 𝜀0𝜒1𝐸2(𝑡) = 𝜀0𝜒1𝐸202(1 + cos(2𝜔𝑡)) (14) A filter (e.g., indium phosphide wafer) is inserted in the THz beam path to remove the high frequency component and changing the equation to 𝑃𝑛𝑙(𝑡) = 𝜀0𝜒1𝐸202. (15) When activated by an ultra-short optical pulse, this nonlinear polarisation term is activated for the duration of the optical pulse. Thus, an electric field, with sub-picosecond duration, having THz-level bandwidth is created. For additional information on optical rectification, I recommend the text by Dr. David G. Cooke [155]. 3.4 Terahertz Detection The detection of THz radiation for THz-TDS is achieved by utilising a THz detector. Terahertz detectors are devices that measure THz radiation by leveraging the forward processes of the photoconductive effect of semiconductors or the electro-optic effect of nonlinear optical crystals. The working principle of THz detection for both photoconductive and electro-optic detectors are examined in Chapter 3.4. 33 3.4.1 Photoconductive Detection The Photoconductive THz detector is seen on Figure 3.4.1.1. The photoconductive THz detector comprises of a pellicle beam splitter (BS), a parabolic mirror (PM), a gallium arsenide semiconductor wafer patterned with surface electrodes that are connected to an ammeter and ground. This photoconductive detector measures, by inference, THz electric field using the 'forward' photoconductive process. The operation of this device is as follows: the photoconductive THz detector utilises incident 𝐸THz as a bias electric field, ?⃗? bias, without the need for an applied Vbias to the electrodes. The electrodes are instead attached to an ammeter for subsequent current measurements. The 𝐸THz beam is overlapped with the probe beam path laser pulse, ?⃗? opt(𝜔𝑡), using a pellicle beam splitter. These overlapped beams are focused using a gold-sputtered parabolic mirror, ideally suited for THz radiation, though functional for optical laser beams. Terahertz radiation is absorbed by glass, thus silvered backed glass plates (i.e., standard mirrors) are not sufficient for THz reflection or THz focusing using conventional glass lenses. The overlapped and focused beams, ?⃗? opt(𝜔𝑡) and ?⃗? THz(𝑡), are synchronised in time, with t = t1 for both signals, and strike the gallium arsenide component of the photoconductive THz detector. Such that, the applied THz electric field biases the gallium arsenide semiconductor, which produces a measurable current for the duration of optical excitation by a pulsed laser. The current magnitude is proportional to the intensity of applied THz electric field, that is, 𝐼ph ∝ ?⃗? THz(𝑡). The laser pulse, ?⃗? opt(𝜔𝑡), and ?⃗? THz(𝑡) are of similar timescales, permitting only a portion of the 𝐸THz signal to be measured at any given time corresponding to the peak of ?⃗? opt(𝜔𝑡). The inference of THz radiation is accomplished using a time-resolved measurement scheme. The time-resolved measurement scheme allows for many point measurements of the THz signal. The ?⃗? opt(𝜔𝑡) and ?⃗? THz(𝑡) pulsed signals generated, at mode-locked laser repetition frequency (e.g., 80 MHz), with high degree of repeatability sufficient for the time-resolved measurement scheme. The time-resolved measurement scheme is performed 34 Figure 3.4.1.1 The photoconductive detector process is shown. The terahertz pulse is shown in grey and the optical probe pulse is shown in red. 35 by measuring the gallium arsenide current at many varying degrees of time delay (i.e., t = t2, …, t = tn) between overlapped and synchronized ?⃗? opt(𝜔𝑡) and ?⃗? THz(𝑡). The time differential between the laser pulse ?⃗? opt(𝜔𝑡) (i.e., topt = t1, t2, …, tn) and THz pulse, ?⃗? THz(𝑡) (i.e., tTHz ≡ t1) is achieved by increasing the distance of the probe beam path using an optical delay stage; such that, ∆t = tTHz - topt = 0, t1, …, tn-1. The culmination of current data points from measured different THz electric field events are constructed into a single THz signal. Figure 3.4.1.1 depicts a representation of these delayed THz and laser pulse events for an example case where t = t1, t2, and t3. The probe pulses are delayed in time as such and are seen in the inset figure underneath a THz pulse signal. Dashed lines connecting the peaks of the laser pulses to the relative portion of THz signal are shown. The time-resolved measurement scheme is also used in the electro-optic detection of THz. 3.4.2 Electro-Optic Detection The electro-optic THz detector [156] is seen on Figure 3.4.2.1. The electro-optic THz detector comprises the following: a pellicle beam splitter (BS), a parabolic mirror (PM), a zinc telluride nonlinear crystal (i.e., ZnTe), collimating lens, quarter wave-plate (i.e., circular polariser), polarisation beam splitter (i.e., Wollaston prism), and a differential mode balanced silicon photodiode. The electro-optic detector measures, by inference, THz electric field using the 'forward' electro-optic process. The operation of this device is as follows: the configuration of the BS and PM allow for the THz electric field, ?⃗? THz(𝑡), and probe beam pulse, ?⃗? opt(𝜔𝑡), to overlap and become incident onto the zinc telluride nonlinear crystal. The probe beam pulse is generated having a (relative) diagonal type linear polarisation state by the mode-locked fiber laser. Meaning, a majority of the probe beam photons oscillate within a 45° X-Y plane— 36 Figure 3.4.2.1 The electro-optic terahertz detection process. The terahertz pulse is shown in grey and the optical probe pulse is shown in red. 37 diagonal type linear polarisation state being the net magnitude of 0° X-plane polarised photons oscillating in-phase with 90° Y-plane polarised photons. The incidence of the THz electric field enables the 'forward' electro-optic process to occurs, such that the Pockels effect transpires within the zinc telluride. The Pockels effect causes the zinc telluride to manifest a variation in birefringence proportional to the magnitude of incident THz electric field [157]. Birefringence is the property of a transparent material to have different refractive indices for different polarisations states of light. That is to say, zinc telluride by influence of ?⃗? THz(𝑡), will decrease the permissible propagation speed (i.e., increase in refractive index) of either horizontal or vertical components of polarised, ?⃗? opt(𝜔𝑡), by differing amounts. For example, THz excited zinc telluride will phase delay the X-plane polarisation component of X-Y diagonal polarised ?⃗? opt(𝜔𝑡). The consequence of this phase delay is that the net angle of oscillation for X-Y plane diagonal polarised light will change from 45° to 20°, for instance. (These values are exaggerated for expository purposes.) A zinc telluride crystal with 500 μm thickness and a 780 nm pulsed laser corresponds to minimal phase mismatch, such that, there is negligible distortion of roughly 3 THz bandwidth THz pulses. This 25° difference in polarisation is illustrated on Figure 3.4.2.1, within the inset figure, labeled under the 'A' case polarisation state. When ?⃗? THz(𝑡) is not present on zinc telluride, the net polarisation of ?⃗? opt(𝜔𝑡) is illustrated at an example case of 0° (depicted as a red arrow). When ?⃗? THz(𝑡) is incident onto zinc telluride, the net polarisation of ?⃗? opt(𝜔𝑡) is illustrated at 25° (depicted as a grey arrow). Once ?⃗? opt(𝜔𝑡) propagates through zinc telluride, this beam is collimated by a lens and interacts with a circular polariser. The circular polariser significantly phase delays the X-plane or Y-plane component of net X-Y plane diagonally polarised light by a full quarter wave. The outcome of a quarter wave phase delay is circular polarised light. Circular polarised light has the net polarisation changing though all 360° for one period of optical wavelength, 𝜔𝑡—represented as the red symmetrically circular under 'B' case polarisation state from Figure 3.4.2.1. Again, when ?⃗? THz(𝑡) is present, the net circular polarisation changes 38 from symmetrically circular to elliptically circular, as seen by the grey elliptical arrow under 'B' case polarisation state on Figure 3.4.2.1. The circular polariser is needed so that the X-plane and Y-plane ?⃗? opt(𝜔𝑡) components can later be separated without attenuation of either component—as would be the case by using a standard linear polarising filter. Finally, the circular or elliptical polarised ?⃗? opt(𝜔𝑡) interacts with the Wollaston prism, which directs the new X-plane and Y-plane components down different paths to be measured by a balanced photodiode. The 'C' and 'D' polarisation states on Figure 3.4.2.1 show equal magnitude X-plane and Y-plane components (red arrows) when ?⃗? THz(𝑡) is zero. The differential feature of the balanced photodiode measures and subtracts these two identical magnitude signals giving a zero net signal while rejecting random noise signals common to single element detectors. Non zero ?⃗? THz(𝑡) corresponds to nonequal magnitude X-plane and Y-plane ?⃗? opt(𝜔𝑡) components (grey arrows), with the difference measured by the balanced photodiode being proportional to the magnitude of THz electric field incident onto the zinc telluride. The time-resolved measurement scheme is used in the electro-optic THz detection device. The operation of the time-resolve measurement scheme was discussed in Chapter 3.4.1, with the illustrative inset for temporally offset THz electric field, ?⃗? THz(𝑡) and probe beam, ?⃗? opt(𝜔𝑡), pulses seen on Figure 3.4.2.1. 3.5 Terahertz Measurement and Terahertz Spectroscopy Terahertz spectroscopy makes use of THz measurements with and without a sample present, and is used to determine the absorption coefficient and refractive index of a sample over the THz bandwidth of the THz pulse (or over some portion of the THz bandwidth). Unique sample characteristics can be evaluated by studying the absorption of THz radiation at specific frequencies [158]. For example, myoglobin has a strong THz signal at approximately 2 THz [159]. Terahertz absorption studies can be performed using THz-TDS systems. These systems can uncover the absorption coefficient and refractive index of THz radiation 39 for a sample at many frequencies; however, system parameters like dynamic range and maximum absorption coefficient should be established and appreciated when interpreting THz-TDS results. The configuration, operation, and data interpretation a THz-TDS system is discussed the remaining Chapter 3. The complete THz-TDS system is illustrated on Figure 3.5.1. The THz-TDS system depicts a fiber pulsed laser (i.e., mode-locked laser), which generates 780 nm 100 fs pulses, at a repetition frequency of 80 MHz. The initial beam from the laser is split into two separate beam paths, via a beam splitter (BS), which are the pump beam and the probe beam. The pump beam is used for sample excitation, whereas, the probe beam is used for THz detection. This THz-TDS system is configured to operate via photoconductive THz emission and an electro-optic electro-optic THz detection architectures. The pump beam is reflected off of various mirrors, some of which reside on the optical delay stage, until interaction with a microscope objective lens. The objective lens focuses the pump beam onto the photoconductive THz emitter (i.e., PC THz emitter). The conductive electrodes of the photoconductive THz emitter has a potential difference, Vb, applied as a bias voltage—being a square waveform with frequency required for subsequent lock-in detection. The square voltage waveform is generated by a function generator and inverting op-amp circuit (not seen on figure). The photoconductive THz emitter generated THz radiation and is collimated and refocused, with parabolic mirrors (PM), onto the sample under test. Some THz frequencies are absorbed within the sample, with the remaining THz radiation being transmitted onto another pair of PM, passing through a BS, and focused onto a zinc telluride crystal (i.e., ZnTe crystal), used for electro-optic detection of THz. The probe beam is reflected off the BS, overlapping with the THz beam, and focused onto the zinc telluride crystal for electro-optic detection of THz. The electro-optic detection of THz necessitates the polarisation of probe beam to be modulated in proportion to THz radiation; as is achieved by the zinc telluride THz interaction effects (i.e., Pockels effect). The probe beam polarisation is further processed, using a circular polariser and a Wolliston prism, for separation of X-plane and Y-plane polarisation components. The ratio between separated X-plane and Y-plane probe beam polarisation components are proportional to the intensity of THz radiation incident on zinc telluride nonlinear crystal. This ratio is 40 Figure 3.5.1 A terahertz time-domain spectroscopy system. 41 measured by a balanced silicon (Si) photodiode, which differences the two beams leaving the Wolliston prism. This measurement is performed many times, at various time differences between probe beam pulse and pump beam pulse, for the time-resolved measurement scheme. The time difference between pulses is achieved by increasing the distance the pump beam travels. The pump beams travel distance is increased by scanning through the delay stage positions, represented in Figure 3.5.1 as ∆x. The measured THz signals, via the balanced photodiode, are conditioned using a current preamp (not seen on figure), lock-in amplifier (not seen on figure), and are recorded using a DAQ connected to a computer, which records the delay stage position. A THz-TDS system is used to determine the absorption coefficient and refractive index of a sample for a spectrum of THz frequencies. The calculation of the absorption coefficient requires the measurement of the THz electric field for both the sample, ?⃗? sam(𝑡), and of free space for reference, ?⃗? ref(𝑡). The sample and reference time-domain THz electric field signals are converted, using the Fourier transform, into the frequency-domain. The amplitude ratio, 𝐴(𝑓) =|?⃗? sam(𝑓)|/|?⃗? ref(𝑓)| , is the quotient between the sample and reference THz electric field. This ratio is required to derive the absorption coefficient, 𝛼(𝑓), for THz-TDS. The absorption coefficient is described by 𝛼(𝑓) = −2𝑑ln(|?⃗? sam(𝑓)||?⃗? ref(𝑓)|(𝑛(𝑓) + 1)24𝑛(𝑓)), (16) as reported in Jepsen and Fischer [160]. This equation requires the following properties to be additionally known for successful calculation: the reciprocal of the sample thickness, 𝑑−1, and the sample refractive index, 𝑛(𝑓). The sample refractive index, as a function of frequency, is established using the phase-delay information, 𝜙(𝑓), as captured from the sample THz electric field measurements. The refractive index equation is described as 𝑛(𝑓) = 1 + 𝑐2𝜋𝑓𝑑𝜙(𝑓). (17) 42 In the early stages of THz-TDS research, it was thought that refractive index and absorption coefficient where sufficient for THz spectroscopy analysis. However, a noteworthy contribution by Jepsen and Fischer [160] established the caveat of system dynamic range, and therefore maximum absorption coefficient, contributes to THz spectroscopy analyses. Specifically, it was determined that evaluation of a sample absorption coefficient, 𝛼(𝑓), is only valid when residing below the maximum absorption coefficient, 𝛼max. The alpha max value corresponds to the dynamic range, 𝐷𝑅, of the THz-TDS system. Alpha max is described as 𝛼max =2𝑑 ln (DR4𝑛(𝑛 + 1)2) . (18) The equation for dynamic range 𝐷𝑅 =|?⃗? ref(𝑓)|noise floor , (19) is set by the Fourier transform of the measured THz pulse, normalized to the noise floor. Dynamic range can be thought of as a function of the bandwidth for a THz-TDS system. Terahertz electric fields measured within the bandwidth, reside above the noise floor measurement noise floor, and below the maximal signal amplitude producible by the reference THz pulse, for a given frequency. With this information THz electric field data can be converted into frequency-domain graphs appropriate for absorption coefficient analyses [161]. 3.5.1 Terahertz Time-Domain Spectroscopy Measurements on Water Vapour The following provides an examination of a typical THz-TDS experiment analysing water vapour, and establishes the experimental basis of much of the proposed work. The data is reformed from my coauthored work published in IEEE Journal of Selected Topics in Quantum Electronics [9] and used here to illustrate THz-TDS through a photoconductive emitter and photoconductive detector setup. Water molecules have a high absorption to THz radiation, being ideally-suited for an exposition experiment, due 43 to its abundance within room temperature air. Water vapour found in air is used as the 'sample', and the reference signal is taken when nitrogen has purged the sample chamber—voiding the chamber of air and therefore water vapour. The pertinent experimental data for this examination are shown as time-domain and frequency-domain graphs. Figure 3.5.1.1(a) depicts the THz electric field, ?⃗? ref(𝑡), for the reference pulse in the time-domain. The reference pulse is captured without the majority of water vapor found in air, as achieved by a nitrogen purge of the sample measurement chamber. The THz pulse is shown as a large spike in electric field starting at approximately 12 picoseconds. The THz pulse quickly returns to baseline with minor oscillations for the remainder of the measurement scan time window. Figure 3.5.1.1(b) depicts the THz electric field, |?⃗? ref(𝑓)|, for the reference pulse in the frequency-domain. This frequency spectrum is shown as curve with a roll-off characteristic starting at 0.50 THz. The downward spikes are at 1.70 THz and 2.40 THz correspond to the aforementioned minor oscillations in the time-domain. Figure 3.5.1.2(a) depicts the THz electric field, ?⃗? sam(𝑡), for the sample pulse in the time-domain, i.e., the THz pulse passed through the vapour-rich environment. The sample pulse is captured with the majority of water vapor found in air, as achieved by conducting the THz scan without the use of the sample enclosure and nitrogen. The THz pulse is shown as a large spike in electric field magnitude starting at approximately 12 picoseconds. The THz pulse quickly returns to baseline with significant oscillations for an additional 40 picoseconds, with minor oscillations for the remainder of the measurement scan time window. Figure 3.5.1.2(b) depicts the magnitude of the THz electric field, |?⃗? sam(𝑓)|, for the sample pulse in the frequency-domain. This frequency spectrum is shown as curve with a roll-off characteristic starting at 0.50 THz. The many downward spikes correspond to the aforementioned significant oscillations in the time-domain. The downward spikes are commonly referred to as absorption lines; which coincide with THz attenuation due to resonance-absorption interaction with THz wavelengths, molecular structures, and 44 Figure 3.5.1.1 (a) a measured terahertz pulse vs. time and (b) the same terahertz pulse vs. frequency. This is for a vapour free environment. 45 Figure 3.5.1.2 (a) a measured terahertz pulse vs. time and (b) the same terahertz pulse vs. frequency. This is for a vapour-present environment. 46 vibrational modes (mode transitions) of water vapor, for the given frequency. Furthermore, there are notable absorption peaks beyond 3.0 THz that reside a plateau of the frequency spectrum. This plateau is associated with the noise floor of the THz spectroscopy measurement scan. Figure 3.5.1.3 depicts the dynamic range (i.e., DR) as a function of |?⃗? ref(𝑓)|. The noise floor of the dynamic range has been normalized to a value of one. The noise floor is denoted with a yellow dashed line. The dynamic range measurement establishes the bandwidth of all valid THz absorption measurements. The concept of dynamic range is extended in terms of absorption coefficient, 𝛼max, as depicted on Figure 3.5.1.4. Figure 3.5.1.3 The dynamic range of the measurement is shown as a black curve and the noise floor is shown as a yellow-dashed line. Figure 3.5.1.4 shows the absorption coefficient, 𝛼, as a function of frequency within the THz regime. The maximum absorption coefficient possible for this THz-TDS system, 𝛼max, is denoted with the red trace. The absorption coefficient for water vapour is denoted with the blue trace. The maximum absorption coefficient is derived from the dynamic range of the system. Thus, any absorption coefficient that is of greater magnitude than 𝛼max is considered impermissible in post experimental absorption coefficient analyses. The water vapour absorption lines are well above the 𝛼max beyond 3.0 THz frequency and thus are not trusted to produce quantified results for absorption. 47 Figure 3.5.1.4 The absorption coefficient of water vapour (α) is shown in blue and the maximum measurement (αmax) is shown in red. Figure 3.5.1.5 shows the water vapour absorption coefficient, 𝛼, as a function of THz frequency. Seven representative and distinct absorption peaks have been chosen for comparison with a known database of water vapour absorption frequencies. These frequencies are denoted with cardinal letters and compared to the associated absorption frequencies found within the HITRAN database for water molecules [162]. This data is summarized in Table 3.5.1.1 below. Table 3.5.1.1 Nominal Water Molecule Absorption Frequencies for HITRAN versus THz-TDS experimental data. Water Molecule Absorption Frequencies HITRAN Database THz-TDS Experimental Data 0.5573 THz 0.5625 THz "A" 0.7526 THz 0.7500 THz "B" 0.9886 THz 0.9875 THz "C" 1.1140 THz 1.1125 THz "D" 1.1640 THz 1.1625 THz "E" 1.2080 THz 1.2125 THz "F" 1.4120 THz 1.4125 THz "G" 48 Figure 3.5.1.5 The absorption coefficient is shown for a water vapour sample. Characteristic absorption peaks are indicated with cardinal lettering A through G. Table 3.5.1.1 summarises a subset of the main water molecule absorption frequencies found within the high-resolution transmission molecular absorption (HITRAN) database (left column). The water vapour absorption coefficient frequencies observed from the experimental THz-TDS data (illustrated in Figure 3.5.1.5) are listed (middle column). The cardinal lettering (right column) that relates the measured absorption peaks from Figure 3.5.1.5 to their associated frequencies (middle column) is shown. There is approximate agreement between the HITRAN and experimental THz-TDS absorption frequencies 3.6 Finite-Difference Time-Domain Theory The propagation of electromagnetic waves through media can be simulated using a finite-difference numerical method. In particular, the FDTD method is often used, such that, Maxwell's equations are modeled numerically using finite-difference approximations (i.e., a FDTD electromagnetic simulation), as described by Taflove [163]. 49 The fundamental FDTD electromagnetic simulation utilises the Yee algorithm as defined by Yee [164], whereby, the derivative operators of Maxwell's third and fourth equations are replaced with finite-difference approximations, becoming the update equations in the FDTD electromagnetic simulation. Here, the finite-difference approximation of Maxwell's fourth equation, for one dimension, is presented with the finite-difference substituted in place of the spatial and temporal derivative operators 𝐻y| 𝑘+1 2⁄ 𝑛− 𝐻y| 𝑘−1 2⁄ 𝑛∆𝑧= − 𝜀0𝐸x| 𝑘 𝑛+1 2⁄ −𝐸x| 𝑘 𝑛−1 2⁄∆𝑡 . (20) The corresponding update equation to calculate the electric field is 𝐸x| 𝑘 𝑛+1 2⁄ = 𝐸x| 𝑘 𝑛−1 2⁄ −∆𝑡𝜀0∆𝑧(𝐻y| 𝑘+1 2⁄ 𝑛− 𝐻y| 𝑘−1 2⁄ 𝑛) . (21) The finite-difference approximation of Maxwell's third equation, for one dimension, is presented with the finite-difference substituted in place of the spatial and temporal derivative operators 𝐸x| 𝑘+1 𝑛+1 2⁄ − 𝐸x| 𝑘 𝑛+1 2⁄∆𝑧= − 𝜇0𝐻y| 𝑘+1 2⁄ 𝑛+1− 𝐻y| 𝑘+1 2⁄ 𝑛∆𝑡 . (22) The corresponding update equation to calculate the magnetic field is 𝐻y| 𝑘+1 2⁄ 𝑛+1= 𝐻y| 𝑘+1 2⁄ 𝑛−∆𝑡𝜇0∆𝑧(𝐸x| 𝑘+1 𝑛+1 2⁄ − 𝐸x| 𝑘 𝑛+1 2⁄ ) . (23) These equations are for a one-dimensional FDTD electromagnetic simulation corresponding to a Yee grid where the propagation of the electric and magnetic fields are calculated for alternating spatial and temporal steps [165–168]. These update equations are implemented to solve a wave propagating along the Z-axis. Thus, the electric field is confined to the X-axis and the magnetic field is confined to the Y-axis, which corresponds to alternating rows of the Yee gird. Figure 3.6.1 depicts an explanatory diagram of a Yee grid scheme for a one-dimensional FDTD electromagnetic simulation. The Yee grid encompasses the iterative calculations, via the update equations, for the electric field, Ex, and the magnetic field, Hy, for a change in space (i.e., ∆z), denoted with k, and a change in time (i.e., ∆t), denoted with n. 50 Figure 3.6.1 A depiction of a Yee grid scheme for a one-dimensional finite-difference time-domain electromagnetic simulation. 51 Using the Yee grid scheme, the Ex component is calculated, at the current time interval n and spatial interval k, using two spatially adjacent Hy components located at k ‒ 0.5 and k + 0.5 spatial intervals, for a previous time interval of n ‒ 0.5. Likewise, the Hy component is calculated, at the current time interval n + 0.5 and spatial interval k + 0.5, using two spatially adjacent Ex components located at k and k + 1 spatial intervals, for a previous time interval of n. This process is repeated for every spatial interval within the Yee grid until the desired number of time intervals have elapsed [164]. A demonstration of wave propagation via a one-dimensional FDTD electromagnetic simulation is shown within Chapter 5 as Figure 5.4.1. The FDTD electromagnetic simulation via calculation of electric and magnetic fields (i.e., field components) using a Yee grid scheme, requires information from the orthogonal field components at the adjacent k spatial intervals, at the previous n time interval. The required field component information at the k + 0.5 spatial interval is not available beyond the boundary of the Yee grid. This problem can be managed using a variety of methods. One such method is the implementation of a Dirichlet boundary condition. Here, the unknown field components outside the Yee grid are set to a zero value, causing total reflections at the Dirichlet boundary. These reflections can be undesirable and can cause inaccurate modeling of a structure. The reflections can be removed using an absorbing boundary condition method [169] for a one-dimensional FDTD electromagnetic simulation by modifying the update equations at the boundary of the Yee grid. However, an absorbing boundary condition method is not ideal for multiple angles of incidents when implemented in two-dimensional and 3D FDTD electromagnetic simulations [170]. This problem can be addressed for two-dimensional and 3D FDTD electromagnetic simulations by using the perfectly matched layer method [171]. A perfectly matched layer is applied along the boundary of the Yee grid and attenuates incident waves to a negligible magnitude before reflection into the simulation space. The standard implementation of the one-dimensional FDTD electromagnetic simulation, as briefly introduced and described above, is applied to complement the experimental works found in Chapters 5 and 6 of this thesis. 52 3.7 Chapter Conclusions In this chapter, the experimental framework was shown for THz-TDS and THz operation through emission and detection of THz waves. Terahertz emitters and detectors were discussed. Experimental THz-TDS measurements were shown for a water vapour sample and prove to be in approximate agreement with HITRAN database values. The fundamental operation of the one-dimensional FDTD electromagnetic simulation was briefly discussed, as this topic is relevant to the theoretical and experimental work found in Chapter 5 and Chapter 6. 53 Chapter 4: A Comprehensive Study of Three-Dimensional Printing Materials over the Terahertz Regime: Absorption Coefficient and Refractive Index Characterisations This chapter provides a consolidative and comprehensive THz-TDS measurement study performed on twenty-four 3D printing filament materials. This experimental study of material analyses is presented in the following subchapters: Background (Chapter 4.1), Revisiting of Experimental Terahertz Method and Visualisation of Terahertz Time-Domain Spectroscopy System Configuration (Chapter 4.2), The Terahertz Time-Domain Spectroscopy Method (Chapter 4.3), Polylactic Acid Filament Materials (Chapter 4.4), Common Alternatives to PLA Filament Materials (Chapter 4.5), Flexible Filament Materials (Chapter 4.6), Dissolvable Support Filament Materials (Chapter 4.7), Nylon Filaments Materials (Chapter 4.8), Packaging Thermoplastic Filament Materials (Chapter 4.9), Non-Standard Filament Materials (Chapter 4.10), Sample Images of 3D Printed Materials (Chapter 4.11), Summary of Absorptive and Refractive Properties and Product details on 3D Printed Filament Materials (Chapter 4.12), Absorption Coefficient, Refractive index, and Loss Tangent Analysis of 3D Printed Materials (Chapter 4.13), Chapter Conclusions (Chapter 4.14). Elements of this thesis chapter were first published in the following article: A comprehensive study of 3D printing materials over the terahertz regime: Absorption coefficient and refractive index characterisations, Optical Materials Express, vol. 12, pp. 3379-3402, 2022. © 2022 Optica Publishing Group. Additionally, elements of this thesis chapter were presented as the following conference proceeding: Terahertz time-domain spectroscopy of 3D printed materials, 2022 Proceedings of Photonics North. 4.1 Background Generation of THz radiation has become increasingly accessible over time. The research and development of THz applications is ongoing, often requiring the use of THz compatible optical components. At the same time, rapid prototyping 3D printing systems are now commercially accessible and are capable of printing resolutions on the order of the THz wavelengths. Thus, 3D printing systems can be leveraged for use in creating novel THz optical components in varied experiments and applications. The filament material used in 3D printing systems dictates the absorptive and refractive properties of the 3D 54 printed THz optical component. The commercial release of filament materials is continuous, year after year, inducing a need for literature to stay current with characterising these filament materials over the THz gap. In this Chapter, THz-TDS is used to characterise the absorptive and refractive properties of 3D printing materials over the THz gap. Additionally, a consolidative and comprehensive aggregation of THz-TDS measurements of twenty-four 3D printing materials is presented in this Chapter. A comparison of THz-TDS measurements for thick and thin samples provides for verification of measurement accuracy. The measured THz bandwidth of these samples is extended by up to 1.2 THz. Furthermore, to the author's best knowledge, this work puts forward the first THz-TDS measurements of polyvinyl butyral (PVB), polyetherimide (PEI), and low temperature polycaprolactone (LT PCL) filament materials. This work primarily focuses on FFF 3D printed materials, rather than stereolithography 3D printed materials. Terahertz optical components are constructed from materials that are known to be THz compatible, such as quartz [172], silicon [173], and polytetrafluoroethylene (PTFE) [174]. These THz compatible materials are often implemented with predefined/standard geometries, as shaping of these materials for THz research can be challenging. Fortunately, such a challenge can be mitigated by fabrication equipment that is capable of rapid prototyping [175]. Emergence of novel materials for rapid prototyping (i.e., AM) is ongoing [176], with characterisation of these materials in the THz gap being advantageous for assessing potential use in THz applications [177]. The typical filament materials used for FFF 3D printers are PLA filament material [178], ABS filament material [179], and PETG filament material [180]. Typical 3D printed materials that are used for vat polymerization based 3D printers are acrylate [181] and methacrylate [182] photopolymer resins. The FFF and stereolithography based 3D printing systems are capable of printing resolutions on the micrometre scale, which is being leveraged in radiofrequency and photonics research applications [183] [184]. The spatial resolution of modified FFF 3D printers can be as low as 100 µm [185] (with ubiquitous consumer grade systems achieving 250 µm resolution) and the spatial resolution of industrial grade stereolithography 3D printers can be below 20 µm [186] (with 100 µm resolution being common with ubiquitous consumer grade systems). These lower limits for feature size of 20 to 100 µm are comparable to 55 wavelengths in the THz spectrum. This makes 3D printing systems well suited to the fabrication of THz optical components. The aim of this Chapter 4 is to expand upon the measurements noted in Table 2.1.1 from Chapter 2.1 and to fill in literature gaps with THz-TDS characterisations of additional filament materials. 4.2 Revisiting of Experimental Terahertz Method and Visualisation of Terahertz Time-Domain Spectroscopy System Configuration A collection of twenty-four 3D printing filament materials are assessed for THz absorptive and refractive properties using the THz-TDS method. When possible, the 3D printing filament materials are chosen to have the corresponding natural filament colour, or otherwise with a white filament colour. These material samples are printed from commercially available 3D printer filament into 25.4 mm diameter disks at an approximate target thickness for two of the following dimensions: 300 µm, 700 µm, 1400 µm, or 2100 µm. The FFF 3D printer is configured to operate at an infill ratio of one hundred percent, producing an approximately solid sample disk. The samples are printed with a generic FFF 3D printer (IIIP 15365) capable of a maximum extruder temperature of 250°C, an X-Y axis resolution of 200 µm, and a Z-axis layer height configuration set to 175 µm. The sample and reference THz electric field measurements are taken in a nitrogen enclosure to mitigate water vapor effects in the THz frequency spectrum. The THz-TDS method is performed in free space, using the THz system configuration displayed in Figure 4.2.1(a). This uses a photoconductive emitter and electro-optic detector, as described in Chapter 3.5. A 3D computer rendered image of the THz-TDS system is shown as an experimental optomechanical setup on an optical table, with two distinct laser beam paths—the pump beam (Pump), required for photoconductive THz emission, and the probe beam (Probe), required for electro-optic THz detection. The exact component configuration of this system is shown by the top view image in Figure 4.2.1(b). Here, two 780 nm wavelength laser beams, being the pump and probe beams, are generated and sent onto the optical table via an ultrafast Ti:Sapphire pulsed laser (Spectra-Physics Mai Tai HP, MKS Instruments Inc., Massachusetts, USA), with a rated pulse duration of <100 fs, and rated repetition rate of 80 MHz. 56 Figure 4.2.1 (a) A three-dimensional model of the terahertz time-domain spectroscopy setup is shown upon an optical table. (b) A top-view of the three-dimensional model of the terahertz time-domain spectroscopy setup is shown. The abbreviation labels are as follows: pump laser beam (Pump), probe laser beam (Probe), microscope objective (MO), photoconductive emitter (PE), parabolic mirror (PM), THz beam path (THz), three-dimensional printed sample material (Sample), pellicle beam splitter (BSpel), electro-optic crystal (EO), lens (L), mirror (M), quarter wave plate (QW), polarisation beam splitter (BSpol), and balanced silicon photodiode (PDsi). 57 The pump beam is directed into a microscope objective (MO) and focused onto the electrodes of a gallium arsenide THz photoconductive emitter (PE), biased with a 100 Vpk-pk square wave of known frequency, fbias. The obtained THz signal from the electro-optic detection is from lock-in detection to fbias. The PE, excited by the pump beam, generates THz radiation (shown in yellow) in a point source emission pattern. This point source of THz radiation is projected onto a parabolic mirror (PM) and shapes the THz point source into a collimated THz beam path. The collimated THz beam path is then incident upon and passes through a sample of 3D printing material (Sample) and continues to pass through a pellicle beam splitter (BSpel). At the same time, the probe beam is directed using standard mirrors (M) onto the BSpel and overlapped spatially with the THz beam path—and subsequently is overlapped temporally using an optical delay stage (IMS600CCHA, MKS Instruments Inc., Massachusetts, USA; not shown on figure). Both the THz beam (THz) and the probe beam are focused by the second PM onto a zinc telluride electro-optic crystal (EO) that is cut to <110> orientation. Consequently electro-optic detection is achieved, where the magnitude of the incident THz radiation is inferenced by a proportional change of probe beam polarisation state within the electro-optic crystal. The modulated probe beam is now recollimated by a lens (L) projected onto a quarter-wave plate (QW). The now circular or elliptical polarisation of the probe beam (in the presence of THz) is induced by the phase delay of a quarter wavelength, with the horizontal or vertical polarisation components of the probe beam separated by a polarising beam splitter (BSpol). The polarisation components of the probe beam are measured by a balanced silicon photodiode (PDSi). The measured optical signal is differentiated and transduced by the PDSi for isolation and acquisition from a lock-in amplifier at fbias (SR830, Stanford Research Systems, California, USA; not shown on figure). 4.3 The Terahertz Time-Domain Spectroscopy Method Two measurements on two different thicknesses is important because it can reveal any variation in the measurement, although variation between measurements is minimal throughout this study. An example measurement is shown of the well-characterised PLA filament material to demonstrate the above concepts. Figure 4.3.1 shows the absorption spectra and the maximum measurable absorption spectra for sample 58 thicknesses of approximately 1400 µm (thick) and 700 µm (thin). Note from this figure that the results for the thick and thin PLA filament materials extend up to different maximum measurable frequencies, at 1.4 to 1.7 THz, respectively, due to their overall losses, at high and low levels, respectively. This distinction will be seen throughout the remainder of this work. The results of Figure 4.3.1 are in agreement with other measurements of the well-studied PLA material [63] [64]. This comparison to literature reveals that the THz-TDS setup is well calibrated. The oscillations present in the maximum absorption coefficient curves of Figure 4.3.1, i.e., the max blue and red dashed lines, are due to reflections from the electro-optic crystal which is a <110> zinc telluride crystal of 500 m thickness. An estimate of the free-spectral range associated with this oscillation shows the free-spectral range to be approximately 0.1 THz, and this is consistent with the 0.1 THz spacing of local maxima/minima in the oscillations of the Figure 4.3.1 curves. This free-spectral range effect is much less in subsequent absorption coefficient curves, as these calculations divide amplitude of sample and reference measurements, thus largely removing the free-spectral range effect. Ultimately, to use any 3D printed material as a THz optical component, one must have knowledge of its overall absorptive and refractive properties. Therefore, THz-TDS is performed on a 3D printed sample, rather than on its fundamental material. The printed sample will show the ultimate properties of the fabricated device. Therefore, the results that are presented will be representative of a realistic printed object and characterise the overall effective absorption and refraction of the system. Any variation in absorption measurements is minimal, and the measurement is performed with multiple thicknesses, with similar absorption and refraction characteristics observed. Effects of the gap between each layer of samples of 3D materials has been previously studied for the THz regime [68]. Naftaly et al. states that although there will be both higher loss coefficient and scattering loss for 3D printed materials, these effects will counteract each other. 59 Figure 4.3.1 The absorption coefficient (solid curves) and alpha max. (dotted curves) are each shown for polylactic acid (PLA) filament material with approximate sample thicknesses of 700 µm (blue) and 1400 µm (red). 4.4 Polylactic Acid Filament Materials Polylactic acid is a common filament material for consumer grade FFF printers [187]. In Figure 4.4.1 The standard PLA filament material is compared with non-standard PLA filament materials that are manufactured with blended metallic particles ranging from five to eight percent by volume. The samples are fabricated with FFF. The standard PLA of Figure 4.4.1(a) is measured with a bandwidth of B = ∆f = fmax – fmin = 1.76 THz – 0.20 THz = 1.56 THz. (The bandwidth for each filament material can be seen in Table 4.12.1.) This PLA filament material is compared for filament materials blended with copper (PLA Cu) in Figure 4.4.1(b), blended with iron (PLA Fe) in Figure 4.4.1(c), and blended with tungsten (PLA W) in Figure 4.4.1(d). The corresponding absorption coefficients and refractive indices are displayed for target sample thicknesses being approximately 700 μm and 1400 μm. The plots for the absorption coefficient and refractive index are displayed up to the maximum measurable frequency (as the intersection of absorption coefficient and alpha max.). Similar absorptive properties are observed across these samples in Figure 4.4.1. There is a notable change in refractive index between the PLA filament material and PLA Cu filament material, from 1.54 to 1.79, respectively. 60 Figure 4.4.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample materials: (a) polylactic acid (PLA) filament material, (b) PLA filament material with embedded copper (PLA Cu) particles, (c) PLA filament material with embedded iron (PLA Fe) particles, and (d) PLA filament material with embedded tungsten (PLA W) particles. 61 The absorption coefficient and refractive index are important parameters for the application of 3D printed materials for the fabrication of THz optical components. Typically, a material with higher refractive index and lower absorption is desirable for optimal performance of 3D printed THz optical components [188]. This is because higher refractive index materials will refract light at more extreme angles than those of lower refractive index materials for the same thickness of material. Thus, the desired THz beam shaping can be accomplished with less material and less absorption of THz radiation, allowing higher efficiency of THz transmission. For this Chapter work and its application, it is deemed that a 3D printer filament material will be effective for use in THz optical components only up to a maximum permissible frequency, wherein the absorption coefficients at or below this frequency are less than 10 cm-1. This 10 cm-1 value comes about through an analysis of a nominal THz optical component. Such a component may have an order of magnitude greater size than a 300 m wavelength (corresponding to 1 THz frequency), being 3 mm. Under these conditions, full absorption (defined here as being attenuation of intensity below five percent of initial value) will occur when absorption coefficient is 10 cm-1. Thus this 10 cm-1 absorption coefficient represents a threshold between THz-desirable and THz-undesirable materials. For materials exhibiting comparable absorption coefficients, it is deemed the material with the higher refractive index to be preferable. The results of the THz-TDS of PLA filament material, PLA Cu filament material, PLA Fe filament material, and PLA W filament material indicate that these materials can be effective for use in THz optical components up to maximum permissible frequencies of 0.54 THz, 0.48 THz, 0.46 THz, and 0.52 THz, respectively. In Figure 4.4.2, two non-standard PLA filaments are compared: PLA filament material embedded with pine tree particles (PLA Pine) in Figure 4.4.2(a); and PLA filament material embedded with electrically conductive particles (PLA Cond.) in Figure 4.4.2(b). The samples are fabricated with FFF. The corresponding absorption coefficients and refractive indices are displayed for target sample thicknesses of approximately 700 μm and 1400 μm. The plots for the absorption coefficient and refractive index are displayed until the absorption coefficient intersects alpha max. Due to limitations manifesting from high 62 Figure 4.4.2 The absorption coefficient and refractive index are shown for the approximate sample thicknesses of 300 µm, 700 µm, and 1400 µm for the following sample filament materials: (a) polylactic acid filament material embedded with pine wood particles (PLA Pine) and (b) PLA filament material embedded with conductive particles (PLA Cond.). 63 absorption coefficient and/or low alpha max., the PLA Cond. filament material is measured for a single sample with a thickness of approximately 300 μm. This is because thicker samples of PLA Cond. filament material reach alpha max. at the minimal measurable THz frequency. The PLA Cond. filament material has a high refractive index (i.e., 2.38), but its absorption is not ideal for THz optical components needing strong transmission [188]. Nonetheless, such a material may be of use below the THz spectrum, i.e., below 0.3 THz, where its absorption is low [188]. Continuous wave THz sources could be used here at frequencies of 0.1 THz, 0.2 THz, or 0.3 THz (Terasense Group, Inc. San Jose, California, USA). These match the aforementioned lower absorption range of some 3D printed filament materials. The results of THz-TDS of the PLA Pine filament material and PLA Cond. filament material indicate that these materials can be effective for use in THz optical components up to maximum permissible frequencies of 0.56 THz, and a frequency below the minimum measured frequency, i.e., fTHz < fmin, respectively. That is, PLA Cond. filament material is highly absorptive to THz radiation and is thus not desirable for transmission based 3D printed THz optical components. 4.5 Common Alternatives to PLA Filament Materials Common alternatives to the PLA filament materials are compared in Figure 4.5.1. The figure shows PETG filament material in Figure 4.5.1(a), ASA filament material in Figure 4.5.1(b), ABS filament material in Figure 4.5.1(c), and polycarbonate co-polyester (PC CPE) filament material in Figure 4.5.1(d). The samples are fabricated with FFF. The corresponding absorption coefficients and refractive indices are displayed for two of three target sample thicknesses being approximately 700 μm, 1400 μm, and 2100 μm. Again, the plots for the absorption coefficient and refractive index are displayed until the absorption coefficient has intersected with alpha max. The results are comparable for both absorption coefficient and refractive index across these samples. The results of THz-TDS of the PETG filament material, ASA filament material, ABS filament material, and PC CPE filament material indicate that these materials can be effective for use in THz optical 64 Figure 4.5.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lightest respective colour), 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample materials: (a) polyethylene terephthalate glycol (PETG) filament material, (b) acrylonitrile styrene acrylate (ASA) filament material, (c) acrylonitrile butadiene styrene (ABS) filament material, and (d) polycarbonate co-polyester (PC CPE) filament material. 65 Figure 4.6.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample materials: (a) thermoplastic elastomer filament material (TPE) and (b) thermoplastic polyurethane filament material (TPU). 66 components up to maximum permissible frequencies of 0.68 THz, 0.69 THz, 0.70 THz, and 0.66 THz, respectively. 4.6 Flexible Filament Materials In Figure 4.6.1, the absorptive and refractive properties are shown for commercially available flexible filament materials, being TPE filament material with polyurethane Figure 4.6.1(a), and thermoplastic polyurethane (TPU) filament material in Figure 4.6.1(b). The samples are fabricated with FFF. The corresponding absorption coefficients and refractive indices are displayed for target sample thicknesses approximately of 700 μm and 1400 μm. Again, the plots for the absorption coefficient and refractive index are displayed until the absorption coefficient intersects with alpha max. The results are comparable for both absorption coefficient and refractive index across these samples. The results the THz-TDS of the TPE filament material and TPU filament material indicate that these materials can be effective for use in THz optical components up to maximum permissible frequencies of 0.52 THz and 0.52 THz, respectively. 4.7 Dissolvable Support Filament Materials Figure 7 depicts the absorptive and refractive properties of the dissolvable support filament materials: PVA filament material in Figure 4.7.1(a) and HIPS filament material in Figure 4.7.1(b). The samples are fabricated with FFF. These materials are often used to support the structure of complex components printed in other materials using a dual extruder FFF 3D printer. The support material is dissolved within the appropriate solvent. The solvent used for the PVA filament material is water, and the solvent used for the HIPS filament material is limonene. The corresponding absorption coefficients and refractive indices are displayed for target sample thicknesses of approximately 700 μm and 1400 μm. Again, the plots for the absorption coefficient and refractive index are displayed until the absorption coefficient intersects alpha max. 67 Figure 4.7.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample materials: (a) polyvinyl alcohol (PVA) filament material and (b) high impact polystyrene (HIPS) filament material. 68 The absorptive and refractive properties of these samples are very different. The difference in refractive index is 0.26 at 1.0 THz. At the same time, the PVA filament material shows high absorption, at 30.6 cm-1 for 1.0 THz, whereas the HIPS filament material shows low absorption, at 3.50 cm-1 for 1.0 THz, as listed in Table 4.12.1. The results of THz-TDS of the PVA filament material and HIPS filament material indicate that these materials can be effective for use in THz optical components up to maximum permissible frequencies of 0.52 THz and 1.43 THz, respectively 4.8 Nylon Filaments Materials Figure 4.8.1 displays the absorptive and refractive properties of the filament materials blended with different grades of nylon, being Nylon 910 filament material in Figure 4.8.1(a) and Nylon 230 filament material in Figure 4.8.1(b). The samples are fabricated with FFF. The corresponding absorption coefficients and refractive indices are displayed for target sample thicknesses of approximately 700 μm and 1400 μm. Again, the plots for the absorption coefficient and refractive index are displayed until the absorption coefficient has intersected with alpha max. The absorptive and refractive properties of these two samples are comparable. The results of the THz-TDS of Nylon 910 filament material and Nylon 230 filament material indicate that these materials can be effective for use in THz optical components up to maximum permissible frequencies of 0.48 THz and 0.52 THz, respectively. 4.9 Packaging Thermoplastic Filament Materials Figure 4.9.1 depicts the absorptive and refractive properties of the filaments blended with materials common within commercial and consumer packaging, such as PP filament material in Figure 4.9.1(a), and HDPE filament material in Figure 4.9.1(b). The samples are fabricated with FFF. The corresponding absorption coefficients and refractive indices are displayed for two target sample thicknesses selected from approximately 700 μm, 1400 μm, and 2100 μm. There is a high degree of overlap between the 1400 μm 69 Figure 4.8.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample materials: (a) Nylon 910 filament material and (b) Nylon 230 filament material. 70 and 2100 μm plots for the HDPE filament material. The plots for the absorption coefficient and refractive index are displayed until the absorption coefficient intersects alpha max. The absorption coefficient of the PP filament material data displays minor peaks associated with water vapor vibrational absorption, although they do not change the trend of the plotted data. The absorptive and refractive properties of these samples are similar, with a difference in refractive index of 0.23 at 1.0 THz. The PP filament material has high absorption coefficients for 1.0 THz and 2.0 THz, at 8.70 and 28.31 cm-1, respectively, in comparison to the HDPE filament material, at 1.2 and 2.39 cm-1, respectively. (See Table 4.12.1 for absorptive and refractive data for 1.0 THz.) High density polyethylene filament material has low absorption across the THz bandwidth, making it suitable for use in 3D printing of THz optical components. Although HDPE can be temperamental to work with due to warping, Chong et al. suggests several ways to mitigate these issues in Table 2 of their work [189]. The results of THz-TDS of the PP filament material and HDPE filament material indicate that these materials can be effective for use in THz optical components up to maximum permissible frequencies of 1.04 THz, and above the maximum measured frequency. This indicates that HDPE filament material is very low loss and is acceptable for use in transmission based 3D printed optical components across the entire measured THz frequency bandwidth. 4.10 Non-Standard Filament Materials Figure 4.10.1 depicts the absorptive and refractive properties of LT PCL filament material in Figure 4.10.1(a) and PVB filament material in Figure 4.10.1(b). The samples are fabricated with FFF. The corresponding absorption coefficients and refractive indices are displayed for target sample thicknesses of approximately 700 μm, and 1400 μm. The plots for the absorption coefficient and refractive index are displayed until the absorption coefficient intersects alpha max. To the author's best knowledge, this is the first THz absorptive and refractive characterisations of the LT PCL filament material and PVB filament material. The high refractive index (i.e., 1.89 at 1.0 THz) 71 Figure 4.9.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lightest respective colour), 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample filament materials: (a) polypropylene (PP) filament material and (b) high density polyethylene (HDPE) filament material. 72 Figure 4.10.1 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lighter respective colour) and 1400 µm (darker respective colour) for the following sample filament materials: (a) low temperature polycaprolactone (LT PCL) filament material and (b) polyvinyl butyral (PVB) filament material. 73 of LT PCL filament material is promising for THz optical elements in the 0.2 to 0.5 THz range, given the low absorption coefficients in this range. The material LT PCL can be highlighted as an interesting material, given its unique properties, being that it has relatively high refractive index (approx. n = 2), rather than the lower refractive indices (approx. n = 1.5) of many of the other 3D printed materials. This could therefore be a useful material for refractive-based applications, such as rapid prototyping of lenses and diffraction gratings. The absorptive and refractive properties of PVB filament material outperform those of the standard PLA filament material, reaching a lower maximum absorption coefficient over a broader THz frequency range, making it useful for THz optical components where higher THz transmission is preferable [160]. The results of the THz-TDS of LT PCL filament material and PVB filament material indicate that these materials can be effective for use in THz optical components up to maximum permissible frequencies of 0.4 THz and 0.82 THz, respectively. Figure 4.10.2 shows the absorptive and refractive properties of polymethylmethacrylate (PMMA) filament material (i.e., acrylic filament material). The samples are fabricated with FFF. Such acrylic is often used in optical applications as a waveguide over the visible spectrum. The corresponding absorption coefficients and refractive indices are displayed for target sample thicknesses of approximately 1400 μm and 2100 μm. The plots for the absorption coefficient and refractive index are displayed until the absorption coefficient intersects alpha max. The results of THz-TDS of the PMMA filament indicate that this material can be effective for use in THz optical components up to a maximum permissible frequency of 0.68 THz. Figure 4.10.3 depicts the absorptive and refractive properties of photopolymer liquid resin for stereolithography printers (i.e., SLA), in Figure 4.10.3(a), and PEI filament material, in Figure 4.10.3(b). The Figure 4.10.3(a) results are performed on a SLA material sample that is fabricated with a ELEGOO Saturn 3D printer. The Figure 4.10.3(b) results are performed on a PEI material sample that is fabricated with a heated hydraulic press. The corresponding absorption coefficients and refractive index are displayed for target sample thicknesses of approximately 700 μm, 1400 μm, and 2100 μm. The plots for the absorption 74 coefficient and refractive index are displayed until the absorption coefficient intersects alpha max. To the author's best knowledge, this is the first THz absorptive and refractive characterisations of the PEI filament material. Figure 4.10.2 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample materials: polymethylmethacrylate (PMMA) filament material. The PEI filament material is designed for high performance 3D printers with printing temperatures in excess of 290°C. The FFF 3D printer used in this experiment has a maximum extruder temperature of 250°C, which is insufficient to melt the PEI filament material. This challenge is mitigated by melting down and compressing the PEI filament material into a solid cylindrical disk sample (i.e., PEI material sample) with a heated hydraulic press (Model: 4122, CARVER Inc., Indiana, USA). The obtained PEI material samples are fabricated for two different target thicknesses and are characterised via THz-TDS over the THz gap. To facilitate the comprehensive aggregation of filament material absorptive and refractive data, two samples of different thickness of photopolymer liquid resin are produced (i.e., SLA material samples) using the stereolithography additive process and are characterised with THz-TDS. The SLA material samples are printed with an ELEGOO Saturn 3D printer. In this experiment, both the SLA and PEI material samples are completely solid. 75 Figure 4.10.3 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 700 µm (lightest respective colour), 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample materials: (a) photopolymer liquid resin for stereolithography printers (i.e., SLA) and (b) polyetherimide (PEI) filament material. 76 The results of the THz-TDS of SLA and PEI material samples indicate that these materials can be effective for use in THz optical components up to maximum permissible frequencies of 0.68 THz and 0.66 THz, respectively. Figure 4.10.4 shows the absorptive and refractive properties of COC filament material. The samples are fabricated with FFF. The corresponding absorption coefficients and refractive indices are displayed for target sample thicknesses of approximately 1400 μm and 2100 μm. The plots for the absorption coefficient and refractive index are displayed until the absorption coefficient intersects alpha max. Figure 4.10.4 The absorption coefficient (blue curves) and refractive index (green curves) are shown for the approximate sample thicknesses of 1400 µm (medium respective colour), and 2100 µm (darkest respective colour) for the following sample materials: cyclic olefin copolymer (COC) filament material. 4.11 Sample Images of Three-Dimensional Printed Materials The images of the 3D printed materials are shown in Figure 4.11.1. The images are taken with a digital microscope and a scalebar is included to shown the size of the images. 77 Figure 4.11.1 Images of the three-dimensional printed material samples are shown. 78 4.12 Summary of Absorptive and Refractive Properties and Product Details on Three-Dimensional Printed Materials In addition to the presented 3D printed filament materials, there are many other materials of interest for THz applications, including TOPAS, Teflon, and Zeonex. These materials are thoroughly characterised by Saiful Islam et al. [190] with full THz-TDS characterisation for absorption coefficient and refractive index. Table 1 summarises the absorption coefficient and refractive index measurements of all the filament materials under test at a frequency of 1.0 THz and a target sample thickness of approximately 1400 μm. This summarises absorption coefficient and refractive index at a frequency of 1 THz, shows the maximum permissible frequency, shows the minimum and maximum measured frequency, and shows the measured THz bandwidth (being the difference between the maximum and minimum measured frequencies). To note trends and provide comparisons it is helpful to look at this one specific wavelength of 1 THz. The frequency 1 THz is chosen as this is below the maximum measurable frequency for all samples, and thus has a value of each sample for absorption coefficient and refractive index. Additionally, the choice of 1 THz follows the methods of Jin et al. [191], which sets a convention of setting loss tangent analyses at 1 THz frequency. A loss tangent analysis is presented later in this Chapter. To aid in the application of this work, specific material details are summarised. Table 4.12.1 shows the filament material acronym, the corresponding filament material name, the product name with material colour (where available on produce specification sheet), and the product brand name. The filament material acronym from Table 4.12.2 are used as labels on previous figures of this Chapter. 79 Table 4.12.1 Summary of absorption coefficient, refractive index, maximum permissible frequency, minimum and maximum measured THz frequency, and measured THz bandwidth. Filament Material Absorption Coefficient Extinction Coefficient Refractive Index Maximum Permissible Frequency Minimum and Maximum Measured Frequency Measured THz Bandwidth α(1.0 THz), [cm-1] † κ(1.0 THz) n(1.0 THz) † f(α = 10 [cm-1]), [THz] † (fmin , fmax) , [THz] ‡ B = ∆f = fmax – fmin , [THz] ‡ PLA 32.6 0.078 1.54 0.54 (0.20, 1.76) 1.56 PLA Cu 38.4 0.092 1.79 0.48 (0.20 , 1.58) 1.38 PLA Fe 41.6 0.099 1.70 0.46 (0.20, 1.64) 1.44 PLA W 34.5 0.082 1.67 0.52 (0.20, 1.60) 1.40 PLA Pine 29.2 0.070 1.58 0.56 (0.20 , 1.48) 1.28 PLA Cond.* 255 0.608 2.38 <fmin (0.20 , 0.96) 0.76 PETG 18.8 0.045 1.61 0.68 (0.20, 1.58) 1.38 ASA 20.2 0.048 1.54 0.69 (0.20, 2.40) 2.20 ABS 19.6 0.047 1.47 0.7 (0.20 , 2.56) 2.36 PC CPE 20.9 0.050 1.62 0.66 (0.20 , 2.12) 1.92 TPE 31.2 0.074 1.61 0.52 (0.20, 2.46) 2.26 TPU 29.3 0.070 1.62 0.52 (0.20 , 2.16) 1.96 PVA 30.6 0.073 1.74 0.52 (0.20, 1.86) 1.66 HIPS 3.50 0.008 1.48 1.43 (0.50, 2.66) 2.16 Nylon 910 30.9 0.050 1.66 0.48 (0.20 , 2.00) 1.80 Nylon 230 30.9 0.073 1.63 0.52 (0.20 , 2.02) 1.82 PP 8.70 0.021 1.34 1.04 (0.60 , 2.16) 1.56 HDPE 1.20 0.003 1.57 >fmax (0.50 , 3.0) 2.50 LT PCL 56.2 0.134 1.89 0.4 (0.20 , 1.32) 1.12 PVB 14.4 0.034 1.55 0.82 (0.20 , 2.78) 2.58 PMMA 23.1 0.055 1.53 0.68 (0.20, 1.66) 1.46 SLA 23.3 0.056 1.61 0.68 (0.42, 2.70) 2.28 PEI 15.0 0.036 1.75 0.66 (0.20 , 2.76) 2.56 COC 2.29 0.005 1.50 2.60 (0.20 , 2.60) 2.40 *Due to αmax limitations, α and n quoted at 0.96 THz for target sample thickness of 300 μm. †For a target sample thickness of approx. 1400 μm. ‡For the target sample thickness (i.e., approx.. 700 μm, 1400 μm, or 2100 μm,) that produced the largest measureable THz bandwidth. 80 Table 4.12.2 Summary of filament material information. Filament Material Acronym Filament Material Name Product Name with Material Color Product Brand Name PLA Polylactic Acid PLA 3D Printer Filament – White AMZ3D PLA Cu Polylactic Acid, Copper Fill Copper Filled Standard PLA Filament 3DPrintingCanada PLA Fe Polylactic Acid, Iron Fill Iron Filled Standard PLA Filament 3DPrintingCanada PLA W Polylactic Acid, Tungsten Fill Tungsten Filled Standard PLA Filament 3DPrintingCanada PLA Pine Polylactic Acid, Pine Wood Fill EasyWood Filament – Pine Formfutura PLA Cond. Polylactic Acid, Conductive Fill Conductive PLA Proto-Pasta PETG Polyethylene Terephthalate Glycol EconoFil – PETG Filament – White Filaments.ca 3DPrintingMaterials ASA Acrylonitrile Styrene Acrylate ASA Filament – White AzureFilm ABS Acrylonitrile Butadiene Styrene EconoFil – ABS Filament – White Filaments.ca 3DPrintingMaterials PC CPE Polycarbonate Co-Polyester Easy PC CPE Filament – Natural Filaments.ca 3DPrintingMaterials TPE Thermoplastic Elastomer Filaflex 82A – White Recreus TPU Thermoplastic Polyurethane TPU Flexible Filament – White SainSmart PVA Polyvinyl Alcohol PVA Filament – Natural Filaments.ca 3DPrintingMaterial HIPS High Impact Polystyrene HIPS Filament – Natural Filaments.ca 3DPrintingMaterials Nylon 910 Nylon Based Polymer Blend Alloy 910 Filament – Natural Taulman3D Nylon 230 Nylon Based Polymer Blend Nylon 230 Filament – Natural Taulman3D PP Polypropylene Centaur PP Filament – Natural Formfutura HDPE High Density Polyethylene HDPE Filament – Natural Filaments.ca 3DPrintingMaterials LT PCL Low Temperature Polycaprolactone PCL Low Temperature Filament – Natural Filaments.ca 3DPrintingMaterials PVB Polyvinyl Butyral PVB Filament – White Filaments.ca 3DPrintingMaterials PMMA Polymethylmethacrylate HIRMA Acrylic Filament – Transparent TreeD SLA Photopolymer Liquid Resin Professional UV Resin – Grey Peopoly PEI Polyetherimide ULTEM PEI – Natural Filaments.ca 3DPrintingMaterials COC Cyclic Olefin Copolymer CREAMELT® COC – Transparent CREAMELT® - 3D Printing Materials 81 4.13 Absorption Coefficient, Refractive Index, and Loss Tangent Analysis of Three-Dimensional Printed Materials The absorption coefficient data versus loss tangent (at 1 THz) is shown in Figure 4.13.1 with Figure 4.13.1(a) showing 24 materials, and Figure 4.13.1(b) showing all but the highest absorption coefficient material. The loss tangent is tan  =2𝑛𝑐4𝜋𝑓 𝑛2 − (𝑐4𝜋𝑓 )2 , (24) where n is refractive index, c is the vacuum speed of light, f is the frequency, and  is the absorption coefficient. The loss tangent analysis reveals several noteworthy material relationships. The PLA filament material embedded with electrically conductive particles (i.e., PLA Cond.) is particularly absorptive (i.e., absorption coefficient beyond 250 cm-1). This is as one would expect given that the free electrons and high conductivity will severely attenuate a THz electromagnetic wave, particular given the relatively close match of the plasma frequency. The PLA material has covalent bonding, lactic acid monomer, and is within the polymer class polyesters. The LT PCL filament material represents the next regime of interest with absorption coefficient beyond 50 cm-1. The PLA family of materials is spread from approximately 25-45 cm-1 and consists of: PLA; PLA blended with pine tree particles, PLA Pine; PLA blended with iron, PLA Fe; PLA blended with copper, PLA Cu; and PLA blended with tungsten, PLA W. In general, the integration of metal tends to trend up to higher absorption while the integration of wood (e.g., pine) tends to trend down to lower absorption of the THz wave. Given the high absorption of metals [192] and the low absorption of wood for THz [193], this result is consistent with expectations. There is a cluster of materials (other than PLA) in the 25-35 cm-1 regime, including Nylon 230 and Nylon 910 filament materials and TPE filament material, TPU filament material, and PVA filament material. 82 Figure 4.13.1 Absorption coefficient versus loss tangent is shown 83 Figure 4.13.2 Refractive index versus loss tangent is shown. 84 Figure 4.13.3 Extinction coefficient versus loss tangent is shown. 85 The next cluster of materials is in the 10-25 cm-1 regime, including photopolymer liquid resin for stereolithography printers (i.e., SLA), PMMA filament material, PC CPE filament material, ASA filament material, ABS filament material, PETG filament material, PVB filament material, and PEI filament material. Of particular importance and relevance to application in THz optical components is materials with absorption coefficient below 10 cm-1, and this includes the cluster of 3D printed materials that includes: PP filament material, HIPS filament material, COC filament material, and HDPE filament material. In Figure 4.13.2, the refractive indices versus loss tangent (at 1 THz) is shown with Figure 4.13.2(a) showing 24 materials, and Figure 4.13.2(b) showing all but the highest refractive index material. Most of the samples fall within the refractive index range of 1.3-1.9. In Figure 4.13.3, the extinction coefficient versus loss tangent (at 1 THz) is shown with Figure 4.13.3(a) showing 24 materials, and Figure 4.13.3(b) showing all but the highest refractive index material. Extinction coefficient, κ(f), is defined as 𝜅(𝑓) =100𝑐((𝑓))4𝜋𝑓 . (25) The mean and standard deviation, for three samples of HIPS and COC filament material, was determined for absorption coefficient and refractive index at 1.0 THz, rounded to 3 significant figures (αHIPS: M = 4.51 cm-1, SD = 0.717 cm-1; nHIPS: M = 1.50, SD = 0.0357; αCOC: M = 1.56 cm-1, SD = 0.641 cm-1; nCOC: M = 1.51, SD = 0.0127). Cunningham et al. reports α = 0.25 cm-1 and n = 1.53 at 1.0 THz for bulk COC material [70]. Farman et al. reports α = 9 cm-1 and n = 1.59 at 1.0 THz for bulk PS material [69]. From the above data the reproducibility is quantified. The comparison to Cunningham and Farman show differing values, therefore, the bulk form of the materials and the 3D printed form of the materials are different. As such, Chapter 4 focuses on bringing measurements of 3D printed forms of materials into the literature. 86 4.14 Chapter Conclusions This Chapter presented THz-TDS measurements in a comprehensive study of twenty-four 3D printer materials. The work also presented a comparison of thick and thin samples for THz-TDS measurements—establishing verification of measurement accuracy. Such work extended the measured THz bandwidth beyond prior reported data. At the same time, the work put forward the first THz-TDS measurements, to the author's best knowledge, ASA filament material, PVB filament material, LT PCL filament material, and PEI filament material. It is hoped that this work will become a useful resource in the assessment of absorptive and refractive properties for 3D printing filaments and their suitability for custom THz optics. The THz-TDS results shown in this work indicated that the four best 3D printer filament materials, from the collection measured here, are the HDPE filament material, HIPS filament material, COC filament material, PP filament material. These AM filament materials exhibit relatively low absorption at higher THz frequencies, in comparison to the other AM filament materials evaluated in this study. 87 Chapter 5: Terahertz Bragg Structures Fabricated with Additive Manufacturing This Chapter investigates the development and characterisation of THz Bragg structure devices (i.e., interference filters) fabricated with additive manufacturing. This Chapter is organised as follows: Background (Chapter 5.1), Terahertz Time-Domain Spectroscopy of High Impact Polystyrene Filament Material (Chapter 5.2), Terahertz Bragg Structure Geometry (Chapter 5.3), Operation of Finite-Difference Time-Domain Electromagnetic Simulation (Chapter 5.4), Terahertz Experimental Testbed for Characterisation of 3D printed Bragg Structures (Chapter 5.5), Terahertz Bragg Structure Operation (Chapter 5.6), Material Absorption Considerations (Chapter 5.7), Comparison to Other Techniques (Chapter 5.8), Chapter Conclusions (Chapter 5.9). Elements of this thesis Chapter were first published in the following article: Terahertz Bragg structures fabricated with additive manufacturing, Applied Optics, vol. 62, pp. 4465-4473, 2023. © 2023 Optica Publishing Group. Additionally, elements of this thesis Chapter were presented as the following conference proceeding: Far-infrared Bragg device, 2023 Proceedings of Photonics North. 5.1 Background A THz Bragg structure design for THz frequencies fabricated with FFF 3D printing is presented in this Chapter. The chosen 3D printing material is high impact polystyrene (HIPS) filament material. High impact polystyrene is chosen for its suitable refractive index (n = 1.48 at 1.0 THz) and absorption coefficient (α = 4 cm-1 at 1.0 THz) (i.e., being superior to that of PLA filament material), as previously reported [57]. The THz Bragg structure is formed from alternating layers of HIPS filament material and free space, and held structurally secure with a supportive structure on its periphery. The THz Bragg structure is investigated theoretically in the time-domain and frequency-domain using a FDTD software simulation. The THz Bragg structure is investigated experimentally in the time-domain and frequency-domain using a THz setup based on a gallium arsenide photoconductive antenna (for THz emission), parabolic mirrors (for THz collimation), and a zinc telluride electro-optic crystal (for THz detection). Ultimately, the THz Bragg structure is shown 88 to have favourable performance, with controllable rejection at targeted frequencies (i.e., notch filter behaviour). The main purpose of this Chapter is to establish the methodologies required for developing and testing THz Bragg components. This is shown with the material HIPS, and Chapter 6 will subsequently use this methodology to thoroughly compare HIPS and COC THz Bragg components. In addition, (to the author's knowledge) this Chapter and corresponding journal article [59] presented the first fully-3D-printed THz Bragg structure (i.e., not a composite of individual 3D printed parts [138]) in the literature. The THz Bragg structure is also shown for a smaller (N = 6) and larger (N = 18) number of material layers. The main contributions of this Chapter are as follows. A HIPS THz Bragg structure is introduced that can be designed as desired via FFF-based 3D printing. The Chapter establishes this structure theoretically through FDTD electromagnetic simulations, with analysis in time- and frequency-domain. The work experimentally demonstrates the THz Bragg structure for two designs having wide and narrow frequency-domain spacings, showing tunability of frequency rejection in a transmitted THz beam. The work experimentally demonstrates the frequency designs for the THz Bragg structure for six and eighteen HIPS filament material layers, showing tunability of frequency rejection efficiency. This overall analysis approach can then be applied for HIPS and COC, which is done in Chapter 6. Rapid prototyping capability for THz components is expanded through this Chapter. 5.2 Terahertz Time-Domain Spectroscopy of High Impact Polystyrene Filament Material An ideal THz compatible material for THz photonic devices will have absorption coefficient that is a (relatively) low value and refractive index that is well beyond that of free-space. Such absorption coefficient and refractive index properties will allow transmission of THz and manipulation of THz, respectively. Such a material is the HIPS filament material. Figure 5.2.1 shows THz-TDS of HIPS filament material, a low absorption 3D printing material over the THz regime, and contrasts to that of acrylonitrile butadiene styrene (ABS), a high absorption 3D printing material over the THz regime. The ABS material is selected from the various high absorption coefficient materials studied in Chapter 4 because it is a readily 89 Figure 5.2.1 The absorption coefficient (blue) and refractive index of (yellow) are shown for the high impact polystyrene (HIPS) filament material used in the three-dimensional printing of the experimental terahertz Bragg structure. The absorption coefficient (red) and refractive index (black) of acrylonitrile butadiene styrene (ABS) filament material is displayed. A trendline (not shown), approximating the absorption coefficient (blue) of high impact polystyrene filament material, over the 0.5 THz to 1.2 THz spectrum, is established with a slope of 4.5 cm-1/THz. available 3D material that represents a commonly used 3D printing material. In Figure 5.2.1, additional THz-TDS data sets are shown (beyond those of Chapter 4) for HIPS and ABS. For HIPS, there is an increasing absorption coefficient that is low overall (below 10 cm-1) across the THz frequencies with a corresponding consistent and high refractive index. Figure 5.2.1. shows data that HIPS has two properties: low absorption and suitably high refractive index. Furthermore, the comparatively higher absorption coefficient of ABS filament material is also shown on Figure 5.2.1 (i.e., 21 cm-1 at 1 THz), with a corresponding refractive index. A trendline (not shown on Figure 5.2.1), approximating the absorption coefficient of the HIPS filament material, is established with a 4.5 cm-1 per THz slope for subsequent analyses, as discussed in Chapter 5.7. Another material with these material properties is HDPE, however, the difficulty of using this material with 3D printing is well documented and it has inferior printability [189]. Therefore, HIPS is chosen as it has superior printability. (Ultimately a further improvement is seen with COC in Chapter 6, once these methodologies are established.) The HIPS filament 90 material is a particular reliable material for 3D printing of THz photonic devices, i.e., it is a dimensionally constant FFF printing material. In this work, the HIPS filament material is printed with the Prusa i3 MK3S+ 3D printer (Prusa Research, Prague, CZ), using the 50 µm Z-axis layer resolution setting (corresponding to a feed rate of 0.33 mm3/s) and a extrusion nozzle with an orifice diameter of 0.4 mm. The fabricated THz Bragg structures are stored in airtight containers to mitigate the potential for the absorption of water vapor. 5.3 Terahertz Bragg Structure Geometry Figure 5.3.1 shows the THz Bragg structure for a number of material layers, N. In Figure 5.3.1(a) the isometric-view (left) and top-view (right) is shown for a THz Bragg structure with N = 6 HIPS filament material layers. Figure 5.3.1(b) shows an expanded top-view and defines the layer parameters, for filament material of refractive index n2 of thickness d2, and free-space of refractive index n1 of thickness d1, which are repeated N times. That is, the N parameter is the number of spatial periods in the structure. For example, a value of N = 4 would have four pairs of HIPS and air layers, and would have a total thickness of Nd2 + (N-1)d1 = 4d2 + 3d1 (omitting the final air layer). These Bragg layer parameters define the frequency response of the THz Bragg structure. The frequency response has frequency-domain spacing of removed frequencies of the transmission spectra that follow ∆𝐹 =𝑐2𝑑1𝑛1=𝑐2𝑑2𝑛2 , (26) where ∆F is the frequency-domain spacing, c is the vacuum speed of light, and thicknesses, d1 and d2, and refractive indices, n1 and n2, are defined as shown in Figure 5.3.1. The rejection of the selected frequencies is more pronounced as the number of material layer interfaces increase [194]. 91 Figure 5.3.1 An overview of the terahertz Bragg structures are shown. (a) The N = 6 material layer terahertz Bragg structure is shown for a three-dimensional (left) and a top-view (right). (b) An enlarged top-view image of the terahertz Bragg structure is shown, with high impact polystyrene material layers and air gap thicknesses with refractive indices being d2, n2, and d1, n1, respectively. (c) The N = 18 material layer THz Bragg structure is shown for a three-dimensional view. 92 5.4 Operation of Finite-Difference Time-Domain Electromagnetic Simulation In this Chapter, the THz Bragg structure is investigated in terms of its theoretical response to a THz pulse in the time- and frequency-domain. This is accomplished using a FDTD electromagnetic simulation. Here, an example case of a THz Bragg structure having N = 3 material layers of (free-space) refractive index n1 = 1.00 and thickness d1 = 600 µm, with spacing of refractive index n2 = 1.48 and distance d2 = 400 µm. A comparison of all mentioned THz Bragg structure dimensions, refractive indices, and frequency-domain spacings, is provided in Table 5.6.1, for this example case, and for the later explored experimental Bragg structures. The FDTD electromagnetic simulation is written in one physical dimension with electric field (displayed in Figure 5.4.1) and magnetic field (not displayed in Figure 5.4.1) and iteratively solves Maxwell's equations numerically. The simulation assumes that there is normal incidence between the propagated THz pulse and the THz Bragg structure. Furthermore, it is assumed there is no energy loss due to material absorption, such that all incident electric field energy is measured as either reflected or transmitted from the THz Bragg structure. The FDTD electromagnetic simulations use a discretisation size of 8.5 m (chosen to be well below the smallest wavelength later evaluated experimentally). This follows norms set about by Taflove and Hagness [195]. Absorption in FDTD is considered in Appendix A. The FDTD electromagnetic simulation is presented in Figure 5.4.1. The FDTD electromagnetic simulation injects a THz pulse that is monophasic and Gaussian in shape with a full-width-at-half-maximum of 0.5 ps, which therefore contains frequencies in the THz regime. Figure 5.4.1 (a)-(d) show the progression of the THz pulse time-steps of 3.4, 9.3, 15.3, and 67.8 ps after the start of the simulation. The transmitted electric field becomes a pulse train because of the interaction of the interfaces of the material layers through Fresnel transmission and reflection coefficients. This transmitted pulse train is absent of frequencies that originate with the injected THz pulse. This behaviour is apparent when analysing the natural logarithm intensity ratio, |Et(f) |2/|Ei(f) |2, where Et(f) is the transmitted electric field, and Ei(f) is the incident electric field on the THz Bragg structure. This is shown in Figure 5.4.1(e), with pronounced rejection at the expected frequencies as determined by the frequency-domain spacing, ∆F = 0.25 THz. This simulation is used and modified to compare with several experimentally characterised THz Bragg structures. 93 For a one-dimensional FDTD electromagnetic simulation, there is an assumption of infinite symmetry in the two dimensions not aligning with the optical axis. Therefore, such FDTD simulation is not modeling a true Gaussian spatially profiled beam. An experimental terahertz pulse is likely a spatial Gaussian profiled beam. Therefore, this could be a reason for slight differences between theory and experiment. 94 Figure 5.4.1 A simplified example of the terahertz Bragg structure is theoretically investigated with a finite-difference time-domain simulation as shown for multiple time intervals. (a) A Gaussian electric field pulse (blue) is propagated through free-space toward three material layers of high impact polystyrene filament material (yellow) surrounding two air gap layers. (b-c) The Gaussian electric field pulse is propagating through the high impact polystyrene layers. (d) Sufficient time has elapsed for all transmitted and reflected electric field energy to be recorded. (e) The theoretical frequency-domain spectrum of the natural logarithm intensity ratio is shown having frequency rejection at four distinct frequency bands. 95 5.5 Terahertz Experimental Testbed for Characterisation of Three-Dimensional Printed Bragg Structures The THz Bragg structure is characterised with a THz experimental testbed, as shown in Figure 5.5.1. The THz experimental testbed makes use of an ultrafast pulsed laser of wavelength 780 nm which is divided into pump and probe beams. The probe beam is temporally delayed to perform an ultrafast time-resolved measurement. The pump beam is focused through a microscope objective lens (MO) onto a photoconductive THz emitter (PE). A pulsed THz beam emerges and is collimated between two parabolic mirrors (PM). The pulsed THz beam, having a horizontal polarisation which is parallel to the surface of the optical table, passes through the THz Bragg structure device, with interactions being along the one-dimensional optical axis (being left-to-right in the Figure 5.5.1 image). In Figure 5.5.1, an expanded 3D inset view of a THz Bragg structure is displayed (outlined in blue) above the schematic of the THz experimental testbed. A pellicle beam splitter (BSpel) is also between the two parabolic mirrors and allows the probe beam to be overlapped onto the pulsed THz beam. The result undergoes electro-optic sampling using the following components: electro-optic crystal (EO), quarter wave plate (QW), polarising beam splitter (BSpol), and balanced silicon photodiode (PDsi). Several mirrors (M) and a lens (L) are included throughout the THz experimental testbed. 5.6 Terahertz Bragg Structure Operation The THz Bragg structures, fabricated with 3D printing using the HIPS filament material, are characterised up to 1.2 THz using the THz experimental testbed. The fabricated geometry of the THz Bragg structures manifests as wide and narrow frequency responses (i.e., wide and narrow frequency-domain spacings, ∆F), with substantial rejection of targeted frequencies within the THz spectrum. The above-mentioned THz Bragg structures are evaluated experimentally, for both N = 6 layer and N = 18 layer variations, as shown respectively in Figure 5.3.1(a) and Figure 5.3.1(c), and compared with theoretical results that are produced from the FDTD electromagnetic simulations. 96 Figure 5.5.1 A graphical overview of the terahertz experimental testbed is shown with the following functional components: microscope objective (MO), photoconductive terahertz emitter (PE), parabolic mirror (PM), terahertz beam path (THz), pellicle beam splitter (BSpel), electro-optic crystal (EO), quarter wave plate (QW), polarisation beam splitter (BSpol), balanced silicon photodiode (PDsi), mirror (M), lens (L), pulsed laser pump beam (Pump), and pulsed laser probe beam (Probe). The terahertz Bragg structure is shown within the optical axis of the terahertz beam path (THz) and shown as an expanded inset image (outlined in blue). 97 Using (26), a structure can be made for desired rejection peaks. There will be two F values (frequency spacing between peaks) investigated, corresponding to two pairs of structures (ultimately, four individual structures). The first two structures are designed to have wide frequency spacing of F = 0.2 THz, and are 3D printed to create these structures with alternating layers of thickness d2 = 500 m (HIPS material with refractive index of n2 = 1.48) and d1 = 750 m (air with refractive index of n1 = 1.0) with either N = 6 or N = 18 spatial periods. The second two structures have narrow frequency spacing of F = 0.17 THz, and this is created with structures with alternating layers of thickness d2 = 600 m (HIPS material with refractive index of n2 = 1.48) and d1 = 900 m (air with refractive index of n1 = 1.0) with either N = 6 or N = 18 spatial periods. These cases are summarised in Table 5.6.1. Table 5.6.1 Dimensions and properties of the terahertz Bragg structures. Case N (mat. layers) d1 [m] (air) d2 [m] (HIPS) n1 (air) n2 (HIPS) ∆F [THz] (freq. spacing) example simulation 3 600 400 1.00 1.48 0.25 wide ∆F Bragg structure 6 750 500 1.00 1.48 0.20 wide ∆F Bragg structure 18 750 500 1.00 1.48 0.20 narrow ∆F Bragg structure 6 900 600 1.00 1.48 0.17 narrow ∆F Bragg structure 18 900 600 1.00 1.48 0.17 The experimental and theoretical response of the THz Bragg structures fabricated for wide frequency-domain spacing is presented in Figure 5.6.1. Here, the simulated natural logarithm intensity ratio of a N = 6 layer THz Bragg structure is provided in Figure 5.6.1(a). The theoretical response (red) is manifested as six frequency rejection peaks, within 1.2 THz. The theoretically calculated ∆F frequency-domain spacing is 0.20 THz, as per (26). The percent error between the theoretical ∆F frequency-domain spacing and the average ∆F frequency-domain spacing, as determined from the FDTD electromagnetic simulation, is 0.2 %. 98 The corresponding experimental characterisation of the fabricated N = 6 layer (yellow) and N = 18 layer (blue) THz Bragg structure is presented in Figure 5.6.1(b) with targeted F = 0.2 THz, as a function of the natural logarithm intensity ratio. The N = 6 layer and N = 18 layer THz Bragg structure show close agreement in terms of the measured ∆F frequency-domain spacing of the natural logarithm intensity ratio. That is, the observed frequency peaks from the N = 6 layer and N = 18 layer THz Bragg structures overlap closely. Furthermore, the percent error between the theoretical and average measured ∆F frequency-domain spacing, of the N = 6 layer, and N = 18 layer THz Bragg structures, is 4 %, and 4 %, respectively. An improved efficiency of frequency rejection is associated with an increased number of material layers in the THz Bragg structure. For the N = 6, d1 = 750 m, d2 = 500 m THz Bragg structure (targeted F = 0.2 THz), the ∆F values are 0.194, 0.188, 0.194, 0.200, and 0.189 THz, which average to be 0.193 THz. For the N = 18, d1 = 750 m, d2 = 500 m THz Bragg structure, and the ∆F values are 0.172, 0.215, 0.185, 0.195, and 0.195 THz, which average to be 0.192 THz. The corresponding time-domain data for the above-mentioned N = 6, and N = 18, layer THz Bragg structures are provided for completeness, as seen in Figure 5.6.2. For Figure 5.6.2(a), with the physically smaller N = 6 structure, the incident THz electric field, Ei(t), signal is represented in red over a 160 picosecond timescale (i.e., equating to a sufficient optical delay-line translation of 24 mm), along with the transmitted THz electric field, Et(t), signal being represented in blue. For Figure 5.6.2(b), with the physically larger N = 18 structure, the incident THz electric field, Ei(t), signal is represented in red over a longer 400 picosecond timescale (i.e., equating to a sufficient optical delay-line translation of 60 mm), along with the transmitted THz electric field, Et(t), signal being represented in blue. This longer time window is used to capture the full time-domain signal. The experimental and theoretical response of the THz Bragg structures fabricated for a narrow frequency-domain spacing is presented in Figure 5.6.3. 99 Figure 5.6.1 (a) The theoretical natural logarithm intensity ratio of the N = 6 layer terahertz Bragg structure is shown in red for the wide frequency-domain spacing. (b) The theoretical natural logarithm intensity ratio of the N = 18 layer terahertz Bragg structure is shown in red for the wide frequency-domain spacing. (c) The experimental characterisation of the terahertz Bragg structure with wide frequency-domain spacing is presented here for both N = 6 layer (yellow) and N = 18 layer (blue) variations. 100 Figure 5.6.2 The incident electric field (red), Ei(t), and transmitted electric field (blue), Et(t), time-domain data is presented for the (a) N = 6 and (b) N = 18 layer terahertz Bragg structures corresponding to wide frequency-domain spacing, F = 0.20 THz. 101 Here, a natural logarithm intensity ratio of a N = 6 layer THz Bragg structure is provided in Figure 5.6.3(a). The theoretical response (red) is manifested as seven frequency rejection peaks, within 1.2 THz. The theoretically calculated ∆F frequency-domain spacing is 0.17 THz, as per (26). The percent error between the theoretical ∆F frequency-domain spacing and the average ∆F frequency-domain spacing, as determined from the FDTD electromagnetic simulation, is 0.2 %. The corresponding experimental characterisation of the fabricated N = 6 layer (yellow) and N = 18 layer (blue) THz Bragg structure (targeted F = 0.17 THz) is presented in Figure 5.6.3(c), as a function of the natural logarithm intensity ratio. The N = 6 layer and N = 18 layer THz Bragg structure show close agreement between them with respect to the measured ∆F frequency-domain spacing of the natural logarithm intensity ratio. That is, the observed frequency peaks from the N = 6 layer and N = 18 layer THz Bragg structures overlap. Furthermore, the percent error between the theoretical and average measured ∆F frequency-domain spacing, of the N = 6 layer, and N = 18 layer THz Bragg structures, is 2 %, and 2 %, respectively. An improved efficiency of frequency rejection is associated with an increased number of material layers in the THz Bragg structure. For the N = 6, d1 = 900 m, d2 = 600 m THz Bragg structure, the ∆F values are 0.163, 0.163, 0.169, 0.156, 0.169, and 0.166 THz, which average to be 0.164 THz. For the N = 18, d1 = 900 m, d2 = 600 m THz Bragg structure, the ∆F values are 0.161, 0.167, 0.175, 0.158, 0.162, and 0.165 THz, which average to be 0.165 THz. The corresponding time-domain data for the above-mentioned N = 6, and N = 18, layer THz Bragg structures are provided for completeness, as seen in Figure 5.6.4. For Figure 5.6.4(a), the (smaller) N = 6 structure data is shown with the incident THz electric field, Ei(t), signal is represented in red over a 160 picosecond timescale (i.e., equating to a sufficient optical delay-line translation of 24 mm), Et(t), signal being represented in blue. For Figure 5.6.4(b), with the physically larger N = 18 structure, the incident THz electric field, Ei(t), signal is represented in red over a longer 400 picosecond timescale, along with the transmitted THz electric field, Et(t), signal being represented in blue. 102 Figure 5.6.3 (a) The theoretical natural logarithm intensity ratio of the N = 6 layer terahertz Bragg structure is shown in red for the narrow frequency-domain spacing. (b) The theoretical natural logarithm intensity ratio of the N = 18 layer terahertz Bragg structure is shown in red for the narrow frequency-domain spacing. (c) The experimental characterisation of the terahertz Bragg structure with narrow frequency-domain spacing is presented here for both N = 6 layer (yellow) and N = 18 layer (blue) variations. 103 Figure 5.6.4 The incident electric field (red), Ei(t), and transmitted electric field (blue), Et(t), time-domain data is presented for the (a) N = 6 and (b) N = 18 layer terahertz Bragg structures corresponding to narrow frequency-domain spacing, F = 0.17 THz. 104 5.7 Material Absorption Considerations In Figure 5.6.1, the upper frequency regime is more subject to unwanted peaks than the low frequency regime. This is because the higher frequencies are approaching the maximum measurable frequency for a transmission measurement. In general, such measurements can only show data up to when the amplitude of the transmitted electrical field, Et(f), is at the noise floor. If the transmitted electric field is below the noise floor, the natural logarithm intensity ratio = − ln (|𝐸t(𝑓)|2|𝐸i(𝑓)|2) (27) function will show the maximum measurable value, which is maxmeasurement = − ln (noise floor|𝐸i(𝑓)|2) (28) This follows the analysis set out in the fundamental THz work of Jepsen and Fischer [160]. Equation (27) is the natural logarithm of the transmittance, which is the ratio between transmitted and incident power. Figure 5.7.1(a), shows the incident and reference spectra. Figure 5.7.1(b) shows the maximum measurable value and repeat the frequency response for the, N = 18 F = 0.20 THz, THz Bragg structure. one can observe for the high frequency regime (beyond 0.8 THz) that the measurement is close to the maximum measurable value (and therefore Et(f) is close to the noise floor), and therefore more subject to random fluctuations which are unwanted noise features. In Figure 5.7.1(b), the black dashed line represents the absorption (from the Figure 5.2.1 THz-TDS investigation of HIPS) for a thickness of Nd2, where N = 18 and d2 = 500 m. This shows that the upward trending of the Figures. 5.6.1 and 5.6.3 is attributable to material absorption in the HIPS layers. This can be reduced by use of emerging THz compatible 3D printing materials, such as COC filament material [73], which is investigated in Chapter 6 and compared to HIPS filament material performance for THz Bragg structures and THz Bragg superstructures. 105 Figure 5.7.1 (a) The measured incident (red) and transmitted (blue) terahertz frequency spectra are shown, for the N = 18 layer terahertz Bragg structure, with alternating layer dimensions d1 = 750 µm and d2 = 500 µm. (b) The natural logarithm intensity ratio (blue), corresponding to the above-mentioned terahertz Bragg structure, is presented here. A linear trendline approximating the absorption of HIPS filament material, for a sum total material thickness equivalent to this terahertz Bragg structure, is indicated as a dashed line. The maximum detectable natural logarithm intensity ratio is displayed in red. 106 5.8 Comparison to Other Techniques It is possible to fabricate such a THz Bragg structure using subtractive manufacturing, e.g., through laser micromilling [196] or computer numerical control milling [197]. However, such techniques subtract material, and therefore waste material. In contrast, the THz Bragg structures investigated in this Chapter are fabricated using additive manufacturing. Thus material is added only in the amount that is required. Additionally, the use of a 3D printer encourages such devices to be rapidly prototyped, encouraging further scientific exploration of 3D printed THz components, in contrast to mass manufacturing techniques such as injection molding [198]. In Cruz et al., the authors make a Bragg fiber with 3D printing which can reject frequencies similarly to THz Bragg structures [114]. However, the THz Bragg structures investigated in this Chapter operate for free-space THz transmission, and therefore can be applied in free-space THz communications [199] or sensor applications [200]. Liu et al. [201] makes use of graphene material and Headland et al. [202] makes use of silicon material for Bragg structures operating over THz wavelengths. Unfortunately, such materials do not lend themselves to 3D printing and rapid prototyping. One can also compare to Bragg structures for other wavelengths, such as visible and infrared [203]. Such structures can be used for mixing optical wavelengths and biosensing over submicron wavelengths. They would be made with materials that are optically-transparent, whereas the THz Bragg structure involves materials that are transparent over the THz regime. However, in terms of applications, optical and infrared Bragg structures find communication and sensing to be two of the most common applications, as is envisioned for the presented work in the THz regime. 5.9 Chapter Conclusions A THz Bragg structure was introduced that was fabricated with 3D printing from HIPS filament material. The THz Bragg structure was theoretically investigated using FDTD electromagnetic simulations 107 for analysis in both the time- and frequency-domains. The Chapter demonstrated the tunability of this THz Bragg structure by experimentally characterising two different geometric designs, manifesting as a wide and narrow frequency spacings in the frequency-domain, for frequency rejection in a transmitted THz beam. The Chapter experimentally demonstrated the frequency designs with the THz Bragg structure for six and eighteen HIPS filament material layers, showing designability of frequency rejection efficiency as shown through the natural logarithm intensity ratio. This work demonstrated the advantageous use of FFF-based 3D printing for fabrication of frequency-tunable THz compatible components, as can be implemented in future THz technologies. 108 Chapter 6: Terahertz Components by Additive Manufacturing: Material and Fabrication Characterisations Realised Through Bragg Structures This work explores device characterisations of Bragg structures and superstructures for the THz regime that are 3D printed with two filament materials, HIPS and COC. The underlying frequency responses are shown that come about due to the material absorption and chosen 3D printing resolution. This thesis chapter is organised as follows: Background (Chapter 6.1), Terahertz Time-Domain Spectroscopy of HIPS and COC Filament Material (Chapter 6.2), Terahertz Bragg Superstructure Geometry (Chapter 6.3), Terahertz Bragg Superstructure Operation (Chapter 6.4), Theoretical Finite-Difference Time-Domain Simulation (Chapter 6.5), HIPS Bragg Superstructure Experimental Results (Chapter 6.6), COC Bragg Superstructure Experimental Results (Chapter 6.7), Effect of Printing Resolution (Chapter 6.8), and Chapter Conclusions (Chapter 6.9). Elements of this thesis Chapter were accepted as the following article: Terahertz components by additive manufacturing: Material and fabrication characterizations realized through Bragg structures, IEEE Transactions on Terahertz Science and Technology, 2024, accepted. © 2024 IEEE. Additionally, elements of this thesis Chapter were presented as the following invited conference proceeding: Terahertz components through additive manufacturing, 2023 Proceedings of Photonics North. 6.1 Background As stated throughout this thesis, 3D printing is an additive manufacturing process of particular interest for THz photonic elements, as 3D printers are capable of fabricating structures with feature sizes on the order of THz wavelengths [204]. Fused filament fabrication (FFF) style 3D printers are capable of fabricating structures with resolutions less than 100 µm [185] (which can be well-suited for THz wavelengths) and can print a wide variety of available filament materials (which can be well-suited to use for a wide variety of THz photonic elements). However, many FFF filament materials are not well-explored in THz literature, particularly for demonstration as THz filters through their frequency responses. 109 As discussed previously in this thesis, the selection of FFF filament material for use in a THz photonic element must balance two factors. First, a filament material, intended for fabrication of THz photonic elements, should be selected to have appropriate refractive and absorptive properties. The selection process of THz compatible filament materials can be facilitated by recent studies evaluating 3D printer filament materials over the THz region [57]. Filament materials having low absorption (i.e., low loss) and refractive indices sufficiently beyond the free-space refractive index are of particular important for applications of 3D printed THz photonic elements. The use of low loss 3D printing filament materials have been applied to THz photonic elements, with demonstrations of waveguides [73] and diffractive elements [91]. Chapter 5 demonstrated a THz Bragg structure (two alternating materials with the same temporal period) using HIPS [59]. However, more intricate THz Bragg structures, such as the THz Bragg superstructure (two alternating materials with substantially different temporal periods) have not been demonstrated. The second factor to balance is that a filament material should have ease of printing, i.e., the fabricated structure should be dimensionally similar to the intended design. High impact polystyrene is a filament material that is widely available, having adequately low absorption coefficient [57] (initially shown in Chapter 4) versus the desirably-low absorption coefficient of high density polyethylene (HDPE) filament material, with desirable printability over that of HDPE filament material. The HDPE filament material is difficult to 3D print due to thermal contraction, warping, and printer bed adhesion failures [189] [205]. Squires and Lewis comment on the desirability of HIPS for THz applications, with its (relatively) low absorption and high printability [64]. However, there is an opportunity for improvement beyond HIPS filament material as it has non-negligible absorption in the THz region, e.g., 4 cm-1 absorption coefficient at 1 THz. In contrast to both HDPE and HIPS filament materials, COC filament material possesses the ideal low absorption coefficient, similar to that of other polyolefin filament materials (i.e., HDPE), and has desirable printability like polylactic acid and HIPS filament materials [73]. The investigation of THz technologies fabricated with 3D printing is appreciable and ongoing for various THz photonic elements. This exploration of 3D printed THz photonic elements includes THz lenses, e.g., THz Powel lenses [81], THz Fresnel lenses [206], and THz lens arrays [97]. Additionally, 3D printing 110 is being leveraged to fabricate THz diffraction gratings [207] [91], THz polarisers [208] [209] [66], and THz polarisation beam splitters [210]. Moreover, 3D printed THz waveguides [73] [211] and THz hollow core waveguides [212] [213] [104] have been characterised. Additional characterisations have been performed for 3D printed THz waveguides incorporating Bragg structure geometries [113] [214], with one such Bragg fiber exhibiting increased THz-TDS sensitivity of lactose powder [116]. As noted in Chapter 2, research on standalone Bragg structures (i.e., without incorporation into waveguides) as 3D printed THz photonic elements is emerging, with publications on this topic. Specifically, Revuri et al. have developed a THz Bragg structure, whereby they manually assemble components that are initially 3D printed, using high loss PLA filament material [138]. Revuri and colleagues show their Bragg structure operating over 0.3 THz to 0.75 THz for two peaks of frequency rejection. Chapter 5 reported a 3D printed THz Bragg structure fabricated, as a singular component from lower loss HIPS filament material [59] (i.e., not requiring additional assembly post 3D printing, in contrast to Revuri et al.). Chapter 5 aimed this Bragg structure design to extend operation over the THz spectrum showing six peaks of frequency rejection over 0.1 THz to 1.2 THz. Beyond the contributions Chapter 5, Chapter 6 makes the following contributions. Chapter 6 revisits THz-TDS of HIPS and COC filament materials to highlight the low absorption coefficient of COC filament material. The low absorption coefficient is further highlighted with an experimental demonstration several THz Bragg superstructures for both HIPS and COC filament materials, with reference to theoretical FDTD responses. Through this demonstration, this Chapter fabricates, demonstrates, and analyses multiple designs of the THz Bragg superstructures. These multiple designs can be used to quickly fabricate THz Bragg superstructures with wide and narrow frequencies responses, which can be used for a variety of applications. This Chapter also extensively investigates printing resolution considerations for THz components. Specifically, THz Bragg structures are chosen, which have wide spacing between frequency features, to demonstrate the affected spectra from the underlying limitations of printing resolution. Several printing resolutions are explored, ranging from 50 µm to 400 µm. This is performed for both HIPS and COC THz Bragg structures and show lessened performance with increasing resolution. 111 6.2 Terahertz Time-Domain Spectroscopy of High Impact Polystyrene and Cyclic Olefin Copolymer Filament Materials The contrast in material response between HIPS and COC filament materials can be highlighted through THz-TDS analyses, initially explored in Chapter 4 and revisited here for further clarity. This THz-TDS extracts the refractive index and absorption coefficient of the filament materials through the respective phase spectra and magnitude spectra of the incident and transmitted THz pulses [160]. The THz-TDS results are presented in Figure 6.2.1(a) for 1 mm thick samples in open air conditions and in Fig. 6.2.1 (b) for 5 mm thick samples in nitrogen purged conditions. The THz-TDS samples are prepared as 3D printed samples fabricated using a one hundred percent infill setting, such that the diameter of the cylinder samples is fabricated on the X- and Y-axes plane on the 3D printer bed. The height of the cylinder samples is fabricated in the Z-axis direction of the 3D printer bed, with the minimum Z-axis layer resolution setting of 0.05 mm. Here, the refractive index of HIPS filament material, nHIPS, and refractive index of COC filament material, nCOC, are seen to be similar taking on a value of approximately 1.5. This indicates that the photonic performance of a THz Bragg superstructure or structure made from either material will possess similar spectral features, with the exception of losses due to differences in absorption coefficient. Such a difference can also be seen in Figure 6.2.1 through the stark difference between the absorption coefficient of HIPS, αHIPS, and the absorption coefficient of COC, αCOC. Averaging the Fig. 6.2.1(a) and 6.2.1(b) data, the values at 1 THz frequency are αHIPS = 5 cm-1, nHIPS = 1.5, αCOC = 2 cm-1, and nCOC = 1.5, which are consistent with literature values [73] [64] [215]. The contrast between the two absorption coefficients is pronounced at higher frequencies, e.g., a difference between 4 cm-1 and 2 cm-1 at 1 THz for HIPS and COC, respectively. This difference in absorption coefficient is also seen later in this Chapter in the experimental results of Chapter 6.6 and Chapter 6.7. Both HIPS and COC filament materials are of high printability for fabricating dimensionally accurate structures. The THz-TDS is performed in a THz experimental testbed, as shown in Figure 6.2.2. This THz experimental testbed can have THz-TDS samples, THz Bragg superstructures (left inset), or THz Bragg structures (right inset) inserted in the path of the THz beam (horizontal polarisation). 112 Figure 6.2.1 The terahertz time-domain spectroscopy results for high impact polystyrene (HIPS) filament material (black) and cyclic olefin copolymer (COC) filament material (grey) are shown for (a) open air conditions and (b) nitrogen purge conditions. The corresponding absorption coefficient, α, and refractive index, n, are represented as, striated curves, and solid curves, respectively. 113 Figure 6.2.2 A 3D view of the THz experimental testbed is shown with components: microscope objective (MO), photoconductive terahertz emitter (PE), parabolic mirror (PM), terahertz beam path (THz), pellicle beam splitter (BSpel), electro-optic crystal (EO), quarter wave plate (QW), polarisation beam splitter (BSpol), balanced silicon photodiode (PDsi), mirror (M), lens (L). The pump beam (Pump) and probe beam (Probe), shown in red, originate from a 780 nm 100 fs pulsed laser (not shown). The terahertz Bragg superstructure (Bragg Device) is shown within the optical axis of the terahertz beam path (THz) and shown as an expanded inset image (outlined in green). The terahertz Bragg structure, which can replace the terahertz Bragg superstructure, is shown as an inset image (outlined in blue). 114 6.3 Terahertz Bragg Superstructure Geometry One example design, of the THz Bragg superstructures to be 3D printed, is shown in Figure 6.3.1. Figure 6.3.1(a) shows a 3D view of a computer drafted model of the THz Bragg superstructure with illustrative time-domain incident (blue) and transmitted (red) THz pulses. The incident THz pulse, ETHz,INC, interacts with N = 4 material layers, then exits the THz Bragg superstructure as a transmitted THz pulse, ETHz,TRN. The material layers of the THz Bragg superstructure are bound within two stabilising side reinforcements, all attached to a bottom plate, having additional surfaces for optical table mounting. Figure 6.3.1(b) shows the top-view of the THz Bragg superstructure, with drafting lines indicating, d1, the air gap spacing, and d2, the material layer thickness, with respective refractive indices n1 and n2. These parameters are fundamental to the operation of the THz Bragg superstructure, as will be discussed in Chapter 6.4. A THz Bragg structure, not shown in Figure 6.3.1, (shown in Figure 5.3.1) can be made by selecting n1d1 = n2d2, i.e., that the gaps adhere to optical length equalization. The Bragg superstructures in this work are printed using the PrusaSlicer software, for the Prusa i3 MK3S+ 3D using the 50 µm resolution setting (corresponding to a feed rate of 0.33 mm3/s) and 0.4 mm nozzle. The Bragg superstructures are fabricated, such that, the width of the material layers, having thickness d2, are fabricated in the X- and Y-axes plane on the printer bed. The default 0.45 mm extrusion width resolution setting for the X- and Y-axes plane is maintained in the PrusaSlicer software to fabricate the Bragg superstructures. The Bragg superstructure material layers consist of many X- and Y-axes plane slices concatenated in the Z-axis direction. Appendix Figure B.1 shows the THz Bragg superstructure with respect to the polarisation of the THz beam. 6.4 Terahertz Bragg Superstructure Operation The THz Bragg superstructure response is shown here. Details for the THz Bragg structure response can be found in literature [59]. A nominal time-domain experimental response is shown in Figure 6.4.1 for a THz Bragg superstructure made from COC filament material with d1 = 14.01 mm, d2 = 1.12 mm, and N = 4. The incident THz pulse, ETHz,INC(t), is the blue curve and the transmitted THz pulse, ETHz,TRN(t), is the 115 Figure 6.3.1 Overview images of the geometry and function of terahertz Bragg superstructure is presented. (a) The terahertz Bragg superstructure is represented as a three-dimensional view, with corresponding incident (blue) and transmitted (red) THz electric field pulses, being ETHz,INC, and ETHz,TRN, respectively. (b) A top-view representation of the terahertz Bragg superstructure geometry is shown for air, n1, and material, n2, interfaces having distances, d1, and d2, respectively. 116 Figure 6.4.1 The experimental time-domain results of the terahertz Bragg superstructure, fabricated from cyclic olefin copolymer filament material, are shown for the design case corresponding to narrow Fmajor and narrow Fminor frequency periodicities in the terahertz spectrum. The time-domain experimental results are represented for both incident (blue), and transmitted (red), terahertz electric field pulses for: (a) 400 picosecond time scale, and (b) 100 picosecond timescale. Shown in (c) and (d) are FDTD time-domain results. 117 red curve. The time-domain responses are displayed for 0 to 400 ps (full data shown) and 0 to 100 ps (zoomed in, partial data shown) in Figure 6.4.1(a) and Figure 6.4.1(b), respectively. For comparison, Figs. 4(c) and 4(d) show FDTD time-domain results for a Bragg superstructure with d1 = 14 mm, d2 = 1 mm, N = 4, n1 = 1, and n2 = 1.5. The incident and transmitted time-domain pulses are expressed in the frequency-domain as Ei(f) and Et(f), respectively, which are used in the natural logarithm intensity ratio, being from equation (27) in Chapter 5. Figure 6.4.2 An illustrative depiction of the theoretical natural logarithm intensity ratio for the terahertz Bragg superstructure is shown as a function of frequency. The frequency-domain features of interest, being the wide and narrow frequency peak spacing's, are represented as ∆Fmajor and ∆Fminor, respectively. The natural logarithm intensity ratio shows how a THz Bragg superstructure responds as a function of frequency. Such a nominal (theoretical) frequency response is shown in Figure 6.4.2 for demonstrative purposes. Here, numerous rejection peaks manifest in the frequency-domain with underling periodicities. The first underling periodicity is ∆𝐹major =𝑐2𝑑2𝑛2 , (29) and is only dependant on the properties of the material layers. This is similar to (26) from Chapter 5 for THz Bragg structures. The vacuum speed of light is denoted as c. The second underlying periodicity is ∆𝐹minor =𝑐2𝑑1𝑛1 + 2𝑑2𝑛2 ≈ 𝑐2𝑑1𝑛1 , (30) 118 which is primarily dependant on the properties of the air gaps. The various THz Bragg superstructures explored in the remainder of this Chapter will show wide and narrow ∆Fmajor and ∆Fminor based on their geometries. Table 6.5.1 Terahertz Bragg superstructure; results and experimental parameters. Bragg super-structure Frequency Description d1 [mm] (air) d2 [mm] (mat.) n1 (air) n2 (mat.) ∆Fmajor [THz] (freq. spacing) ∆Fminor [THz] (freq. spacing) FDTD (a) narrow ∆Fmajor narrow ∆Fminor 14.00 1.00 1.0 1.5 0.100 0.010 FDTD (b) wide ∆Fmajor narrow ∆Fminor 14.00 0.75 1.0 1.5 0.133 0.010 FDTD (c) narrow ∆Fmajor wide ∆Fminor 10.10 1.00 1.0 1.5 0.100 0.013 HIPS (a) narrow ∆Fmajor narrow ∆Fminor 14.00 1.12 1.0 1.5 0.093 0.010 HIPS (b) wide ∆Fmajor narrow ∆Fminor 14.02 0.92 1.0 1.5 0.113 0.010 HIPS (c) narrow ∆Fmajor wide ∆Fminor 10.07 1.11 1.0 1.5 0.093 0.013 COC (a) narrow ∆Fmajor narrow ∆Fminor 14.01 1.12 1.0 1.5 0.097 0.010 COC (b) wide ∆Fmajor narrow ∆Fminor 14.01 0.91 1.0 1.5 0.117 0.010 COC (c) narrow ∆Fmajor wide ∆Fminor 10.11 1.11 1.0 1.5 0.096 0.013 6.5 Theoretical Finite-Difference Time-Domain Simulation This Chapter continues with investigations of three simulated superstructures, three experimental superstructures made from HIPS filament material, and three experimental superstructures made from COC filament material. Three different designs are selected to demonstrate how ∆Fmajor and ∆Fminor can manifest from subtle variations in the fabricated geometry. This is important for application-specific device fabrication. Design (a) has narrow ∆Fmajor and narrow ∆Fminor due to large d1 and large d2 values. Design (b) has wide ∆Fmajor and narrow ∆Fminor due to a small d1 and large d2 values. Design (c) has narrow ∆Fmajor and 119 Figure 6.5.1 The theoretical results of the finite-difference time-domain electromagnetic simulation of an ideal (lossless) terahertz Bragg superstructure is shown for three frequency designs. The theoretical natural logarithm intensity ratio is displayed for a terahertz Bragg superstructure having (a) narrow ∆Fmajor and narrow ∆Fminor, (b) wide ∆Fmajor and narrow ∆Fminor, (c) and narrow ∆Fmajor and wide ∆Fminor. 120 wide ∆Fminor due to a large d1 and small d2 values. The theoretical responses are shown for a perfect lossless case. The HIPS filament material experimental responses demonstrate a lossy case. The COC filament material experimental responses demonstrate a low loss case. All cases, and their respective properties, are summarised in Table 6.5.1. Figure 6.5.1(a)-(c) shows the abovementioned designs (a)-(c) for a standard FDTD simulation implemented in one dimension. Although FDTD computes time-domain data, our simulation performs a Fourier transform on this data to produce spectra. The vertical axis in Fig. 6.5.1 is the natural logarithm of the intensity ratio, as previously defined in equation (1). The theoretical response has consistent amplitudes across the 0.1-1.0 THz frequency range—there is no underlying absorption. Figure 6.5.1(b) and Fig. 6.5.1(c) show the response for Design (b) and Design (c) and all these various designs can be used for applications requiring partitioning of the THz spectrum in different and specific ways. The FDTD simulation does not incorporate absorption, and such a modification is a point of potential future work. The FDTD simulation follow a process outlined by Rumpf [216]. The details for this 1D FDTD simulation are as follows: It has a spatial grid resolution of 10 µm (being well below the THz wavelengths), a temporal step resolution of 16.66 fs, such that, the temporal step resolution is the grid resolution divided by two times the speed of light. A Gaussian pulse source is leveraged to act as the THz pulse in this simulation, having a duration of 500 fs. A pair of one-dimensional absorbing boundary conditions are used at the extreme ends of the spatial grid, such that, the electric and magnetic fields at the boundaries are adjusted to become such fields from two time-steps prior. The total simulation undergoes 100,000 time-steps, going well beyond the time required to evaluate all significant resonant electric and magnetic field interactions with the Bragg superstructure. 6.6 High Impact Polystyrene Bragg Superstructure Experimental Results Figure 6.6.1 shows experimental results for the three designs of the THz Bragg superstructures fabricated with lossy HIPS filament material. Design (a) is made with large d1 = 14.00 mm and large d2 = 121 Figure 6.6.1 The experimental results of the terahertz Bragg superstructure, fabricated from lossy high impact polystyrene filament material, is shown for three frequency designs. The natural logarithm intensity ratio is displayed for a high impact polystyrene terahertz Bragg superstructure having (a) narrow ∆Fmajor and narrow ∆Fminor, (b) wide ∆Fmajor and narrow ∆Fminor, (c) and narrow ∆Fmajor and wide ∆Fminor. 122 Figure 6.7.1 The experimental results of the terahertz Bragg superstructure, fabricated from cyclic olefin copolymer filament material, is shown for three frequency designs. The natural logarithm intensity ratio is displayed for a cyclic olefin copolymer terahertz Bragg superstructure having (a) narrow ∆Fmajor and narrow ∆Fminor, (b) wide ∆Fmajor and narrow ∆Fminor, (c) and narrow ∆Fmajor and wide ∆Fminor. 123 1.12 mm with its frequency response shown in Figure 6.6.1(a). From equation (29) and (30), a narrow ∆Fmajor = 0.089 THz and a narrow ∆Fminor 0.010 THz are expected. These values are consistent with their experimentally-measured counterparts shown in Table 6.5.1. The troughs do not reach consistent minima throughout the demonstrated frequency range. This is due to the high absorption coefficient of HIPS filament material, particularly at high frequencies. Design (b) is made with large d1 = 14.02 mm and small d2 = 0.92 mm with its frequency response shown in Figure 7.7.1(b). From equation (29) and (30), a wide ∆Fmajor = 0.109 THz and a narrow ∆Fminor = 0.010 THz are expected. Design (c) is made with small d1 = 10.07 mm and large d2 = 1.11 mm. With its frequency response shown in Figure 7.7.1(c). From equation (29) and (30), a narrow ∆Fmajor = 0.090 THz and wide ∆Fminor = 0.013 THz are expected. Designs (b) and (c) also show the high absorption coefficient from the HIPS filament material (measured in Figure 6.2.1), which is undesirable. This high absorption coefficient manifests itself as an underlying linear increase in the natural logarithm intensity ratio. Additional loss, as compared to the ideal simulation reported in Chapter 6.5, is likely due to scattering (Appendix A). 6.7 Cyclic Olefin Copolymer Bragg Superstructure Experimental Results Figure 6.7.1, shows experimental results for the three designs of the THz Bragg superstructures, however, now using low loss COC filament material. From this low loss COC filament material, this should represent the best experimental response and the closest match to the Figure 6.7.1 theoretical results. Design (a) is made with large d1 = 14.01 mm and large d2 = 1.12 mm with its frequency response shown in Figure 6.7.1(a). From equation (29) and (30), a narrow ∆Fmajor = 0.089 THz and a narrow ∆Fminor = 0.010 THz are expected. These values are consistent with their experimentally-measured counterparts shown in Table 6.5.1. The trough minima are shown to be much more consistent throughout the demonstrated frequency range. This is due to the low absorption coefficient of COC, particularly at high frequencies. Design (b) is made with large d1 = 14.01 mm and small d2 = 0.91 mm with its frequency response shown in Figure 6.7.1(b). From equation (29) and (30), a wide ∆Fmajor = 0.110 THz and a narrow ∆Fminor = 0.010 THz are 124 expected. Design (c) is made with small d1 = 10.11 mm and large d2 = 1.11 mm with its frequency response shown in Figure 6.7.1(c). From equation (29) and (30), a narrow ∆Fmajor = 0.090 THz and a wide ∆Fminor = 0.013 THz are expected. Designs (b) and (c) also show the low absorption coefficient from the COC filament material as measured in Figure 6.2.1, which is desirable. Overall, the stark contrast in absorption between Figure 6.6.1 and Figure 6.7.1 shows the benefits of COC filament material over that of HIPS filament material. For either filament material, THz Bragg superstructures can be designed with differing frequency periodicities according to the needs of the application. This can be achieved in rapid prototyping, given the use of 3D printing. 6.8 Effect of Printing Resolution The 3D printing resolution is a crucial parameter to analyse, given that the fine resolution (50 µm) structures take drastically longer to print than the coarse resolution (400 µm) structures, being 375 minutes (i.e., greater than six hours) versus 35 minutes (i.e., less than one hour), respectively. This dramatic contrast can make the difference between 3D printing being a viable rapid prototyping technology for THz components or not being viable at all. The resolution study aims to answer questions regarding the effect of resolution on performance of components over the THz regime. Thus for both HIPS and COC filament materials, the study includes the following 3D printer resolutions: 50, 100, 150, 200, 250, 300, 350, and 400 µm. Terahertz Bragg structures [59] are selected due to their widely spaced loss peaks. These resolutions can be above or below the wavelengths of the (broadband) THz pulses. For HIPS, the results are presented in Figure 6.8.1. A behaviour is shown similar to a pseudo lowpass filter, i.e., the loss peaks associated with the lower frequencies are less affected than the loss peaks associated with the higher frequencies. This is summarised in Table 6.8.1. Here, the loss of the peaks decreases as 3D printing resolution increases, and this is particularly true for high frequency loss peaks. Higher frequencies than the limiting resolution frequency (Fres = c/ndres), where c is the free-space speed of light) are particularly affected. Stop-band width (SBW) is affected in a similar way. In the insets of Figure 6.8.1, scanning electron microscope (SEM) images are 125 shown to corroborate the feature size of the printing resolution, as input into the 3D printer. Thus, the fabrication results of the 50-400 µm range of Z-axis resolution settings can be observed in the SEM inset images on Figure 6.8.1 and Figure 6.8.2, for HIPS filament material and COC filament material, respectively. The 50-400 µm range of Z-axis resolution settings are applied in the PrusaSlicer software. The resolution study continues through an analysis of COC THz Bragg structures with the same 3D printer resolutions. This is presented in Figure 6.8.2. The same pseudo lowpass behaviour is observed whereby the loss peaks associated with the lower frequencies are better maintained than the ones associated with higher frequencies (not calculated as they are undefined beyond Fres). This is summarised in Table 6.8.2. The loss of the peaks decreases as 3D printing resolution increases, and this is particularly true for high frequency loss peaks. Higher frequencies than the resolution frequency are affected the most. To quantify the results of Table 6.8.1 and Table 6.8.2 further and compare the maximum measured peak frequency location, e.g., 19F0 for 50 µm resolution HIPS, 15F0 for 150 µm resolution HIPS, the percent errors can be found between experimental values and the calculation. This percent error for the experimental values averages to be 0.7% and 0.3% for Table 2 and 3, respectively. Each of the frequency rejection peaks in Table 6.8.1 and Table 6.8.2 for the THz Bragg structure response correspond to the F0 odd integer multiple fundamental frequency modes. The dimensions of these THz Bragg structures are fabricated to the specifications of d1 = 900 µm, d2 = 600 µm, n1 = 1.0 , n2 = 1.5, for N = 10 material layers. The THz Bragg structures adhere to optical length equalization, such that, n1d1 = n2d2. The frequency-domain response of the THz Bragg structures exhibits frequency rejection peaks following odd-integer multiples of the fundamental frequency mode being, F0, 3F0, 5F0, …, 21F0, where the fundamental is at 𝐹0 =𝑐(2𝑛2𝑑2 + 2𝑛1𝑑1) (31) Each of the frequency rejection peaks in Table 6.8.1 and Table 6.8.2 for the THz Bragg structure response correspond to the above-mentioned fundamental frequency modes. These frequency rejection peaks have a 126 theoretical SBW [217] of SBW = 4𝜋𝐹0 sin−1 |𝑛1𝑛2− 1𝑛1𝑛2+ 1| . (32) The SBW is determined in the FDTD simulations and experimentally as the full-width-at-half-maximum. The difference between frequency rejection peaks, ∆F, follows ∆𝐹 = 2𝐹0 =𝑐2𝑛2𝑑2 , (33) which is an expansion of equation (26) from Chapter 5 to connect with the fundamental frequency. The theoretical loss of each frequency rejection peak can be derived from the transmission-to-incident intensity ratio [217] for a Bragg reflection of multiple refractive index changes following |𝐸t(𝑓)|2|𝐸i(𝑓)|2= 1 − (1 − 𝑛1𝑛22(𝑁)1 + 𝑛1𝑛22(𝑁))2 . (34) The theoretical loss, L, is found through 𝐿 = ln (|𝐸i(𝑓)|2|𝐸t(𝑓)|2)2.303 . (35) This equation has the division by 2.303 as a conversion between a base 10 logarithm and natural logarithm. The loss of the FDTD simulation and experimental data is found from dividing the natural log intensity ratio by 2.303. From the data of Table 6.8.1 and Table 6.8.2, and the visual trend in Figure 6.8.1 and Figure 6.8.2 (with affected spectra being highlighted in grey shading), shows the dramatic impact of the resolution. The Table 6.8.1 and Table 6.8.2 results display SBW values only up to the cutoff imposed by Fres. Figure 6.8.1 and Figure 6.8.6 show a visibly distorted frequency response beyond the Fres value. 127 Figure 6.8.1 The experimental results of the terahertz Bragg structure, fabricated with high impact polystyrene filament material, are shown. The terahertz response (blue) is displayed along with the maximum measurable value (red), for each corresponding fabrication pitch resolution, dres.: 50 µm, 100 µm, 150 µm, 200 µm, 250 µm, 300 µm, 350 µm, and 400 µm. A SEM image showing the terahertz Bragg structure fabrication pitch resolution is shown. Each inset image was taken at the same SEM magnification and each image is a 1,000 µm (vertical image height) by 1,000 µm (horizontal image width) for overall 1 mm2 area. The grey region of the terahertz spectrum indicates the frequency regime equal to and above the resolution frequency, Fres.. 128 Table 6.8.1 Terahertz Bragg structure, fabricated with high impact polystyrene filament material; results and experimental parameters. HIPS Filament Material Freq. [THz] 3Fo 5Fo 7Fo 9Fo 11Fo 13Fo 15Fo 17Fo 19Fo 0.2499 0.4165 0.5831 0.7497 0.9163 1.083 1.250 1.416 1.583 Theory SBW 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 ∆F 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 𝐿 2.916 2.916 2.916 2.916 2.916 2.916 2.916 2.916 2.916 FDTD SBW 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 ∆F 0.1651 0.1664 0.1677 0.1664 0.1666 0.1666 0.166 0.1665 0.1655 𝐿 2.880 2.913 2.891 2.883 2.911 2.911 2.910 2.916 2.923 dres. = 50 µm Fres.= 4.00 THz SBW 0.0250 0.0200 0.0200 0.0188 0.0150 0.0200 0.0250 0.0200 0.0613 ∆F 0.1625 0.1625 0.1638 0.1613 0.1650 0.1688 0.1588 0.1638 0.1750 𝐿 2.298 2.702 3.204 2.509 2.446 1.842 1.852 1.639 1.472 dres. = 100 µm Fres.= 2.00 THz SBW 0.0225 0.0188 0.0188 0.0175 0.0200 0.0158 0.0270 0.0110 0.0420 ∆F 0.1650 0.1638 0.1625 0.1650 0.1663 0.1638 0.1638 0.1600 0.1550 𝐿 2.503 3.204 2.470 2.771 2.112 1.851 1.073 0.8430 0.9403 dres. = 150 µm Fres.= 1.33 THz SBW 0.0213 0.0150 0.0163 0.0213 0.0200 0.0200 0.0180 ∆F 0.1650 0.1638 0.1650 0.1650 0.1613 0.1625 0.1650 𝐿 2.615 3.372 2.194 1.349 0.8632 0.5293 0.9073 dres. = 200 µm Fres.= 1.00 THz SBW 0.0188 0.0163 0.0200 0.0213 0.0188 ∆F 0.1675 0.1638 0.1625 0.1650 0.1650 𝐿 2.429 2.712 1.637 0.9755 0.8109 dres. = 250 µm Fres = 0.80 THz SBW 0.0163 0.1143 0.0188 0.0213 ∆F 0.1600 0.1638 0.165 0.1625 𝐿 3.022 1.847 1.398 1.061 dres. = 300 µm Fres.= 0.67 THz SBW 0.0138 0.0113 0.0150 ∆F 0.1650 0.1663 0.1675 𝐿 2.910 2.056 1.199 dres. = 350 µm Fres.= 0.57 THz SBW 0.0163 0.0125 ∆F 0.1700 0.1700 𝐿 2.901 1.545 dres. = 400 µm Fres.= 0.50 THz SBW 0.0150 0.0080 ∆F 0.1675 0.1675 𝐿 2.190 2.348 129 Figure 6.8.2 The experimental results of the terahertz Bragg structure, fabricated with cyclic olefin copolymer filament material, are shown. The terahertz response (blue) is displayed along with the maximum measurable value (red), for each corresponding fabrication pitch resolution, dres.: 50 µm, 100 µm, 150 µm, 200 µm, 250 µm, 300 µm, 350 µm, and 400 µm. A SEM image showing the maximum and minimum terahertz Bragg structure fabrication pitch resolution is shown. Each inset image was taken at the same SEM magnification and each image is a 1,000 µm (vertical image height) by 1,000 µm (horizontal image width) for overall 1 mm2 area. The grey region of the terahertz spectrum indicates the frequency regime equal to and above the resolution frequency, Fres. 130 Table 6.8.2 Terahertz Bragg structure, fabricated with cyclic olefin copolymer filament material; results and experimental parameters. COC Filament Material Freq. [THz] 3Fo 5Fo 7Fo 9Fo 11Fo 13Fo 15Fo 17Fo 19Fo 21Fo 0.2499 0.4165 0.5831 0.7497 0.9163 1.083 1.250 1.416 1.583 1.749 Theory SBW 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 0.0213 ∆F 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 𝐿 2.916 2.916 2.916 2.916 2.916 2.916 2.916 2.916 2.916 2.916 FDTD SBW 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 ∆F 0.1651 0.1664 0.1677 0.1664 0.1666 0.1666 0.166 0.1665 0.1655 0.165 𝐿 2.880 2.913 2.891 2.883 2.911 2.911 2.91 2.916 2.923 2.94 dres. = 50 µm Fres.= 4.00 THz SBW 0.0199 0.0200 0.0150 0.0173 0.0175 0.0190 0.0210 0.0150 0.0140 0.0130 ∆F 0.1624 0.1612 0.1649 0.1674 0.1623 0.1613 0.1640 0.1660 0.1685 0.1700 𝐿 3.223 2.675 3.236 2.414 2.245 1.959 1.479 1.620 1.567 1.571 dres. = 100 µm Fres.= 2.00 THz SBW 0.0212 0.0175 0.0175 0.0200 0.0175 0.0250 0.0160 0.0110 0.0100 ∆F 0.1699 0.1649 0.1624 0.1624 0.1613 0.1648 0.1665 0.1665 0.1670 𝐿 2.561 3.149 2.508 2.104 2.423 1.738 1.901 1.914 1.479 dres. = 150 µm Fres. = 1.33 THz SBW 0.0150 0.0100 0.0051 0.0175 0.0188 0.0200 0.0170 ∆F 0.1699 0.1674 0.1649 0.1637 0.1655 0.1648 0.1610 𝐿 3.284 3.732 2.366 1.878 1.565 1.313 1.094 dres. = 200 µm Fres. = 1.00 THz SBW 0.0200 0.0163 0.0162 0.0150 0.0200 ∆F 0.1674 0.1674 0.1662 0.1649 0.1649 𝐿 2.726 2.227 1.737 1.160 0.8867 dres. = 250 µm Fres. = 0.80 THz SBW 0.0175 0.0150 0.0150 0.0150 ∆F 0.1649 0.1662 0.1674 0.1674 𝐿 2.949 2.191 1.245 1.073 dres. = 300 µm Fres. = 0.67 THz SBW 0.0175 0.0162 0.0175 ∆F 0.1624 0.1662 0.1699 𝐿 2.509 1.834 1.163 dres. = 350 µm Fres. = 0.57 THz SBW 0.0125 0.0137 ∆F 0.1674 0.1674 𝐿 3.274 2.092 dres. = 400 µm Fres. = 0.50 THz SBW 0.0187 0.0125 ∆F 0.1674 0.1674 𝐿 2.200 1.577 131 The connection between printing time, printing resolution, and Fres is shown in Figure 6.8.3 for three potential Bragg structures and Bragg superstructures. The connection between build rate, printing resolution, and Fres is shown in Figure 6.8.4 for the three potential Bragg structures and Bragg superstructures. The printing time and build rate is calculated using the PrusaSlicer software for a Prusa i3 MK3S+ 3D printer. For this 3D printer, the external perimeter feed rates of 0.33, 0.86, 1.57, 2.04, 2.48, 4.02, 4.59, and 5.14 mm3/s correspond to the printer resolution settings, dres, of 50, 100, 150, 200, 250, 300, 350, and 400 µm, respectively. 132 Figure 6.8.3 Three potential Bragg structures and Bragg superstructures, with N material layers, are evaluated for (a) the print time versus printing resolution, and (b) the print time versus the resolution frequency, Fres. 133 Figure 6.8.4 Three potential Bragg structures and Bragg superstructures, with N material layers, are evaluated for (a) the build rate versus printing resolution, and (b) the build rate versus the resolution frequency, Fres. 134 6.9 Chapter Conclusions This Chapter first revisited THz-TDS of HIPS and COC filament materials. From these results, the low absorption coefficient of COC filament material was reshown. This Chapter demonstrated several THz Bragg superstructures for both HIPS and COC filament materials, to show the contrast in performance and mitigation of unwanted absorption for a THz photonic element. This Chapter also provided a 3D printing resolution study, showing the connection between the difficulty to preserve Bragg spectra features with increasing 3D printing resolution, for THz Bragg structures made from both HIPS and COC filament materials. These results highlighted the importance of COC filament material for rapid prototyping of THz Bragg superstructures and demonstrate printing resolution limitations. Such THz Bragg superstructures can be fabricated using 3D printing and designed for the needs of a specific application. Terahertz Bragg structures and superstructures both lend themselves to applications in sensing and communications. I hope that the outcomes of this thesis will help researchers make design choices while undergoing rapid prototyping for THz experiments. I will make some broad recommendations below. Terahertz Bragg structures and superstructures made from HIPS filament material are suitable for low THz frequencies and low cost applications. Terahertz Bragg structures and superstructures made from COC filament material are suitable for high THz frequencies and applications that can tolerate higher costs. The printing resolution of 0.05 mm is suitable for high THz frequency applications where long fabrication times can be tolerated. The printing resolution of 0.40 mm is suitable for low THz frequency applications where short fabrication times are required. 135 Chapter 7: Thesis Contributions and Future Work This Chapter provides a summary of the contributions found in each Chapter of this thesis. In addition potential avenues of future work are discussed. 7.1 Summary of Thesis Contributions The body of the thesis is Chapters 2-6. Chapter 2 provided a literature review. Chapter 3 provided relevant fundamental knowledge. Chapters 4-6 provided novel contributions to the literature. These contributions are listed and discussed below. Chapter 4 presented an experimental study characterising AM filament materials with a THz-TDS free-space optical system. The contributions presented are as follows: i. Twenty-four additive manufacturing materials were characterised with THz-TDS and consolidated into a single study, with the results disseminated in a journal article. This filled the literature gap of material characterisations and keeping the current THz science literature abreast of new AM filament materials. For many materials, the Chapter extended the measured THz bandwidths compared to prior reported data. ii. The THz absorption and THz refractive index properties of the twenty-four characterised AM filament material were evaluated for their appropriateness towards application as THz structures and devices. It was determined that from the twenty-four characterised filament materials, HDPE filament material, HIPS filament material, COC filament material, and PP filament material, showed lower THz absorption, being less than 10 cm-1 at 1.0 THz. The aforementioned low absorption filament materials are selected as being suitable for use as 3D printed THz devices and structures. The HIPS and COC filament materials were identified as the top candidates, as HDPE is difficult to 3D print and PP has the highest absorption coefficient of these four filament materials. iii. To the author's best knowledge, the first reported THz-TDS characterisations of the following AM filament materials where presented in this Chapter and established in the literature: These filament 136 materials are ASA filament material, PVB filament material, LT PCL filament material, and PEI filament material. Chapter 5 presents an experimental study evaluating the design, fabrication, and characterisation of THz Bragg structures, having optical path length equalization, fabricated with AM via HIPS filament material. The contributions presented are as follows i. Two THz Bragg structures (each with two numbers of material layers) were developed, having unique frequency designs, and were implemented and investigated theoretically, with FDTD electromagnetic simulations, and experimentally, with a THz experimental testbed. ii. The response of these THz Bragg structures were thoroughly analysed in the time-domain and frequency-domain. It was shown that these two THz Bragg structures manifested a wide and narrow frequency rejection peak placement in corresponding the THz frequency-domain response of a transmitted THz beam. iii. It was demonstrated that FFF AM is applicable to the creation of frequency selective THz devices whilst utilising THz compatible filament materials. Chapter 6 presented an experimental study of THz Bragg structures Bragg superstructures fabricated with HIPS and COC filament materials via AM. The contributions presented are as follows. i. It was shown that a THz Bragg superstructure, being (intentionally) without optical path length equalization, can be implemented with FFF AM and suitable filament materials. ii. Terahertz Bragg superstructures were demonstrated for both HIPS and COC filament materials, with performance comparison of both materials for fine frequency features. There was an observation of (undesirable) high THz absorption for such application with HIPS filament material and (desirable) low THz absorption for such application with COC filament material. iii. The AM fabrication resolution was studied using the THz Bragg structure, for eight fabrication resolutions ranging from 50 µm to 400 µm, for both HIPS and COC filament materials. This 137 established the association between preservation of spectral features of the corresponding THz response and fabrication resolution of the Bragg structure. A lower AM fabrication resolution was found to preserve the higher frequency features in the THz response. 7.2 Future Work The future work recommendations for this thesis work are summarised here. The recommendation for future work is as follows. i. The library of AM filament materials is ever expanding, therefore, the THz characterisations for any new AM filament materials can be performed on a continual basis to update the contributions of this thesis. ii. Development and application of additional frequency selective THz structures fabricated with FFF based AM for applications is recommended for future work. Two potential avenues for application are in sensing and communications. iii. 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Express 31, 21706 (2023). 160 Appendices Appendix A Absorption can be incorporated into a FDTD electromagnetic simulations using the Debye model, as demonstrated by Taflove et al. [167]. The Debye model utilises a frequency dependant complex permittivity, 𝜀(𝜔), defined as 𝜀(𝜔) = 𝜀∞ + 𝜀s − 𝜀∞ 1 − 𝑗𝜔𝜏=𝐷x(𝜔)𝐸x(𝜔) , (36) where 𝜀s is the low frequency permittivity (i.e., dielectric constant), 𝜀∞ is the high frequency permittivity (i.e., refractive index squared), and 𝜏 is the Debye relaxation time constant. The inverse Fourier transform of the Debye model of (36) renders the following differential equation, as described by Taflove [167], being 𝐷x + 𝜏d𝐷xd𝑡= 𝜀s𝐸x + 𝜏𝜀∞d𝐸xd𝑡 . (37) The corresponding FDTD electromagnetic simulation update equation is 𝐸x| 𝑘 𝑛+1 2⁄ = ∆𝑡 + 2𝜏2𝜏𝜀∞ + 𝜀s∆𝑡𝐷x| 𝑘 𝑛+1 2⁄ +∆𝑡 − 2𝜏2𝜏𝜀∞ + 𝜀s∆𝑡𝐷x| 𝑘 𝑛−1 2⁄ + 2𝜏𝜀∞ − 𝜀s∆𝑡2𝜏𝜀∞ + 𝜀s∆𝑡𝐸x| 𝑘 𝑛−1 2⁄ . (38) Here, the electric field component, 𝐸x| 𝑘 𝑛+1 2⁄ , i.e., E, is defined with respect to the electric flux density component, 𝐷x| 𝑘 𝑛+1 2⁄ , of the same time-step, as well as the electric field and electric flux density components of the previous time-step, 𝐸x| 𝑘 𝑛−1 2⁄, and, 𝐷x| 𝑘 𝑛−1 2⁄, respectively. Equation (38) is implemented in a 1D FDTD update scheme following D→E→H. Thus, the magnetic field component, 𝐻y| 𝑘+1 2⁄ 𝑛+1 , i.e., H, is defined as 𝐻y| 𝑘+1 2⁄ 𝑛+1= 𝐻y| 𝑘+1 2⁄ 𝑛−∆𝑡𝜇0∆𝑧(𝐸x| 𝑘+1 𝑛+1 2⁄ − 𝐸x| 𝑘 𝑛+1 2⁄ ) , (39) 161 and the electric flux density component, 𝐷x| 𝑘 𝑛+1 2⁄, i.e., D, is defined as 𝐷x| 𝑘 𝑛+1 2⁄ = 𝐷x| 𝑘 𝑛−1 2⁄ −∆𝑡∆𝑧(𝐻y| 𝑘+1 2⁄ 𝑛− 𝐻y| 𝑘−1 2⁄ 𝑛) . (40) The abovementioned update equations are implemented in a 1D FDTD electromagnetic simulation for an N = 4 material layer Bragg superstructure (as shown in Figure 6.4.1). The Debye complex permittivity values were chosen from the literature to model HIPS [218] [219] and COC [220] materials. The frequency-domain result for HIPS and COC Bragg superstructures are shown in Figure A.1 and Figure A.2, respectively. The experimental data in Figure A.1(b) and Figure A.2(b) is reproduced from Figure 6.6.1(a) and Figure 6.6.2(b). This is for the 1D FDTD electromagnetic simulation with the parameters ∆𝑡 = 6.67 fs,∆𝑧 = 4 μm; Bragg superstructure: d1 = 14.0 mm, d2 = 1.01 mm; COC material: 𝜀∞ = 2.25 , 𝜀s = 2.36 , 𝜏 = 1.2⨉10−14 s ; HIPS material: 𝜀∞ = 2.25 , 𝜀s = 2.55, 𝜏 = 1.3⨉10−14 s. The discrepancy between subfigures (a) and (b), for Figure A.1 and Figure A.2, is assumed to be mainly from scattering. Figure A.1 (a) The frequency-domain result of a 1D FDTD electromagnetic simulation modeling a Bragg superstructure comprised of HIPS material is shown. (b) The experimental frequency-domain result of a Bragg superstructure fabricated from HIPS filament material is shown. 162 Figure A.2 (a) The frequency-domain result of a 1D FDTD electromagnetic simulation modeling a Bragg superstructure comprised of COC material is shown. (b) The experimental frequency-domain result of a Bragg superstructure fabricated from COC filament material is shown. A one-dimensional FDTD electromagnetic simulation was performed for a THz Bragg superstructure (where d1 = 14.0 mm, d2 = 1.00 mm), with and without loss, shown in Figure A.4 and Figure A.3, respectively. The corresponding frequency-domain results are shown in terms of (a) transmittance, (b) reflectance, and (c) loss. Figure A.3 is for the case without loss, where the summation of transmittance and reflectance is equal to one. Figure A.4 is for the case that simulates loss using the Debye model for HIPS material, such that, the summation of transmittance, reflectance, and loss, is equal to one. Scattering is not simulated with this FDTD analysis. 163 Figure A.3 The frequency-domain result of a 1D FDTD electromagnetic simulation modeling a Bragg superstructure for an ideal case is shown in terms of (a) transmittance, (b) reflectance, and (c) loss. 164 Figure A.4 The frequency-domain result of a 1D FDTD electromagnetic simulation modeling a Bragg superstructure comprised of HIPS material is shown in terms of (a) transmittance, (b) reflectance, and (c) loss. 165 Appendix B The THz Bragg superstructure is shown as a 3D model for a front view. The corrugated surface is representative of the 400 µm fabrication resolution. The polarisation orientation of the incident THz beams utilised in Chapter 5 and Chapter 6 is parallel to the red axis arrow. Figure B.1 A front view representation of the THz Bragg superstructure is shown.
Thesis/Dissertation
eng
Electrical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Collier, Christopher Michael
Terahertz characterisations and analyses of additive manufacturing materials and structures
Text