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Additional imaging examples, comparison of various algorithms and a brief description of Sigmoid functions

In the past few decades, the Terahertz range (0.1−10 THz) has gained interest for its many applications in astronomy, non-destructive testing, imaging, security and many other fields. With the current availability of non-cryogenic, table-top Terahertz (THz) sources and receivers, THz systems with peak dynamic ranges between 120 − 140 dB have become commonplace due to their broad frequency coverages over a few octaves. However, there is a severe lack of affordable, broadband characterisation tools, like vector network analysers. Electronic systems in a hollow metallic waveguide configuration yet offer the largest dynamic range, however, they are comparatively narrowband. At least five different waveguide rectangular (WR)-configurations (WR-1.5 to WR-0.65) are necessary for a frequency coverage between 0.5 − 1.5 THz, along with the corresponding frequency-extender modules, which become exponentially expensive with increasing operational frequency. A particularly costly component of an electronic system with on-chip measurement capability is the ground-signal-ground (G-S-G) probes that wear off and have to be regularly replaced. Therefore, free-space setups are implemented where possible. Traditionally employed optical components in free-space setups, such as lenses and parabolic mirrors, make THz systems bulky and create hurdles for miniaturisation and integration. For instance, a 10 × 10 μm2 large active device needs an antenna and a silicon lens to operate in free-space configuration, which enlarges it by at least 6 orders of magnitude. In order to circumvent both the limitations of a hollow metal waveguide and the unhandiness of a free-space setup, we propose in this thesis a dielectric waveguide architecture and an integrated photoconductive receiver topology to manufacture a (semi-) integrated, broadband, continuous-wave vector network analyser driven by standard 1550 nm telecom lasers. Enhanced by digital post-processing techniques, the photonic vector network analyser (PVNA) features an operational bandwidth between 0.5−1.5 THz without the need of exchanging any bands. The thesis first explores the applicability of free-space PVNAs in material characterisation and imaging at THz frequencies that will later serve as a benchmark for the integrated PVNA. For homogeneous, plane-parallel dielectric devices under test (DUTs), the measured scattering parameters (S-parameters) feature Fabry-Pérot oscillations. Fitting these oscillatory features allows the extraction of the physical thickness of the DUT with a precision of λ/15, 000 and proves such high precision by visualising a Siemens star as thin as 50 nm using a bandwidth between 0.6 − 0.8 THz. For characterising multilayered samples, where calculation of analytical Fabry-Pérot functions is cumbersome, we propose scattering transfer parameter (T-parameter)-based modelling and vectorial optimisation algorithms and apply them in estimating the thickness and refractive index of each layer of a 5-layered distributed Bragg reflector (DBR) structure with ∼ 0.6% error margin. The digital signal processing techniques demonstrably improve the operational bandwidth and dynamic range (DNR) of continuous-wave (CW) THz systems, such as the free-space PVNA, by ∼ 30% and 20 dB, respectively, without any significant increase in the measurement time. The waveguide architecture miniaturises the free-space PVNA by transforming the free-space THz beam to a guided one. The waveguides are highly-resistive float-zone silicon (HRFZ-Si)-based rectangular, dielectric structures with a 200 × 50 μm2 cross-section. High density polyethelene (HDPE) or crystalline quartz (Qz) substrates provide mechanical stability to the waveguide and ease their further integration with active devices, especially with Vivaldi antenna (VA)-coupled THz receivers manufactured in-house from erbium arsenide/indium (aluminium) galium arsenide (ErAs:In(Al)GaAs) photoconductors. The single-mode bandwidths of the waveguides are between 0.45 − 0.7 THz and 0.5 − 0.75 THz when supported by HDPE and Qz substrates, respectively. We operate the waveguides in the overmoded regime, but suppress the generation of undesired higher-order modes (HOMs) at bends by using ≳ 4 mm bend radii for circular bends or ≳ 2.3 mm for sine-squared bends. The tapered structures for free-space in-coupling and quasi near-field out-coupling using VA-coupled active devices further suppress the excitation of HOMs. The coupling efficiency to VA-coupled receivers is 5 − 14 dB higher than free-space coupling between 0.4 − 1.05 THz. The operational bandwidth of the waveguides in their fundamental mode with free-space in-coupling and direct out-coupling is between 0.45 − 1.5 THz, where the upper boundary is solely given by the decreasing dynamic range (DNR) with increasing frequency. The VA-coupled THz receivers are only 0.23 × 0.9 × 0.03 mm3 large and do not require silicon lenses to operate, easing integration to planar system-on-chip (SOC) architectures. Finally, the thesis presents a (semi-) integrated 1.5-port PVNA using the waveguide architecture and VA-coupled, ErAs:In(Al)GaAs-based receivers. A commercial P-I-N diode-based THz source is used in the free-space configuration due to the unavailability of appropriate materials to fabricate powerful VA-coupled THz sources. Despite of the 10−13 dB in-coupling losses, the operational bandwidth of the PVNA extends between 0.5−1.5 THz, demonstrated by a characterised whispering gallery mode (WGM) resonator, where the entire HRFZ-Si structure is fabricated together. We successfully characterise a THz fibre Bragg grating and two cavity resonators using the PVNA setup between 0.45 − 1.2 THz, where the measured S-parameters match excellently with simulated models in CST® microwave studio. Furthermore, we demonstrate a coupling mechanism to rectangular hollow metallic (RHM) waveguides that enable on-chip measurements of integrated electronic circuits using commercially available wafer probes in G-S-G configuration between 0.45 − 1.1 THz, without changing any setup components. In closing, the thesis briefly discusses the current pitfalls of the 1.5-port architectures and the modifications necessary to assemble a 2-port PVNA.

Conventional continuous-wave Terahertz imaging and thickness resolution systems often rely on the Fabry-Pérot resonances generated in the sample being imaged. As the samples become thinner, larger frequency sweeps are necessary for their visualisation. In this work, we demonstrate a post-processing technique employing zero-padding of a smaller frequency sweep between frequency intervals as low as 10 GHz up to intervals of 200 GHz, conducted between 0.6-0.8 THz, to emulate the thickness resolution generally achieved by orders of magnitude larger frequency ranges.