Abstract-Subwavelength thick ultrahigh-Q terahertz disc microresonators

Dominik Walter Vogt, Angus Harvey Jones, Thomas Alan Haase, and Rainer Leonhardt

 (a) Schematic illustration of a THz disc resonator with subwavelength thickness. The insert depicts 2 orders of magnitude of the normalized electric field distribution of the fundamental TM mode of a disc resonator with 12 mm diameter and 66.5 μm thickness at 0.6 THz on a logarithmic scale. The HRFZ-Si disc is indicated with the grey solid line. (b) Simulated intrinsic 𝑄$Q$ factor 𝑄0$Q_0$ for two discs with 6 mm diameter and 72 μm thickness (blue dots) and 12 mm diameter and 66.5 μm thickness (orange dots). The green-shaded area indicates the 𝑄0$Q_0$ of a solid sphere with 6 mm diameter. For simplicity, a constant permittivity corresponding to a material absorption of 𝛼=0.006 cm−1$\alpha =0.006{\mathrm{cm}}^{-1}$ is assumed. (c) Optimal disc thickness (black) and maximal intrinsic 𝑄$Q$ factor (brown) for diameters from 6 to 60 mm at a design frequency of about 560 GHz. The green-shaded area shows the intrinsic 𝑄$Q$ factors for solid sphere resonators. (d) FSRs of the disc resonators for diameters from 6 to 60 mm with optimal thicknesses (blue) and solid spheres (green). The solid lines are interpolations of the simulated data points to guide the eye.

https://www.osapublishing.org/prj/abstract.cfm?uri=prj-8-7-1183

Artificial structures that exhibit narrow resonance features are key to a myriad of scientific advances and technologies. In particular, exploration of the terahertz (THz) spectrum—the final frontier of the electromagnetic spectrum—would greatly benefit from high-quality resonant structures. Here we present a new paradigm of terahertz silicon disc microresonators with subwavelength thickness. Experimental results utilizing continuous-wave THz spectroscopy establish quality factors in excess of 120,000 at 0.6 THz. Reduction of the disc thickness to a fraction of the wavelength reduces the losses from the silicon substrate and paves the way to unparalleled possibilities for light–matter interaction in the THz frequency range.

© 2020 Chinese Laser Press

Abstract-Free-space coupling to symmetric high-Q terahertz whispering-gallery mode resonators

Dominik Walter Vogt, Angus Harvey Jones, and Rainer Leonhardt


https://www.osapublishing.org/ol/abstract.cfm?uri=ol-44-9-2220

We report on the coupling of a free-space Gaussian beam to symmetric high-quality (Q) whispering-gallery mode resonators (WGMRs) for terahertz (THz) radiation. We achieve very high excitation efficiencies up to 50% to THz WGMs with a Q-factor of 1.5×104$1.5\times {10}^4$ at 0.7 THz. The high coupling efficiencies have been realized by leveraging a Gaussian beam with a nearly diffraction-limited focal spot, as well as readily available low-loss, high-index silicon spheres with diameters comparable to the wavelength. The results convincingly underline the viability of free-space coupling in the THz frequency range.

© 2019 Optical Society of America

Abstract-Coherent Continuous Wave Terahertz Spectroscopy Using Hilbert Transform

Dominik Walter Vogt, Miro Erkintalo, Rainer Leonhardt,

https://link.springer.com/article/10.1007/s10762-019-00583-3

Coherent continuous wave (CW) terahertz spectroscopy is an extremely valuable technique that allows for the interrogation of systems that exhibit narrow resonances in the terahertz (THz) frequency range, such as high-quality (high-Q) THz whispering-gallery mode resonators. Unfortunately, common implementations are impaired by deficiencies in the used data analysis schemes. Here, we show that these deficiencies can be conveniently overcome using the Hilbert transform, and we unveil the theoretical foundations of the method. In particular, by establishing that signals encountered in typical experiments are closely related to analytic signals, we demonstrate that Hilbert transform is applicable even when the envelope varies rapidly compared to the oscillation period. Compelling results from experimental measurements and numerical simulations confirm the broad applicability of the described method.
Coherent continuous wave (CW) terahertz spectroscopy is an extremely valuable technique that allows for the interrogation of systems that exhibit narrow resonances in the terahertz (THz) frequency range, such as high-quality (high-Q) THz whispering-gallery mode resonators. Unfortunately, common implementations are impaired by deficiencies in the used data analysis schemes. Here, we show that these deficiencies can be conveniently overcome using the Hilbert transform, and we unveil the theoretical foundations of the method. In particular, by establishing that signals encountered in typical experiments are closely related to analytic signals, we demonstrate that Hilbert transform is applicable even when the envelope varies rapidly compared to the oscillation period. Compelling results from experimental measurements and numerical simulations confirm the broad applicability of the described method.

Abstract-Anomalous blue-shift of terahertz whispering-gallery modes via dielectric and metallic tuning

Dominik Walter Vogt, Angus Harvey Jones, Harald G. L. Schwefel, and Rainer Leonhardt

https://www.osapublishing.org/ol/abstract.cfm?uri=ol-44-6-1319

The vast majority of resonant systems show a red-shift for the resonance frequency when a perturbation, e.g., losses, is introduced to the system. In contrast, here we report for the first time, to the best of our knowledge, the experimental demonstration of both red- and anomalous blue-shifting of whispering-gallery modes (WGMs) using dielectric and metallic substrates. The maximum blue-shift is more than three times as large as the expected red-shift, proving that the anomalous blue-shift is more than a peculiar curiosity. The experiments are performed in the terahertz frequency range with coherent continuous-wave spectroscopy. The results establish dielectric and metallic tuning as a novel and viable approach to tune high-quality WGMs and provide valuable insights into the anomalous blue-shift of WGM cavity systems. The tuning capabilities for these compact monolithic resonators are of significant interest for fundamental science and technological applications alike.

© 2019 Optical Society of America

Abstract-Prism coupling of high-Q terahertz whispering-gallery-modes over two octaves from 0.2 THz to 1.1 THz

Dominik Walter Vogt, Angus Harvey Jones, Harald G. L. Schwefel, and Rainer Leonhardt

Fig. 1 (a) Schematic of the CW THz spectroscopy system with fiber coupled photo-conductive antennas (PCAs) using two-inch diameter s-p THz lenses to focus the THz radiation onto the base of the HRFZ-Si prism. The length of the base of the prism is about 13 mm. The spherical HRFZ-Si WGMR is mounted on a 3D manual translation stage, and the position is observed using two microscope cameras. (b) and (c) show the corresponding top and side view, respectively, of the 8 mm HRFZ-Si sphere next to the HRFZ-Si prism. Please note that (c) is focused on the prism surface.

https://www.osapublishing.org/oe/abstract.cfm?uri=oe-26-24-31190

We report on prism coupling of high-quality (high-Q) terahertz (THz) whispering-gallery modes (WGMs) in spherical high resistivity float zone grown silicon (HRFZ-Si) resonators over two octaves from 0.2 THz to 1.1 THz. The WGMs are excited using a HRFZ-Si prism and show unprecedented quality factors of up to 2.2 × 104. A detailed discussion of the phase-and mode-matching criteria of the prism coupling scheme implemented in the continuous wave THz spectroscopy system is presented. The results provide numerous op

portunities for passive ultra-broadband high-Q devices operating in the THz frequency range.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Abstract-Mode identification for ultra high-Q terahertz whispering-gallery modes

Dominik Walter Vogt and Rainer Leonhardt

https://www.osapublishing.org/abstract.cfm?uri=CLEO_QELS-2018-JW2A.74

We report on the identification of terahertz whispering-gallery modes (WGMs) using the phase information from coherent continuous-wave (CW) spectroscopy. The demonstrated WGM has an ultra high quality (Q) factor of 1.5 × 104 at 0.62 THz.

© 2018 The Author(s)

Abstract-Ultra-high Q terahertz whispering-gallery modes in a silicon resonator

Dominik Walter Vogt, Rainer Leonhardt

https://arxiv.org/abs/1802.00549

We report on the first experimental demonstration of terahertz (THz) whispering-gallery modes (WGMs) with an ultra high quality (Q) factor of 1.5×104 at 0.62THz. The WGMs are observed in a high resistivity float zone silicon (HRFZ-Si) spherical resonator coupled to a sub-wavelength silica waveguide. A detailed analysis of the coherent continuous wave (CW) THz spectroscopy measurements combined with a numerical model based on Mie-Debye-Aden-Kerker (MDAK) theory allows to unambiguously identify the observed higher order radial THz WGMs.

Abstract-Dielectric bubble whispering gallery mode terahertz resonator

 Dominik Walter Vogt,  Rainer Leonhardt

http://ieeexplore.ieee.org/document/8067041/

Micro ring and micro bubble resonators are of enormous importance in the optical regime [1], [2], however little work has yet been done in the terahertz (THz) realm [3]. In this work we present simulations and measurements of whispering gallery modes (WGMs) in a dielectric bubble resonator at THz frequencies. The resonators are numerically analyzed with both finite element method as well as Mie scattering theory. The experiments are performed with a continuous wave THz spectrometer. At critical coupling a very high Q-factor of more than 400 at 0.465 THz is experimentally observed. The measured Finesse of the THz bubble resonator is ~ 9. The enormous potential of bubble WGM THz resonators for sensing applications are discussed.

Abstract-Fano resonances in a high-Q terahertz whispering-gallery mode resonator coupled to a multi-mode waveguide

Dominik Walter Vogt and Rainer Leonhardt

https://www.osapublishing.org/ol/abstract.cfm?uri=ol-42-21-4359

We report on Fano resonances in a high-quality (𝑄$Q$) whispering-gallery mode (WGM) spherical resonator coupled to a multi-mode waveguide in the terahertz (THz) frequency range. The asymmetric line shape and phase of the Fano resonances detected with coherent continuous-wave (CW) THz spectroscopy measurements are in excellent agreement with the analytical model. A very high 𝑄$Q$ factor of 1600, and a finesse of 22 at critical coupling is observed around 0.35 THz. To the best of our knowledge this is the highest 𝑄$Q$ factor ever reported for a THz WGM resonator.

© 2017 Optical Society of America

Abstract-Terahertz whispering gallery mode bubble resonator

Dominik Walter Vogt and Rainer Leonhardt

https://www.osapublishing.org/optica/abstract.cfm?uri=optica-4-7-809

Whispering gallery mode (WGM) resonators are compelling optical devices; however, they are nearly unexplored in the terahertz (THz) domain. In this Letter, we report on THz WGMs in quartz glass bubble resonators with a subwavelength wall thickness. An unprecedented study of both the amplitude and phase of THz WGMs is presented. The coherent THz frequency domain measurements are in excellent agreement with a simple analytical model and results from numerical simulations. A high finesse of 9 and a quality (𝑄$Q$) factor exceeding 440 at 0.47 THz are observed. Due to the large evanescent field, the high 𝑄$Q$-factor THz WGM bubble resonators can be used as a compact, highly sensitive sensor in the intriguing THz frequency range.

© 2017 Optical Society of America