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Coherent Continuous Wave Terahertz Spectroscopy Using Hilbert Transform

  • Dominik Walter VogtEmail author
  • Miro Erkintalo
  • Rainer Leonhardt
Article
  • 31 Downloads

Abstract

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.

Keywords

Terahertz spectroscopy Continuous wave Hilbert transform 

Notes

Acknowledgements

M. Erkintalo acknowledges support from the Rutherford Discovery Fellowships of the Royal Society of New Zealand.

References

  1. 1.
    Yi-Wen Liu. Hilbert transform and applications. In Fourier Transform Applications. InTech, 2012.Google Scholar
  2. 2.
    De-Yin Kong, Xiao-Jun Wu, Bo Wang, Yang Gao, Jun Dai, Li Wang, Cun-Jun Ruan, and Jun-Gang Miao. High resolution continuous wave terahertz spectroscopy on solid-state samples with coherent detection. Optics Express, 26(14):17964–17976, 2018.Google Scholar
  3. 3.
    C Hepp, S Lüttjohann, A Roggenbuck, A Deninger, S Nellen, T Göbel, M Jörger, and R Harig. A cw-terahertz gas analysis system with ppm detection limits. In 41st International Conference on Infrared, Millimeter, and Terahrtz waves (IRMMW-THz), pages 1–2. IEEE, 2016.Google Scholar
  4. 4.
    Dominik Walter Vogt and Rainer Leonhardt. Ultra-high Q terahertz whispering-gallery modes in a silicon resonator. APL Photonics, 3(5):051702, 2018.Google Scholar
  5. 5.
    G Mouret, S Matton, R Bocquet, D Bigourd, F Hindle, A Cuisset, JF Lampin, and D Lippens. Anomalous dispersion measurement in terahertz frequency region by photomixing. Applied Physics Letters, 88(18):181105, 2006.Google Scholar
  6. 6.
    Masayoshi Tonouchi. Cutting-edge terahertz technology. Nature Photonics, 1(2):97, 2007.Google Scholar
  7. 7.
    Damien Bigourd, Arnaud Cuisset, Francis Hindle, Sophie Matton, Eric Fertein, Robin Bocquet, and Gaël Mouret. Detection and quantification of multiple molecular species in mainstream cigarette smoke by continuous-wave terahertz spectroscopy. Optics Letters, 31(15):2356–2358, 2006.Google Scholar
  8. 8.
    A Roggenbuck, H Schmitz, A Deninger, I Cámara Mayorga, J Hemberger, R Güsten, and M Grüninger. Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples. New Journal of Physics, 12(4):043017, 2010.Google Scholar
  9. 9.
    Christian Jansen, Steffen Wietzke, Ole Peters, Maik Scheller, Nico Vieweg, Mohammed Salhi, Norman Krumbholz, Christian Jördens, Thomas Hochrein, and Martin Koch. Terahertz imaging: applications and perspectives. Applied Optics, 49(19):E48–E57, 2010.Google Scholar
  10. 10.
    Nicholas Karpowicz, Hua Zhong, Jingzhou Xu, Kuang-I Lin, Jenn-Shyong Hwang, and XC Zhang. Comparison between pulsed terahertz time-domain imaging and continuous wave terahertz imaging. Semiconductor Science and Technology, 20(7):S293, 2005.Google Scholar
  11. 11.
    Dominik Walter Vogt and Rainer Leonhardt. High resolution terahertz spectroscopy of a whispering gallery mode bubble resonator using hilbert analysis. Optics Express, 25(14):16860–16866, Jul 2017.Google Scholar
  12. 12.
    AL Bingham and D Grischkowsky. Terahertz two-dimensional high-Q photonic crystal waveguide cavities. Optics Letters, 33(4):348–350, 2008.Google Scholar
  13. 13.
    Hou-Tong Chen, Willie J Padilla, Joshua MO Zide, Arthur C Gossard, Antoinette J Taylor, and Richard D Averitt. Active terahertz metamaterial devices. Nature, 444(7119):597, 2006.Google Scholar
  14. 14.
    Frédéric Cohen Tenoudji. Causal Signals—Analytic Signals, pages 177–205. Springer International Publishing, Cham, 2016.Google Scholar
  15. 15.
    Dominik Walter Vogt, Angus Harvey Jones, Harald GL Schwefel, and Rainer Leonhardt. Prism coupling of high-Q terahertz whispering-gallery-modes over two octaves from 0.2 THz to 1.1 THz. Optics Express, 26(24):31190–31198, 2018.Google Scholar
  16. 16.
    Dominik Walter Vogt and Rainer Leonhardt. Terahertz whispering gallery mode bubble resonator. Optica, 4(7):809–812, Jul 2017.Google Scholar
  17. 17.
    Dominik Walter Vogt, Angus Harvey Jones, and Rainer Leonhardt. Thermal tuning of silicon terahertz whispering-gallery mode resonators. Applied Physics Letters, 113(1):011101, 2018.Google Scholar
  18. 18.
    S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard. Coupled whispering gallery mode resonators in the terahertz frequency range. Optics Express, 16(10):7336–7343, May 2008.Google Scholar
  19. 19.
    Jingya Xie, Xi Zhu, Xiaofei Zang, Qingqing Cheng, Lin Chen, and Yiming Zhu. Terahertz integrated device: high-Q silicon dielectric resonators. Optical Materials Express, 8(1):50–58, 2018.Google Scholar
  20. 20.
    Dominik Walter Vogt and Rainer Leonhardt. Fano resonances in a high-Q terahertz whispering-gallery mode resonator coupled to a multi-mode waveguide. Optics Letters, 42(21):4359–4362, 2017.Google Scholar
  21. 21.
    M. L. Gorodetsky and V. S. Ilchenko. Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes. Journal of the Optical Society of America B, 16(1):147–154, Jan 1999.Google Scholar
  22. 22.
    John D Joannopoulos, Steven G Johnson, Joshua N Winn, and Robert D Meade. Photonic crystals: molding the flow of light. Princeton university press, 2011.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsThe University of AucklandAucklandNew Zealand
  2. 2.The Dodd-Walls Centre for Photonic and Quantum TechnologiesAucklandNew Zealand

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