Distinct Gaussian Properties of Multiple Reflections in Extended Hemispherical Lenses

  • Burak OzbeyEmail author
  • Kubilay Sertel


Multiple reflections in an extended hemispherical lens are shown to exhibit distinctly different Gaussian characters. It is demonstrated that the second- and third-order bounces of the electromagnetic fields within the electrically large lens result in contributions with spot sizes and locations that are uncorrelated with the fundamental Gaussian-beam-like radiation from a small antenna located at the lens focus. We present the optical properties (Gaussicities and power levels at the beam waist) of such higher-order lens reflections. The impacts of these reflections on a typical quasi-optical spectroscopy setup are discussed. The relative received power densities are computed and compared with measurements for each higher-order reflection. The agreement between the measurement and theory indicates that the adopted method is a reliable and efficient tool for characterization of the dominant reflections from extended hemispherical lenses.


Lens-integrated antenna Double-slot antenna Extended hemispherical lens THz time domain spectroscopy (THz-TDS) Ray tracing 



The lead author would like to thank the Turkish Fulbright Commission for their support under the Postdoctoral Program Grant.

Funding Information

This work was financially supported by the NSF Division of Elect., Comm. & CyberSystems (EECS-1710977) under the project “Compact polarimetric THz sensor for reflectometric imaging.”


  1. 1.
    Filipovic, D.F., Gearhart, S.S., Rebeiz, G.M.: Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses. IEEE Transactions on Microwave Theory and Techniques 41(10), 1738–1749 (1993). Scholar
  2. 2.
    Filipovic, D.F., Gauthier, G.P., Raman, S., Rebeiz, G.M.: Off-axis properties of silicon and quartz dielectric lens antennas. IEEE Transactions on Antennas and Propagation 45(5), 760–766 (1997). Scholar
  3. 3.
    Alder, C.J., Brewitt-Taylor, C.R., Dixon, M., Hodges, R.D., Irving, L.D.: Microwave and millimetre-wave receivers with integral antenna. IEE Proceedings H: Microwaves Antennas and Propagation 138, 253–257 (1991).CrossRefGoogle Scholar
  4. 4.
    Babakhani, A., Guan, X., Komijani, A., Natarajan, A., Hajimiri, A.: A 77-GHz Phased-Array Transceiver With On-Chip Antennas in Silicon: Receiver and Antennas. IEEE Journal of Solid-State Circuits 41(12), 2795–2806 (2006).CrossRefGoogle Scholar
  5. 5.
    Rui, G., Abeysinghe, D.C., Nelson, R.L., Zhan, Q.: Demonstration of beam steering via dipole-coupled plasmonic spiral antenna. Scientific Reports 3, 2237 (2013).
  6. 6.
    Semenov, A.D., Richter, H., Hubers, H.W., Gunther, B., Smirnov, A., Il’in, K.S., Siegel, M., Karamarkovic, J.P.: Terahertz Performance of Integrated Lens Antennas With a Hot-Electron Bolometer. IEEE Transactions on Microwave Theory and Techniques 55(2), 239–247 (2007). Scholar
  7. 7.
    Sigel, P.H., Dengler, R.J.: The dielectric-filled parabola: A new millimeter/submillimeter wavelength receiver/transmitter front end. IEEE Transactions on Antennas and Propagation 39(1), 40–47 (1991).CrossRefGoogle Scholar
  8. 8.
    Bin, M., Gaidis, M.C., Zmuidzinas, J., Phillips, T.G., LeDuc, H.G.: Low-noise 1 THz niobium superconducting tunnel junction mixer with a normal metal tuning circuit. Applied Physics Letters 68(12), 1714–1716 (1996).CrossRefGoogle Scholar
  9. 9.
    Chantraine-Bares, B., Sauleau, R., Coq, L.L., Mahdjoubi, K.: A new accurate design method for millimeter-wave homogeneous dielectric substrate lens antennas of arbitrary shape. IEEE Transactions on Antennas and Propagation 53(3), 1069–1082 (2005).CrossRefGoogle Scholar
  10. 10.
    Gearhart, S.S., Rebeiz, G.M.: A monolithic 250 GHz Schottky-diode receiver. IEEE Transactions on Microwave Theory and Techniques 42(12), 2504–2511 (1994). Scholar
  11. 11.
    Trichopoulos, G.C., Mosbacker, H.L., Burdette, D., Sertel, K.: A Broadband Focal Plane Array Camera for Real-time THz Imaging Applications. IEEE Transactions on Antennas and Propagation 61(4), 1733–1740 (2013). Scholar
  12. 12.
    Trichopoulos, G.C., Mumcu, G., Sertel, K., Mosbacker, H.L., Smith, P.: A Novel Approach for Improving Off-Axis Pixel Performance of Terahertz Focal Plane Arrays. IEEE Transactions on Microwave Theory and Techniques 58(7), 2014–2021 (2010). Scholar
  13. 13.
    Neto, A., Maci, S., Maagt, P.J.I.d.: Reflections inside an elliptical dielectric lens antenna. IEE Proceedings - Microwaves, Antennas and Propagation 145(3), 243–247 (1998). Scholar
  14. 14.
    Vorst, M.J.M.v.d., Maagt, P.J.I.d., Herben, M.H.A.J.: Effect of internal reflections on the radiation properties and input admittance of integrated lens antennas. IEEE Transactions on Microwave Theory and Techniques 47(9), 1696–1704 (1999). Scholar
  15. 15.
    Vorst, M.J.M.v.d., Maagt, P.J.I.d., Neto, A., Reynolds, A.L., Heeres, R.M., Luinge, W., Herben, M.H.A.J.: Effect of internal reflections on the radiation properties and input impedance of integrated lens antennas-comparison between theory and measurements. IEEE Transactions on Microwave Theory and Techniques 49(6), 1118–1125 (2001). Scholar
  16. 16.
    Wu, X., Eleftheriades, G.V., Deventer-Perkins, T.E.v.: Design and characterization of single- and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications. IEEE Transactions on Microwave Theory and Techniques 49(3), 431–441 (2001). Scholar
  17. 17.
    Poggio, A.J., Miller, E.K.: Integral equation solutions for three dimensional scattering problems. Pergamon Press, NY (1973).CrossRefGoogle Scholar
  18. 18.
    Ozbey, B., Sertel, K.: Effects of internal reflections on the performance of lens-integrated mmW and THz antennas. In: 2018 International Applied Computational Electromagnetics Society Symposium (ACES) (2018).
  19. 19.
    Ozbey, B., Sertel, K.: Reflection characteristics of an extended hemispherical lens for THz time domain spectroscopy. In: 2019 International Workshop on Antenna Technology (iWAT) (2019).
  20. 20.
    Kominami, M., Pozar, D., Schaubert, D.: Dipole and slot elements and arrays on semi-infinite substrates. IEEE Transactions on Antennas and Propagation 33(6), 600–607 (1985). Scholar
  21. 21.
    Balanis, C.A.: Advanced Engineering Electromagnetics. John Wiley & Sons Inc (1989).Google Scholar
  22. 22.
    Kong, J.A.: Electromagnetic Wave Theory. John Wiley & Sons Inc, New York (1986).Google Scholar
  23. 23.
    Sertel, K., Trichopoulos, G.C.: Non-contact metrology for mm-wave and thz electronics. In: P. Fay, D. Jena, P. Maki (eds.) High-Frequency GaN Electronic Devices, chap. 10, pp. 283–299. Springer, Cham (2019).Google Scholar
  24. 24.
    Virginia Diodes, I.: Nominal Horn Specifications (2006).
  25. 25.
    Johansson, J.F., Whyborn, N.D.: The diagonal horn as a sub-millimeter wave antenna. IEEE Transactions on Microwave Theory and Techniques 40(5), 795–800 (1992).CrossRefGoogle Scholar

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

Authors and Affiliations

  1. 1.ElectroScience LaboratoryThe Ohio State UniversityColumbusUSA

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