Study on Planar Whispering Gallery Dielectric Resonators. I. General Properties

  • Giuseppe Annino
  • Mario Cassettari
  • Massimo Martinelli


Several basic properties of homogeneous planar Whispering Gallery dielectric resonators are investigated through a general approach. In particular the values for the minimum and maximum allowed radius, defined by irradiation and dielectric losses, respectively, are obtained in terms of the complex dielectric constant of the involved media. The same approach is employed in the analysis of the limit allowed frequencies of a fixed family of mode, leading to the definition of the “ideal” frequency band. The role of the transverse mode is then discussed, and the “effective” frequency band is introduced and determined both in simple disc and circular ring resonators. The extension of the effective band is limited at least by a factor 3, in terms of decades, in comparison to the extension of the ideal one; this limitation, due to the presence of transverse modes, can be overcome using suitable designed nonhomogeneous resonators, as discussed in a following companion paper.

Dielectric resonators whispering gallery modes planar homogeneous structures working frequency band circular ring resonators 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    C. Vedrenne and J. Arnaud, “Whispering-Gallery modes in dielectric resonators”, Proc. Inst. Elect. Eng., vol. 129, pt. H, no. 4, pp. 183-187, (1982).Google Scholar
  2. 2).
    G. Annino, D. Bertolini, M. Cassettari, M. Fittipaldi, I. Longo, and M. Martinelli, “Dielectric properties of materials using whispering gallery dielectric resonators; Experiments and perspectives of ultrawideband characterization”, J. Chem. Phys., vol. 112,no. 5, pp.2308-2314, (2000).Google Scholar
  3. 3).
    G. Annino, M. Cassettari, M. Fittipaldi, I. Longo, M. Martinelli, C.A. Massa, and L.A. Pardi, “High-Field, Multifrequency EPR Spectroscopy Using Whispering Gallery Dielectric resonators”, J. Magn. Reson., vol. 143, pp. 88-94, (2000).Google Scholar
  4. 4).
    A. Tredicucci, C. Gmachl, F. Capasso, D.L. Sivco, S. Chu, A.L. Hutchinson, and A.Y. Cho, “Very long wavelength (λ approximately=16 µm) whispering gallery mode microdisk lasers”, Electron. Lett., vol.36,no.4; pp. 328-330, (2000).Google Scholar
  5. 5).
    G.H.V. Rhodes, B.B. Goldberg, M.S. Unlu, S.T. Chu, and B.E. Little, “Internal spatial modes in glass microring resonators”, IEEE J. Selected Top. Quantum Electr., vol. 6, pp. 46-53, (2000). B.E. Little, S.T. Chu, J.V. Hryniewicz, and P.P. Absil, “Filter synthesis for periodically coupled microring resonators”, Opt. Lett., vol. 25, pp. 344–346, (2000).Google Scholar
  6. 6).
    R.D. Richtmyer, J. Appl. Phys., “Dielectric Resonators”, vol. 10, pp. 391-398, (1939).Google Scholar
  7. 7).
    D. Kremer, “Modeling of non-radiative dielectric waveguides and double disk resonators made up of uniaxial anisotropic dielectrics by the method of lines”, AEU-Int. J. Electron. Commun., vol.52,no.6, pp.347-54, (1998).Google Scholar
  8. 8).
    G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Whispering Gallery Modes in Dielectric Resonator: Characterization at Millimeter Wavelength”, IEEE Trans. Microwave Theory Tech., vol. 45,no. 11, pp. 2025-2034, (1997).Google Scholar
  9. 9).
    G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “Analysis of stacked whispering gallery dielectric resonators for submillimeter ESR spectroscopy”, Chem. Phys. Lett., vol. 281, pp. 306-311, (1997).Google Scholar
  10. 10).
    H. Peng, “Study of Whispering Gallery Modes in Double Disk Sapphire Resonators”, IEEE Trans. Microwave Theory Tech., vol. 44, pp. 848-853, (1996).Google Scholar
  11. 11).
    J.R. Wait, “Electromagnetic Whispering Gallery Modes in a Dielectric Rod”, Radio Sci., vol. 2, pp. 1005-1017, (1967).Google Scholar
  12. 12).
    F.G. Reick, “The optical whispering mode of polished cylinders and its applications in laser technology”, Appl Opt., vol. 4, pp. 1395-1399, (1965).Google Scholar
  13. 13).
    L.V. Weinstein, “Open Resonators and Open waveguides”, Boulder, CO: Golem, (1969).Google Scholar
  14. 14).
    C.J.F. Böttcher and P. Bordewijk, “Theory of Electric Polarization” Vol. 2, (Elsevier, Amsterdam, 1978), Chapter 8.Google Scholar
  15. 15).
    M. Born and E. Wolf, “Principles of Optics”, (Pergamon Press, London, 1959), Chapter 7.Google Scholar
  16. 16).
    V.S. Boriskina and I.A. Nosich, “Radiation and absorption losses of the whispering-gallery-mode dielectric resonators excited by a dielectric waveguide”, IEEE Trans. Microwave Theory Tech., vol. 47, pp. 223-231, (1999).Google Scholar
  17. 17).
    G.N. Watson, “A Treatise on the Theory of Bessel Functions”, Cambridge University Press, (1952).Google Scholar
  18. 18).
    G. Annino, M. Cassettari, I. Longo, and M. Martinelli, “FIR laser measurements at 240 GHz on a whispering gallery dielectric resonator”, Int. J. Infrared Millim. Waves, vol. 19, 605-620, (1998).Google Scholar
  19. 19).
    D. Kajfez and P. Guillon, “Dielectric Resonators”, Norwood, MA: Artech House, Chapter 4, (1986).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Giuseppe Annino
    • 1
  • Mario Cassettari
    • 1
  • Massimo Martinelli
    • 1
  1. 1.Istituto di Fisica Atomica e Molecolare (now: Istituto per i Processi Chimico-Fisici), CNRPisaItaly

Personalised recommendations