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Mathematical analysis of whispering gallery modes in graded index optical micro-disk resonators

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An Erratum to this article was published on 08 December 2020

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Abstract

We study from a theoretical point of view whispering gallery modes (WGM) in graded index micro-disk resonators where the refractive optical index varies with the radial position. Using a quantum mechanical analogy, we highlight three different behaviors for the WGM depending on the sign of a key parameter expressed as the ratio of the refractive index value to its derivative at the cavity boundary. This results in three asymptotic expansions of the resonances for large polar mode index providing first-approximations of WGM in a simple and quick way. Besides, these expansions yield a theoretical fundation to considerations of V.S. Ilchenko, A.A. Savchenkov, A.B. Matsko, L. Maleki, J. Opt. Soc. Am. A 20, 157 (2003), about three sorts of effective potentials for TE modes in a dielectric sphere.

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  • 08 December 2020

    The affiliations for the article are corrected.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of California, Merced, 5200 North Lake Road, Merced, CA, 95343, USA

    Stéphane Balac, Monique Dauge & Zoïs Moitier

  2. UNIV. RENNES, CNRS, FOTON-UMR 6082, Enssat, 22305, Lannion, France

    Yannick Dumeige & Patrice Féron

Authors
  1. Stéphane Balac
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  2. Monique Dauge
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  3. Yannick Dumeige
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  4. Patrice Féron
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  5. Zoïs Moitier
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Correspondence to Stéphane Balac.

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Balac, S., Dauge, M., Dumeige, Y. et al. Mathematical analysis of whispering gallery modes in graded index optical micro-disk resonators. Eur. Phys. J. D 74, 221 (2020). https://doi.org/10.1140/epjd/e2020-10303-5

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  • DOI: https://doi.org/10.1140/epjd/e2020-10303-5

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