Abstract
Whispering gallery modes [WGM] are resonant modes displaying special features: They concentrate along the boundary of the optical cavity at high angular frequencies and they are associated with (complex) scattering resonances very close to the real axis.
As a classical simplification of the full Maxwell system, we consider two-dimensional Helmholtz equations governing transverse electric [TE] or magnetic [TM] modes. Even in this 2D framework, very few results provide asymptotic expansion of WGM resonances at high angular frequency.
In this work, using multiscale expansions, we design a unified procedure to construct asymptotic quasi-resonances and associate quasi-modes that have the WGM structure in disk cavities with a radially varying optical index. We show using the black-box scattering approach that quasi-resonances are asymptotically close to true resonances.
More specifically, using a Schr\"odinger analogy we highlight three typical behaviors in such optical micro-disks, leading to three distinct asymptotic expansions for the quasi-resonances and quasi-modes.
1 avril 2020
10 juin 2021
IMA Journal of Applied Mathematics,
Oxford University Press (OUP)
86 (6), 1212-1265 (2021)
On line
DOI: 10.1093/imamat/hxab033
