Asymptotic expansions of Whispering Gallery Modes in graded index optical micro-cavities

Stéphane Balac (1) , Monique Dauge (1) , Zoïs Moitier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We are interested in resonance frequencies of two dimensional dielectric cavities-a component of optical micro-resonators-and more specifically in resonances corresponding to whispering gallery modes (WGM). WGM are optical waves with high polar mode index, circling around the cavity and almost perfectly guided by total internal reflection. For a cavity of general shape with a varying optical index n (graded index optical cavity), using a phase amplitude ansatz, we have obtained asymptotic expansions of resonances as the polar mode index becomes large. We have also found sufficient conditions linking the curvature of the cavity boundary and the optical index for such expansions to hold.

Mots clés: Helmholtz transmission problem; Resonances; WKB method

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Balac, Monique Dauge, Zoïs Moitier. Asymptotic expansions of Whispering Gallery Modes in graded index optical micro-cavities. 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation ( WAVES 2019), Aug 2019, Vienna, Austria. ⟨hal-03830626⟩