Mathematical investigations of resonances in optical micro-resonators

Zoïs Moitier (1) , Stéphane Balac (1) , Eric Darrigrand (1) , Monique Dauge (1) , Yvon Lafranche (1) , Fabrice Mahé (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We investigate the computation of whispering gallery modes in optical micro-resonators. From a mathematical point of view, this leads to the computation of the complex resonances of dielectric micro-cavities in the sense of the scattering theory. We consider here the 2D case where the scattering problem consists of the Helmholtz equation in R 2 with discontinuities of the normal derivative at the cavity boundary and with the outgoing wave condition at infinity. The computational domain is made finite by the use of perfectly matched layers (PML) compatible with the outgoing wave condition, which results in a non self-adjoint problem. Discretization is then achieved by the Finite Element Method. We show theoretical and numerical results for 2D geometries of the micro-cavity.

Mots clés: Scattering resonances; Optical micro-resonators; Finite Element Method; PML

Domaines: Analyse numérique [math.NA]

Zoïs Moitier, Stéphane Balac, Eric Darrigrand, Monique Dauge, Yvon Lafranche, et al.. Mathematical investigations of resonances in optical micro-resonators. ICCEM 2018 - IEEE International Conference on Computational Electromagnetics , Mar 2018, Chengdu, China. ⟨hal-01715438v1⟩