Monique Dauge (Rennes) - 14 December 2020
Автор: Cardiff Analysis
Загружено: 2020-12-14
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CARDIFF ANALYSIS SEMINAR 14 December 2020
Monique Dauge (Rennes)
Whispering Gallery Modes in radially symmetric micro-resonators: Asymptotic analysis and numerical computation
This investigation is originally motivated by optical devices called micro-resonators, the core of which is a dielectric cavity. Scattering resonances of such a cavity play an important role in properties of the micro-resonator. As in examples given in the literature, we consider radially symmetric cavities with a radially variable optical index (disks, annuli, spheres). Transmission problems of Helmholz type appear. By separation of variables, one obtains families of Schrödinger type equations with the polar mode index m as parameter. When m gets large, eigenmodes concentrate at the bottom of the effective potential well, often at the boudary of the cavity, and give rise to Whispering Gallery Modes.
In this talk, we present asymptotic expansions of associated resonances as m gets large, according to 3 distinct cases discriminated by an effective curvature. We also present numerical computations.
From ongoing work with Stéphane Balac and Zoïs Moitier.
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