### Study at high frequencies of a stratified waveguide

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Anne-Sophie Bonnet-BenDhia,
Gabriel Caloz,
Monique Dauge,
Fabrice Mahé
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A waveguide in integrated optics is defined by its refractive index. The guide is assumed to be invariant in the propagation direction while in the transverse direction it is supposed to be a compact perturbation of an unbounded stratified medium. We are interested in the high frequency modes guided by this device.
We consider the problem under the assumptions of weak guidance, so that it reduces to a two dimensional eigenvalue problem for a scalar field. While a general study has been done in a previous paper, our goal here is to present an asymptotic study at high frequencies, which illustrates the dispersive character of the stratified guide. We will give the limit as the frequency tends to infinity of the guided modes and characterize this limit as the solution of an eigenproblem. The technical difficulty lies in the stratified character of the unbounded reference medium.

Preprint IRMAR, Univ. Rennes (Jan. 1999)

*IMA Journal of Applied Mathematics* ** 66 **, 2001, 231--257.