Study at high frequencies of a stratified waveguide

A waveguide in integrated optics is defined by its refractive index. The gu ide is assumed to be invariant in the propagation direction while in the tr ansverse direction it is supposed to be a compact perturbation of an unboun ded 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 (Bonnet-BenDhia et al., IM AJAM 60, 1998), our goal here is to present an asymptotic study at high fre quencies, which illustrates the dispersive character of the stratified guid e. We will give the limit as the frequency tends to oo of the guided modes and characterize this limit as the solution of an eigenproblem. The technic al difficulty lies in the stratified character of the unbounded reference m edium.