Study at high frequencies of a stratified waveguide

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the high frequency modes guided by thisdevice. We consider the problem under the assumptions of weak guidance,so that it reduces to a two-dimensional eigenvalue problem fora scalar field. While a general study has been done in a previouspaper (Bonnet-BenDhia et al., IMAJAM 60, 1998), our goal hereis to present an asymptotic study at high frequencies, whichillustrates the dispersive character of the stratified guide.We will give the limit as the frequency tends to of the guidedmodes and characterize this limit as the solution of an eigenproblem.The technical difficulty lies in the stratified character ofthe unbounded reference medium.