Abstract

We consider the solutions of the Helmholtz equation in the two-dimensional space in the presence of an unbounded thin waveguide layer with a high contrast index of refraction. We are interested in the identification of some parameters of the waveguide from its response to a localized excitation. This is related to some inverse problems appearing in seismology for layered media and in optical or sound probing of laminated media. In this study, for identification purposes, we will exploit an interesting phenomenon. When the medium is excited by an external point source in a wide range of frequencies, it can be observed that at some given frequencies the behavior of the solution abruptly changes. To properly characterize this phenomenon, we perform an asymptotic analysis of the explicitly solution of the Helmholtz equation, in the two-dimensional space, in the presence of an unbounded waveguide. This is a joint work with Eric Bonnetier, Faouzi, Triki and Axel Osses.