An Open Waveguide with a Thin High Contrast Core Layer: Asymptotic Analysis and Inverse Detection Problem

We investigate the Helmholtz equation in a two dimensional open waveguide with a thin and high contrast core layer. We develop an asymptotic analysis of the Green function of the problem, and through it we identify and characterize the appearance of resonant frequencies. For waves originating outside of the core, the waveguide response at these resonant frequencies is vastly different than the response at non-resonant frequencies. Using this phenomenon and multifrequency measurements containing the first resonance, we propose, theoretically analyze, and numerically validate a reconstruction algorithm to identify the location, thickness and index of refraction of the core layer.