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Shape defect detection in wave guides via modal representations

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RNTW04 - Synergistic workshop on Rich and Nonlinear tomography aimed at drawing together all strands of both methods and applications with new insights

We present a multi-frequency inversion method to reconstruct defects in a waveguide. Starting with the acoustic case, we use a Born approximation to reconstruct three types of defects, which are localized, smooth, and have small amplitude, from multifrequency wave field measurements of propagating modes : a local perturbation of the optical index inside the waveguide, a bent, or a localized bump. We also consider the case of resonant frequencies, where we derive  the asymptotic structure of the solution, and try to extract from it information on possible shape defects. Finally, we consider the generalization of our approach to 2D elastic waveguidesor 3D elastic plates.This is joint work with Angèle Niclas (Ecole Polytechnique), Laurent Seppecher and Gregory Vial (both from Ecole Centrale Lyon).

This talk is part of the Isaac Newton Institute Seminar Series series.

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