On the Inverse Problem for Scattering of Electromagnetic Radiation by a Periodic Structure

Abstract

We consider a smooth perturbation δ (x, y, z) of a constant background permittivity = 0 that varies periodically with x, does not depend on y, and is supported on a finite-length interval in z. We investigate the theoretical and numerical determination of such perturbation from (several) fixed frequency y-invariant electromagnetic waves.By varying the direction and frequency of the probing radiation a scattering matrix is defined. By using an invariant-imbedding technique we derive an operator Riccati equation for such scattering matrix. We obtain a theoretical uniqueness result for the problem of determining the perturbation from the scattering matrix.We also investigate a numerical method for performing such reconstruction using multi-frequency information of the truncated scattering matrix. This relies on ideas of regularization and recursive linearization. Numerical experiments are presented validating such approach.

Analytical Expressions for Numerical Characterization of Semiconductors per Comparison with Luminescence

“…Quasi-periodic structures can also be addressed by a Green’s functions formalism as shown in Ref. [ 28 ].…”