On the Inverse Problem for Scattering of Electromagnetic Radiation by a Periodic Structure.
Jorge P. Zubelli | Castellano Pérez, Luis Orlando
Inverse Problems | Inverse Scattering | Periodic Structures | Diffraction
We consider a smooth perturbation $\delta\epsilon(x,y,z)$ of a constant background permittivity $\epsilon=\epsilon_0$ 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.