Preprint A175/2002
On the Inverse Problem for Scattering of Electromagnetic Radiation by a Periodic Structure.

Jorge P. Zubelli | Castellano PĂ©rez, Luis Orlando

**Keywords: **
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.