We consider a smooth perturbation deltais an element of(x, y, z) of a constant background permittivity is an element of = is an element of(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. [References: 41]
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