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On the Inverse Problem for Scattering of Electromagnetic Radiation by a Periodic Structure
Author(s) -
Castellano Pérez L. O.,
Zubelli Jorge P.
Publication year - 2003
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.t01-1-00230
Subject(s) - scattering , mathematical analysis , inverse scattering problem , uniqueness , mathematics , linearization , perturbation (astronomy) , electromagnetic radiation , regularization (linguistics) , physics , inverse problem , optics , quantum mechanics , nonlinear system , computer science , artificial intelligence
We consider a smooth perturbation δε( x , y , z ) of a constant background permittivity ε=ε 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.