## Abstract

We consider a smooth perturbation δe(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.

Original language | British English |
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Pages (from-to) | 115-166 |

Number of pages | 52 |

Journal | Studies in Applied Mathematics |

Volume | 111 |

Issue number | 2 |

DOIs | |

State | Published - Aug 2003 |