Invariant imbedding and Cauchy system of scattering function in searchlight problem in rugged terrain

Ueno, S.; Wang, A.P.; Toho, Makoto

doi:10.1016/s0898-1221(99)00148-0

Cited by 1 publication

(2 citation statements)

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“…For convenience, we assume that our scatterer has its support in B 0 for some fixed B 0 > 0. In the first case, according to Lemma 2 any sequence c ∈ Y B 0 defines an incident field via (17). The corresponding scattered field can be represented in the form (19) in + B 0 for some sequence d ∈ X B 0 .…”

Section: The Scattering Matrixmentioning

confidence: 99%

“…The basic ingredient will be an invariant-imbedding argument [8] following the same circle of ideas in [11], which dealt with the compact supported perturbation case. This technique has been used in a number of different contexts, such as the analysis of wave propagation in the time domain [12][13][14], scattering by anisotropic media [15], and the solution of nonlinear integro-differential equations [16,17] to cite a few. Let us denote by q z :…”

Section: The Matrix Riccati Equationmentioning

confidence: 99%

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On the Inverse Problem for Scattering of Electromagnetic Radiation by a Periodic Structure

Perez

Zubelli

2003

Stud Appl Math

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We consider a smooth perturbation δ (x, y, z) of a constant background permittivity = 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.

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Section: The Scattering Matrixmentioning

confidence: 99%