Fourier Transform of the Lippmann-Schwinger Equation: Solving Vectorial Electromagnetic Scattering by Arbitrary Shapes

Frederic Gruy, Victor Rabiet and Mathias Perrin ()
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Frederic Gruy: Ecole Nationale Supérieure des Mines de St. Etienne, Centre SPIN, F-42100 Saint-Etienne, France
Victor Rabiet: Ecole Nationale Supérieure des Mines de St. Etienne, Centre SPIN, F-42100 Saint-Etienne, France
Mathias Perrin: Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France

Mathematics, 2023, vol. 11, issue 22, 1-23

Abstract: In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulated in the direct space R n (typically n = 2 or n = 3 ). In the article, we rigorously computed the Fourier transform of the vectorial Lippmann–Schwinger equation in the space of tempered distributions, S ′ ( R 3 ) , splitting it in a singular and a regular contribution. One eventually obtains a simple equation for the scattered field in the Fourier space. This permits to draw an explicit link between the shape of the scatterer and the field through the Fourier Transform of the body indicator function. We compare our results with accurate calculations based on the T-matrix method and find a good agreement.

Keywords: electromagnetic scattering; integral equation; singular integral; Fourier Transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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