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Fourier transform of the Lippmann-Schwinger equation for 3D Vectorial Electromagnetic Scattering : a direct relationship between fields and shape

Abstract : In classical Physics, the Lippmann-Schwinger equation links the field scattered by an ensemble of particles-of arbitrary size, shape and material-to the incident field. This singular vectorial integral equation is generally formulated and solved in the direct space R n (typically, n = 2 or n = 3), and often approximated by a scalar description that neglects polarization effects. Computing rigorously the Fourier transform of the fully vectorial Lippmann-Schwinger equation in S (R 3), we obtain a simple expression in the Fourier space. Besides, we can draw an explicit link between the shape of the scatterer and the scattered field. This expression gives a general, tridimensional, picture of the well known Rayleigh-Sommerfeld expression of bidimensional scattering through small apertures.
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https://hal.archives-ouvertes.fr/hal-03043716
Contributor : Mathias Perrin <>
Submitted on : Monday, December 7, 2020 - 2:06:56 PM
Last modification on : Friday, December 11, 2020 - 3:46:58 AM

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  • HAL Id : hal-03043716, version 1

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Frédéric Gruy, Mathias Perrin, Victor Rabiet. Fourier transform of the Lippmann-Schwinger equation for 3D Vectorial Electromagnetic Scattering : a direct relationship between fields and shape. 2020. ⟨hal-03043716⟩

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