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

Frédéric Gruy (1, 2) , Mathias Perrin (3, 3) , Victor Rabiet (4)

1 ENSM ST-ETIENNE - Ecole Nationale Supérieure des Mines de St Etienne
2 LGF-ENSMSE - Laboratoire Georges Friedel
3 LOMA - Laboratoire Ondes et Matière d'Aquitaine
4 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Optique [physics.optics]; Physique mathématique [math-ph]

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⟩