Multiple light scattering in a two-dimensional medium with large scatterers

Abstract

A study is presented of the two-dimensional case of light propagation in a turbid medium involving sharply anisotropic one-center scattering in accordance with the Heney-Greenstein law, with strong absorption (when the photon absorption length is shorter than the transport length). An exact analytic solution that takes into account fluctuations of the photon paths is obtained within the framework of the small-angle approximation for the transfer equation in the case of a light beam normally incident upon the plane surface of the medium. The parameters of the radiation distribution (angular spectrum and attenuation coefficient) for the deeppropagating mode are analyzed in detail.

Light propagation in a two-dimensional medium with large inhomogeneities

“…(9) can be solved analytically only for some specific phase functions, in particular, for phase functions decreasing with the angle by specific power laws (see [12,16]). …”

“…Following the method used in [12,16], I construct a general solution to Eq. (9) as the eigenfunction expansion:…”

“…The factorization of the intensity into the zand θ-dependent terms corresponds to the asymptotic regime of multiple scattering. In this regime, the angular distribution (normalized to unity) of light no longer varies with the depth [12,15].…”

“…(15)], the eigenfunctions Φ n ω and Φ v ω have definite parity (or, more precisely, for the continuous spectrum such eigenfunctions can be constructed). In the case of normal incidence, the intensityĨz; θ and its Fourier transformĨ z; ω are even functions of the variables θ and ω, respectively, and the odd eigenfunctions make no contribution to the expansion (16) [12,16] and c 2m1 0, where the parameter s is defined by Eq. (21).…”

“…Of particular interest is the multiple light scattering in various lowdimensional disordered systems [8][9][10][11][12][13][14][15][16][17][18][19], including artificial two-dimensional media [20], nematic liquid crystals [21], and biological tissues [7,22].…”