Nonscalar elastic light scattering from continuous random media in the Born approximation

Abstract

A three-parameter model based on the Whittle-Matérn correlation family is used to describe continuous random refractive-index fluctuations. The differential scattering cross section is derived from the index correlation function using nonscalar scattering formulas within the Born approximation. Parameters such as scattering coefficient, anisotropy factor, and spectral dependence are derived from the differential scattering cross section for this general class of functions.

Fig. 1

Index correlation functions for some values of m.

Fig. 2

Above: An example differential scattering cross section plotted in spherical coordinates. The incident wave propagates from left to right and the polarization is such that electric field is in the vertical plane. The dimple is located at the origin. Below: Comparison of the rotationally averaged σ_up (inner) corresponding to unpolarized incidence and the scalar wave approximation σ_sw (outer) for kl_c = 0.1 (isotropic scattering) shown left, and kl_c = 1 (forward scattering) shown right.

Fig. 3

Wavelength normalized scattering coefficient μ_s/k as a function of wavelength normalized index correlation length kl_c. Inset shows the normalized mean free path kl_s = k/μ_s dependence. It should be noted that although no limit is shown for μ_s, the value is inherently limited by the requirement that l_s > l_c. This weak scattering limit requires that the value of dn²(kl_c)² ≪ 1.

Fig. 4

Reduced scattering coefficient as a function of index correlation length (each normalized by wavelength).

Fig. 5

Plots of ${\mu }_s^{\prime }$ vs kl_c with and without the dipole factor.