Coherent backscattering enhancement in refracting media: diffusion approximation

Abstract

The weak localization (coherent backscattering enhancement) phenomenon in media with graded refraction index is investigated within the diffusion approximation. The obtained analytic results are compared with numerical solutions by finite-difference and Monte Carlo calculations.

Weak Localization in Media with Refractive-Index Gradient: the Diffusion Approximation

“…On the basis of these results, the well-known asymptotic expressions for the peripheral regions of the coherent backscattering cone [9] were extended to the case of inhomogeneous media. A solution to the coherent backscattering problem in the diffusion approximation [8], which is similar to the well-known result [10] for the media with uniform refractive index, was also found.…”

“…Due to the approximations and assumptions, the solution obtained in [8] is not in good agreement with the results of numerical simulation by the finite-difference technique and the Monte-Carlo method. In particular, unlike the results of calculation by numerical methods, this solution is fully invariant with respect to the sign of the refractive-index gradient of the medium.…”

“…In this paper, following [7,8], we restrict ourselves to considering the refractive index of the form…”

“…The transfer of radiation from point 1 to point 2 was described by the Green's function of the radiation transfer equation in the diffusion approximation (dotted line in the diagram), and the complete solution was then calculated by integration over the coordinates of the points 1 and 2 (the first and the last scatterings in the medium). In [8], this solution was directly generalized to the case of a medium with refractive-index gradient. In the interval of the ray trajectory in the medium after the point 2 (the last scattering), the refractive effects were neglected.…”

“…First analytical and numerical results on weak localization in inhomogeneous media have recently been published [7,8]. In the case of a strongly elongated scattering indicatrix, asymptotic solutions of the scalar radiative transfer equation in the low-angle approximation were obtained for the main fundamental types of sources, including planar monodirected, point monodirected, and point isotropic ones [7].…”