Multiple Scattering of Light in Superdiffusive Media

Light transport in superdiffusive media of finite size is studied theoretically. The intensity Green’s function for a slab geometry is found by discretizing the fractional diffusion equation and employing the eigenfunction expansion method. Truncated step length distributions and complex boundary conditions are considered. The profile of a coherent backscattering cone is calculated in the superdiffusion approximation.

Figure 1

Normalized Green’s function $f(x,x_0)$ for a slab with $L=5$, $x_0=L/3$, $M=300$, $D_{\alpha }=1$, and absorbing boundaries, computed for various values of $\alpha$.

Figure 2

Normalized Green’s function $f(x,x_0)$ for a slab with $\alpha =1.5$, $L=5$, $x_0=L/3$, $M=300$, and $D_{\alpha }=1$, computed for various values of (a) $l_{\max }$ and (b) the reflectance $R$ on the left boundary.

Figure 3

Normalized coherent albedo for a slab with $L=5$, $M=300$, and $D_{\alpha }=1$, computed for various values of $\alpha$. When $\alpha$ is decreased, the contribution of long paths to the backscattering cone is larger, leading to a sharper cusp and to tails that fall down more slowly (but still go to zero for $\theta =\pm \pi /4$). A zoomed view of the top of the curves is shown in the inset.