Random Walk of Polarized Light in Turbid Media

We study the propagation of polarized light in turbid media as a random walk of vector photons. Both propagation and polarization directions of light are found to isotropize, following a power law of the number of scattering events. The characteristic length scale governing light isotropization and linear depolarization, the isotropization length $l_p$, is derived using the exact Mie scattering for spherical particles. A simple relation $l_p/l_t\simeq 2.8-2.5g$ is obtained for Rayleigh-Gans scatterers where $l_t$ is the transport mean free path and $g$ is the mean cosine of scattering angles.

Figure 1

The eigenvalues ${\lambda }_{\pm }$ versus the size parameter of Mie scatterers for various relative refractive index $m$. Size parameter is defined as $2\pi a/\lambda$ where $a$ is the radius of the particle and $\lambda$ is the wavelength of light in the background medium.

Figure 2

The ratio of the characteristic length $l_p$ of light becoming isotropic in its polarization and propagation directions over the transport mean free path $l_t$ versus (a) size parameter $x$ and (b) relative refractive index $m$. The inset in (a) shows $l_p/l_t\simeq 2.8-2.5g$ for particles with modest refractive index and average cosine $g\le g_0\sim 0.72$.