Multiple scattering of polarized light in uniaxial turbid media with arbitrarily oriented linear birefringence

The effective scattering Mueller matrices obtained by the simulation were simplified to the reduced matrices and factorized using the Lu-Chipman polar decomposition, which afforded the polarization parameters in two dimensions. In general, the scalar retardance around the illumination point of a pencil beam shows a broad azimuthal dependence with an offset. Photons may behave quite differently under the birefringence according to their polarization state. In contrast, when the birefringence is oriented along the y axis in the plane parallel to the surface (x-y) plane, for example, the azimuthal dependence of the scalar retardance shows clear maxima along the x and y axes and sharp valleys between the maxima. Photons propagating in the medium probably experience the retardance in nearly the same way, when they are polarized linearly and circularly. Moreover, the polarization parameters generally become nonsymmetric with respect to the plane perpendicular to both the x-y plane and the plane containing the birefringence axis, which suggests that the pathway of the lateral propagation of photons from the illumination point to the surrounding is slightly oblique upward relative to the x-y plane.