Symmetric relationship of multiple scattering in birefringent slab media: Monte Carlo simulation

The symmetry relationship of the reduced effective scattering Mueller matrix was examined in two dimensions for uniaxial turbid slab media using a Monte Carlo simulation. For forward scattering, a matrix form corresponding to a reciprocal position of the mirror image of a particle is generally observed in spite of the orientation of the birefringence axis. For backward scattering, a reciprocal form is obtained when the birefringence axis is parallel to the slab surface, while it does not when the birefringence axis is inclined to the slab surface. Although the matrix form primarily satisfies reciprocity for multiple scattering in turbid media, it may be transformed into the observed matrix form due to the scattering geometry. Moreover, the Jones matrices for these scattering geometries take forms satisfying symmetry relationships corresponding to those for the Mueller matrix, which was supported by the relative magnitudes of simulated birefringences for uniaxial turbid slab media.