Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer.

The symmetry theorems on the complete forward and backward scattering Mueller matrices for light scattering from a single dielectric scatterer (as opposed to an ensemble of scatterers) are systematically and thoroughly analyzed. Symmetry operations considered include discrete rotations about the incident direction and mirror planes not coinciding with the scattering plane. For forward scattering we find sixteen different symmetry shapes (not including the totally asymmetric one), which may be classified into five symmetry classes, with identical reductions in the forward scattering matrices for all symmetry shapes that fall into the same symmetry class. For backward scattering we find only four different symmetry shapes, which may be classified into only two symmetry classes. The forward scattering symmetry theorems also lead to a symmetry theorem on the total extinction cross section. Based on the conclusions of this work it should be possible to design quick and nondestructive methods for the identification of certain small objects, when suitable partial information about the objects to be identified is already available. A promising practical example is given.