AN EXTENSION OF THE MUELLER SCATTERING MATRIX TO NONLINEAR LIGHT-SCATTERING

We present a new method of analyzing the polarization dependence of nonlinear light scattering (2 in, 1 out), which generalizes the 4 x 4 Mueller matrix used in linear scattering. We apply it to the case of an isotropic ensemble of anisotropic scatterers, obtaining a ''super-Mueller matrix'' of dimension 4 x 4 x 4. Limiting ourselves to coplanar scattering, we show that two subsets of the elements of this matrix have properties closely analogous to properties found in the linear Mueller matrix; namely, (1) sensitivity to the helicity of the scatterer, and (2) sensitivity to imaginary quantities not arising from the complex vector potential of the light; namely, the damping constant, retardative interactions, and an external magnetic field. These elements are all characterized by an odd number of diagonal intensity modulation indices.