Co-polarized and Cross-polarized Scattering of an Off-axis Focused Gaussian Beam by a Spherical Particle. 1. Exact GLMT Formalism

In static and dynamic light scattering, it has frequently been claimed that cross-polarized scattering cannot occur for single-scattering by a homogeneous spherical particle. Although this is true for both plane wave and on-axis Gaussian beam incidence, we show that cross-polarized scattering does occur when the beam is translated off-axis incidence perpendicular to the scattering plane. We find that the existence of cross-polarized scattering is a direct result of the breaking of the circular symmetry of the beam with respect to the center of the particle when the beam is translated off-axis in wave theory, and to the constraint of the incident beam being a solution of Maxwell's equations.