We have developed a 3D Finite Difference Time Domain (FDTD) algorithm to model obliquely incident waves
through arbitrary birefringent and dichroic media with transverse periodic boundaries. Beginning with arbitrary
conductivity and permittivity tensors, we employed the split-field method (SFM) to enable broadband sources
with oblique incidence. We terminate our boundaries with a uniaxial perfectly matched layer (UPML) in one
dimension and periodic boundaries in the other two dimensions. The algorithm is validated via several case
studies: a polarizer pair, a twisted nematic liquid crystal, and an array of conducting particles. Using this
approach, we simulate for the first time polarization gratings with light obliquely incident in directions orthogonal
to the grating vector (i.e., at oblique angles outside the normal diffraction plane).