Determination of the eigenpolarizations in arbitrary diffraction orders of planar periodic structures under arbitrary incidence

The determination of eigenpolarizations is a crucial issue in the study of functional nanomaterials and nanostructures for polarization control, such as the newly emergent chiral metamaterials with artificial optical activity. Here we propose the approaches for determining the eigenpolarizations in an arbitrary diffraction order of any planar periodic structure (PPS) under arbitrary incidence. First, a simple analytical approach based on symmetry considerations is developed for discriminating the eigenpolarizations of the directly transmitted light of any PPS under normal incidence, by dividing the PPSs into 10 categories according to the group theory. Then a general numerical approach is established to rigorously solve the eigenpolarizations of any diffraction order of a PPS under any angle of incidence. Examples are demonstrated to show the effectiveness of the approaches.