Physics of High Contrast Gratings: A Band Diagram Insight

We generalize the theoretical modelling of high contrast gratings (HCGs) to arbitrary incidence angle. We unveil the HCG band diagram with HCG supermode formulism, and present the intriguing connections between HCG and 1D photonic crystal (PhC). We show, for the first time, HCG and PhC can be unified in the same theoretical analysis architecture. They differentiate themselves by operating at different regimes in the band diagram. The HCG band diagram not only provides a powerful tool to study both HCG and PhC, but also to design various optical components with different functionalities on the HCG-based optoelectronics platform.