How is a grating defined?
Gratings exist at the planar interface between two infinite half spaces, the superstrate, and the substrate. The superstrate is characterized by a single real number, it’s index of refraction. The superstrate must be non absorbing. The substrate is characterized by a real or complex index of refraction. If the substrate is absorptive, then the transmitted diffraction orders are defined at the top surface of the substrate, where they decay exponentially away as they propagate down into the substrate. The grating region consists of an arbitrary number of material layers that sit on top of the substrate. The superstrate sits on top of the grating layers. Each (arbitrary thickness) layer of the grating consists of a number of uniform materials that are repeated periodic with a period P (the same for all layers). For a traditional grating the layer is periodic in X and uniform in Y. For crossed gratings the layer is periodic in X and (independently) in Y. Each material is characterized by a
