Internal mechanism of perfect-reflector-backed dielectric gratings to achieve 100% diffraction efficiency

The work started 20 years ago [Appl. Opt.42, 6255 (2003)APOPAI0003-693510.1364/AO.42.006255] investigating the physical mechanism of multilayer dielectric reflection gratings to achieve 100% diffraction efficiency is completed to offer much deeper insight than before. How different scattering matrix elements of the top periodic surface corrugation contribute to the -1st-order efficiency of such a compound grating is unveiled analytically using a minimum set of real parameters. The two diffraction amplitudes transmitted through the top corrugation play a dominant role in enabling 100% diffraction efficiency. Simple necessary and sufficient conditions for 100% efficiency are derived. Moreover, the role of the reflection phase of the perfect reflector, including the contribution of the optical path between the top corrugation and the reflector, is emphasized.