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

The work started 20 years ago [Appl. Opt. 42, 6255 (2003)] investigating the physical mechanism of multilayer dielectric reflection gratings to achieve 100% diffraction efficiency is extended to offer much deeper insight than before. How different diffraction amplitudes of the top surface corrugation contribute to the −1st-order efficiency of such a grating is shown analytically using a minimum set of real parameters. The two diffraction amplitudes transmitted through the corrugation play a dominant role in enabling DE = 100%. The necessary and sufficient condition for 100% efficiency is derived, and a very simple sufficient condition is also given. Moreover, the role of the reflection phase of the perfect-reflector, including the contribution due to optical path between the corrugation and the reflector, is emphasized.