Semi-analytic theory of high-efficiency multilayer dielectric gratings

A semi-analytic theory of multilayer dielectric gratings (MLDGs) is presented. Analytic formulas for the -1st-order diffraction efficiency of an MLDG being 100% and greater than a preset value are given in terms of the scattering matrix elements of the top surface-relief grating (TG). The important role of the combined reflection phases is highlighted. The need to secure high reflectances of the multilayer stack at the two angles of incidence below the TG and the need to supply a sufficient number of aperiodic layers in the multilayer substrate for phase matching are emphasized. Three numerical examples of 100% efficient MLDGs, obtained without optimizing the TG, are presented, illustrating the accuracy and generality of the theory.