BRAGG-FRESNEL MULTILAYER GRATINGS - ELECROMAGNETIC THEORY

We develop an electromagnetic analysis and its numerical implementatio n for gratings of arbitrary shape etched into a plane multilayer. The multilayer consists of a stack of identical bilayers, each bilayer inc luding two materials (dielectrics and/or metals) with different thickn esses. The analysis is based on the differential theory of gratings, w hich is generalized to the case of many superimposed gratings by compu tation of the T matrix of each elementary grating linking the field ab ove the modulated region to the field below it. The product of all the T matrices gives the T matrix of the stack, from which the outgoing w ave condition permits derivation of the grating efficiencies. The meth od, developed for TE polarization, can be used throughout the entire s pectrum, but it is particularly useful in the soft-x-ray region. Examp les of performances of multilayer gratings in this spectral domain are computed.