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Integral method for echelles covered with lossless or absorbing thin dielectric layers.

We make a generalization of the integral method in the electromagnetic theory of gratings to study diffraction by echelles covered with dielectric lossless or absorbing layers. Numerical examples are given that show that, as in the resonance domain, the diffraction efficiency is more complicated than being a simple product of lossless diffraction efficiency curves and plane surface reflectivity.