We make a generalization of the integral method in the electromagnetic theo
ry of gratings to study diffraction by echelles covered with dielectric los
sless or absorbing layers. Numerical examples are given that show that, as
in the resonance domain, the diffraction efficiency is more complicated tha
n being a simple product of lossless diffraction efficiency curves and plan
e surface reflectivity. (C) 1999 Optical Society of America.