Numerical solution of integral equations for the surface current on perfectly conducting echelette-type diffraction gratings is used for comparison with the results of five approximate-analysis techniques. The edge singularity of the current for the P(E∥) polarization and the relatively large current in the shadow region for the S(H∥) polarization give some insight into the rather restricted limits of validity of the perturbation, scalar diffraction, and physical-optics techniques. Two more-general approaches, based on the Rayleigh hypothesis of using only outward-diffracted orders, while considerably more versatile, are found to be at best of marginal use in studying the physical phenomena associated with typical echelette gratings.
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