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(EII]) polarization and the relatively large current in the shadow region for the S(HII) 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.
H. A. KALHOR and A. R. NEUREUTHER, "Comparison of Approximate-Analysis Techniques for Diffraction Gratings," J. Opt. Soc. Am. 62, 1444-1448 (1972)