A comparative study of the Rayleigh hypothesis and analytic continuation methods as applied to sinusoidal gratings

Two methods are investigated for solving the problem of plane-wave diffraction by gratings with sinusoidal profiles. The first is based on an extension of the Rayleigh hypothesis, and the second employs an analytic continuation technique for computing the field in regions in which the Rayleigh hypothesis breaks down. Some numerical results are presented to compare the two methods.