Full wave analysis of plane wave diffraction by a finite sinusoidal grating: E-polarization case

Plane wave diffraction studies of a finite sinusoidal grating have previously assumed that the grating length is large in wavelengths and the depth of its corrugations is small compared to a wavelength. This paper introduces a rigorous technique, the Method of Analytical Regularization (MAR), which removes these restrictions. The solution obtained by this method is free from limitations on the parameters of sinusoidal grating and possesses the capability to achieve predetermined accuracy of computations uniformly in a wide frequency band. The results of previous studies, which employed the Wiener-Hopf technique combined with a perturbation method, are compared with those obtained by the MAR; excellent concordance of results in the common parameter regimes of applicability of both methods is found. The different regimes of applicability of each approach are identified; within these, the MAR provides effective and efficient solutions to benchmark problems for testing other approximate techniques.