Plane-wave expansions used to describe the field diffracted by a grating: comments

It is shown that (1) the exceptional numerical efficiency of the Rayleigh–Fourier method for h/d (h is the height and d is the period of a sinusoidal grating) as large as 0.5 could not have been discovered by Petit and Cadilhac in 1966 and (2) the Rayleigh least-squares method does not converge numerically for all h/d, these facts being in contradication to the assertions made by Hugonin et al. [ J. Opt. Soc. Am.71, 593 ( 1981)].