On Rayleigh's Theory of Sinusoidal Diffraction Gratings

It is shown that the Meecham-Yasuura numerical method is not a valid indicator of the possibilities of the Rayleigh theory. In this way, Petit showed that the Rayleigh theory is useful only if the amplitude/period (h/d) ratio does not exceed approximately 0·144. Actually, the application of the Fourier method, proposed by Rayleigh himself, enables the theory of the latter to be used, with success, for h/d attaining at least 0·35, regardless of the polarization. This is demonstrated by comparisons with results obtained by other authors from rigorous integral equation methods.