Introduction

The first theoretical studies of scattering by diffraction gratings are due to Lord Rayleigh. His “Theory of Sound” Volume 2, 2nd Edition, published in 1896 [18]*, contains an analysis of the scattering of a monochromatic plane wave normally incident on a grating with a sinusoidal profile. In a subsequent paper [19] he extended the analysis to oblique incidence. Rayleigh assumed in his work that in the half-space above the grating the reflected wave is a superposition of the specularly reflected plane wave, a finite number of secondary plane waves propagating in the directions of the higher order grating spectra of optics, and an infinite sequence of evanescent waves whose amplitudes decrease exponentially with distance from the grating. The validity of Rayleigh’s assumption for general grating profiles was realized in the early 1930’s [10], following Bloch’s work [4] on the analogous problem of de Broglie waves in crystals. Waves of this type will be called Rayleigh-Bloch waves (R-B waves for brevity) in this work.