Theoretical and numerical study of diffraction on electromagnetic optics VI. Obliquely incident t.e.-polarized Gaussian beams on a finite grating with conducting substrate

Diffraction of an obliquely incident TE-polarized Gaussian beams by N equally spaced slits (finite grating) with conducting substrate is treated. The substrate can be either vacuum or conductor. The diffracted and scattered patterns, the transmission and reflection coefficients, and the normally diffracted energy are analyzed as a function of several optogeometrical parameters. Particularly, the coupling between slits and the influence of the substrate is considered. We have found that, when the substrate is a conductor, the grating equation in reflection predicts with good precision the angular positions of the orders of a finite grating; the angular positions of these orders are independents of the beam width, the spot position on the finite grating, and the conductivity of the substrate. Besides, the envelope of the reflected energy is conserved constant when the position of the spot is changed.