Spatial modifications of Gaussian beams diffracted by reflection gratings

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Abstract
By using an angular spectral representation, we show that the fields of Gaussian beams scattered by reflection gratings differ markedly from those predicted by geometrical considerations. We find that, in general, each diffracted beam exhibits a lateral displacement, a focal shift, and an angular deflection; in addition, the size of the beam width is enlarged or reduced. The beam changes are largest if the incidence angle is phase matched to a leaky wave that may be supported by the grating. This phase condition is identical to that for which Wood’s anomalies of the resonant variety occur if plane waves, instead of bounded beams, are incident. By evaluating the spatial modifications of beams diffracted at a canonic grating structure consisting of a sinusoidal reactance plane, we show that the magnitudes of the beam effects can be considerably large. We also examine the special case of blazed diffracted orders and find that their corresponding beams are not extinguished completely but appear with reduced intensity and strong profile distortion.