It is known that near grating anomalies of the resonance type a beam may undergo a lateral shift of the order of the beam width, and a pulse may be delayed by a time of the order of the pulse duration. These numerical investigations are extended to Rayleigh anomalies that occur when, upon variation of the wavelength or the angle of incidence, an additional propagating diffraction order emerges. It is shown that delays and displacements are 1 order of magnitude smaller than in the resonance case. However, with increasing beam width (or pulse duration), the lateral displacement (or the temporal delay) can become large.
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