New property in the diffraction of Hermite–Gaussian beams by a finite grating in the scalar diffraction regime: Constant-intensity angles in the far field when the beam center is displaced through the grating

We study the diffraction of Hermite–Gaussian beams by N equally spaced slits (finite grating) in a planar screen by means of the Rayleigh–Sommerfeld theory in the scalar diffraction regime. We find in the far field the existence of constant-intensity angles when the incident-beam position on the screen is changed. We have determined the optimal conditions under which this new diffraction property can be achieved. Also, a novel effect called the constant-intensity-angles-collapse effect is presented, in which the constant-intensity angles collapse to the minima of the diffraction pattern when the incident spot size is enlarged. For the grating case, deep dips at the maxima of the diffraction patterns of Hermite–Gaussian beams are predicted. Also, for a grating we have found that large segments of these diffraction patterns are independent of the incident-beam position (called constant-intensity curves). The results of this report may be useful for considering unstable vibrational systems in which constant intensities at some angular direction of the far field are required.