Resonant diffraction gratings for spatial differentiation of optical beams

Diffraction of a two-dimensional optical beam from a resonant diffraction grating is considered. It is shown that at certain resonance parameters the diffraction grating allows for spatial differentiation and integration of the incident beam. The parameters of the diffraction grating for spatial differentiation of optical beams in the transmission geometry are calculated. It is shown that the differentiating diffraction grating allows the conversion of the two-dimensional beam into the two-dimensional Hermite-Gaussian mode. The presented results of numerical modelling are in good agreement with the proposed theoretical description. The use of the considered resonant diffraction gratings is promising for solving the problems of all-optical data processing.