Spatial integration of optical beams using phase-shifted Bragg grating

The diffraction of a 2D optical beam upon a multilayer Bragg structure is considered. It is shown that phase-shifted Bragg grating can perform spatial integration in transmission of a 2D incident beam in the vicinity of the angular frequency associated with the excitation of a quasi-guided mode confined to the defect layer. The integration is fulfilled with an exponential weight function which fades away as the quality factor of the resonance increases. Beam propagation simulation results are in close agreement with provided theoretical description.