Spatial optical integrator based on phase-shifted Bragg gratings

We present a theoretical study of a new application of a phase-shifted Bragg grating (PSBG) in transmission mode as a spatial optical integrator. The PSBG consists of two identical Bragg gratings separated with a phase-shift defect layer. It is shown that PSBG enables performing the operation of spatial integration of the profile of the 2D incidence beam with a central spatial frequency close to the propagation constant of a quasiguided mode localized in the defect layer. The spatial integration is performed with an exponential weight function, the decay rate of which is determined by the quality factor of the resonance. The rigorous electromagnetic simulations demonstrate good agreement between numerical results and the given theoretical description.