Abstract
We consider diffraction of a three-dimensional (3D) spatiotemporal optical pulse by a phase-shifted Bragg grating (PSBG). The pulse diffraction is described in terms of signal propagation through a linear system with its transfer function determined by the reflection or transmission coefficient of the PSBG. It is shown that a PSBG can perform temporal differentiation in reflection and temporal integration in transmission of a 3D spatiotemporal optical pulse envelope. Second order differentiation of the incident pulse envelope is achieved using two differentiating PSBGs separated by a vacuum layer with the optical thickness of a quarter of the Bragg wavelength. The possibility of performing the said operations are confirmed by rigorous simulation results.
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