Ultra-Wideband Temporal Differentiators Based on Phase-Shifted Fiber Bragg Gratings

We introduce a simple and general photonics (all-fiber) approach for designing practical arbitrary-order time differentiators. Specifically, we demonstrate that the N^th time derivative of an input optical waveform can be obtained by reflection of this waveform in a single uniform fiber Bragg grating (FBG) incorporating N pi-phase shifts properly located along its grating profile. The design procedure of an arbitrary-order optical time differentiator based on a multiple-phase-shifted FBG is described and numerically demonstrated for up to third-order time differentiation. Our simulations show that the proposed approach can provide optical operation bandwidths in the tens-of-GHz regime using readily feasible FBG structures.