A simple and general approach for designing practical all-optical (all-fiber) arbitrary-order time differentiators is introduced here for the first time. 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 π-phase shifts properly located along its grating profile. The general design procedure of an arbitrary-order optical time differentiator based on a multiple-phase-shifted FBG is described and numerically demonstrated for up to fourth-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.
©2007 Optical Society of America
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