Arbitrary-Order Ultrabroadband All-Optical Differentiators Based on Fiber Bragg Gratings

We introduce a general approach for designing ultrabroadband arbitrary-order all-optical (all-fiber) time differentiators based on the use of fiber Bragg gratings (FBGs). Specifically, we numerically demonstrate that an Nth-order time differentiator can be implemented using a single specially apodized highly dispersive linearly chirped FBG operated in transmission. A concatenated reflection phase-shifted FBG is also required for implementing any odd-order differentiator. Our numerical simulations show that accurate and efficient time differentiation of optical signals with bandwidths up to a few hundreds of gigahertz can be realized using readily feasible FBG structures.