Long-period grating assisted fractional differentiation of highly chirped light pulses

We experimentally demonstrate the possibility to perform a fractional differentiation of arbitrary order on a given light pulse by propagation through a single long-period grating. A simple analytical expression is obtained also, relating the fractional order of differentiation with the parameters of the long-period grating. A secant hyperbolic like pulse of 23 ps time width with a chirp parameter of −30 was successfully fractionally differentiated to the 0.5th order. The proposal was corroborated experimentally and numerically. The device may find applications in real time phase recovery.