Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer

In this work we demonstrate both, experimentally and theoretically, that a long-period grating-based in-fiber modal interferometer can perform an all-optical arbitrary-order fractional differentiation. Experimentally, we fractionally differentiated to the 0.5th order a secant hyperbolic-like pulse of 23 ps time width provided by a 1039.5 nm emission wavelength modelocked fiber laser, with a chirp parameter of −30. An analytical expression relating the fractional order of differentiation n with the characteristics of the modal interferometer was also derived, with the purpose to simplify the design procedure. The proposal was corroborated also numerically. This device may find applications in real time phase recovery.