Design of an ultra-broadband all-optical fractional differentiator with a long-period fiber grating

We propose an all-optical in-fiber ultra-broadband fractional differentiator. We numerically demonstrate that a long-period grating inherently performs the temporal fractional differentiation on an optical pulse propagating in the fundamental fiber mode, within a certain spectral bandwidth around the resonance frequency. The device shows a good accuracy calculating the fractional time derivatives of the complex field of THz-bandwidth optical pulses.