Proposal of a Phase-Shift Fiber Bragg Grating as an Optical Differentiator and an Optical Integrator Simultaneously

We show analytically and numerically that a practically realizable phase-shift fiber Bragg grating (PS-FBG) can function as a temporal first-order optical differentiator and a temporal first-order optical integrator at the same time. The PS-FBG working in reflection implements the differentiation and working in transmission implements the integration. We provide both the generalized conditions for a PS-FBG functioning as a first-order optical differentiator and a first-order optical integrator. The proposed PS-FBG can perform the time differential and integral of the complex envelope of an arbitrary input optical signal with high accuracy, respectively.