We propose and analyze a first-order optical differentiator based on a fiber Bragg grating (FBG) in transmission. It is shown in the examples that a simple uniform-period FBG in a very strong coupling regime (maximum reflectivity very close to 100%) can perform close to ideal temporal differentiation of the complex envelope of an arbitrary-input optical signal.
Preciado, M. A., & Muriel, M. A. (2008). Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission. Optics Letters, 33(21), 2458-2460. https://doi.org/10.1364/OL.33.002458