It is demonstrated that a uniform fiber Bragg grating (FBG) working in the linear regime inherently behaves as an optical temporal integrator over a limited time window. Specifically, the reflected temporal waveform from a weak-coupling uniform FBG is proportional to the time integral of an (arbitrary) optical pulse launched at the component input. This integration extends over a time window fixed by the duration of the squarelike temporal impulse response of the FBG. Ultrafast all-optical integrators capable of accurate operation over nanosecond time windows can be implemented using readily feasible FBGs. The introduced concepts are demonstrated by numerical simulations.
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