Proposal of time-resolved chirp-measurement through all-optical in-fiber mathematical operators

We propose a simple technique to measure in the time domain the magnitude of frequency chirp of high-speed temporal complex waveforms. The technique relies in the properties of three time-domain chirp-sensitive operations: the Hilbert transform, the integration, and the differentiation, all of them analyzed in its integer and fractional counterpart. The implementation of these operations through fiber Bragg gratings is also discussed. We numerically prove the viability of this technique.