Abstract
We theoretically demonstrate by using fractional calculus tools the linking between the instantaneous phase profile of a given temporal optical pulse and its photonics semi-differintegration, i.e. a 0.5th-order differentiation/integration. In both cases, the signal's temporal phase can be retrieved by simple dividing two temporal intensity profiles, namely the intensities of the input and output pulses of a spectrally-shifted 0.5th-order differentiator/integrator. In both cases, we obtained simple analytical expressions for the instantaneous frequency profile. We numerically prove the viability of these proposals.
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