Evolution of Amplitude Fluctuation in Fractional Temporal Talbot Effect

Temporal Talbot phenomena occur when a periodic optical pulse train propagates through a dispersive medium with a proper dispersion amount, which includes integer and fractional orders depending on the dispersion amount. The fractional temporal Talbot (FTT) effect has attracted great interest because of its potentials in repetition rate multiplication of optical pulse train and passive amplification of short pulses. In this paper, we investigate the evolution of amplitude fluctuation in FTT systems from the viewpoint of the frequency-dependent fading of pulse train envelope. It is found that the envelope frequency response of FTT is different from that of integer orders since there is waveform-to-waveform phase profile in the output pulse train in FTT systems. The noise reduction phenomenon in FTT systems is analyzed based on the derived frequency response. A closed-form expression of the noise reduction ratio is derived for the first time based on the analysis of the noise power spectral density. With the given model, we are able to predict the fluctuation suppression effect in FTT systems more precisely.