Statistical analysis of incoherent pulse shaping.

The performance of incoherent pulse shaping based on temporal gating and dispersive propagation of a broadband incoherent optical source is analyzed. The average temporal intensity of the dispersed gated source is essentially proportional to the spectral density of the incoherent source scaled along the temporal axis; therefore temporal waveforms are synthesized by spectral density modulation of the incoherent source. Although the coherence time of the shaped waveform is longer than that of the initial incoherent source, the shaped-intensity probability density function at any given time is identical to the probability density function of a polarized incoherent source. This restricts the signal-to-noise ratio of the shaped waveform to 1. Statistical analysis describes how the signal-to-noise ratio is affected by polarization multiplexing and averaging over multiple realizations of the incoherent process. The signal-to-noise ratio of high-speed electric waveforms generated by photodetection of the shaped optical waveform is described.