Theoretical spectrum of noisy optical pulse trains

The intensity of an ideal optical pulse train is often modeled as an exact periodic repetition of a given pulse-shape function with constant amplitude and width. Therefore, the ideal intensity power spectrum is a pure line power spectrum. However, spontaneous-emission noise due to amplification media, electronic noise due to modulators, or even intentional modulations result in period-to-period fluctuations of the pulse amplitude, width, or arrival time. The power spectrum of this so-called noisy optical pulse train is then composed of a line spectrum added to a band spectrum. This study shows that the optical pulse train intensity is cyclostationary under usual assumptions on the fluctuations. This property allows us to derive the exact optical pulse train power spectrum. A general closed-form expression that takes into account the three noise manifestations (jitter, amplitude, and width modulations) is provided. Particular expressions are given for usual cases of interest such as the jitter and amplitude modulation model, for given fluctuation probability distributions, and pulse-shape functions.