Coherence theory of noise in ultrashort-pulse trains

We study the influence of noise in ultrashort-pulse trains in terms of the concepts of optical coherence theory. Specifically, we consider the effects of temporal partial coherence and the timing jitter, including their possible statistical dependence. Analytical expressions for the optical power spectrum, average intensity, mutual coherence function, and the cross-spectral density function of different partially coherent pulse trains affected by stationary noise are given. We show that the new frequencies appearing due to the presence of noise are always fully uncorrelated, unless they are separated by an integral multiple of the repetition rate of the pulses in the train. We also find that spikes appear in the optical power spectrum when the noise and timing jitter are correlated.