Analysis of shot noise in the detection of ultrashort optical pulse trains

We present a frequency domain model of shot noise in the photodetection of ultrashort optical pulse trains using a time-varying analysis. Shot-noise-limited photocurrent power spectral densities, signal-to-noise egressions, and shot-noise spectral correlations are derived that explicitly include the finite response of the photodetector. It is shown that the strength of the spectral correlations in the shot noise depends on the optical pulsewidth, and that these correlations can create orders-of-magnitude imbalance between the shot-noise-limited amplitude and phase noise of photonically generated microwave carriers. It is also shown that only by accounting for spectral correlations can shot noise be equated with the fundamental quantum limit in the detection of optical pulse-to-pulse timing jitter.