Excess noise in optical pulses in non-Hermitian mode-locked laser systems

Summary form only given. We present a comprehensive fully quantum mechanical model, with self-consistent numerical simulations, for the noise in optical pulses in both linear and non-linear (including dynamic gain/loss saturation) mode-locked laser systems in which the time evolution operator for the pulse fluctuations is not Hermitian. Our results show that the excess noise factor can be quite large. In semiconductor mode-locked lasers this factor can exceed 10 for the mean square timing and frequency noise. We construct quantum mechanical operators for the pulse photon number, phase, frequency and timing fluctuations, and show that in non-Hermitian systems these fluctuation operators have first order contributions from eigen-modes of all order. This is a novel result since in Hermitian mode-locked systems to first order only the first two eigen-modes contribute to these fluctuation operators. We also show that the spectra of the pulse energy and timing fluctuations obtained by measuring the spectrum of the photo-detector current noise are exactly the spectra of the energy and timing fluctuation operators that we construct, and contain significant contributions from higher order eigen-modes.