The quantum-limited comb lineshape of a mode-locked laser: Fundamental limits on frequency uncertainty

We calculate the quantum-limited shape of the comb lines from a mode-locked Ti:sapphire laser using experimentally-derived parameters for the linear response of the laser to perturbations. The free-running width of the comb lines is found across the laser spectrum. By modeling the effect of a simple feedback loop, we calculate the spectrum of the residual phase noise in terms of the quantum noise and the feedback parameters. Finally, we calculate the frequency uncertainty in an optical frequency measurement if the limiting factor is quantum noise in the detection of the optical heterodyne beat.