Noise of mode-locked lasers

Abstract

In recent years, many solid-state lasers have been mode-locked successfully, using the additive pulse mode-locking (APM) principle. It has been shown that, under appropriate approximations, the theory of APM is congruent with that of saturable absorber mode-locking, supplemented by self-phase modulation and group velocity dispersion. When the shortest pulses are achieved, the pulses behave like transform-limited solitons, perturbed by the gain-bandwidth limiting and the APM action. In this limit, a perturbation theory is feasible that is closely related to that of soliton perturbation theory. Noise is handled by perturbation theory; an adiabatic perturbation of the pulse changes its amplitude, phase, carrier frequency and timing. Contrary to soliton perturbations, amplitude and frequency perturbations of mode-locked solitary pulses do not persist but shed some of their energy into the continuum. This is a consequence of the gain saturation and gain-bandwidth limitation not encountered with solitons (nonlinear Schrodinger equation). The timing experiences a random walk, and so does the phase. The latter leads to a Lorentzian line-shape of the resonant cavity modes, similar to that of a free-running oscillator. The spectrum of the amplitude and frequency are Lorentzian because both have nonzero relaxation times. The frequency relaxes to the center frequency of the gain, the amplitude to the value required to equate gain to loss.