Optical Comb Dynamics and Stabilization

The spectrum of a mode-locked laser consists of a comb of equidistantly spaced frequencies. This comb has only two degrees of freedom, its offset frequency at zero and the spacing of the teeth of the comb. While the spacing of the frequencies is simply determined by the repetition rate of the laser and can be relatively easily controlled, the offset frequency is governed by phase differences between the carrier and the envelope of the pulses during one round trip through the laser cavity. This carrier-envelope offset (CEO) phase is measured via heterodyning different harmonics of the mode-locked laser spectrum. In an unstabilized laser, this CEO phase exhibits very strong noise and can fluctuate several thousand radians in only one second. We provide an analysis of CEO phase-noise contributions and track their origin. The passive stability with respect to CEO fluctuations can be greatly improved by suitable cavity design, which greatly simplifies the stabilization of the CEO phase. Recent efforts on carrier-envelope stabilization are reviewed and some limitations are outlined.