Stabilized pulse spacing in soliton lasers due to gain depletion and recovery

We consider the interpulse dynamics in harmonic passively mode-locked soliton lasers and find that gain depletion in conjunction with its recovery provides an effective repulsion force between adjacent solitons by imparting a group-velocity drift proportional to the interpulse spacings. Analytic descriptions for both the two-pulse and N-pulse per round-trip configurations demonstrate the stability of the equally spaced condition. These theoretical findings, which are supported by experimental results, hold in the limit where cavity losses and perturbations are small per round trip so that the weak gain depletion and recovery mechanisms can dominate the interpulse interactions.