Integrable model of asynchronous mode-locking

In the mid-1990s, the Ultrafast Optics group at MIT discovered the phenomenon of asynchronous mode-locking using an erbium-doped fiber laser with nonzero dispersion, Kerr nonlinearity, and a phase modulator. The modulator was detuned several kHz from a 1 GHz cavity harmonic. Stable short pulses (1 ps) were observed, but the pulses were found to exhibit oscillatory timing and frequency. As the phase modulation function sweeps by the pulses, they are alternately chirped positively and negatively, and dispersion results in pulse oscillations in time. With small detuning, a soliton could be trapped in the potential well created by the phase modulator. In the asynchronous mode-locking case, the detuning is too great for trapping to occur