Cage Solitons

The theoretical framework of the Haus master equation of passive mode-locking is revisited. Reformulating the equation in the frequency domain as coupled ordinary differential equations, the complete set of fundamental soliton solutions is surveyed. For large values of anomalous dispersion, this leads to the well known bell-shaped solutions originally found by inverse scattering. Closer to zero dispersion, mode-locked spectra are affected by the available gain bandwidth, and solitons with Bessel-like temporal profiles are found. These spectrally caged solitons match previously unexplained pulse characterization measurements of few-cycle oscillators and mode-locked fiber lasers in the normal dispersion regime. Moreover, the frequency domain formalism suggests that a phase lock between the modes can even be established in the absence of saturable absorption. This finding may explain numerous mysterious experimental reports of mode-locking or comb formation in passive microring resonators and semiconductor lasers. Therefore our frequency-domain approach sheds new light into soliton physics from a completely different perspective.