Dynamics of multifrequency mode-locking driven by homogenous and inhomogenous gain broadening effects

A complete characterization is given of the effects of homogeneous and inhomogeneous gain broadening on the mode-locking dynamics and stability of a laser operating simultaneously at N frequency channels. Using a low-dimensional model for the wavelength-division multiplexing interactions of the governing cubic-quintic master mode-locking equation, the interplay of the gain dynamics can be completely classified. This gives a simple way to characterize the laser performance and the parameter regimes under which stable multifrequency operation can be achieved. The analysis shows that a small amount of inhomogeneous gain broadening is critical for the multifrequency operation. The model further provides a simple framework for understanding the stability of mode-locked pulses at multiple frequencies, thus contributing to the characterization of the increasingly important and timely technology of dual-frequency and multifrequency mode-locked laser cavities.