Self-starting microring laser solitons from the periodic cubic complex Ginzburg-Landau equation

Dissipative Kerr solitons are optical pulses propagating in a nonlinear dielectric waveguide without dispersing. These attractive properties have spurred much research into integrated soliton generation in microring resonators at telecom wavelenghts. However, these solitons are generated via external pumping of a nonlinear medium, which limits system compactness and the wavelength coverage. Recently it was shown that dissipative Kerr solitons can be generated directly in the gain medium of mid-infrared semiconductor ring lasers, where the energy is supplied via electrical pumping. These technological advances enable a new route towards the monolithic generation of diverse light states in a wide frequency range, requiring insight into the conditions necessary for achieving control over the system. In this work, we study in depth the phase diagram of such systems, exhibiting fast gain dynamics and no external pumping, and which are described by the complex cubic Ginzburg-Landau equation with periodic boundary conditions. While previous studies have focused on large system sizes, we here focus on finite ring sizes leading to a modification of the phase space and enlargement of the region for stable soliton formation. In addition to localized, dispersion-less soliton pulses on a finite background, breather solitons are predicted to occur under feasible experimental conditions. This enables monolithic generation of solitions in electrically pumped media such as quantum cascade lasers, extending the availability of soliton sources to mid-infrared and terahertz frequencies which are very attractive for molecular spectroscopy, free-space communication, imaging, and coating thickness measurements.