Mode locking of the Hermite-Gaussian modes of a nanolaser

Mode locking is predicted in a nanolaser cavity forming an effective photonic harmonic potential. The cavity is substantially more compact than a Fabry-Perot resonator with a comparable pulsing period, which is here controlled by the potential. In the limit of instantaneous gain and absorption saturation, mode locking corresponds to a stable dissipative soliton, which is very well approximated by the coherent state of a quantum mechanical harmonic oscillator. This property is robust against noninstantaneous material response and nonzero phase-intensity coupling.