Theoretical demonstration of Brillouin lasing effect in racetrack resonators based on germanium waveguides in the mid-infrared.

In this Letter, we present a theoretical investigation of integrated racetrack Brillouin lasers based on germanium waveguides that are buried in silicon nitride and operate at a wavelength of 4 μm. General design equations in a steady-state regime have been carried out to determine the threshold power and the emitted Stokes power as a function of the resonance mismatch and coupling factor. The pulling effect as induced by the Brillouin gain dispersion and the pushing effects originated by SPM and XPM effects have been accurately investigated to predict the lasing frequency.