Lasing in ring resonators by stimulated Brillouin scattering in the presence of nonlinear loss

We theoretically investigate lasing due to stimulated Brillouin scattering in integrated ring resonators. We give analytic expressions and numerical calculations for the lasing threshold for rings in the presence of for both linear and nonlinear loss. We demonstrate the operation of the ring in the different regimes of amplification and lasing, and show how these regimes depend on the coupling to the ring and on the nonlinear parameters. In the case of nonlinear losses, we find that there can exist an upper threshold to the lasing regime where the losses are dominated by free-carrier absorption. We also find that nonlinear losses can inhibit Brillouin lasing entirely for certain ranges of coupling parameters, and we show how the correct ranges of coupling parameters can be calculated and optimized for the design of integrated Brillouin lasers.