Stimulated Brillouin scattering in integrated ring resonators

We investigate stimulated Brillouin scattering (SBS) in ring resonators that exhibit linear and nonlinear losses. We present both analytic and numerical tools that can be used to compute the amplification and lasing threshold for the SBS-induced Stokes line. We show that, for both linear and nonlinear losses, there is a maximum achievable SBS amplification, and we show how this depends on the parameters of the ring and on the material parameters. We also study the relation between the critical coupling and input pump power to achieve amplification in various situations. We present simplified models that can be used to accurately predict the nonlinear behavior of the ring and consequently estimate the pump power required to achieve the optimum gain in a range of technologically important situations.