Bistability and Self-Pulsation in Free-carrier Driven Optical Microcavities with All Nonlinear Losses

Continuous-wave pumped micro-optical resonators have been vastly exploited to produce frequency comb (FC) utilizing Kerr effect. Most of the materials used to build photonic platforms exhibit nonlinear losses such as, multi-photon absorption, free-carrier absorption and free-carrier dispersion which can strongly affect the nonlinear characteristics of the devices viz. micro-resonators. In this work, we have developed analytical formulation to make quick estimation of the steady-state behavior, optical bistability, and self-pulsation phenomena in presence of nonlinear losses. Higher-order (>3) characteristic polynomial of intra-cavity power describing the steady-state homogeneous solution of the modified Lugiato Lefever Equation are discussed in detail. We derive the generalized analytical expressions for the threshold of normalized pump detuning to initiate the optical bistability, a necessary condition for the FC generation.