  Continuous-wave pumped optical microresonators have been vastly exploited to
generate frequency comb (FC) utilizing the Kerr nonlinearity. Most of the
nonlinear materials used to build photonic platforms exhibit nonlinear losses
such as multi-photon absorption, free-carrier absorption (FCA), and
free-carrier dispersion (FCD) which can strongly affect the nonlinear
characteristics of the devices made out of these materials. In this work, we
model the Kerr FC based on modified Lugiato-Lefever Equation (LLE) along with
the rate equation and develop analytical formulations to make quick estimations
of the steady-state, modulation instability (MI) gain, bandwidth and the
dynamics of Kerr Frequency-Comb (FC) in presence of nonlinear losses. Our
analytical model is valid over a broad wavelength range of interest as it
includes the effects of all nonlinear losses. Higher order (>3) characteristic
polynomial of intra-cavity power describing the steady-state homogeneous
solution of the modified LLE are discussed in detail. We derive the generalized
analytical expressions for the threshold of normalized pump detuning to
initiate the optical bistability which is a necessary condition for the FC
generation. Free-carrier dispersion-led nonlinear cavity detuning is observed
through the reverse Kerr-tilt of the resonant-peaks. We further deduce the
expressions for the threshold pump intensity and the range of possible cavity
detuning for the initiation of the MI when all the nonlinear losses are
present. To corroborate our analytical findings, LLE along with the rate
equations are solved numerically through split-step Fourier method. Our
theoretical study can explain several experimental results which are previously
reported and thereby is able to provide a better understanding of the comb
dynamics.
