Free-carrier-driven Kerr frequency comb in optical microcavities: Steady state, bistability, self-pulsation, and modulation instability

Abstract

Continuous-wave pumped optical microresonators have been vastly exploited to generate a frequency comb (FC) utilizing the Kerr nonlinearity. Most of the nonlinear materials used to build photonic platforms exhibit nonlinear losses such as multiphoton absorption, free-carrier absorption, and free-carrier dispersion which can strongly affect their nonlinear performances. In this work, we model the Kerr FC based on a modified Lugiato-Lefever equation (LLE) along with the rate equation and develop analytical formulations to make a quick estimation of the steady state, bistability, self-pulsation, and modulation instability (MI) gain and bandwidth in the presence of nonlinear losses. The analytical model is valid over a broad wavelength range as it includes the effects of all nonlinear losses. Higher-order (>3) characteristic polynomials of intracavity power describing the steady-state homogeneous solution of the modified LLE are discussed in detail. We derive the generalized analytical expressions for the threshold (normalized) pump detuning that initiates the optical bistability when nonlinear losses are present. Free-carrier dispersion-led nonlinear cavity detuning is observed through the reverse Kerr tilt of the resonant peaks. We further deduce the expressions of the threshold pump intensity and the range of possible cavity detuning for the initiation of the MI considering the presence of nonlinear losses. The proposed model will be helpful in explaining several numerical and experimental results which have been previously reported and thereby will be able to provide a better understanding of the comb dynamics.

Analysis of Kerr comb generation in silicon microresonators under the influence of two-photon absorption and fast free-carrier dynamics

“…In the absence of FCA, i.e., for σ = 0, Eq. ( 12) is consistent with results from previous studies investigating the impact of TPA on modulation stability [18,19]. Similarly, maintaining only FCA-related terms in Eq.…”

“…We further develop and numerically validate a design for a silicon-photonic Kerr comb source that has a free spectral range (FSR) of 100 GHz and a threshold pump power of 12 mW and that should even be suitable for dissipative Kerr-soliton (DKS) comb formation. It turns out that the incorporation of fast free-carrier dynamics changes the behavior of the optical waveforms in the microresonator to a notable degree, whereas the conditions for MI are essentially unaffected and remain consistent with the findings from simpler models [17][18][19].…”

“…In a bifurcation study of the LLE [37], r = 1/ √ 3 was also found as a threshold value for the TPA parameter preventing bifurcations from the steady-state solution a(t , τ ) = a 0 . Further, r < 1/ √ 3 is also a necessary condition for bistability of the continuous-wave (cw) intracavity power A = |a 0 | 2 as a function of the detuning ζ [18]. Note also that other investigations previously described the impact of the TPA parameter on the intracavity power A required for MI in the presence of TPA and FCA [17] and in the presence of TPA only, see again [18,19].…”

“…For wavelengths in the midinfrared, Kerr comb formation in silicon microresonators under the influence of three-photon absorption and free-carrier absorption was already experimentally demonstrated [16]. In contrast to that, at NIR telecommunication wavelengths, Kerr generation comb in silicon microresonators is impaired by two-photon absorption (TPA) and subsequent free-carrier absorption (FCA) and has so far only been investigated theoretically [17][18][19]. Interestingly, Ref.…”

All-Optical Graphene-Based Modulation of Surface Plasmon Polaritons via Modulation Instability for Secure Optical Communication

“…It appears through a quasi-periodic state (convective MI) and then progresses within a growing amplitude (absolute MI), a prior state to the chaotic regime [3][4][5][6][7]. MI seems to be undesirable but can on the other hand be useful for applications in supercontinuum generation [8][9][10], sideband generation [11], frequency comb generation [12][13][14] and optical modulation [15][16].…”