Stability and variational analysis of cavity solitons under various perturbations

Abstract

We theoretically investigate the dynamics and stability of a temporal cavity soliton (CS) excited inside a silicon-based microresonator that exhibits free-carrier generation as a results of two-photon absorption (TPA). The optical propagation of the CS is modelled through a mean field Lugiato-Lefever equation (LLE) coupled with an ordinary differential equation accounting for the generation of free carriers owing to TPA. The CS experiences several perturbations (like intrapulse Raman scattering (IRS), TPA, free-carrier absorption (FCA), free-carrier dispersion (FCD) etc.) during its round-trip evolution inside the cavity. We develop a full variational analysis based on Ritz optimization principle which is useful in deriving simple analytical expressions describing the dynamics of individual pulse parameters of the CS under perturbation. TPA and FCA limit the efficient comb generation and modify the stability condition of the CS. We determine the critical condition of stability modification due to TPA and derive closed form expressions of the saturated amplitude and width of stable CS. The CS experiences FCD which leads to a temporal acceleration resulting in spectral blue-shift. Exploiting the variational analysis we estimate these temporal and spectral shifts. We also include IRS in our perturbation theory and analytically estimate the frequency red-shifting. Finally we study the effect of pump-phase-modulation on stable CS. All our analytical results are found to be in good agreement with the numerical data obtained from the full solution of LLE. arXiv:1905.05960v1 [physics.optics]

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].…”

“…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]. In both cases, the required intracavity (IC) FIG.…”

“…Similarly, maintaining only FCA-related terms in Eq. (12) leads to relations that have previously been derived for resonators impaired by free carriers only [19]. We simplify the further analysis, by treating as a continuous non-negative real-valued variable, even though it was originally defined as an integer parameter ∈ N + .…”

“…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.…”