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]

We adopt a variational technique to study the dynamics of perturbed dissipative solitons, whose evolution is governed by a Ginzburg-Landau equation (GLE). As a specific example of such solitons, we consider a silicon-based active waveguide in which free carriers are generated through twophoton absorption. In this case, dissipative solitons are perturbed by physical processes such as third-order dispersion, intrapulse Raman scattering, self-steepening, and free-carrier generation. To solve the variational problem, we adopt the Pereira-Stenflo soliton as an ansatz since this soliton is the exact solution of the unperturbed GLE. With this ansatz, we derive a set of six coupled differential equations exhibiting the dynamics of various pulse parameters. This set of equations provides considerable physical insight in the complex behavior of perturbed dissipative solitons. Its predictions are found to be in good agreement with direct numerical simulations of the GLE. More specifically, the spectral and temporal shifts of the chirped soliton induced by free carriers and intrapulse Raman scattering are predicted quite accurately. We also provide simple analytic expressions of these shifts by making suitable approximations. Our semi-analytic treatment is useful for gaining physical insight into complex soliton-evolution processes.

Photonic crystal fibers doped with silver nanoparticles exhibit a Kerr nonlinearity that can be positive or negative depending on the input wavelength and vanishes at a specific wavelength. The existence of negative nonlinearity allows soliton formation even in the normal-dispersion region of the fiber, and the zero-nonlinearity wavelength (ZNW) acts as a barrier for the Raman-induced red shift of solitons. We adopted variational principle to understand the role of zero-nonlinearity point on Raman red-shift and verified its prediction numerically for fundamental and higher-order solitons. We show how the simultaneous presence of a ZNW and a zero-dispersion wavelength affects soliton evolution inside such fibers and find a number of unique features like the position and the spectral bandwidth of the dispersive wave that change with the location of the ZNW.

Abstract-The Ginzburg-Landau (GL) equation is in general not integrable by the inverse scattering method and support solitary-wave solution, called dissipative soliton (DS). We numerically demonstrate that, a DS can radiate dispersive waves (DWs) in presence of third-order dispersion (TOD). We propose a silicon-based active waveguide that excites stable DSs. Energy can be transferred from these stable DS to linear DWs when a resonance condition is achieved. The dynamics of the DS is governed by the complex GL equation which we solve numerically for different operational parameters. Numerical solution of the perturbed GL equation exhibits multiple radiations, when the stable DS is allowed to propagate through a large distance. We theoretically derive a special phase-matching relation that can predict the frequencies of these multiple radiations, which are found numerically. In our theoretical and numerical calculations we include the role of free carriers which appear inside semiconductor waveguides as a consequence of two-photon absorption (TPA). We demonstrate that apart from TOD, TPA and gain dispersion are two additional parameters that can control the radiation emitted by DS. The DS-mediated radiation is different in nature and demands an intuitive understanding. In this work we try to provide some insights of this fascinating radiation phenomenon by elaborate analytical and numerical calculations.

We present a scheme for ground-state cooling of a mechanical resonator by simultaneously coupling it to a superconducting qubit and a cavity field. The Hamiltonian describing the hybrid system dynamics is systematically derived. The cooling process is driven by a red-detuned ac drive on the qubit and a laser drive on the optomechanical cavity. We have investigated cooling in the weak and the strong coupling regimes for both the individual system, i.e., qubit assisted cooling and optomechanical cooling, and compared them with the effective hybrid cooling. It is shown that hybrid cooling is more effective compared to the individual cooling mechanisms, and could be applied in both the resolved and the unresolved sideband regimes.