Search results for "Nonlinear"
showing 10 items of 3684 documents
Switching Dynamics of Dark Solitons in Kerr Microresonators
2019
Dissipative Kerr solitons (DKS) are localized structures in optical resonators that arise from a double balance between dispersion and Kerr effect, and linear loss and parametric gain [1]. The periodic nature of DKS corresponds to frequency combs. DKS can be generated in high-Q microresonators for diverse applications, from coherent communications to precision frequency synthesis [1]. Most studies of DKS have focused on microresonator cavities operating in the anomalous dispersion regime, where the waveforms correspond to bright soliton pulses. Coherent microresonator combs can also be formed in the normal dispersion regime [2]. The time-domain waveform corresponds to a localized dark-pulse…
Kerr effect as a tool for the investigation of dynamic heterogeneities
2006
We propose a dynamic Kerr effect experiment for the distinction between dynamic heterogeneous and homogeneous relaxation in glassy systems. The possibility of this distinction is due to the inherent nonlinearity of the Kerr effect signal. We model the slow reorientational molecular motion in supercooled liquids in terms of non-inertial rotational diffusion. The Kerr effect response, consisting of two terms, is calculated for heterogeneous and for homogeneous variants of the stochastic model. It turns out that the experiment is able to distinguish between the two scenarios. We furthermore show that exchange between relatively 'slow' and 'fast' environments does not affect the possibility of …
Counter-propagating difference-frequency generation in diamond with terahertz fields
2013
The nonlinear interaction of terahertz (THz) pulses with optical fields in Kerr, gaseous media is a key ingredient for broadband THz detection schemes [1]. Terahertz field-induced second harmonic generation in solid-state media has also been considered for THz detection and as a tool e.g. for liquid dynamics investigations [2,3], while four-wave mixing has been addressed as a possible mechanism for THz generation [4,5]. © 2013 IEEE.
Vectorial Kerr-cavity solitons.
2000
It is shown that a Kerr cavity with different losses for the two polarization components of the field can support both dark and bright cavity solitons (CS’s). A parametrically driven Ginzburg–Landau equation is shown to describe the system for large-cavity anisotropy. In one transverse dimension the nonlinear dynamics of the bright CS’s is numerically investigated.
Statistical characterization of the internal structure of noiselike pulses using a nonlinear optical loop mirror
2016
Abstract In this work we study statistically the internal structure of noiselike pulses generated by a passively mode-locked fiber laser. For this purpose, we use a technique that allows estimating the distribution of the amplitudes of the sub-pulses in the bunch. The technique takes advantage of the fast response of the optical Kerr effect in a fiber nonlinear optical loop mirror (NOLM). It requires the measurement of the energy transfer characteristic of the pulses through the NOLM, and the numerical resolution of a system of nonlinear algebraic equations. The results yield a strongly asymmetric distribution, with a high-amplitude tail that is compatible with the existence of extreme-inte…
Numerical simulation of Kerr nonlinear systems : analyzing non-classical dynamics
2019
Abstract We simulate coherent driven free dissipative Kerr nonlinear system numerically using Euler’s method by solving Heisenberg equation of motion and time evolving block decimation (TEBD) algorithm, and demonstrate how the numerical results are analogous to classical bistability. The comparison with analytics show that the TEBD numerics follow the quantum mechanical exact solution obtained by mapping the equation of motion of the density matrix of the system to a Fokker-Plank equation . Comparing between two different numerical techniques, we see that the semi-classical Euler’s method gives the dynamics of the system field of one among two coherent branches, whereas TEBD numerics genera…
Effect of nonequilibrium charge screening in A + B ? 0 bimolecular reactions in condensed matter
1993
The formalism of many-particle densities developed earlier by the present authors is applied to the study of the cooperative effects in the kinetics of bimolecular A +B--*0 reactions between oppositely charged particles (reactants). It is shown that unlike the Debye-Hiickel theory in statistical physics, here charge screening has essentially a nonequilibrium character. For the asymmetric mobility of reactants (DA=0, D~4:0) the joint spatial distribution of similar immobile reactants A reveals at short distances a singular character associated with their aggregation. The relevant reaction rate does not approach a steady state (as it does in the symmetric case, DA=DB), but increases infinitel…
Kolmogorov-Arnold-Moser–Renormalization-Group Analysis of Stability in Hamiltonian Flows
1997
We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.
Bayesian estimation of the specific shear and bulk viscosity of the quark-gluon plasma with additional flow harmonic observables
2021
The transport properties of the strongly coupled quark-gluon plasma created in ultrarelativistic heavy-ion collisions are extracted by Bayesian parameter estimate methods with the latest collision beam energy data from the CERN Large Hadron Collider. This Bayesian analysis includes sophisticated flow harmonic observables for the first time. We found that the temperature dependence of specific shear viscosity appears weaker than in the previous studies. The results prefer a lower value of specific bulk viscosity and a higher switching temperature to reproduce additional observables. However, the improved statistical uncertainties both on the experimental data and hydrodynamic calculations wi…
An invariant analytic orthonormalization procedure with applications
2007
We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct $g(x)\in L^2(\Bbb{R})$ in such a way the functions $g_{\underline n}(x)=e^{ian_1x}g(x+an_2)$, $\underline n\in\Bbb{Z}^2$ and $a$ some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice naturally associated to the procedure in this analysis.