Search results for "nonlinear"
showing 10 items of 3684 documents
Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion
2014
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; %favors the mechanism of pattern formation with respect to the classical linear diffusion case; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude o…
Phase Domains and Spatial Solitons in Degenerate Optical Parametric Oscillators with Injection
2000
The stability of phase domains and spatial solitons in DOPO under the presence of an injected signal is investigated. The injected signal prevents the nondegenerate regime and, for a particular value of the phase, preserves the equivalence between the two homogeneous states, allowing the domain formation and, in particular, the stability of solitons. The main conclusion is that injection facilitates the experimental observation of solitons in degenerate OPOs.
Pattern formation in a complex Swift-Hohenberg equation with phase bistability
2016
We study pattern formation in a complex Swift Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems submitted to a kind of forcing dubbed rocking when the instability is towards long wavelengths. Applications include two-level lasers and photorefractive oscillators. Under rocking, the original continuous phase symmetry of the system is replaced by a discrete one, so that phase bistability emerges. This leads to the spontaneous formation of phase-locked spatial structures like phase domains and dark-ring (phase-) cavity solitons. Stability of the homogeneo…
Directional Second Harmonic Generation Controlled by Sub-wavelength Facets of an Organic Mesowire
2018
Directional harmonic generation is an important property characterizing the ability of nonlinear optical antennas to diffuse the signal in well-defined region of space. Herein, we show how sub-wavelength facets of an organic molecular mesowire crystal can be utilized to systematically vary the directionality of second harmonic generation (SHG) in the forward scattering geometry. We demonstrate this capability on crystalline diamonoanthraquinone (DAAQ) mesowires with subwavelength facets. We observed that the radial angles of the SHG emission can be tuned over a range of 130 degrees. This angular variation arises due to spatially distributed nonlinear dipoles in the focal volume of the excit…
Switching dynamics of dark-pulse Kerr comb states in optical microresonators
2019
Dissipative Kerr solitons are localized structures that exist in optical microresonators. They lead to the formation of microcombs --- chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion microresonators. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we report the discovery of reversible switching between coherent dark-pulse Kerr combs, whereby distinct states can be accessed deterministically. Furt…
Nonlocality threshold for entanglement under general dephasing evolutions: A case study
2015
Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence depending only on the purity of the initial state. We then utilize these thresholds in a paradigmatic …
Diffusion front capturing schemes for a class of Fokker–Planck equations: Application to the relativistic heat equation
2010
In this research work we introduce and analyze an explicit conservative finite difference scheme to approximate the solution of initial-boundary value problems for a class of limited diffusion Fokker-Planck equations under homogeneous Neumann boundary conditions. We show stability and positivity preserving property under a Courant-Friedrichs-Lewy parabolic time step restriction. We focus on the relativistic heat equation as a model problem of the mentioned limited diffusion Fokker-Planck equations. We analyze its dynamics and observe the presence of a singular flux and an implicit combination of nonlinear effects that include anisotropic diffusion and hyperbolic transport. We present numeri…
Fabrication of polarizing photonic crystal fibres and photonic crystal fibre tapers: Applications
2007
We report the fabrication of an anisotropic photonic crystal fibre with polarization properties and photonic crystal fibre tapers for supercontinuum generation. The anisotropy of the fibre was created by enlarging four airholes next to the silica core. Different polarization regimes as a function of the geometric parameters, including polarizing behaviour at 1.55 mum, were obtained. In the second part of the paper, we report the fabrication of photonic crystal fibre tapers. We present experimental results on supercontinuum generation in photonic crystal fibre tapers using quasi-continuous pump pulses of 7 ns duration at 532 nm and at 1064 nm.
Nonlinear Characterisation of an AsSe Chalcogenide Holey Fiber
2009
oral session TuA " Highly Nonlinear Fibers " [TuA1]; International audience; We report the nonlinear characterization of a chalcogenide holey fiber, based on the AsSe glass composition. A nonlinear coefficient as high as 15 000 W-1 km-1 has been measured.
An E-plane EBG waveguide for dispersion compensated transmission of short pulses
2007
The resolution of radar applications can significantly suffer from pulse broadening along the propagation in homogeneous hollow waveguides. The latter occurs due to the strongly dispersive nature of the fast waves in the waveguides. A low-cost solution to this problem is here proposed, employing an EBG type of waveguide, compatible with traditional E-plane fabrication techniques. By means of an example, here we demonstrate the reduction of the pulse spreading as it propagates along this type of waveguide.