Nonlocal Media Research Articles

Solitons in weakly nonlocal media with cubic-quintic nonlinearity

The propagation of optical beams in weakly nonlocal media with cubic-quintic nonlinearity is studied. The exact solutions for bright and dark solitons are found. The general solutions are implicit, and they are expressed in terms of the elliptic integrals. In particular cases, the solutions are written explicitly in terms of the hyperbolic functions. The dependence of the beam parameters and the soliton shapes on the system parameters is analyzed. The role of nonlocality on the soliton stability is investigated.

Spatial soliton switching in strongly nonlocal media with longitudinally increasing optical lattices

We present the impact of imprinted longitudinally gradually increasing optical lattices on the soliton mobility in strongly nonlocal nonlinear media. Based on the Ehrenfest theorem in quantum mechanics, we show that the introduction of a longitudinal modulation offers an opportunity for soliton steering. The position of the output channel can be varied by small changes of the growth rate, a property that might find applications in optical switching schemes. Numerical simulations confirm the theoretical result.

Evolution of superposition solitons and breathers in strongly nonlocal nonlinear media

Abstract We analyzed and obtained the condition to form a new kind of two-dimensional solitons with complex structure named as “superposition solitons and breathers” in strongly nonlocal media based on the analytical and numerical investigations. Furthermore we investigated how such solitons and breathers persist and are robust when degree of nonlocality is gradually decreased when taken the fully nonlinear system, then we can find such solitons by using the method.

Soliton control in inhomogeneous nonlocal media

In this paper, we have addressed a new way to achieve soliton control, such as compression (or broadening) and fission. More concretely, nonlocality management technique has been adopted, and different control purposes can be realized by controlling corresponding nonlocal parameter. Essentially, nonlocality management should be classified into nonlinearity management.

Self-trapping of two-dimensional vector dipole solitons in nonlocal media

We study the self-trapping of the superposition of two-dimensional vector dipole solitons in nonlocal media with an arbitrary degree of nonlocality. We apply the variational approach to find the exact solution of such vector dipole solitons and investigate their stability by using directly numerical simulations. The dynamics of such vector solitons are also compared with a scalar vortex. We show the nonlocality induces an attractive force which can completely stabilize the vector dipole solitons.

Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media

We address the properties of optical solitons in thermal nonlinear media with a local refractive index defect that is capable to trap solitons launched even close to the sample boundary despite the boundary-mediated forces that tend to deflect all beams toward the center of the sample. We show that while such forces become more pronounced with increasing the input beam power the defect can trap only light below a critical power above which solitons are ejected. The dynamics of soliton ejection and the subsequent propagation may be controlled.

Three-dimensional spatiotemporal solitary waves in strongly nonlocal media

We construct a class of three-dimensional strongly nonlocal spatiotemporal solitary waves of the nonlocal nonlinear Schrödinger equation, by using superpositions of single accessible solitons as initial conditions. Evolution of such solitary waves, termed the accessible light bullets, is studied numerically by choosing specific values of topological charges and other solitonic parameters. Our numerical results reveal that in strongly nonlocal nonlinear media with a Gaussian response function, different classes of accessible spatiotemporal solitons can be generated and controlled by tailoring different soliton parameters.

Accessible solitary wave families of the generalized nonlocal nonlinear Schrödinger equation

Two-dimensional accessible solitary wave families of the generalized nonlocal nonlinear Schrodinger equation are obtained by utilizing superpositions of various single accessible solitary solutions. Specific values of soliton parameters are selected as initial conditions and the superposition of known single solitary solutions in the highly nonlocal regime are launched into the nonlocal nonlinear medium with a Gaussian response function, to obtain novel numerical solitary solutions of improved stability. Our results reveal that in nonlocal media with the Gaussian response the higher-order spatial accessible solitary families can exist in various forms, such as asymmetric necklace, asymmetric fractional, and symmetric multipolar necklace solitons.

Gap solitons in optical lattices embedded into nonlocal media

We analyze the existence, stability, and mobility of gap solitons (GSs) in a periodic photonic structure built into a nonlocal self-defocusing medium. Counter-intuitively, the GSs are supported even by a highly nonlocal nonlinearity, which makes the system quasi-linear. Unlike local models, the variational approximation (VA) predicts the GSs in a good agreement with numerical findings, due to the suppression of undulating tails of the solitons.

Buckling of elastic beams on non-local foundation: A revisiting of Reissner model

The buckling of an axially loaded elastic beam resting on linearly elastic non-local medium is analytically studied in this paper. We show that Reissner foundation model can be expressed in an integral format therefore inducing the non-local character of this elastic foundation model. The variational format of Reissner model is given, leading to meaningful natural and higher-order boundary conditions. Physical arguments are detailed for the mathematical identification of the non-local constitutive law associated to the reaction soil medium. Buckling solutions are obtained in case of simply supported elastically founded column, and the sensitivity of the solution to the choice of higher-order boundary conditions is specifically studied. The scale effects are highlighted for this non-local model.

Frustrated Brownian Motion of Nonlocal Solitary Waves

We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.

The propagation of dipole solitons in highly nonlocal medium

This paper studies the propagation of dipole solitons in highly nonlocal medium by using the variational method. It finds that the dipole solitons will be stable when the input power obeys a restrict value. When the incident power does not satisfy the stable conditions, the nonlocal accessible dipole solitons will undergo linear harmonic oscillation. It shows such evolution behaviours in detail.

Erratum: Pulsating behavior of an optical beam induced by initial phase-front curvature in strongly nonlocal media [Phys. Rev. A76, 043833 (2007)

Erratum: Pulsating behavior of an optical beam induced by initial phase-front curvature in strongly nonlocal media [Phys. Rev. A<b>76</b>, 043833 (2007)

Existence and blow-up of solutions for a non-local filtration and porous medium problem

AbstractWe consider a non-local filtration equation of the formand a porous medium equation, in this case K(u) = um, with some boundary and initial data u0, where 0 &lt; p &lt; 1 and f, f′, f″ &gt; 0. We prove blow-up of solutions for sufficiently large values of the parameter λ &gt; 0 and for any u0 &gt; 0, or for sufficiently large values of u0 &gt; 0 and for any λ λ 0.

The pulsating propagation of spatial soliton in strongly nonlocal optical lattice

Based on the nonlocal nonlinear Schrdinger equation, which is the evolution equation of propagation of spatial soliton in the nonlocal media, the pulsating propagation of spatial solitons in one-dimensional strongly nonlocal optical lattice are researched numerically by the split-step Fourier method. The pulsating propagation period of spatial soliton is analyzed for different parameters of propagation, such as the initial energy of the beam, the nonlocality degree, the modulation degree of lattice, the period of the transverse modulation and the asymptotic rate of the longitudinal modulation of linear refractive index. And the inherent physical mechanisms of pulsating propagation of spatial soliton are discussed for the different parameters of lattice structure. Furthermore, the controllable switching behavior of spatial optical soliton has been achieved in the strongly nonlocal optical lattice with longitudinal modulation of linear refractive index.

Non local theory of excitations applied to the Hubbard model

We propose a nonlocal theory of single-particle excitations. It is based on an off-diagonal effective medium and the projection operator method for treating the retarded Green function. The theory determines the nonlocal effective medium matrix elements by requiring that they are consistent with those of the self-energy of the Green function. This arrows for a description of long-range intersite correlations with high resolution in momentum space. Numerical study for the half-filled Hubbard model on the simple cubic lattice demonstrates that the theory is applicable to the strong correlation regime as well as the intermediate regime of Coulomb interaction strength. Furthermore the results show that nonlocal excitations cause sub-bands in the strong Coulomb interaction regime due to strong antiferromagnetic correlations, decrease the quasi-particle peak on the Fermi level with increasing Coulomb interaction, and shift the critical Coulomb interaction UC2 for the divergence of effective mass towards higher energies at least by a factor of two as compared with that in the single-site approximation.

初始波前曲率对强非局域介质中光束演化的影响

初始波前曲率对强非局域介质中光束演化的影响

Grow-up of critical solutions for a non-local porous medium problem with Ohmic heating source

We investigate the behaviour of solution u = u(x, t; λ) at λ = λ* for the non-local porous medium equation \({u_t = (u^n)_{xx} + {\lambda}f(u)/({\int_{-1}^1} f(u){\rm d}x)^2}\) with Dirichlet boundary conditions and positive initial data. The function f satisfies: f(s),−f ′ (s) > 0 for s ≥ 0 and sn-1f(s) is integrable at infinity. Due to the conditions on f, there exists a critical value of parameter λ, say λ*, such that for λ > λ* the solution u = u(x, t; λ) blows up globally in finite time, while for λ ≥ λ* the corresponding steady-state problem does not have any solution. For 0 < λ < λ* there exists a unique steady-state solution w = w(x; λ) while u = u(x, t; λ) is global in time and converges to w as t → ∞. Here we show the global grow-up of critical solution u* = u(x, t; λ*) (u* (x, t) → ∞, as t → ∞ for all \({x\in(-1,1)}\).

Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media

We investigate the propagation of spatial solitons in cylindrical strongly nonlocal media by a method of image beam of light. The dynamic force of the soliton steering resulting from the boundary effect is equivalent to the force between the soliton beam and the image beam. The trajectory of the soliton is analytically studied, which is in good agreement with the experimental results.

TELL IT NOT IN HARRISBURG, PUBLISH IT NOT IN THE STREETS OF TAMPA

A framing analysis was performed on 22 local news reports identified in 90 newscasts carried by television stations covering the Federal Communications Commission's (FCC) public hearings on media ownership held in Harrisburg, PA and Tampa, FL in 2007. It revealed two frames: one portraying the hearings as “unimportant” and another suggesting that “media consolidation is not a problem.” Taking into account that the stations are owned by non-local media conglomerates, the findings of this study imply that maintaining broadcasters independent of the networks serves the diversity of viewpoints in a market, especially regarding issues in which media conglomerates have a vested interest.