Arbitrary Degree Of Nonlocality Research Articles

Generation of solitons in media with arbitrary degree of nonlocality using an optimization procedure

Using a recently developed technique based on the Rayleigh-Ritz optimization principle, we generate solitons for media with an arbitrary degree of nonlocality. We demonstrate that it is possible to obtain a plethora of complex self-trapped beams using known solutions to the harmonic oscillator for one-dimensional (1D), 2D, and 3D systems, but working directly with a generalized nonlinear nonlocal Schr\odinger equation. We compare the parameters obtained variationally between the phenomenological Gaussian response and other more realistic nonlocal responses. We report that, for both kinds of nonlocal models, our approach obtains variational solutions that can remain self-trapped for certain conditions. We corroborate that, in general, the soliton dynamics can be different between the Gaussian response and the more realistic media for an arbitrary degree of nonlocality.

Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

Completely stable two-dimensional ring dark soliton in nonlocal media with an arbitrary degree of nonlocality are investigated. The exact solution of the ring dark solitons is obtained with the variational method and a cylindrical nonlocal response function. The analytical results are confirmed by directly numerical simulations. We also analytically and numerically study the expansion dynamics of the gray ring dark solitons in detail.

Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality

The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.

Spatial optical soliton in (1 + 2)-dimensional synthetic nonlocal nonlinear media

This paper studies the propagation of Gaussian-shaped optical beams in (1+2)-dimensional synthetic nonlocal media by variational approach. The evolution equations for the parameters of the optical beam are obtained and the critical power of forming a soliton is found. The optical soliton can be formed in “focusing–focusing” synthetic nonlocal media with arbitrary degree of nonlocality. However, we find that σ2 must be grater than a certain value which was depended on the other material parameters of the “focusing–defocusing” synthetic nonlocal media. The analytical results were confirmed by the numerical results.

The interaction of dark solitons with competing nonlocal cubic nonlinearities

The interaction of dark solitons under competing cubic nonlinearities is investigated with an arbitrary degree of nonlocality. Employing the approximately variational technique, the analytical relations for the interaction of dark solitons is obtained in the whole range of degree of nonlocality. It is shown that the competing self-focusing nonlinearity enhances the repulsive force of the interaction, whereas, the competing self-defocusing nonlinearity strengthens the attractive force of the interaction. All the analytically theoretical results have also been demonstrated by direct numerical simulations with split step Fourier transform.

Polarized vector dark solitons in nonlocal Kerr-type self-defocusing media

We study the polarized vector dark-type solitons in nonlocal self-defocusing media with an arbitrary degree of nonlocality. The relations between the soliton parameters and the representation of the transverse velocity of vector dark solitons in the whole range of degree of nonlocality is analytically obtained. We also demonstrate the propagation properties of the polarized vector dark solitons numerically.

Stabilization of counter-rotating vortex pairs in nonlocal media

The dynamics of vector vortex pairs with explicit and hidden vorticity in nonlocal media with an arbitrary degree of nonlocality is investigated analytically and numerically. We show that the stability dynamics of the vortex pairs depends crucially upon their total angular momentum, the topological charge, and the degree of nonlocality. In particular, we show that nonlocality eliminates the splitting of the vortex pairs, improves their propagation stability, and leads to formation of stationary bound states of vortex pairs.

Instability suppression of clusters of vector-necklace-ring solitons in nonlocal media

We study the instability suppression of vector-necklace-ring soliton clusters carrying zero, integer, and fractional angular momentums in nonlocal nonlinear media with an arbitrary degree of nonlocality. We show that the combination of nonlocality and mutual trapping of soliton constituent components can completely stabilize the vector-necklace-ring soliton clusters which are otherwise only quasistable in local media. Our results may be useful to studies of the novel soliton states in Bose-Einstein with dipolar long-range interactions.

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.

Analytical theory of dark nonlocal solitons

We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality.

HIGHLY NONLOCAL OPTICAL SOLITONS AND THEIR OBSERVATION IN NEMATIC LIQUID CRYSTALS

We investigate 2-dimensional spatial optical solitons in media exhibiting a large nonlocal response coupled with a self-focusing nonlinearity. To this extent, with reference to a specific system in undoped nematic liquid crystals, we develop a general theory of spatial solitons in media with an arbitrary degree of nonlocality and carry out experimental observations to validate the model. The remarkable agreement between predictions and data yields evidence of narrow-waist solitons, revealing an important connection between nonparaxiality and nonlocality and emphasizing the role of nonlocality.