Nonlocal Nonlinear Media Research Articles

Asymmetric multi-vortex solitons in nonlocal nonlinear media

This paper introduces a series of asymmetric multi-vortex solitons, which made up of Gaussian beam and embedded multi off-axis shift vortex, in nonlocal nonlinear media. The analytical expression of the soliton trajectory is derived, and the other propagation properties, such as the intensity distribution, the rotating period, and the orbital angular momentum (OAM) are all investigated. It is found that the initial displacement of the soliton mass center, which can be controlled by selecting the appropriate shift values of the off-axis vortexes, can determine the trajectory of the optics beam. The OAM also depending on the shift values of the vortexes. Obviously, the controllable propagation of the asymmetric multi-vortex beam has important academic value and application prospect in optical switches, or be used as optical tweezers and wrenches.

Propagation of self-accelerating Hermite complex-variable-function Gaussian wave packets in highly nonlocal nonlinear media

The evolution dynamic properties of self-accelerating Hermite complex-variable-function Gaussian (SHCG) wave packets in highly nonlocal nonlinear media are investigated. Analytical results from a $$(3+1)$$ -dimensional Snyder–Mitchell model show that various SHCG wave packets carrying multi-order vortices rotate smoothly. Increasing the distribution factor will cause the intensity layout to cluster more closely around the center, while the vortices will be farther away. The SHCG wave packets can reverse the positions of their temporal side lobes. The role of the power ratio in determining the rotation period and the angular velocity is also discussed. Furthermore, numerical results of the nonlocal nonlinear Schrodinger equation are simulated to illustrate the effects of different nonlocalities and initial perturbations. The SHCG wave packets show interesting features during propagation, which can provide new ideas for the regulation of the multi-dimensional optical field.

Accessible solitons in three-dimensional parabolic cylindrical coordinates

A class of self-similar beams, named three-dimensional (3D) spatiotemporal parabolic accessible solitons, are introduced in the 3D highly nonlocal nonlinear media. We obtain exact solutions of the 3D spatiotemporal linear Schrödinger equation in parabolic cylindrical coordinates by using the method of separation of variables. The 3D localized structures are constructed with the help of the confluent hypergeometric Tricomi functions and the Hermite polynomials. Based on such an exact solution, we graphically display three different types of 3D beams: the Gaussian solitons, the ring necklace solitons, and the parabolic solitons, by choosing different mode parameters. We also perform direct numerical simulation to discuss the stability of local solutions. The procedure we follow provides a new method for the manipulation of spatiotemporal solitons.

Managements of scalar and vector rogue waves in a partially nonlocal nonlinear medium with linear and harmonic potentials

We consider a ( $$2+1$$ )-dimensional nonautonomous-coupled nonlinear Schrodinger equation, which includes the partially nonlocal nonlinearity under linear and harmonic potentials. Via a projecting expression between nonautonomous and autonomous equations, and utilizing the bilinear method and Darboux transformation method, we find diversified exact solutions. These solutions contain the nonlocal rogue wave and Akhmediev or Ma breather solutions, and the combined solution which describes a rogue wave superposed on an Akhmediev or Ma breather. By adjusting values of diffraction, width and phase chirp parameters of wave, the maximum value of the accumulated time can be modulated. When we compare the maximum value of the accumulated time with that of the excitation position parameters, we study the management of scalar and vector rogue waves, such as the excitations of full shape, early shape and climax shape for rogue waves.

Propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams in nonlocal nonlinear media

In this paper, the propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams (AHSGB) in strongly nonlocal nonlinear media are discussed. The propagation expression of the AHSGB is theoretically derived and the evolution characteristics of the light intensity distribution, the beam width, and the phase curvature are analyzed by using mathematical and numerical methods. We find that the parameters of the hyperbolic sinusoidal function, the initial power and the initial position are important factors that influence the propagation behavior of the beam.

Propagation of hollow sinh-Gaussian beams in strongly nonlocal nonlinear media

Based on the Snyder-Michell model and using the ABCD matrix description of a strongly nonlocal nonlinear media (SNNM), the propagation properties of hollow sinh-Gaussian beams (HsGBs) through SNNM are investigated. The propagation formula, the second-order intensity moment beam width and the critical power for an on-waist incident HsG beam in SNNM are derived. The evolution of the intensity distribution pattern and the beam width of the HsGB are illustrated, graphically and analyzed with numerical examples. It is found that the HsGB pattern evolves periodically during propagation in SNNM, and its evolution behavior is strongly affected by the initial beam power and beam parameters. For a critical input power, the beam width keeps invariant during propagation, which can be regarded as a HsGB-soliton.

Z-scan analytical expressions for weak thick nonlocal nonlinear media

Analytical expressions for the on-axis normalized transmittance and total transmittance z-scan of thick nonlocal nonlinear media illuminated by a Gaussian beam are obtained in this paper. The corresponding thin media transmittance expressions and the distributed lens method are used together with the assumption that the nonlocal media exhibits weak nonlinear absorption and refraction in order to obtain the formulas. The obtained expressions enable the consideration of different degrees of nonlocality and the reproduction of the results reported for local media.

Controllable soliton transition and interaction in nonlocal nonlinear media

Two kinds of controllable evolutions of optical solitons are predicted in nonlocal nonlinear media by gradually tuning the characteristic length of response function. On the one hand, the solitons can smoothly transit among the ones of different widths. On the other hand, two parallel out-of-phase solitons can be conveniently tailored to attract or repel each other. In addition, numerical results demonstrate that all the transitions of fundamental and multipole solitons can be physically realized in actual nonlocal media, such as nematic liquid crystal, and are stable against noise. Obviously, control soliton widths and interactions have important research opportunities and application prospects in signal processing and transmission.

Propagation dynamics of tripole breathers in nonlocal nonlinear media

We demonstrate the propagation dynamics of optical breathers in nonlinear media with a spatial nonlocality, which is governed by the nonlocal nonlinear Schrodinger equation, by employing the variational approach. Taking a tripole breather as an example, the approximate analytical solution is obtained and the physical propagation properties, such as the evolution of the critical power, the spot size, the wavefront curvature, and the intensity distribution of the breather, have been discussed in detail. The physical reasons for the evolution of the tripole breathers are analyzed by borrowing the ideas from Newtonian mechanics. It is found that the analytical results obtained by the variational approach agree well with the numerical results of the nonlocal Schrodinger equation for the strong nonlocal case, especially when the incident power approaches the critical power.

Propagation properties of quadrupole breather in nonlinear media with a nonlocal exponential-decay response

We investigate the propagation properties of quadrupole breather in nonlinear media with a nonlocal exponential-decay response by using the variational method and the equivalent particle method. The analytical solution of the quadrupole breather is obtained. The breather beamwidth, the wavefront curvature, the intensity pattern, and the comparisons between the analytical quadrupole breather solution and the numerical simulations of the nonlocal nonlinear Schrödinger equation in the case of highly nonlocal nonlinearity are analyzed. The results show that the analytical solution is in good agreement with the numerical simulations at near-critical power incidence. Furthermore, we find that the envelope of the difference value curve between the analytical solution and the numerical simulation can be described as a logarithmic function under different input powers. It is useful for further understanding the propagation properties of optical breathers in nonlocal nonlinear media and might be of interest to the applications in error analysis and precision measurements.

Stable solution of induced modulation instability

In this paper,we discussed the nonlinear evolution of modulation instability and the steady-state process of induced modulation instability in sine-oscillatory response nonlocal nonlinear media. With plane wave plus perturbation as initial conditions, we simulated the long-term evolution of modulation instability in the nonlocal nonlinear Schrodinger equation with sine-oscillatory response numerically. For the input of modulated wave, the approximate analytical solution of the stable solution of the equation is obtained under the assumption that only the fundamental wave and the first harmonic wave are present. For the input of modulated wave with arbitrary harmonic waves, we obtained the exact numerical solution of the stable solution of the induced modulation instability.

Dynamics engineering of spatial beams in nonlocal nonlinear media

We addressed the mobilities of spatial beams in nonlocal nonlinear media with the aid of the analogy to the particles described by Newtonian mechanics. Various dynamics for spatial beam are predicated by equivalent kinematic laws, including the harmonic vibrations due to the off-centered shifts, the circular and elliptical motions to the combination of off-centered shifts and initial phase chirps, which can be equivalently regarded as the Hooke's force and the transverse velocities in mechanics, respectively. By a purposive engineering of several beams, we can achieve a variety of rotating clusters, such as clusters with opposite rotating directions along different circular orbits and those exhibiting both revolving and spinning rotations simultaneously. The predications about dynamics of spatial beams are confirmed by the numerical simulations.

Asymmetric propagation of solitons in nonlinear media with gradual nonlocality

We investigate the propagation of solitons in homogeneous nonlocal nonlinear media and in media with gradual nonlinear nonlocality. We calculate the width and the maximum amplitude of solitons during propagation and demonstrate that solitons will propagate asymmetrically in the medium with gradual nonlinear nonlocality. Moreover, the propagation of solitons in the nonlinear medium with gradual nonlocality is independent of the forms of monotonically gradual nonlocalities. Finally, we investigate the ratio of width magnification quantitatively and demonstrate that the soliton with a particular input power maintains its width in one direction and suffers strong expansion in another direction.

Controlling effect of vector and scalar crossed double-Ma breathers in a partially nonlocal nonlinear medium with a linear potential

We follow our interest in a nonautonomous (2+1)-dimensional coupled nonlinear Schrodinger equation with partially nonlocal nonlinear effect and a linear potential, and get a relational expression mapping nonautonomous equation into autonomous one. Further applying the Darboux method, we find affluent vector and scalar solutions, including the crossed double-Ma breather solution. Regulating values of initial width, initial chirp and diffraction parameters so that the maximal value of accumulated time changes to compare with values of peak positions, we actualize the controlling effect of vector and scalar crossed double-Ma breathers including the complete shape, crest shape and nascent shape excitations in different linear potentials.

Instability suppression of vector vortex solitons in nonlocal nonlinear media

We studied the instability suppression of vector vortex solitons (VVS), comprised of two incoherently coupled vortices with different topological charges $m$ in thermal nonlocal nonlinear media with cylindrical symmetry. Using linear stability analysis, we found that the azimuthal instability of the higher-order ($|m|\ensuremath{\ge}3$) vortex can be suppressed and even eliminated because of the presence of the other lower-order ($|m|\ensuremath{\le}2$) vortex, including the fundamental beam. The VVS will be stable when the power ratio of the lower-order vortex exceeds a threshold. We also found that stable VVS exists in some combinational states with opposite-sign charges (${m}_{1}=\ensuremath{-}1$, ${m}_{2}\ensuremath{\ge}3$) when the two vortex components have equal Gaussian beam widths.

Controllable propagation path of imaginary value off-axis vortex soliton in nonlocal nonlinear media

Both imaginary value off-axis solitons and imaginary value off-axis vortex solitons are analytically obtained in nonlocal nonlinear media. The imaginary value off-axis solitons can do the snakelike propagations resulting from that the soliton phase $$\Theta $$ are period functions, and the propagation paths (including propagation directions and reverse points) of such solitons can be controlled by selecting the appropriate imaginary values b and c. Due to the position-changed vortex phase, the imaginary value off-axis vortex solitons revolve clockwise or counterclockwise along the controllable elliptical trajectories of different orientations depending on their imaginary off-axis shifts. The controllable vortexes may be used as optical tweezers and wrenches, and the controllable mass centers may have potential application in all-optical controlling.

Multi-pole solitons in nonlocal nonlinear media with fourth-order diffraction

This paper studies the existence and stability of solitons in nonlocal nonlinear media (NNM) with the fourth-order diffraction, and reveals that the coupling constant of the fourth-order diffraction plays a significant role in destabilizing the propagations of the solitons. Such as in the local nonlinear media, the fundamental solitons are stable in the low coupling constant domains, but cannot exist in the high coupling constant regions. For the exponential-decay response, the maximal number of peaks in stable multipole solitons are dipole and quadrupole in NNM with and without the fourth-order diffraction, respectively. For the Gaussian-shaped response, the solitons exhibit novel structures, where the inner humps of the tripole and quadrupole solitons decrease as the β decreases. The evolutions of solitons with perturbation are also investigated to confirm their stability.

Vectorial effect on the evolution of fractional-order vector vortex beams in a strongly nonlocal nonlinear medium.

Propagation of a vector vortex optical field (VVOF) with both fractional order of polarization topological charge $m$m and fractional order of vortex topological charge $n$n with spatially variant states of polarization (SoP) in a strongly nonlocal nonlinear medium (SNNM) is studied. The optical field always evolves reciprocally with a cycle of stretch and shrink in a SNNM with dark stripes forming at $z=t\pi {z_p}$z=tπzp ($t$t denotes an integer number, and ${{z}_p}$zp is a parameter that depends on the initial power of the VVOF and the material constant associated with the response function), as a result from the coherent superposition of the vortices with different order of topological charges and weighting coefficients. In particular, the conversions between linear and circular polarization components occur during propagation, and the converted SoP distributions in different propagation distances depend closely on the topological charges and the initial powers. The evolutions of the Stokes parameters of the fractional-order VVOF (FO-VVOF) during propagation in a SNNM show that the spatial distributions of different polarization components are closely related to the topological charges, the initial powers and the propagation distances, implying that the FO-VVOF can be regarded as a superposition of two different fractional-order vortices with orthogonal circular polarization components. These results provide new strategies on tailoring polarization states in a structured optical field with fractional topological charges.

Elliptic fundamental, dipole and vortex solitons in nonlocal nonlinear media with linear anisotropic diffraction

Elliptic fundamental, dipole and vortex solitons in nonlocal nonlinear media with linear anisotropic diffraction are investigated analytically and numerically. In particular we do this for the whole range of degrees of nonlocality. Analytical solutions for the solitons are obtained with the variational approach. The dynamics of elliptic solitons are also numerically demonstrated with the split-step Fourier transform method. With the help of linear anisotropic diffraction, stable elliptic fundamental and dipole solitons can be obtained. However, elliptic vortex solitons are always unstable and transfer into spiraling elliptic vortex solitons.

Spatiotemporal solitons in cold Rydberg atomic gases with Bessel optical lattices

A scheme is proposed to generate stable spatiotemporal solitons (STs) in a cold Rydberg atomic system with a Bessel Lattice (BL) potential, by utilizing electromagnetically induced transparency (EIT). We investigate the existence and stability of these three-dimensional (3D) STs supported by BL in nonlocal nonlinear media. The results show that the system can support slow STs with low light intensity. We also find that the BL strength and the degree of nonlocality of the nonlinearity, which can be tuned in the system, can be used to control these STs and their propagation behaviors.