Soliton switching in inhomogeneous nonlocal media

We address a simple way to achieve routing of optical spatial solitons via soliton interactions in the inhomogeneous nonlocal media. We reveal that the variation of the nonlocality disturbs the solitons pairs and splits them into two individual solitons which have the same escape angle but opposite deflection directions. In particular, the escape angle monotonically increases with the increase of the nonlocality variation rate. We demonstrate that the soliton pairs could form self-consistent waveguides that are able to controllably guide a weak signal by any output positions.     

Incoherent solitons in strongly nonlocal media: The coherent density theory

We study the properties of one dimension incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. Following the coherent density theory, we obtain an exact solution of such incoherent solitons. The spatial width of the incoherent solitons is related to the incoherent angular power spectrum θ₀ as well as the incident power. The evolution properties of the intensity profile and the coherence characteristics are also discussed in detail when the solitons undergo periodic harmonic oscillation.     

Propagation and interaction of beams with initial phase-front curvature in highly nonlocal media

In this paper, an exact Gaussian solution with initial phase-front curvature for the 1 + 2D Snyder–Mitchell linear model is presented. It is found that the propagation of the beam in bulk strongly nonlocal media is deeply affected by the initial phase-front curvature, which can cause the pulsating behavior of Gaussian beam, and lead to the occurrence of the periodic interference pattern during the interaction of two Gaussian beams. It is useful for further understanding the properties of optical beam in strongly nonlocal media and may be applied to precision measurement.     

Nonautonomous “rogons” in the inhomogeneous nonlinear Schrödinger equation with variable coefficients

The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schrödinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained solutions can be used to describe the possible formation mechanisms for optical, oceanic, and matter rogue wave phenomenon in optical fibres, the deep ocean, and Bose-Einstein condensates, respectively. Moreover, the snake propagation traces and the fascinating interactions of two nonautonomous rogons are generated for the chosen different parameters. The obtained nonautonomous rogons may excite the possibility of relative experiments and potential applications for the rogue wave phenomenon in the field of nonlinear science.     

Optical vortices in self-focusing Kerr nonlinear media

In this work we numerically compare the interaction of optical vortices (OVs) in self-defocusing and self-focusing Kerr nonlinear media. We find that the basic scenarios (attraction/repulsion, translation/rotation vs. background) in the interaction of two and three vortices with equal and alternative topological charges (TCs) are the same in both media. However, the vortex dynamics under self-focusing conditions is influenced by the reshaping of the surrounding part of the background. Square structure of OVs with alternating TCs is found to be stable with respect to the vortex positions in self-focusing media. This elementary cell is successfully generalized in a large square array of OVs with alternative TCs which brings ordering in the multiple filamentation of the background beam in self-focusing conditions.     

Incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media

We theoretically investigate the propagation of incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media. It is found that multipole-mode soliton pairs with arbitrary different orders of Hermite-Gaussian shape can exist when the total power of two beams equals the critical power and the ratio of the beam widths for the Gaussian part is inversely proportional to the square root of the ratio of the wave numbers. When the total power does not equal the critical power, the Hermite-Gaussian breather pair exists and their beam widths evolve analogously. For general cases where the ratio of the beam widths is arbitrary, soliton-breather pairs or breather-breather pairs can be formed and their beam widths evolve synchronously in-phase or out-of-phase. Numerical simulations directly based on the nonlocal nonlinear Schrödinger equation are conducted for comparison with our theoretical predictions. The numerical stability analysis shows the higher-order Hermite-Gaussian solitons can not be stable for small nonlocality or for some media like liquid crystals.     

Two-dimensional spatial solitons in highly nonlocal nonlinear media

We investigate, analytically and numerically, a class of novel higher-order spatial solitons in two transverse-dimensions, in highly nonlocal nonlinear media. The stability of these solutions in propagation is confirmed by direct numerical simulation. Our results demonstrate that the higher-order spatial solitons in highly nonlocal nonlinear media can exist in various forms, such as the fundamental solitons, vortex-ring solitons, multipole solitons, and fractional solitons.     

Kummer solitons in strongly nonlocal nonlinear media

We solve the three-dimensional (3D) time-dependent strongly nonlocal nonlinear Schrödinger equation (NNSE) in spherical coordinates, with the help of Kummer's functions. We obtain analytical solitary solutions, which we term the Kummer solitons. We compare analytical solutions with the numerical solutions of NNSE. We discuss higher-order Kummer spatial solitons, which can exist in various forms, such as the 3D vortex solitons and the multipole solitons.     

Multiwavelength fiber laser with ultradense wavelength spacing based on inhomogeneous loss with assistance of nonlinear polarization rotation

We demonstrate a multiwavelength fiber laser with ultradense wavelength spacing and ultrabroad bandwidth based on inhomogeneous loss mechanism with assistance of nonlinear polarization rotation. The inhomogeneous loss, implemented by incorporating a section of highly nonlinear fiber (HNLF) and a Sagnac filter in the laser cavity, can balance mode competition in erbium-doped fiber and result in ultradense multiwavelength generation. The bandwidth of the multiwavelength spectrum is greatly broadened owing to the intensity-dependent loss induced by nonlinear polarization rotation. Stable multiwavelength lasing with wavelength spacing of 0.08 nm and wavelength number up to 254 is achieved at room temperature. Moreover, multiwavelength tuning is realized through modifying polarization-dependent cavity loss.     

All-optical switch and limiter based on nonlinear polarization in Mach-Zehnder interferometer coupled with a polarization-maintaining fiber-ring resonator

A novel all-optical switch based on nonlinear polarization mechanism using polarization-maintaining fiber ring with a polarization rotator is proposed. Optical switching with low threshold of mW order and optical limiting with broader limiting range, less fluctuation, higher damage threshold and response speed are demonstrated numerically. The deterioration of switching and the improvement of limiting originating from losses are also studied. Considering the tradeoff between switching power and bandwidth, the way to increase bandwidth is discussed.     

Azimuthal modulational instability of vortices in the nonlinear Schrödinger equation

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady-state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS. We briefly show how to extend the method to encompass nonlocal nonlinearities that tend to stabilize such solutions.     

Non-quantum liquefaction of coherent gases

We show that a gas-to-liquid phase transition at zero temperature may occur in a coherent gas of bosons in the presence of competing nonlinear effects. This situation can take place in atomic systems like Bose-Einstein condensates in alkali gases with two-body and three-body interactions of opposite signs, as well as in laser beams which propagate through optical media with Kerr (focusing) and higher order (defocusing) nonlinear responses. The liquefaction process takes place in the absence of any quantum effect and can be formulated in the framework of a mean field theory, in terms of the minimization of a thermodynamic potential. We study from a thermodynamic point of view all the stationary solutions of the cubic-quintic nonlinear Schrödinger equation which describes our system. We show that solitonic localized solutions connect the gaseous and liquid phases. Furthermore, we also perform a numerical simulation in the presence of linear gain and three-body recombination where a rich dynamics, including the emergence of self-organization behavior, is found.     

Elliptic incoherent spatial solitons and their interactions in strongly nonlocal media with an anisotropic nonlocality

We investigate the propagation and interaction of elliptic incoherent spatial solitons (EISS) in strongly nonlocal kerr media with an anisotropic nonlocality based on the coherent density approach. An exact analytical solution of such EISS is obtained; the results show that such EISS can form with both isotropic and anisotropic coherence. Moreover, we find that the interaction properties of EISS are very similar to that of their coherent counterpart. Some numerical examples are presented and pertinent physics features are addressed.     

Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates

We study the properties of the ground state of nonlinear Schrödinger equations with spatially inhomogeneous interactions and show that it experiences a strong localization on the spatial region where the interactions vanish. At the same time, tunneling to regions with positive values of the interactions is strongly suppressed by the nonlinear interactions and as the number of particles is increased it saturates in the region of finite interaction values. The chemical potential has a cutoff value in these systems and thus takes values on a finite interval. The applicability of the phenomenon to Bose-Einstein condensates is discussed in detail.     

Incoherently coupled vector dipole soliton pairs in nonlocal media

We investigate the incoherently and strongly coupled Manakov vector dipole soliton pairs in nonlocal nonlinear media. We use variational approach, to describe analytical properties of these solutions in a strongly nonlocal regime. We show that the presence of fundamental component improve stability of the dipole nonlocal soliton. In the limit of highly nonlocal nonlinearity, the evolution behaviors of the vector solitons is determined by their total power.     

A tunable nonlinear optical loop mirror with feedback using linear highly birefringent fiber in the loop

The dynamics of a nonlinear optical loop mirror (NOLM) with feedback using a high birefringence fiber in the loop are investigated. The effect of rotating input polarization angle on the output power and polarization angle is numerically examined, illustrating the sensitivity of the NOLM with feedback to the input’s polarization state, as well as the polarization chaos present with sufficient input powers. The inclusion of a polarization-dependant loss in one or both arms of the coupler is also shown to change the output dynamical behaviour of the system.     

Interaction of nonlocal incoherent spatial solitons

We investigate numerically the interaction of nonlocal incoherent spatial solitons in strongly nonlocal kerr media based on the coherent density approach. Numerical simulations show that the incoherent soliton position is very similar to the case of coherent soliton, and show that the incoherence plays an important role in the soliton interaction, while the role of other parameters such as the phase difference, the separation, the extent of nonlocality and the input power play in the interaction is very similar to the case of nonlocal coherent soliton. Some interesting numerical examples are presented to illustrate their interaction behavior further. Pertinent physics features are addressed.     

Temporal behavior of dark spatial solitons in closed-circuit photovoltaic media

We show that the time-dependent nonlinear wave equation in closed-circuit photovoltaic media can exhibit quasi-steady-state and steady-state spatial solitons. We demonstrate that the formation time of open-circuit quasi-steady-state and open-circuit steady-state dark solitons decreases with an increase in the intensity ratio of the soliton, which is the ratio between the soliton peak intensity and the dark irradiance. We find that for the time-dependent nonlinear wave equation that exhibits only an open-circuit steady-state dark soliton, changing the electric current density J₀ does not generate quasi-steady-state dark solitons and affects the formation time of steady-state dark solitons and that for the time-dependent nonlinear wave equation that exhibits an open-circuit quasi-steady-state dark soliton, changing J₀ gives rise to three different time evolution regimes of the full width half maximum of the soliton’s intensity. The first regime shows that the formation time of steady-state dark solitons increases with J₀ whereas the formation time of quasi-steady-state dark solitons is independent of J₀. The second regime shows that the formation time of steady-state dark solitons decreases with an increases in J₀ and the formation time of quasi-steady-state dark solitons increases with J₀. The third regime shows that changing J₀ enables only steady-state dark solitons in the time-dependent nonlinear wave equation, of which the formation time increases with J₀.     

Topological solitons and Bloch oscillations in Bose-Einstein condensate

We studied the evolution of topological solitons in the space of its width d and the conjugated momenta l during Bloch oscillations. The unstable solitons are confined in a well with its boundary as four branches of a hyperbola, the stable solitons sit at the four branches of the hyperbola (d · l = 28) which is in agreement with the generalized Heisenberg uncertainty principal Δd · Δl ? Const. The generation, annihilation, and bifurcation of solitons is going on in the well. In studying the behavior of the nonlinear interaction parameter for the stable solitons, it is found that bright solitons and dark solitons alternatively come into action during the breakdown and revival of Bloch oscillations.