Evolution and Stability of Dark Holographic Solitons in Photorefractive Dissipative Systems

The dynamics evolution of dark holographic solutions in a dissipative system is investigated numerically provided that the double balance, i.e. diffraction is balanced by nonlinearity and loss is balanced by gain, is satisfied. The influence of the system parameters, such as the linear loss of the crystal, the external biased field and the angel between input beams, on the stable propagation of soliton beams is discussed numerically. Results show that such solitons can be easily amplified or absorbed by adjusting these system parameters. Furthermore, numerical simulations indicate that dissipative dark holographic solitons are stable for small perturbation on amplitude.     

Vibrating and shaking soliton pairs in dissipative systems

We show that two-soliton solutions in nonlinear dissipative systems can exist in various forms. As with single solitons, they can be stationary, periodic or chaotic. In particular, we find new types of vibrating and shaking soliton pairs. Each type of pair is stable in the sense that the bound state exists in the same form indefinitely.     

Stability of non-degenerate parametric soliton in quadratic media

The non-degenerate solitons due to three-wave mixing in a quadratic medium are analyzed. A new stability criterion for these solitons is found and verified numerically. The influence of the non-paraxial terms on the instability threshold is also discussed.     

Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices

We demonstrated that linearly and nonlinearly amplitude-modulated (chirped) harmonic lattices can support odd and even solitons in both focusing and defocusing saturable media. The modulated lattice modifies the profiles and enlarges the stability domains of solitons, comparing with the unchirped one. Twisted solitons, or “soliton trains” whose profiles exhibit multi-peak structures can also be supported by linearly and nonlinearly chirped lattices. In sharp contrast with periodic lattices, chirped lattices remarkably broaden the existence and stability domains of twisted solitons, especially for solitons with more components. While even solitons in focusing media and twisted solitons in defocusing media are unstable, odd and twisted solitons in focusing media are stable in relatively wide parameter windows. Chirped lattice can be used as a linear guidance to realize the oscillation of solitons which is impossible in unchirped lattice.     

Self-Deflection of Dark Screening Spatial Solitons Based on Higher-Order Space Charge Field

The effects of higher-order space charge field on the self-deflection of dark screening spatial solitons in biased photorefractive crystals are numerically investigated under steady-state conditions. The expression for an induced space-charge electric field including higher-order space-charge field terms is obtained. Numerical results indicate that dark solitons possess a self-deflection process during propagation, and the solitons always bend in the direction of the c axis of the crystal. The self-deflection of dark solitons can experience considerable increase especially in the regime of high bias field strengths.     

Quasi-two-dimensional dark spatial solitons and generation of mixed phase dislocations

This paper presents experimental evidence that orthogonally crossed dark soliton stripes form quasi-two-dimensional spatial solitons with a soliton constant equal to that of singly charged optical vortices. Besides the pairs of oppositely charged optical vortex solitons, the snake instability of the dark formation at moderate saturation is found to lead to generation of steering mixed edge–screw phase dislocations with zero total topological charges. Received: 26 October 1998 / Revised version: 19 January 1999 / Published online: 12 May 1999     

Defect vector gap solitons in photonic lattices

The existence and general properties of different kinds of defect vector gap solitons in one dimensional optically induced photonic defect lattice with focusing saturable nonlinearity in photorefractive crystal are analyzed. The defect is well localized in a single site with two existence forms, namely repulsive and attractive defect. Propagation constants of two beams that compose defect vector gap solitons could be from same gap or from different gaps. We show that some kinds of unstable scalar defect gap solitons could be stabilized by their corresponding vector cases.     

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.     

Gray spatial solitons in biased two-photon photovoltaic photorefractive crystals

This paper predicts that gray spatial solitons can exist in biased two-photon photovoltaic photorefractive crystals. Under appropriate conditions and in the steady state, the gray spatial solitons solution of the optical evolution equation is obtained. The properties associated with these solitons, such as their intensity profile, intensity full width at half-maximum, width, transverse velocity and phase distribution, are discussed as functions of their normalized intensity and degree of “grayness”. Relevant examples are provided.     

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.     

Waveguides induced by steady-state gray solitons in biased photorefractive-photovoltaic crystals

We carry out a theoretical investigation of the properties of waveguides induced by photorefractive one-dimensional steady-state gray spatial solitons (i.e., screening solitons, photovoltaic solitons, and screening-photovoltaic solitons). We demonstrate that waveguides induced by photorefractive steady-state gray spatial solitons are only a single guided mode for both all soliton graynesses and all values of ρ, where ρ is the ratio between the soliton peak intensity and the dark irradiance, and moreover, waveguides induced by gray photovoltaic solitons for closed-circuit condition are also only a single guided mode for all electric current densities. We find that the confined energy near the center of a photorefractive steady-state gray spatial soliton increases with ρ and decreases with an increase in the soliton grayness. We also find that the confined energy near the center of a gray photovoltaic soliton for closed-circuit condition increases with the electric current density. On the other hand, waveguides induced by gray screening-photovoltaic solitons are gray screening soliton-induced waveguides when the bulk photovoltaic effect is neglectable and are gray photovoltaic soliton-induced waveguides when the external bias field is absent.     

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.     

Rotating surface soliton complexes in annular waveguides

We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a π-phase difference between neighboring spots. It is shown that the multipole-mode solitons can rotate steadily upon propagation, and the existence domain is strongly affected by the rotation frequency. The rotation may enhance the stabilization of surface multipole-mode solitons.     

Surface defect gap solitons in superlattices with self-defocusing nonlinearity

We put forward the existence and stability of defect surface gap solitons at the interface between uniform media and an superlattice with self-defocusing nonlinearity. We reveal that the defect plays the significant role in controlling the region of solitons existing. Various solitons are found to be existed in different gaps for different defects. For positive defects, fundamental solitons can exist stably in the semi-infinite gap, and dipole solitons can exist stably in the first gap but they are unstable in the second gap. For zero or negative defects, fundamental and dipole solitons can exist stably in the first gap and the second gap, respectively.     

Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-harmonic generation in photonic crystal fibers

We use cross-correlation frequency-resolved optical gating to obtain spectral-temporal portraits of ultrashort Raman solitons in photonic crystal fibers at telecommunication wavelengths. Power-dependent Raman frequency shifts of 200 nm in 63 mm of fiber are observed accompanied by spectral broadening and 2.5-times soliton compression. Complete time-frequency dynamics at the fundamental wavelength thus visualized enables us to explain the details of the intermodally phase-matched third harmonic generation by the propagating solitons.This revised version was published online in August 2005 with a corrected cover date.     

Discrete light bullets in two-dimensional photonic lattices: Collision scenarios

We report systematic results of collisions between discrete spatiotemporal optical solitons in two-dimensional photonic lattices. We show that the outcomes of collisions strongly depend on the initial soliton parameters, such as their input amplitudes (energies) and their transverse velocities. Four generic outcomes are identified in the study of collisions between discrete light bullets located in the corner, at the edge, and in the center of the photonic lattice: (a) merger of both low and high amplitude solitons into a single one, at small values of the kick parameter (soliton transverse velocity), (b) spreading of low amplitude solitons at intermediate values of the kick parameter, (c) bouncing of high amplitude solitons at intermediate values of the kick parameter, which is accompanied by a sharp modification of input soliton transverse velocities, and (d) quasi-elastic (symmetric) interactions of both low and high amplitude solitons at large values of the kick parameter.     

Two-Dimensional Laguerre--Gaussian Asymmetric Soliton Family in Strongly Nonlocal Media

We demonstrate the existence of a broad class of higher-order Laguerre Gaussian asymmetric spatial optical solitons in strongly nonlocal nonlinear media. Furthermore, we discuss specific values （q = 0） of the modulation depth parameter for different rational values of the topological charge in detail. Our results show that higherorder asymmetry spatial sofiton family can exist in various forms, such as two-dimensional defect haff-solitons, asymmetric single-layer and multi-layer necklace solitons.     

Solitary Wave Evolution of Optical Planar Vortices in Self-Defocusing Photorefractive Media

Solitary wave evolution of optical planar vortices in isotropie self-defoeusing photorefractive media is investigated in detail. We demonstrate that the formation of a planar vortex soliton intensively depends on the diameter and maximum intensity of the input vortex Seam. The exact solutions of planar vortex solitons are obtained due to the Petviashvili iteration method. It is found that, with the increasing soliton maximum intensity, the soliton core will be gradually diminished to a minimum value.     

Interaction of incoherent white-light solitons

We study numerically the formation and interactions of incoherent white-light solitons in a nonlinear media with logarithmic saturable nonlinearity based on the coherent density approach. We find that not only the formation but also the interactions of incoherent white-light solitons are fundamentally a collective effect, where all the frequencies participate in the process, and self-adjust their respective contributions to the formation and interactions. We find that the interactions of incoherent white-light solitons in logarithmic media are always attractive.     

Eigenvalues of the Zakharov-Shabat scattering problem for two separated sech-shaped pulses

It is shown that the initial condition of two separated sech-shaped in-phase pulses in the nonlinear Schrödinger equation, may give rise to not only stationary solitons, but also symmetrically separating solitons, provided the initial distance of separation is large enough. The critical distance between the pulses for which a separating soliton pair can be found for certain amplitudes is derived using a variational approach.