Gap solitons in waveguide arrays.

Dark matter-wave gap solitons of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearities

We overview theoretical and experimental results on spatial optical solitons excited in arrays of nonlinear waveguides. First, we briefly summarize the basic properties of the discrete nonlinear Schrödinger (NLS) equation frequently employed to study spa

We review the theory of light localization due to the combined action of single or double Bragg coupling between dichromatic counterpropagating envelopes and parametric mixing nonlinearities. We discuss existence, stability, and excitation of such localized envelopes. We also investigate the link between stationary gap solitons and input-output response of nonlinear quadratic Bragg gratings. Frustrated transmission and multistable switching is expected to occur under suitable integrable (cascading) limits. Substantial deviations from these conditions lead to the onset of spatial chaos. (c) 2000 American Institute of Physics.

We elaborate a mechanism for the formation of stable solitons of the semi-vortex type (with vorticities 0 and 1 in their two components), populating a finite bandgap in the spectrum of the spin-orbit-coupled binary Bose-Einstein condensate with the Zeeman splitting, in the two-dimensional free space, under conditions which make the kinetic-energy terms in the respective coupled Gross-Pitaevskii equations negligible. Unlike a recent work which used long-range dipole-dipole interactions to construct stable gap solitons in a similar setting, we here demonstrate that stable solitons are supported by generic local interactions of both attractive and repulsive signs, provided that the relative strength of the cross/self interaction in the two-component system does not exceed a critical value ~ 0.77. A boundary between stable and unstable fundamental 2D gap solitons is precisely predicted by the Vakhitov-Kolokolov criterion, while all excited states of the 2D solitons, with vorticities (m, 1 + m) in the two components, m = 1, 2, ..., are unstable. The analysis of the one-dimensional (1D) reduction of the system produces an exact analytical solution for the family of gap solitons which populate the entire bandgap, the family being fully stable. Motion of the 1D solitons in the trapping potential is considered too, showing that their effective mass is positive or negative if the cubic nonlinearity is attractive or repulsive, respectively.

Dark solitons are often overshadowed by bright solitons when optical solitons are discussed, perhaps because they have proven more difficult to control and utilize. Whereas a single bright soliton is formed by a simple packet of light, a dark soliton requires a phase difference between two parts of the packet. The extra effort of controlling the phase, however, allows new and unexpected opportunities. For example, arrays of two-dimensional vortex solitons having no bright soliton analogy are possible. When used as bits of information, dark solitons may be more closely spaced than bright solitons in a one-dimensional system. What is more, dark solitons may, in principle, be observed in weakly nonlinear media because there is no threshold intensity. When consideration is given to light-controlling-light, dark solitons have the advantage that a bright signal may be guided or modulated in a dark region. Dark spatial solitons have been mostly investigated in nonlinear refractive media [1], although they have recently been reported in photorefractive media under a voltage bias.

In this paper, we mainly simulate the characteristics of the ground state dark soliton and the multipole dark soliton in the nonlocal and cubic-quintic nonlinear medium. Firstly, the influences of the degree of nonlocality on the amplitude and the width of the dark soliton in the self-defocusing cubic-and self-focusing quantic-nonlinear medium are studied. Secondly, we find the nonlinear parameters affecting the amplitude values of solitons, but the refractive index induced by the light beam is always a fixed value. The numerical results show that the ground state dark soliton can be propagated stably alone the z axis, and the stable states of the dipole soliton and the dark tri-pole and quadru-pole solitons are stable. However, some quadru-pole dark soliton is unstable after propagating the remote distance. Furthermore, we also discuss the characteristics of the ground state dark soliton and the dark dipole soliton in the local cubic-nonlinear and nonlocal quantic nonlinear media. Both the amplitude and the beam width of the dark ground state soliton and dark dipole soliton are also affected by the degree of nonlocality and nonlinearity. Two boundary values of the induced refractive index change with the variations of the three nonlinear parameters. The dark soliton and the dipole dark soliton are more stable in the self-focusing cubic nonlinear and the nonlocal self-defocusing quantic nonlinear medium than those in the self defocusing cubic nonlinear and nonlocal self-focusing quantic nonlinear medium. The powers of single dark soliton and dark tri-pole soliton decrease monotonically with the increase of propagation constant when the cubic-quintic nonlinearities are certain values and these degrees of nonlocalities are taken different values. Furthermore, we also analyze linear stabilities of various nonlocal spatial dark solitons. And we find that the dipole dark soliton is unstable when the propagation constant is in the region[-0.9,-1.0]. These properties of linear stabilities of other multi-pole dark solitons are the same as their propagation properties.

Guiding and switching by quasi -2D dark spatial solitonsD. Neshev*, A. Dreischuh*, S. Dinev*, L. WindholzTechnical University Graz, Institute ofExperimental PhysicsPetersgasse 16, A-8010 Graz, Austria* permanent address: Sofia University, Department of Quantum Electronics5, J. Bourchier Blvd., BG-1 164 Sofia, BulgariaABSTRACTVariable number of quasi-2D dark spatial solitons of adjustable transverse velocities could be generated by a properchoice of the initial phase profile (odd/even) and width of crossed dark stripes and the background-beam intensity. Thepossibility to branch single input probe beam into ordered structures of subbeams is demonstrated numerically in bulkself'induced-defocusing Kerr nonlinear media.Keywords: nonlinear optics, dark optical solitons, beam guiding, beam branching1. INTRODUCTIONThe dark spatial optical solitons form a specific class of self-supported beams for which the diffraction is compensatedby the beam's self-action in media of negative nonlinearities [1,2J. Because of the negative nonlinear refractive indexcorrection the refractive index itself appears lower in the Dark Spatial Soliton (DSS) wings as compared to this in thevicinity of the intensity-dip. As a consequence, the DSSs should obey guiding properties [3,4]. The same should hold alsofor a quasi-2D DSS formed by two crossed fundamental 1D Odd Dark Spatial Solitons (ODSSs) [5].Characteristic for the 1D black ODSS is the abrupt it-phase shift at the zero-intensity position [2,6J. ffthe phase-jump

The one-particle type temporal soliton exists by maintaining a balance between dispersive linear contributions on the one hand and non-linear effects on the other. The linear contributions occur from processes such as group velocity and polarization mode dispersion. The nonlinear features occur from Kerr, or power law non-Kerr behavior. In addition, a variety of perturbations, such as damping, Brillouin scattering, and Raman effects exist to alter the simple soliton solution. In this paper, we review the propagation of temporal solitons in power law non-Kerr media. This is developed through the higher nonlinear Schroedinger's equation (HNLSE). Also, the fundamentals of multiple-scales are presented that will be used to yield quasi-stationary solitons when perturbations are present. In waveguides, the one-particle type spatial soliton exists by maintaining a balance between the linear propagational diffraction and non-linear self-focusing, while possibly being subjected to a variety of perturbations. Here, we use a spatial optical soliton solution to the nonlinear Schroedinger equation in an inhomogeneous triangular refractive index profile as a small index perturbation to illustrate the oscillation property within a two dimensional waveguide. We determine, from the motion of spatial soliton, its effective acceleration, period of oscillation, and compare results with the Gaussian refractive index profile. Such spatial solitons behave as point masses existing in a Newtonian gravitational potential hole.

The coherent manipulation and control of bright and dark solitons through sodium atomic medium have been investigated in this manuscript. Dark soliton is reported for reflection and bright soliton is reported for transmission pulses with variation in position and driving field parameters through sodium atomic medium. Further the transmission pulse is periodic dark and bright solitonic behaviors and reflection pulse is periodic bright solitonic behavior with variation in the incident angle and Rabi frequency of the control field. Elliptical dark and bright solitons as well as breather types solitons are also investigated for reflection and transmission pulses. The dark soliton in reflection is due to slow light propagation and bright soliton is obtained due to fast light propagation of transmission through the medium. The modified results of the dark and bright solitons are useful for telecommunication and ultra-fast signal routing system.

We investigate analytically and numerically propagation and spatial localization of light in nonlocal media with competing nonlinearities. In particular, we discuss conditions for the modulational instability of plane waves and formation of spatial solitons. We show that the competing focusing and defocusing nonlinearities enable coexistence of dark or bright spatial solitons in the same medium by varying the intensity of the beam.

A nonlinear, coupled, magneto-optic waveguide system supporting bright and dark spatial solitons is investigated to determine the stability and possible application of the resulting bright-dark soliton dynamics. An extensive variational analysis is verified by full numerical simulations. It is discovered that the stability of the magneto-optic coupled states can be exploited to give guaranteed isolator functionality, which could lead to very robust component protection in monolithic integrated circuits.

A novel temporal dark-bright solitons conversion system via an add/drop filter for signal security use

It is predicted that the fundamental spatial solitons, namely bright, dark, and gray solitons associated with photoisomerization, can be formed stably except for antidark solitons. The soliton solutions and the relative properties of these solitons are given in detail. Incoherently coupled bright-dark soliton pairs are also investigated. Both the cases indicate that although the formation of a spontaneous bright soliton based on photoisomerization is impossible, it is, however, possible to form a bright soliton with the joining of a background light or the coupling of another dark soliton. The results provide possible methods of controlling a light with another light.

Gap solitons in a model of a superfluid fermion gas in optical lattices

Self-trapping of light beams in nonlinear self-focusing Kerr media has been explored intensively during the last three decades. The self trapped beams, often in the form of spatial solitons, evolve from nonlinear changes in the refractive index (δn) of the material proportional to the intensity distribution of the light, when the confining effect of the refractive index exactly compensates for the defocusing effect of diffraction. Motivated by experimental results of self-focusing of light beams [1] in the presence of the optical Kerr effect, a theoretical solution for the resulting spatial solitons was found [2,3]. This was followed by demonstrations of self-trapping in vapors [4], liquids [5], and finally, in the last few years, spatial solitons in solid (glass) media [6]. However, the index changes needed for optical-Kerr spatial solitons require high intensities, often exceeding 1 MWatt/cm2. Several other materials, such as slightly-absorbing liquids, exhibit Kerr-like thermal nonlinearities at much lower power densities (Watts/cm2), typically with a negative δn. These materials enabled the observations of dark spatial solitons [7] (narrow dark “notches”) and optical vortex solitons [8,9] (dark solitons were also observed using optical-Kerr nonlinearities in ZnSe [10] at GWatt/cm2 power densities). The most distinct properties of all these Kerr-like solitons are (i) a strong intensity dependence and the existence of a power threshold, and (ii) stability of bright solitons only in a single transverse dimension (consequently, bright Kerr-type solitons can be observed only in a planar waveguide, otherwise the soliton becomes unstable and cannot be observed).KeywordsDark SolitonInput BeamBright SolitonSpatial SolitonPhotorefractive CrystalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.