Dark spatial solitons constructed from modes of linear waveguides

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

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.

We numerically simulate the evolution of the dark-notch-bearing optical beam in the logarithmically saturable nonlinear media based on beam propagation method (BPM). The simulation results indicate that the multiple dark spatial solitons are deep, possible in this type of nonlinear media. The number of multiple dark spatial solitons depends on the width of the dark notch, the initial conditions and the peak intensity of the initial input beam. Under the odd and even initial conditions, the odd and even number sequence of multiple dark spatial solitons can be obtained, respectively. For an input beam with fixed optical intensity, the number of dark solitons increases with the width of the initial input dark notch. The behavior of the multiple dark solitons in this type of media is similar to that in a photorefractive nonlinear crystal.

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.

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.

In the wavelength range shorter than the zero group dispersion point where k!’ is positive, the soliton solution does not exist. However, even in this range of wavelengths, the portion without light, which is produced by chopping a continuous light wave, is known to form a soliton. Such a soliton solution is often called a dark soliton. Dark solitons also appear in space called spatial dark solitons. Spatial dark solitons have interesting applications in the switching and guiding of light beams. We present here. the theoretical and experimental properties of a dark soliton both in time and space.

By using multiple-scale method，we analytically study the nonlinear dynamical properties of an electromagnetically induced transparency medium with three-level atoms and a strong coupling light field. It is shown that a weak probe light beam can form spatial weak-light dark solitons. When it propagates along axial direction，the dark soliton will transforms into a steady spatial weak-light ring dark soliton，which results from the balance of the interplay between beam diffraction and refractive nonlinearity.

The existence of dark and gray spatial solitons in logarithmically nonlinear media is investigated. It is shown that both dark and gray solitons are possible in corresponding nonlinear media. The spatial width for dark solitons is analyzed .It is revealed as follows: the beam width decreases dramatically with increasing power when the peak power is much lower, exhibiting the good nonlinear effects in such cases. The variation of beam width is slow at first and then becomes constant when the peak power continuously increases .

Optical channel waveguides formed by upconverted photobleaching of dye-doped polymer film in regime of dark spatial soliton

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.

We study the evolution of dark spatial solitons by chi((2)): chi((2)) cascaded nonlinearity. The generation and evolution of solitons pairs by the optical branching effect is investigated. It is shown that the number of solitons pairs and the transverse velocity of a given pair depend on the parameters of the input beam. We also investigate the hollows generated in a beam with a uniform background when the two sides of the input beam have various phase difference. It is concluded that dark spatial solitons by chi((2)): chi((2)) cascaded nonlinearity have analog performance compared with that in chi((3)) defocusing Kerr media.

We study analytically and numerically the effect of perturbations on (spatial and temporal) dark optical solitons. Our purpose is to elaborate a general analytical approach to describe the dynamics of dark solitons in the presence of physically important effects which break integrability of the primary nonlinear Schr\"odinger equation. We show that the corresponding perturbation theory differs for the cases of constant and varying backgrounds which support the dark solitons. We present a general formalism describing the perturbation-induced dynamics for both cases and also analyze the influence of several physically important effects, such as linear and two-photon absorption, Raman self-induced scattering, gain with saturation, on the propagation of the dark soliton. As we show, the perturbation-induced dynamics of a dark soliton may be treated as a result of the combined effect of the background evolution and internal soliton dynamics, the latter being characterized by the soliton phase angle. A similar approach is applied to the problem of the dark-soliton propagation on a finite-width background. We analyze adiabatic modification of a dark pulse propagating on a dispersively spreading finite-width background, and we prove analytically that a frequency chirp of the background does not affect the soliton motion. As a matter of fact, the results obtained describe the perturbation-induced dynamics of dark solitons in the so-called adiabatic approximation and, as we show for all the cases analyzed, they are in excellent agreement with direct numerical simulations of the corresponding perturbed nonlinear Schr\"odinger equation, provided the effects produced by the emitted radiation are small.

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.

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

It is known that optical beams can propagate unchanged in the form of self-guided waves or spatial optical solitons due to compensation of the beam diffraction by nonlinearity-induced change in the material refractive index [1]. Many of the properties of spatial optical solitons, including the stability analysis [2] and the inverse scattering technique [3], are unique for the Kerr materials when the nonlinear part of the refractive index nnl(I) depends linearly on the light intensity I, nnl(I) = n2I, where n2 is the so-called Kerr coefficient. However, since the first efforts to observe self-guidence and spatial solitons experimentally, in applications one deals with non-Kerr materials where the dependence nnl(I) is not linear, e.g. it saturation. Recently it has been also shown, theoretically and experimentally, that self-guided beams can be observed in crystals with a strong photorefractive effect [4] and also due to phase-matched parametric interactions in a χ(2) nonlinear medium [5,6]. In many cases, propagation of nonlinear waves in such non-Kerr materials are described by the nonlinear Schrödinger with a more general dependence of the refractive index on the beam intensity. The main purpose of this talk is to present a panoramic overview of different properties of solitary waves in nonKerr materials including the detailed discussion of the stability of (scalar and vector) bright and dark solitons and the soliton coupled states.