Spatial bright–dark soliton steering through waveguide coupling

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.

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 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.

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 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.

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.

Summary form only given. It is well known that bright solitons exist in fibers with anomalous group-velocity dispersion while normal dispersion fiber supports dark solitons. Today dispersion-managed fibers are widely used, and it has been shown that bright solitons, if somewhat modified, exist in such fibers. This is certainly true for path-averaged anomalous dispersion, but it even holds for path-averaged normal dispersion. We have shown just recently that the converse is true for dark solitons: it is not so surprising that they exist for path-averaged normal dispersion but they also exist for path-averaged anomalous dispersion. There is thus an overlap of the stability ranges of dark and bright solitons. This gives us now the opportunity to discuss interactions between dark and bright solitons in one and the same dispersion map. We will here demonstrate a bound state in which a dark soliton is locked between two bright solitons.

Breaking with convention, we construct dark self-guided modes (spatial solitons) from known modal solutions of linear waveguides through a self-consistency procedure rather than by solving a nonlinear differential equation. This approach leads to a physical picture of dark spatial solitons and their analytical representation on the basis of reflectionless plane-wave scattering from a linear dielectric waveguide. The picture applies to solitons of arbitrary cross section propagating within a medium whose refractive index has an arbitrary dependence on intensity. Examples include the first reported dark spatial solitons of a threshold nonlinearity, revealing multiple- and higher-order solitons and a new simple expression for the field of a dark soliton in a Kerr medium.

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.

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.

Soliton explosion is an extremely pulsating behavior of the bright dissipative soliton (DS) in ultrafast lasers. By numerical simulation, we find that the dark soliton (DAS) can coexist with the bright soliton during the exploding process. The collapsed temporal structure of the exploding soliton is induced by the DASs. We reveal the birthing, evolving, and decaying of the DASs inside the bright DS. The time-frequency analysis of the exploding soliton helps us better understand the temporal and spectral structures of the exploding soliton, which might be useful for real-time spectroscopy of the coexisting dark and bright solitons during the soliton explosion.

We show experimentally the existence of bright and dark spatial solitons in semiconductor resonators for excitation above the bandgap energy. These solitons can be switched on, both spontaneously and with address pulses, without the thermal delay found for solitons below the bandgap that is unfavorable for applications. The differences between soliton properties above and below gap energy are discussed.

Under investigation in this paper is a variable-coefficient $$(2+1)$$ dimensional Heisenberg ferromagnetic spin chain equation. Bilinear forms for the bright and dark soliton solutions are respectively obtained. Bright and dark solitons are obtained via the Hirota bilinear method. Features of the bright and dark solitons are discussed. Interaction properties of the bright and dark solitons are discussed via the asymptotic analysis, and stability of the bright and dark solitons is studied via the numerical calculation: (1) Amplitudes of the bright and dark solitons are not related to the coefficient $$\delta _{4}(t)$$ , while the soliton velocities are related to $$\delta _{4}(t)$$ . (2) Interactions between the bright two solitons are shown to be elastic, while interactions between the dark two solitons could be elastic or inelastic, which is determined by the values of $$\rho $$ . (3) Numerical calculation indicates that the bright solitons could not resist the disturbance of small perturbations, while the dark solitons could resist the disturbance of small perturbations.

Using the Lugiato–Lefever model, we base on the hysteresis approach to analyze the coexistence domain of bright and dark solitons in the zero, normal, and anomalous dispersion regimes. Our results also highlight that the fourth-order dispersion term affects the width of the frequency combs of both dark and bright solitons. It also allows the appearance of dispersive waves on the soliton spectra that disappear for high values of the fourth-order dispersion followed by the soliton destabilization into harmonic oscillations and oscillation packages.

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