Spatial bright-dark solitons in transversely magnetized coupled 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

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.

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.

Analytical and numerical solutions that describe the coupling between bright and dark spatial solitons, located in separate planar waveguides are presented. The analytical theory rests upon a well-known variational approach and it is shown to be in good qualitative/semi-quantitative agreement with the exact numerical solutions of the coupled equations of the problem. By manipulating the soliton ‘masses’, through the input power, interesting trajectories for the solitons can be selected. Indeed, these trajectories are shown to possess behaviour patterns that qualify as the first steps in a design of an all-optical scanner. At all stages, the variational solutions are thoroughly checked by the numerical simulations and found to have excellent predictive qualities.

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.

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.

The temperature effects on the evolution and stability of a separate photovoltaic bright–dark soliton pair formed in a serial photovoltaic photorefractive crystal circuit have been investigated. Our numerical results show that adjusting each crystal temperature can affect the dynamical evolution of the soliton formed in the other crystal. For a stable bright–dark soliton pair originally formed in a crystal circuit at given temperatures, when one crystal temperature changes, the soliton supported by the other crystal will evolve into another stable soliton if the temperature change is quite small, whereas it will become unstable and experience larger cycles of compression or break up into beam filaments if the temperature difference is big enough. The bright soliton and dark solitons have their own stable temperature regime.

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.

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.

Optical bistability and observation of bright and dark spatial resonator solitons are reported for a semiconductor microresonator in which the nonlinearity stems from exciton polaritons.

Bright and dark spatial gap solitons are demonstrated in waveguide arrays. These gap solitons travel across the array at zero transverse velocity, in complete analogy with stationary (immobile) temporal gap solitons. Furthermore, the launching configuration for observing these stationary gap solitons is shown to be the analog of an "ideal experiment" for observing stationary temporal gap solitons, never observed so far. A clear distinction is established between the family of Floquet-Bloch solitons in general and discrete solitons in particular, and the limiting case of gap solitons.

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.

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.

Bright pulses and dark solitons coexisting and evolving in a fiber laser with strong normal dispersion have been observed. Experimental results show that there exists a transitional pulse regime with the pulse duty cycle of ∼0.5 that connects the bright pulse and dark soliton regimes. On adjusting polarization states and pump power, the duty cycle of pulses varies so that the laser emits bright, transitional, and dark pulses alternately. It is found that dark solitons are composed of two antiphase square pulses with very large durations and duty cycles. The experimental observations reveal that the bright and dark solitons are not completely isolated from each other. This work could provide a new perspective to the understanding of bright and dark soliton formations as well as their transformations.

We show analytically that bright and dark spatial self-similar waves can propagate in graded-index amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearities. The intensity profiles of the novel waves are identical with those of fundamental bright or dark spatial solitons supported by homogeneous passive waveguides with the same type of nonlinearity. Thus, we reveal a previously unnoticed connection between spatial solitons and self-similar waves. We also suggest that the discovered self-similar waves can be used in a promising scheme for the amplification and focusing of spatial solitons in future all-optical networks.