Modulational instability and solitons in nonlocal media with competing nonlinearities

We study various properties of solutions of an extended nonlinear Schrödinger (ENLS) equation, which arises in the context of geometric evolution problems—including vortex filament dynamics—and governs propagation of short pulses in optical fibers and nonlinear metamaterials. For the periodic initial-boundary value problem, we derive conservation laws satisfied by local in time, weak H2 (distributional) solutions, and establish global existence of such weak solutions. The derivation is obtained by a regularization scheme under a balance condition on the coefficients of the linear and nonlinear terms—namely, the Hirota limit of the considered ENLS model. Next, we investigate conditions for the existence of traveling wave solutions, focusing on the case of bright and dark solitons. The balance condition on the coefficients is found to be essential for the existence of exact analytical soliton solutions; furthermore, we obtain conditions which define parameter regimes for the existence of traveling solitons for various linear dispersion strengths. Finally, we study the modulational instability of plane waves of the ENLS equation, and identify important differences between the ENLS case and the corresponding NLS counterpart. The analytical results are corroborated by numerical simulations, which reveal notable differences between the bright and the dark soliton propagation dynamics, and are in excellent agreement with the analytical predictions of the modulation instability analysis.

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.

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.

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.

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 formation of infrared solitons in graphene under Raman excitation is investigated using density-matrix approach. We find that the unique band structure and selection rules for the optical transitions near the Dirac point can result in extremely strong optical nonlinearity. Theoretical investigations with the aid of slowly varying envelope approximation and perturbation theory clearly indicate the existence of bright and dark solitons in Landau-quantized graphene. Actually, the formation of spatial soliton in such a material is the consequence of the balance between nonlinear effects and the dispersion properties. Also, the corresponding carrier frequency is tunable in the infrared range. These results can make us know better the crossover between optical solitons and graphene metamaterials. The predicted nonlinear optical effect in graphene may provide a new possibility for designing high-fidelity graphene-based information processing device.

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.

Spatial soliton formation in the bulk single-crystal polydiacetylene para-toulene sulfonate has been studied experimentally. The unique nonlinearity of this material at 1600 nm leads to stable solitons below an intensity maximum, and for higher intensities the input beams form a ring and a soliton.

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.

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 report that launching at least two solitons can produce rotating dipoles for a continuum interval of tilts imposed in nonlocal media. Surprisingly, we find that for a higher number of solitons launched and after emission of radiation waves, the beams can decay into rotating dipole solitons.

Since the discovery of photorefractive spatial solitons [1, 2], these non-diffracting waves have been the subject of an intense research effort, because they are particularly interesting for building alloptical diodes, transistors, switches, and all-optical computers. Until now steady-state bright spatial solitons have been observed in BTO [3], SBN [4], InP:Fe [5], KNbO3 [6], KLTN [7], and BaTiO3 [8] crystals. Barium–calcium titanate (BCT) [9, 10] is a promising photorefractive material and an alternative to BaTiO3, which is much easier to grow and does not have any phase transition within the temperature range from 120 C to 100 C. This crystal also possesses slightly larger electrooptic coefficients r13 (20 pm/V) and r33 (130 pm/V) compared to BaTiO3. However, no studies of photorefractive spatial soliton formation have been reported so far in BCT crystals. In this contribution, we investigate photorefractive spatial soliton formation in iron-doped BCT crystals and observe, for the first time to our knowledge, the formation of steady-state two-dimensional (2D) screening solitons in this material. Samples of the congruently melting composition Ba0:23Ca0:77TiO3 are grown in the crystalgrowth laboratory of the Department of Physics at the University of Osnabr€uck [9, 10]. The dimension of our sample that is doped with 290 ppm Fe is 5 5 5 mm3. All surfaces are polished to optical quality. On both faces normal to the c-axis of the crystal, electrodes are prepared with silver paste. The light propagates along the a-axis in our experiment. Our experiments are conducted in a standard setup for soliton formation, in which an external electric field E0 is applied along the ferroelectric c-axis. A frequency-doubled Nd:YAG laser (l 1⁄4 532 nm) is used as the light source. Because of the low dark conductivity of our sample sd 6 10 14 W 1 cm 1 [9], a background illumination is necessary to tune the degree of saturation of the nonlinearity. This ordinarily polarized background light of the same wavelength 532 nm is made spatially incoherent by passing it through a rotating diffuser. The ratio r between the soliton light intensity (extraordinary polarization) and the background irradiance is r 5. The soliton intensity is always kept below 50 mW/cm2 to minimize photovoltaic self-defocusing. Figure 1 shows a characteristic result of 2D soliton formation. In this experiment, the beam intensity is I 30 mW/cm2. The beam diameter at the crystal’s input face is din 14 mm. Without an external electric field E0 applied, the beam width d increases during propagation due to both, phys. stat. sol. (a) 189, No. 1, R4–R5 (2002)