Discrete light bullets in two-dimensional photonic lattices: Collision scenarios

We report systematic results of collisions between discrete spatiotemporal optical solitons in two-dimensional photonic lattices. We show that the outcomes of collisions strongly depend on the initial soliton parameters, such as their input amplitudes (energies) and their transverse velocities. Four generic outcomes are identified in the study of collisions between discrete light bullets located in the corner, at the edge, and in the center of the photonic lattice: (a) merger of both low and high amplitude solitons into a single one, at small values of the kick parameter (soliton transverse velocity), (b) spreading of low amplitude solitons at intermediate values of the kick parameter, (c) bouncing of high amplitude solitons at intermediate values of the kick parameter, which is accompanied by a sharp modification of input soliton transverse velocities, and (d) quasi-elastic (symmetric) interactions of both low and high amplitude solitons at large values of the kick parameter.     

Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices

We demonstrated that linearly and nonlinearly amplitude-modulated (chirped) harmonic lattices can support odd and even solitons in both focusing and defocusing saturable media. The modulated lattice modifies the profiles and enlarges the stability domains of solitons, comparing with the unchirped one. Twisted solitons, or “soliton trains” whose profiles exhibit multi-peak structures can also be supported by linearly and nonlinearly chirped lattices. In sharp contrast with periodic lattices, chirped lattices remarkably broaden the existence and stability domains of twisted solitons, especially for solitons with more components. While even solitons in focusing media and twisted solitons in defocusing media are unstable, odd and twisted solitons in focusing media are stable in relatively wide parameter windows. Chirped lattice can be used as a linear guidance to realize the oscillation of solitons which is impossible in unchirped lattice.     

Higher-order surface solitons in one-dimensional Bessel optical lattices

We demonstrate the existence of higher-order solitons occurring at an interface separating two one-dimensional (1D) Bessel optical lattices with different orders or modulation depths in a defocusing medium. We show that, in contrast to homogeneous waveguides where higher-order solitons are always unstable, the Bessel lattices with an interface support branches of higher-order structures bifurcating from the corresponding linear modes. The profiles of solitons depend remarkably on the lattice parameters and the stability can be enhanced by increasing the lattice depth and selecting higher-order lattices. We also reveal that the interface model with defocusing saturable Kerr nonlinearity can support stable multi-peaked solitons. The uncovered phenomena may open a new way for soliton control and manipulation.     

Solitary Wave Evolution of Optical Planar Vortices in Self-Defocusing Photorefractive Media

Solitary wave evolution of optical planar vortices in isotropie self-defoeusing photorefractive media is investigated in detail. We demonstrate that the formation of a planar vortex soliton intensively depends on the diameter and maximum intensity of the input vortex Seam. The exact solutions of planar vortex solitons are obtained due to the Petviashvili iteration method. It is found that, with the increasing soliton maximum intensity, the soliton core will be gradually diminished to a minimum value.     

Dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals

Using the coherent density approach, we study the dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals. We show that when the full width half maximum (FWHM) of the optical beam’s intensity is increased, the odd incoherent dark beam splits into an odd-number sequence of multiple dark stripes, whereas the even incoherent dark beam splits into an even-number sequence of multiple dark stripes. We find that when more incoherent solitons are generated, the separations between adjacent dark stripes become smaller and the stripes far away from the center become less visible and that for a given physical system and for a given splitting, the separations between adjacent dark stripes decrease with an increase in the intensity FWHM of the optical beam. On the other hand, the dark incoherent soliton splitting in biased photorefractive-photovoltaic crystals is the dark incoherent screening soliton splitting when the bulk photovoltaic effect is neglectable and the dark incoherent closed- and open-circuit photovoltaic soliton splitting when the external bias field is absent.     

Quasi-two-dimensional dark spatial solitons and generation of mixed phase dislocations

This paper presents experimental evidence that orthogonally crossed dark soliton stripes form quasi-two-dimensional spatial solitons with a soliton constant equal to that of singly charged optical vortices. Besides the pairs of oppositely charged optical vortex solitons, the snake instability of the dark formation at moderate saturation is found to lead to generation of steering mixed edge–screw phase dislocations with zero total topological charges. Received: 26 October 1998 / Revised version: 19 January 1999 / Published online: 12 May 1999     

Soliton switching in inhomogeneous nonlocal media

We address a simple way to achieve routing of optical spatial solitons via soliton interactions in the inhomogeneous nonlocal media. We reveal that the variation of the nonlocality disturbs the solitons pairs and splits them into two individual solitons which have the same escape angle but opposite deflection directions. In particular, the escape angle monotonically increases with the increase of the nonlocality variation rate. We demonstrate that the soliton pairs could form self-consistent waveguides that are able to controllably guide a weak signal by any output positions.     

Quasi-stable propagation of vortices and soliton clusters in saturable Kerr media with square-root nonlinearity

Analytical and numerical investigation of the propagation of optical beams in Kerr-like saturable photorefractive media is carried out, utilizing a novel model for the local isotropic part of the space-charge field generated in the medium. Using a variational technique, optimal propagation parameters for the most stable propagation of otherwise unstable single Gaussian, single vortex, and optical soliton cluster beams are determined. Analogy between a ring of identical weakly overlapping solitons and a vortex of the same topological charge is explored.     

Exact domain-wall solitons

We provide exact periodic and soliton solutions of optical domain-wall structures that arise due to modulation instability in a nonlinear medium with normal dispersion.     

Ultraslow optical solitons in a four-level tripod atomic system

We investigate possible formation and propagation of localized, shape-preserving nonlinear optical pulse in a resonant, lifetime-broadened four-level tripod atomic system via electromagnetically induced transparency (EIT). We prove both analytically and numerically that although in anomalous dispersion regimes near resonance a superluminal optical soliton may appear, such soliton suffers serious absorption. However, by choosing appropriate parameters to make the system work in normal dispersion regimes and within an EIT transparency window, ultraslow optical solitons with very low light intensity can form and propagate stably in the system.     

Slowly moving matter-wave gap soliton propagation in weak random optical lattices

We systematically investigate slowly moving matter-wave gap soliton propagation in weak random optical lattices. With the weak randomness, an effective-particle theory is constructed to show that the motion of a gap soliton is similar to a particle moving in random potentials. Based on the effective-particle theory, the effects of the randomness on gap solitons are obtained and the trajectories of gap solitons are well predicted. Moreover, the general laws that describe the movement depending on the weak randomness are obtained. We find that with an increase of the random strength, the ensemble-average velocity reduces slowly and the reflection probability becomes larger. The theoretical results based on the effective-particle theory are confirmed by the numerical simulations based on the Gross-Pitaevskii equation.     

Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers

We present the theory of electrostrictional interaction of soliton pulses in optical fibers. Solitons excite acoustic waves propagating in the direction transverse to the fiber axis. Scattering of optical radiation on these waves leads to a timing jitter of the optical pulses arrival time. We consider this effect as nonlinear self-scattering of light on acoustic waves. Because of the fact that a value of acoustic lifetime can reach a value of about 100 ns self-scattering on acoustic waves can be observed for a single optical pulse as well as for an optical pulse sequence as a whole. The value of single soliton self-frequency shift due to excitation of acoustic waves as a function of soliton duration have been obtained. For soliton duration _sol > 14 ps an acoustic wave soliton self-frequency shift is larger than the Raman soliton self-frequency shift.The obtained theoretical results describe well the long-range interaction of soliton pulse trains in an optical fiber. The value of bit error rate due to electrostrictional interaction of optical pulses in high bit rate, ultra long soliton communication systems have been obtained.     

Properties of Controllable Soliton Switching in Optical Lattices with Longitudinal Exponential-Asymptotic Modulation

The properties of controllable soliton switching in Kerr-type optical lattices with different modulation are investigated theoretically and simulated numerically. The results show that the optical lattices can be available for all-optical soliton switching through utilization for length-scale competition effects. And through longitudinal exponential-asymptotic modulation for the linear refractive index, the properties of soliton switching in the optical lattices can be improved. The number of output channels of soliton switching can be controlled by the parameters such as incident angle, asymptotic rate of longitudinal modulation, guiding parameter and form factor.     

Effects of dark soliton crystal temperature on the self-deflection of bright soliton in a biased serial photovoltaic photorefractive crystal circuit

Based on the theory of one-dimensional separate soliton pairs formed in a serial photovoltaic photorefractive crystal circuit, the effects of the dark soliton crystal temperature on the self-deflection of the bright one in a bright-dark soliton pair are investigated. The numerical results indicate that the spatial shift of the bright soliton can experience obvious increase in their self-deflection with the increase of the temperature of the dark soliton. The self-bending process is further studied using perturbation techniques and the results are found to be good agreement with that obtained by numerical method.     

Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-harmonic generation in photonic crystal fibers

We use cross-correlation frequency-resolved optical gating to obtain spectral-temporal portraits of ultrashort Raman solitons in photonic crystal fibers at telecommunication wavelengths. Power-dependent Raman frequency shifts of 200 nm in 63 mm of fiber are observed accompanied by spectral broadening and 2.5-times soliton compression. Complete time-frequency dynamics at the fundamental wavelength thus visualized enables us to explain the details of the intermodally phase-matched third harmonic generation by the propagating solitons.This revised version was published online in August 2005 with a corrected cover date.     

Photorefractive spatial solitons as waveguiding elements for optical telecommunication

Spatial solitons permit optical waveguiding. This holds true for the soliton write beam (i.e. the driving laser beam), as well as for additional probe beams, which may carry optically encoded information. This feature of spatial solitons is of significant interest for applications in optical telecommunication. We present systematic experimental investigations on single and multiple spatial solitons in the infrared spectral regime (i.e. around optical telecommunication wavelengths), applied as controllable all-optical devices. In particular, we present the implementations of a Y-coupler as an optical signal divider, a switchable Y-coupler as an optical add multiplexer, and a novel design for a 1 × 3 optical beam switch, i.e. applied as a router for infrared signal beams. We report large waveguiding efficiencies up to 40% and transmission rates of 90 Tbit/s in our setups. The presented experimental data are confirmed by numerical simulations.     

Optical beams in lossy non-local Kerr media

It is discussed that optical beams propagate in non-local Kerr medium waveguides with losses. A variational principle is carried out for the 1 + 1-D non-local non-linear Schrödinger equation in the presence of the losses. In the strongly non-local case, the approximate analytical solutions are obtained. The lossy soliton solution shows that, Unlike its local counterpart, such lossy strongly non-local soliton does not possess the adiabatic property anymore. In addition, the general approximate results for non-soliton cases are gained. The comparisons between our approximate analytic solutions and numerical simulations confirm our variational approximate solutions.     

Two-Dimensional Laguerre--Gaussian Asymmetric Soliton Family in Strongly Nonlocal Media

We demonstrate the existence of a broad class of higher-order Laguerre Gaussian asymmetric spatial optical solitons in strongly nonlocal nonlinear media. Furthermore, we discuss specific values （q = 0） of the modulation depth parameter for different rational values of the topological charge in detail. Our results show that higherorder asymmetry spatial sofiton family can exist in various forms, such as two-dimensional defect haff-solitons, asymmetric single-layer and multi-layer necklace solitons.     

(1 + 2)-Dimensional sub-strongly nonlocal spatial optical solitons: Perturbation method

By extending the (1 + 1)-dimensional [(1 + 1)-D] perturbation method suggested by Ouyang et al. [S. Ouyang, Q. Guo, W. Hu, Phys. Rev. E. 74 (2006) 036622] to the (1 + 2)-D case, we obtain a fundamental soliton solution to the (1 + 2)-D nonlocal nonlinear Schrödinger equation (NNLSE) with a Gaussian-type response function for the sub-strongly nonlocal case. Numerical simulations show that the soliton solution obtained in this paper can describe the soliton states in both the sub-strongly nonlocal case and the strongly nonlocal case. It is found that the phase constant and the power of the (1 + 2)-D strongly nonlocal spatial optical soliton with a Gaussian-type response function are both in inverse proportion to the 4th power of its beam width.     

Dynamical Stability of Gap Soliton of One-Dimensional Condensate in Optical Lattices with Strong Interatomic Interaction

By developing the multiple scales method, we analytically study the dynamics properties of gap soliton of Bose- Einstein condensate in optical lattices. It is shown that the gap soliton will appear at Brillouin zone edge of linear band spectrum of the condensates when the interatomic interaction strength is larger than the lattice depth. Moreover, the density of gap soliton starts to be relatively small, while it increases with time and becomes stable.