Self-Deflection of Dark Screening Spatial Solitons Based on Higher-Order Space Charge Field

The effects of higher-order space charge field on the self-deflection of dark screening spatial solitons in biased photorefractive crystals are numerically investigated under steady-state conditions. The expression for an induced space-charge electric field including higher-order space-charge field terms is obtained. Numerical results indicate that dark solitons possess a self-deflection process during propagation, and the solitons always bend in the direction of the c axis of the crystal. The self-deflection of dark solitons can experience considerable increase especially in the regime of high bias field strengths.     

Two-dimensional spatial solitons in highly nonlocal nonlinear media

We investigate, analytically and numerically, a class of novel higher-order spatial solitons in two transverse-dimensions, in highly nonlocal nonlinear media. The stability of these solutions in propagation is confirmed by direct numerical simulation. Our results demonstrate that the higher-order spatial solitons in highly nonlocal nonlinear media can exist in various forms, such as the fundamental solitons, vortex-ring solitons, multipole solitons, and fractional solitons.     

Kummer solitons in strongly nonlocal nonlinear media

We solve the three-dimensional (3D) time-dependent strongly nonlocal nonlinear Schrödinger equation (NNSE) in spherical coordinates, with the help of Kummer's functions. We obtain analytical solitary solutions, which we term the Kummer solitons. We compare analytical solutions with the numerical solutions of NNSE. We discuss higher-order Kummer spatial solitons, which can exist in various forms, such as the 3D vortex solitons and the multipole solitons.     

Waveguides induced by steady-state gray solitons in biased photorefractive-photovoltaic crystals

We carry out a theoretical investigation of the properties of waveguides induced by photorefractive one-dimensional steady-state gray spatial solitons (i.e., screening solitons, photovoltaic solitons, and screening-photovoltaic solitons). We demonstrate that waveguides induced by photorefractive steady-state gray spatial solitons are only a single guided mode for both all soliton graynesses and all values of ρ, where ρ is the ratio between the soliton peak intensity and the dark irradiance, and moreover, waveguides induced by gray photovoltaic solitons for closed-circuit condition are also only a single guided mode for all electric current densities. We find that the confined energy near the center of a photorefractive steady-state gray spatial soliton increases with ρ and decreases with an increase in the soliton grayness. We also find that the confined energy near the center of a gray photovoltaic soliton for closed-circuit condition increases with the electric current density. On the other hand, waveguides induced by gray screening-photovoltaic solitons are gray screening soliton-induced waveguides when the bulk photovoltaic effect is neglectable and are gray photovoltaic soliton-induced waveguides when the external bias field is absent.     

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.     

Gray spatial solitons in biased two-photon photovoltaic photorefractive crystals

This paper predicts that gray spatial solitons can exist in biased two-photon photovoltaic photorefractive crystals. Under appropriate conditions and in the steady state, the gray spatial solitons solution of the optical evolution equation is obtained. The properties associated with these solitons, such as their intensity profile, intensity full width at half-maximum, width, transverse velocity and phase distribution, are discussed as functions of their normalized intensity and degree of “grayness”. Relevant examples are provided.     

Incoherent solitons in strongly nonlocal media: The coherent density theory

We study the properties of one dimension incoherent accessible solitons in strongly nonlocal media with noninstantaneous Kerr nonlinearity. Following the coherent density theory, we obtain an exact solution of such incoherent solitons. The spatial width of the incoherent solitons is related to the incoherent angular power spectrum θ₀ as well as the incident power. The evolution properties of the intensity profile and the coherence characteristics are also discussed in detail when the solitons undergo periodic harmonic oscillation.     

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.     

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.     

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.     

Temporal behavior of dark spatial solitons in closed-circuit photovoltaic media

We show that the time-dependent nonlinear wave equation in closed-circuit photovoltaic media can exhibit quasi-steady-state and steady-state spatial solitons. We demonstrate that the formation time of open-circuit quasi-steady-state and open-circuit steady-state dark solitons decreases with an increase in the intensity ratio of the soliton, which is the ratio between the soliton peak intensity and the dark irradiance. We find that for the time-dependent nonlinear wave equation that exhibits only an open-circuit steady-state dark soliton, changing the electric current density J₀ does not generate quasi-steady-state dark solitons and affects the formation time of steady-state dark solitons and that for the time-dependent nonlinear wave equation that exhibits an open-circuit quasi-steady-state dark soliton, changing J₀ gives rise to three different time evolution regimes of the full width half maximum of the soliton’s intensity. The first regime shows that the formation time of steady-state dark solitons increases with J₀ whereas the formation time of quasi-steady-state dark solitons is independent of J₀. The second regime shows that the formation time of steady-state dark solitons decreases with an increases in J₀ and the formation time of quasi-steady-state dark solitons increases with J₀. The third regime shows that changing J₀ enables only steady-state dark solitons in the time-dependent nonlinear wave equation, of which the formation time increases with J₀.     

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     

Generalized Theory of One-Dimensional Steady-State Optical Spatial Solitons

We present a generalized soliton theory based on the one-dimensional generalized nonlinear Schroedinger equation,from which one can easily obtain the bright, dark, and grey soliton waveforms, and their existence curves. We show that the forming conditions of spatial solitons are directly dependent on the relationship between the index perturbation and the intensity, no matter whether the index perturbation is positive or negative. Some relevant examples are presented when the solitons are supported by the photoisomerization nonlinearity.     

Spatial solitons in a semiconductor microresonator

We show experimentally the existence of bright and dark spatial solitons in a passive quantum-well-semi-conductor resonator of large Fresnel number with mixed absorptive defocusing nonlinearity. Several of the solitons can exist simultaneously as required for applications. Received: 17 November 2000 / Published online: 13 December 2000     

Accessible solitary wave families of the generalized nonlocal nonlinear Schrödinger equation

Two-dimensional accessible solitary wave families of the generalized nonlocal nonlinear Schr?dinger equation are obtained by utilizing superpositions of various single accessible solitary solutions. Specific values of soliton parameters are selected as initial conditions and the superposition of known single solitary solutions in the highly nonlocal regime are launched into the nonlocal nonlinear medium with a Gaussian response function, to obtain novel numerical solitary solutions of improved stability. Our results reveal that in nonlocal media with the Gaussian response the higher-order spatial accessible solitary families can exist in various forms, such as asymmetric necklace, asymmetric fractional, and symmetric multipolar necklace solitons.     

Coherent switching of semiconductor resonator solitons

We demonstrate the switching on and off of spatial solitons in a semiconductor microresonator by injection of light coherent with the background illumination. The results give evidence that the formation of the solitons and their switching are not limited by thermal processes. Received: 11 February 2002 / Revised version: 25 April 2002 / Published online: 8 August 2002     

Photovoltaic solitons in two-photon photorefractive materials under open-circuit conditions

We present the evolution equation of one-dimensional spatial soliton in two-photon photorefractive media under open-circuit conditions. In the steady state regime, our solutions show that the dark and bright photovoltaic spatial solitons can be supported in two-photon photorefractive media under open-circuit conditions.     

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.     

Incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media

We theoretically investigate the propagation of incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media. It is found that multipole-mode soliton pairs with arbitrary different orders of Hermite-Gaussian shape can exist when the total power of two beams equals the critical power and the ratio of the beam widths for the Gaussian part is inversely proportional to the square root of the ratio of the wave numbers. When the total power does not equal the critical power, the Hermite-Gaussian breather pair exists and their beam widths evolve analogously. For general cases where the ratio of the beam widths is arbitrary, soliton-breather pairs or breather-breather pairs can be formed and their beam widths evolve synchronously in-phase or out-of-phase. Numerical simulations directly based on the nonlocal nonlinear Schrödinger equation are conducted for comparison with our theoretical predictions. The numerical stability analysis shows the higher-order Hermite-Gaussian solitons can not be stable for small nonlocality or for some media like liquid crystals.     

Solitons and vortices in lasers

We give in this article the mathematical background for pattern formation in nonlinear active resonators, elucidating the relation of optics with other fields of physics, and demonstrate experimentally the existence, properties, and dynamics of: (i) vortices in lasers, (ii) bright spatial solitons in lasers with saturable absorber, and (iii) spatial solitons in degenerate parametric mixing. All these structures are by definition bistable so that they are potentially useful for parallel optical information processing. Received: 8 June 1998