Subdiffractive discrete cavity solitons

We describe what we believe to be novel types of discrete cavity solitons in nonlinear waveguide arrays that are driven by an external holding beam. We demonstrate that a holding beam with a definite inclination drives the system in a subdiffractive regime and allows the formation of stable discrete cavity solitons. We predict the existence of both bright and dark moving midband discrete cavity solitons for an identical set of system parameters for both focusing and defocusing Kerr nonlinearities.     

Dispersionless envelope lattice solitons on a D-dimensional nonlinear lattice

We show by using the real exponential approach that the d-dimensional discrete nonlinear Schrödinger equation has more general dispersionless envelope lattice soliton solutions than the known bright soliton and kink solutions. Depending on the values of the parameters, the new solutions can describe both bright and dark lattice solitons. Especially, we find novel “W”-like envelope lattice solitons.     

Dark-bright discrete solitons: A numerical study of existence, stability and dynamics

In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions between dark-bright solitons and between a dark-bright one and a dark one. Especially in the latter and in the regime where the underlying lattice structure matters, we find a wide range of potential dynamical outcomes depending on the initial soliton speed.     

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing (SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable.     

The linear and nonlinear optical effects of white light

An overview of our research group’s experimental and theoretical developments is provided on the linear and nonlinear optical effects of white light since 2003. Their work includes the experimental researches on the white light one-dimensional photovoltaic dark spatial solitons and the waveguides and directional couplers induced by them, the circular and elliptic white-light dark spatial solitons and the white-light photorefractive phase masks, two-dimensional white-light photonic lattices and the applicati...     

Frequency characteristics of the dark and bright surface solitons at a nonlinear metamaterial interface

We investigate the generation and properties of dark and bright surface waves at the interface of a conventional medium and a metamaterial. It is shown that the stable dark and bright surface solitons can coexist even when the nonlinear Kerr coefficients of the two media are negative, completely different from those at the interface between two conventional media. Most importantly, both the dark and bright surface solitons exist only within a certain range of the effective refractive index of the metamaterial, greatly depending on the frequency of the electromagnetic wave propagating in it. Therefore, the generation conditions for surface solitons, and the properties of the generated surface solitons such as the peak positions and the intensity of the dark and bright surface solitons, can be controlled by adjusting the structure parameters of the metamaterial and/or the frequency of the electromagnetic wave.     

Two-component coupled photovoltaic soliton pair in two-photon photorefractive materials under open circuit conditions

The existence and nonlinear dynamics of two-component incoherently coupled composite solitons in two-photon photorefractive materials under open circuit conditions have been investigated. In the steady-state regime, these incoherently coupled solitons can propagate in bright–dark, bright–bright and dark–dark configurations. These photovoltaic soliton families can be established provided that the carrier beams share the same polarization and wavelength. The influence of the gating beam on the dynamics of stable solitons is discussed. Numerical simulations show that these solitons are stable for small perturbation on amplitude.     

Bright and dark solitons in a quasi-1D Bose-Einstein condensates modelled by 1D Gross-Pitaevskii equation with time-dependent parameters

We investigate the exact bright and dark solitary wave solutions of an effective 1D Bose-Einstein condensate (BEC) by assuming that the interaction energy is much less than the kinetic energy in the transverse direction. In particular, following the earlier works in the literature Pérez-García et al. (2004) [50], Serkin et al. (2007) [51], Gurses (2007) [52] and Kundu (2009) [53], we point out that the effective 1D equation resulting from the Gross-Pitaevskii (GP) equation can be transformed into the standard soliton (bright/dark) possessing, completely integrable 1D nonlinear Schrödinger (NLS) equation by effecting a change of variables of the coordinates and the wave function. We consider both confining and expulsive harmonic trap potentials separately and treat the atomic scattering length, gain/loss term and trap frequency as the experimental control parameters by modulating them as a function of time. In the case when the trap frequency is kept constant, we show the existence of different kinds of soliton solutions, such as the periodic oscillating solitons, collapse and revival of condensate, snake-like solitons, stable solitons, soliton growth and decay and formation of two-soliton bound state, as the atomic scattering length and gain/loss term are varied. However, when the trap frequency is also modulated, we show the phenomena of collapse and revival of two-soliton like bound state formation of the condensate for double modulated periodic potential and bright and dark solitons for step-wise modulated potentials.     

Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schrödinger (Ablowitz–Ladik) model

We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schrödinger equation of Ablowitz and Ladik. When considered in the complex plane, these two solutions are identical. In the continuum limit, they reduce to known elliptic function solutions. In the long wave limit, the dark one reduces to the collision of two discrete dark solitons, and the bright one to a discrete breather.     

Modulation instability of bright photovoltaic solitons on a partially incoherent background

We present the observation of incoherent anti-dark photovoltaic solitons in LiNbO₃:Fe crystal. This new class of soliton states involves bright photovoltaic solitons on a background beam meeting ?? > 1, where ?? is the ratio of background illumination photovoltaic constant to that of soliton beam. For ?? < 1, dark photovoltaic solitons are generated. Furthermore, this novel type solitons are investigated experimentally by injecting coherent light and partially coherent background of infinite extent. In case of spatial coherence of the background lower than the threshold of incoherent modulation instability, these results indicate that bright photovoltaic solitons can propagate in a stable fashion.     

A train of bright and dark-rogue wave solitons in a polariton fluid with inhomogeneous strength interaction

We solve using the similarity transformation method a one-dimensionless driven-dissipative nonlinear Schrödinger equation to explore the dynamics of the rogue wave solitons generated in a polariton fluid. Under resonant excitation, we predict the existence of the bright and the dark-rogue waves solitons by varying the external pump source parameter. By considering, a time periodic polariton–polariton interaction and adjusting its frequency, the rogue wave soliton trains occur in a polariton fluid. In addition we observe that, the amplitude of the pump power is responsible to the formation of a the train of the bright and the dark rogue waves solitons.     

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.     

Spatial Solitons in 2D Graded-Index Waveguides with Different Distributed Transverse Diffractions

We discuss the nonlinear Schr6dinger equation with variable coefficients in 21） graded-index waveguides with different distributed transverse diffractions and obtain exact bright and dark soliton solutions. Based on these solutions, we mainly investigate the dynamical behaviors of solitons in three different diffraction decreasing waveguides with the hyperbolic, Gaussian and Logarithmic profiles. Results indicate that for the same parameters, the amplitude of bright solitons in the Logarithmic profile and the amplitude of dark solitons in the Gaussian profile are biggest respectively, and the amplitude in the hyperbolic profile is smallest, while the width of solitons has the opposite case.     

Generation of stable bright pulse and the dark soliton interaction in nonlinear left-handed materials

In homogeneous and isotropic nonlinear left-handed materials (LHMs), using the split step Fourier transform method, we demonstrate that two dark electromagnetic solitons which are the solutions of coupled nonlinear Schrödinger equations (CNLS) move along a line toward each other, when the distance between them down to a certain value, the interaction of the two dark solitons can produce a stable bright electromagnetic pulse that behaves like a bright soliton. Although our mathematical analysis shows that the new generated stable bright pulse is not an exact solution of the CNLS, it can propagate steadily in the nonlinear LHMs. And this unusual phenomenon can also be observed in our numerical simulation results by another method.     

DNA adsorption on graphene

We study analytically the properties of the optical absorption and the spatial weak-light solitons in a quantum dot molecule system with the interdot tunneling coupling (ITC). It is shown that, for the linear case, there exists tunneling induced transparency (TIT) in the context of a weak ITC, while the TIT can be replaced by Autler-Townes splitting in the presence of a strong ITC. For the nonlinear case, it is probable to realize the spatial optical solitons even under weak light intensity. Interestingly, we find that there appears transformation behavior between the bright and dark solitons by properly turning both the ITC strength and the detuning of the probe field. Meanwhile, the transformation condition of the bright and dark solitons is obtained. Additionally it is also found that the amplitude of the solitons first descends and then rises with the increasing of ITC strength. Our results may have potential applications for nonlinear optical experiments and optical telecommunication engineering in solid systems.     

First principle theory for cavity solitons in semiconductor microresonators

Cavity solitons are similar to spatial solitons, appearing as localized bright dots in the transverse intensity profile of the electromagnetic field, but they arise in dissipative systems. In this paper we consider a broad-area vertical-cavity semiconductor microresonator, driven by an external coherent field, at room temperature. The active material is constituted by a Multiple Quantum Well GaAs/AlGaAs structure (MQW). We present a set of nonlinear dynamical equations for the electric field and the carrier density valid for both a passive and an active (i.e. with population inversion) configuration. The complex nonlinear susceptibility is derived on the basis of a full many-body theory, with the Coulomb enhancement treated in the Padé approximation. The linear stability analysis of the homogeneous steady states is performed with a generalised approach, and numerical simulations demonstrating the existence of spatial patterns and cavity solitons in experimentally achievable parameter regions are given for the two configurations. Received 18 January 2001     

Bright and dark optical solitons in the nonlinear Schr(o)dinger equation with fourth-order dispersion and cubic-quintic nonlinearity

By the use of an auxiliary equation, we find bright and dark optical soliton and other soliton solutions for the higher-order nonlinear Schr(o)dinger equation (NLSE) with fourth-order dispersion (FOD), cubic-quintic terms, self-steepening, and nonlinear dispersive terms. Moreover, we give the formation condition of the bright and dark solitons for this higher-order NLSE.     

Bright,dark optical and other solitons to the generalized higher-order NLSE in optical fibers

In this paper, we study the generalized higher-order nonlinear Schrödinger equation analytically. We use two integral schemes for conducting this study. Dark, bright, combined dark–bright optical, singular soliton, soliton-like and trigonometric function solutions are successfully constructed. We give the constraint conditions for the existence of valid solutions. The 2D, 3D and the contour graphs for the dark and bright solitons are plotted.     

Subwavelength spatial solitons

We analyze the effects of additional terms in the nonlinear Schr?dinger equation for spatial solitons, directly derived from the Maxwell's equations with the Kerr nonlinearity, on the shapes of bright and dark solitons with a fixed polarization. Combining analytical and numerical methods, we find that the additional terms always render the solitons broader. The most essential result is a fundamental limitation on the width of the subwavelength soliton: The ratio of the FWHM of the bright soliton to the wavelength cannot be smaller than 1/2, and the same ratio for the FWHM of the dark soliton cannot be smaller than 1/4.