Weakly nonparaxial spatial solitons in a medium with Kerr nonlinearity

A version of perturbation theory is developed that intends to determine the field distribution of spatial solitons with a 2D transverse profile in a Kerr medium in the case of small deviations from paraxial conditions. An approximate master equation for transverse components of the electric field in the case of wide solitons is derived. By solving this equation starting from the unperturbed soliton, i.e., Townes mode with linear polarization of radiation, a solution with an axially symmetric field distribution is found. Dependences of the main soliton characteristics on the degree of paraxiality are determined.     

Weakly nonparaxial spatial optical solitons in different mechanisms of Kerr nonlinearity

The structure of spatial (two-dimensional transverse) weakly nonparaxial solitons is determined by solving the Maxwell equations for a medium characterized by different mechanisms of Kerr (cubic) nonlinearity in the approximation of beams with a width greatly exceeding the wavelength of light. Two modes are distinguished for these solitons: a trapping mode, with a constant transverse field profile, and a beating mode, with longitudinal oscillations of the field structure. The angular structure of the field in the beating mode (which is realized when the radiation power slightly exceeds the critical power of self-focusing) is determined.     

Stability of weakly nonparaxial spatial optical solitons in a medium with a Kerr nonlinearity

A variant of perturbation theory is developed to determine the characteristics and stability of transversely two-dimensional spatial solitons in a Kerr medium under conditions of small deviations from paraxial. Distributions of the transverse and longitudinal components of the soliton electric and magnetic fields are obtained. It is shown that the power of a nonparaxial soliton in a Kerr medium increases as the propagation constant increases. A linear analysis is made of soliton stability. In addition to confirming stability, this analysis revealed “internal modes” of nonparaxial solitons and their characteristics were determined.     

One-dimensional nonparaxial bright solitons and their coherent interactions in Kerr media

<正>The existence of one-dimensional bright Kerr solitons is investigated in Kerr media beyond the paraxial approximation. It is found that a nonparaxial soliton with no less than a minimum dimensionless width of about 0.76 can exist, which corresponds to the real width about a wavelength.Besides,the coherent interactions between two nonparaxial bright solitons in Kerr media are also investigated in detail.It is found that their separation and intensity ratio have great influence on the coherent interaction between these two solitons.Furthermore,the effect of the relative phase difference on the nonparaxial interaction is quite different from that on the paraxial interaction.Periodical breath, merging,repulsion,and energy transferring can be realized separately by choosing an appropriate initial relative phase between the coherent solitons.     

Subwavelength spatial solitons in inhomogeneous Kerr media

Propagation of a narrow beam in a periodic Kerr medium is analyzed for an arbitrary relation between the beam width, modulation period, and optical wavelength. Maxwell’s equations used to obtain solutions describing spatial optical solitons, and their basic properties are determined. The results are compared with those obtained by solving the paraxial nonlinear Schödinger equation. Conditions are found under which these models are mutually inconsistent.     

Elliptic incoherent solitons in strongly nonlocal media with anisotropic Kerr nonlinearity

The propagation of elliptic incoherent beam in strongly nonlocal media with noninstantaneous anisotropic Kerr nonlinearity is systematically investigated. Using the mutual coherence function approach, we obtain the existence curve of such solitons and an interesting outcome: correlation characteristics of the elliptic incoherent solitons can be anisotropic as well as isotropic. When the existence conditions of solitons are not satisfied, the elliptic incoherent beam will undergo periodic oscillation. Nonstationary evolution behaviors of the elliptic beam are shown in detail by numerical calculation. It is also obtained that the oscillation periods of the beam in x and y direction are different and the elliptic beam will become circular at some propagation distance under special conditions.     

Counterpropagating spatial solitons in reflection gratings with a longitudinally modulated Kerr nonlinearity

We investigate quasi-Bragg-matched counterpropagating spatial solitons in a reflection grating in the presence of a longitudinally modulated Kerr nonlinearity. The physical interplay of linear reflection and Kerr self-focusing with the modulation in the nonlinearity yields a variety of elaborate self-action mechanisms. We first analytically predict the existence of symmetric soliton pairs supported by a pure Kerr-like effective nonlinearity. We then analytically derive two families of solitons, associated with the linear grating eigenmodes, supported by an effective "incoherent" Kerr-like coupling arising from the exact balance between the modulation in the nonlinearity and the Kerr interaction due to beam interference.     

Thirring optical solitons with Kerr law nonlinearity

The dynamics of Thirring solitons in birefringent fibers with Kerr law nonlinearity is addressed in this paper. An exact 1-soliton solution is obtained. Bright, dark and singular soliton solutions are described.     

非局域克尔介质中空间光孤子的相互作用

研究了强非局域克尔介质中光束的演化规律，通过相位分析得到了空间孤子相互作用所满足 的非局域非线性薛定谔方程的简化近似模型，并获得了双光束传输的解析解.结果表明在传 输过程中相互作用的高斯光束的相位决定于它们的输入总功率.以振幅一强一弱共同传输的 高斯光束为例进行了具体研究，得到了强光和弱光的解析式，相位分析显示弱光在相当短的 传输距离之内能产生大的相移，可以通过对强光能量的调控来实现对弱光的相位调制. 关键词： 非局域克尔介质 空间光孤子 孤子相互作用 相位调制     

Collision between scalar and vector spatial solitons in Kerr media

Experimental observation and numerical results concerning collisions between scalar and vector spatial solitons in a Kerr planar waveguide are presented. It is shown that this configuration allows for the full control of spatial and polarization dynamics of the interacting vector solitons. On the one hand, the ability to achieve polarization control of a single-hump vector soliton is demonstrated. On the other hand, the effect of collision on the spatial symmetry-breaking dynamics of multimode vector solitons is investigated.     

Collision of optical solitons with Kerr law nonlinearity

The intra-channel collision of optical solitons, with Kerr law nonlinearity, is studied by the aid of quasi-particle theory. The perturbation terms considered in this paper are all of Hamiltonian type. It is shown that the soliton–soliton interaction can be suppressed in the presence of these perturbations, namely, the self-steepening, the third-order dispersion, the fourth-order dispersion and the frequency separation between the soliton carrier and the gain-center frequency. The prediction of quasi-particle theory are fully confirmed by direct numerical simulations.     

Nonparaxial spatial solitons and propagation-invariant pattern solutions in optical Kerr media

We investigate nonlinear propagation in the presence of the optical Kerr effect by relying on a rigorous generalization of the standard parabolic equation that includes nonparaxial and vectorial terms. We show that, in the (1 + 1)-D case, both soliton and propagation-invariant pattern solutions exist (while the standard hyperbolic-secant function is not a solution).     

Bright spatial solitons in defocusing Kerr media supported by cascaded nonlinearities

We show that resonant wave mixing that is due to quadratic nonlinearity can support stable bright spatial solitons, even in the most counterintuitive case of a bulk medium with defocusing Kerr nonlinearity. We analyze the structure and stability of such self-guided beams and demonstrate that they can be generated from a Gaussian input beam, provided that its power is above a certain threshold.     

Spatial solitons in Kerr and Kerr-like media

This is a review paper of basic knowledge and recent advances in the area of spatial solitons in Kerr and Kerr-like media. We consider spatial bright and dark solitons, solitons in waveguide geometries, optical bullets, vortex solitons and, briefly, dissipative cases. In our treatment, we use a Hamiltonian approach when considering stability issues.     

Spatial solitons in optofluidic waveguide arrays with focusing ultrafast Kerr nonlinearity

We present an optofluidic nonlinear waveguide array that is fabricated by selectively filling several strands of a photonic crystal fiber with the liquid CCl(4), which exhibits a large focusing ultrafast Kerr nonlinearity. We demonstrate a power dependent formation of a spatial soliton in this novel optofluidic device. The large thermo-optical effect of liquids enables us to control the characteristics of the spatial soliton formation in these nonlinear structures. This opens the road toward flexible designs and the realization of a new class of optofluidic devices with complex nonlinear landscapes and novel effects.     

Nonparaxial dark solitons in optical Kerr media

We show that the nonlinear equation that describes nonparaxial Kerr propagation, together with the already reported bright-soliton solutions, admits of (1 + 1)D dark-soliton solutions. Unlike their paraxial counterparts, dark solitons can be excited only if their asymptotic normalized intensity u2infinity is below 3/7; their width becomes constant when u2infinity approaches this value.     

Propagation of solitons in thermal media with periodic nonlinearity

We address the existence and properties of solitons in layered thermal media made of alternating focusing and defocusing layers. Such structures support robust bright solitons even if the averaged nonlinearity is defocusing. We show that nonoscillating solitons may form in any of the focusing domains, even in those located close to the sample edge, in contrast to uniform thermal media, where light beams always oscillate when not launched exactly on the sample center. Stable multipole solitons may include more than four spots in layered media.     

Spatio-temporal dynamics of multicolor spatial Kerr solitons

We present numerical and experimental results showing the rich and complex spatio-temporal dynamics of multicolor spatial vector soliton generated by stimulated Raman scattering in a Kerr planar waveguide. By taking into account their temporal dimension, we found the precise domain of existence of multicolor soliton whose components are mutually guided and spatio-temporally superimposed. In addition, we observe the Raman Stokes component in the trailing edge of the pump pulse and show that it is associated with the slow-light process induced by the sharp resonance of the Raman gain medium.