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.     

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     

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.     

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.     

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.     

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.     

Engineering of multicolor spatial solitons with chirped-period quasi-phase-matching gratings in optical parametric amplification

We demonstrate the excitation of solitons in a parametric amplifier with enhanced signal content through the use of a chirped-period quasi-phase-matching grating. This technique affords a low soliton threshold at the input end of a parametric amplifier, and the subsequent transformation to a desired soliton that exists at nonzero wave-vector mismatch through the use of a linearly chirped quasi-phase-matching grating. This approach has an advantage over direct excitation of solitons at nonzero wave-vector mismatch in uniform nonlinear materials and holds potential for improving the efficiency and mode quality of high-gain parametric amplifiers.     

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).     

Generation of multicolor vector Kerr solitons by cross-phase modulation, four-wave mixing, and stimulated Raman scattering

We numerically and experimentally show the existence of multicolor vector spatial solitons in a Kerr planar waveguide through the combined effects of cross-phase modulation, four-wave mixing, and stimulated Raman scattering. Mutual spatial guiding of the Raman-Stokes, anti-Stokes, and pump waves is achieved in the high-conversion regime mainly by cross-phase modulation and phase-matched four-wave mixing induced by a power imbalance between Stokes and anti-Stokes components, leading to the generation of a clear-cut sech-shape three-frequency spatial soliton.     

Polarization locking and nonparaxial spatial solitons in media with electronic Kerr nonlinearity

The polarization structure of nonparaxial spatial solitons in a transparent medium with the electronic mechanism of Kerr nonlinearity is studied theoretically. It is demonstrated analytically in the weak nonparaxiality approximation that the regime of polarization locking, in which all the field components have the same propagation constant, is the only stable regime. Estimates of the rate of transition of the initial metastable regime of rotation of the polarization ellipse to the regime of polarization locking are presented. Based on a numerical solution of the nonlinear Maxwell equations, the presence of the nonparaxial regime of polarization locking is confirmed and the main characteristics of the corresponding spatial solitons are obtained.     

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.     

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.     

Spherical solitons in a Kerr medium

Solutions of the complete system of the Maxwell equations for a Kerr medium are found numerically in the form of spherical surface waves—spherical solitons.     

Azimuthally polarized spatial dark solitons: exact solutions of Maxwell's equations in a Kerr medium

Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schro dinger equation, are shown to exist to all nonparaxial orders as exact solutions of Maxwell's equations in the presence of the vectorial Kerr effect. More precisely, we prove the existence of azimuthally polarized, spatial, dark soliton solutions of Maxwell's equations, while exact linearly polarized (2 + 1)D solitons do not exist. Our ab initio approach predicts the existence of dark solitons up to an upper value of the maximum field amplitude, corresponding to a minimum soliton width of about one-fourth of the wavelength.     

Stochastic perturbation of Kerr law optical solitons

The soliton perturbation theory is used to study and analyze the stochastic perturbation of optical solitons, due to Kerr law nonlinearity, in addition to deterministic perturbations of optical solitons that is governed by the nonlinear Schrödingers equation. The Langevin equations are derived and analyzed. The deterministic perturbations that are considered here are of both Hamiltonian as well as of non-Hamiltonian type.     

Effects of varying nonlocality on dynamics of two-component vector spatial solitons

The randomly and the periodically varying weak nonlocalities are investigated by the variational approach in the self-focusing nonlinear media, and their effects are analyzed on the propagation and interaction of the two-component spatial solitons. The results show that they lead to the soliton disintegration and enhance the interaction between the spatial solitons, and their effects depend on the fluctuation strength and the period length of the varying nonlocalities. Finally, the numerical results confirm the theoretical findings.     

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.     

(1+2)维空间光孤子在非局域克尔介质中的传输特性

 从非局域非线性薛定谔方程出发,采用分步傅里叶算法数值讨论了在一定的非局域程度条件下,（1+2）维空间光孤子的传输特性, 数值求解了光孤子各特性参量。假定非局域克尔介质的响应函数为高斯型,得出了在一定的非局域程度条件下空间光孤子的数值解,并数值证明了它们的稳定性。结果表明:（1+2）维光孤子对非局域程度依赖性很强。在一定的非局域程度下,光束能以光孤子态在非局域克尔介质中稳定传输。强非局域时,光孤子的波形是高斯型,其它的非局域程度下,不是高斯型。当非局域程度较弱时,不存在孤子解。