Effect of a small dispersion on self-focusing in a spatially one-dimensional case

The effect of a small dispersion on the self-focusing of solutions of equations of nonlinear geometric optics in a spatially one-dimensional case has been studied. This effect in the leading order is described by a universal special solution of the nonlinear Schrödinger equation, k]which is isomonodromic. The analytical and asymptotic properties of this universal solution have been considered.     

Complex geometrical optics of Kerr type nonlinear media

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.     

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

In the framework of nonlinear wave optics,we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schr?dinger equation.The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method.Taking advantage of the analytical expression,we analyze the influences of various physical parameters on the breathing wave propagation,including the propagation loss and the input power on the beam width,the beam intensity,and the wavefront curvature.Also,the corresponding analytical solutions are obtained.The validity of the analysis results is verified by numerical simulation.This study provides some new insights for investigating beam propagation in lossy nonlinear media.     

FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA

The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.     

高斯光束非线性“热像”效应研究

高功率激光系统中非线性“热像”强度可能达到光学元件损伤阀值，从而对系统的安全运行造成威胁.以往的非线性“热像”现象研究都是基于无限大平面光波背景，但实际系统中传输的是有限束宽光束.本文以高斯光束为例，基于无像差自聚焦理论分析了有限束宽光束的“热像”形成规律.结果表明，高斯光束“热像”的强度与位置在光束腰斑较小时与平面光波情况有明显不同，但光束腰斑较衍射物大得多时，高斯光束可以近似当作平面光波处理.     

强非局域克尔介质中光束传输的变分问题

 在非局域克尔介质中,光束的演化规律服从非局域非线性薛定谔方程。用变分法对此问题进行了重新表述。在强非局域的情况下,通过对介质响应函数进行泰勒展开,可以解析地表示变分问题。束宽的演化规律也可以定性地从光束束宽变分势得出。运用瑞利-里兹方法求解其变分方程,分别求出光束在自散焦和自聚焦介质中的变分解。对于自聚焦介质,当输入功率为某一特定值时,可以得到空间孤子,其束宽在传输过程中保持不变。通过与其他方法得到的解比较表明,变分法是解析讨论光束在非局域非线性介质中演化规律的方法之一。     

New solutions in the theory of self-focusing with saturating nonlinearity

On the basis of an approximate analytic solution of a Cauchy problem for a nonlinear Schrödinger (NLS) equation describing steady-state light beams in a medium with saturating nonlinearity by the method of renormgroup (RG) symmetries, a classification of self-focusing solutions is given depending on two control parameters: the relative contributions of diffraction and nonlinearity and the saturation strength of the nonlinearity. The existence of tube-type self-focusing solutions is proved for an entering beam with Gaussian radial distribution of intensity. Numerical simulation is carried out that allows one to verify the theory developed and to determine its applicability limits.     

External self-focusing,self-bending and optical limiting with thin non-linear media

Analytic solutions are presented for a simple model describing situations where self-focusing and self-bonding of intense optical beams by thin non-linearly refracting media can occur. Physical optics is employed to study effects arising when a non-linear medium is placed in contact with an aperture stop. The feasibility of constructing an optical power limiter by utilizing either external self-focusing or self-bending is discussed.     

基于光线光学的非线性自聚焦现象的仿真分析

采用光线光学方法对非线性自聚焦现象进行仿真, 能够从宏观上直观地体现强激光的传输过程, 同时避免采用近轴近似、自相似近似等. 本文采用在光传输路径上垂直于光轴切片的方法, 将光的非线性传输转化为切片上的光对折射率的调制作用和切片间的线性传输. 在切片端面上统计光强后对量化误差进行了抑制, 而线性传输过程采用了亚当斯法求解光线方程从而解决了龙格库塔法等不能用于非线性光传输仿真的问题. 仿真结果显示, 强激光自聚焦在轴上有多个焦点, 且第一个焦点的位置随光功率的增大而更靠近入射位置; 由于追迹的是实际光线, 故可以得到近轴区以外区域自聚焦及成丝(环)的情况, 这对于强激光系统安全是有重要意义的. 利用已有的同样基于光线追迹方法的光学设计、仿真软件, 可以把非线性自聚焦介质和线性介质结合起来, 仿真光在实际强激光系统中的传输. 关键词： 实际光线追迹 非线性自聚焦 光传输仿真     

Electromagnetic light rays in local dielectrics

An approach to deal with the limit of geometrical optics of electromagnetic waves which propagate in moving nonlinear local dielectric media in the context of Maxwellian electrodynamics is here developed in order to apply to quite general material media. Fresnel equations for the light rays are generically found, and its solutions are intrinsically obtained. The multi-refringence problem is addressed, and no more than four monochromatic polarization modes are found to propagate there.     

Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrodinger equation

A comprehensive analysis is presented of the propagation of symmetry-endowed two-soliton solutions under the influence of various perturbations important in nonlinear optics. Thus, we begin by introducing the analytical expressions of these two-soliton solutions. Then, by considering perturbations which preserve the initial symmetry of the two-soliton solutions, the dependence of the soliton parameters on the propagation distance is determined by using an adiabatic perturbation method. As perturbations of this kind, important for soliton-based communication systems, we consider the bandwidth-limited amplification, nonlinear amplification, and amplitude and phase modulation. Moreover, the results obtained by the adiabatic perturbation method are compared with those obtained by direct numerical simulations of the corresponding governing differential equations. (c) 2000 American Institute of Physics.     

非线性介质中强光对弱光聚焦的控制研究

从理论和实验上分析了强光控制弱光脉冲聚焦的方法, 该方法可以灵活地控制弱光的聚焦过程和特性. 通过研究两光束共同传输, 利用强抽运光在相互作用时为弱探测光提供诱导非线性效应, 从而使弱探测光发生聚焦. 得到了在抽运光保持不变情况下探测光的解析解, 并在实验上得到验证. 进一步研究了强抽运光对弱探测光焦点位置的影响. 结果显示: 通过改变抽运光功率、束宽能够有效地控制弱探测光的聚焦过程和焦点位置. 关键词： 诱导聚焦 自聚焦 非线性折射率     

Ultra-short scalar and vector solitons in self-inductively transparent media

The analytical form of the one-soliton solutions to the Maxwell–Bloch equations is found without the slowly-varying envelope approximation with application to the ultra-short (few-cycle or sub-cycle) light pulses propagating in media of two-level atoms as well as to fluxons in the long Josephson junctions. Also, we discuss the dynamics of the ultra-short vector solitons propagating in specific three-level media and magnetic-flux transmission lines (of two long Josephson junctions sharing a common superconducting plate). Studies of the (ultra-short) pulse collisions lead to the prediction of pulse stability against the collisions. In particular, the collisions of the ultra-short vector solitons are investigated in detail. Their collision-induced polarization transform is found to be similar to the polarization transform of the vector (Manakov) solitons propagating in self-focusing media.     

Localization in the model of contacting media with specific nonlinearity and interface interaction

In this paper, we consider the new model of nonlinear contacting media based on nonlinear Schrodinger equation with point potential and term, which is depended stepwise on field amplitude. Such a model theoretically describes a change in properties of the boundary regions along the interface between a Kerr-type crystal with cubic nonlinearity and a nonlinear medium characterized by abruptly change in dielectric constant depending on field amplitude. The short-range local interaction between wave and interface is taken into account by point potential in nonlinear Schrodinger equation. We obtain two new types of localized states characterized by composite structure consisting of three parts of the field distributions. We find exact and approximate solutions of dispersion equations. We described new properties of the spectrum of localized states arising as a result of the interaction of the wave with the interface and the presence of threshold field of the switching between the medium constants. All results are obtained in an analytical form. The proposed theory can be used to describe the propagation features of intense light beams localized along media interfaces in nonlinear optics, and to describe Bose-Einstein condensates with cubic nonlinearity.     

Solitons in optical lattices with nonlocal nonlinearity

The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.     

高斯光束通过非线性折射和吸收介质的光强分布

以衍射理论为基础,推导并模拟了高斯光束通过非线性折射和吸收效应介质后的远场光强分布。结果表明:入射高斯光束引起的介质折射率变化和光束波前曲率影响介质出射面光束的径向调制相位,安装在焦点前的有自聚焦效应的介质和安装在焦点后的有自散焦效应的介质具有闪耀光栅的能力,使远场出现中心为暗斑外侧为亮环的衍射图样。非线性折射效应为主的介质,其非线性吸收效应的变化同时改变远场衍射图样的数目和光强值,但对于非线性吸收效应为主的介质,衍射图样的数目随吸收效应的变化不明显,吸收效应只影响光强值。