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.     

Gaussian beam diffraction in weakly anisotropic inhomogeneous media

Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.     

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。     

The propagation of a polarized gaussian beam in a smoothly inhomogeneous isotropic medium

In the frame of the eikonal-based complex geometrical optics, which describes the phase front and cross section of a light beam using the quadratic expansion of a complex-valued eikonal, we investigate the transverse deflections of a polarized Gaussian beam (GB) in a smoothly inhomogeneous isotropic medium, which is called the spin Hall effect of the beam. The linear complex-valued eikonal terms are introduced firstly to describe the polarization-dependent transverse shifts of the beam in the inhomogeneous medium. We find that the polarization-dependent transverse shifts of the beams include two parts: one originates from the coupling between the spin angular momentum and the extrinsic orbital angular momentum due to the curve trajectory of the center of gravity of the polarized GB, and the other from the coupling between the spin angular momentum and the intrinsic orbital angular momentum due to the rotation of the beam with respect to the central ray.     

高斯光束在对数型非线性介质中自诱导效应

从标量Helmholtz方程出发,推导了对数饱和非线性介质中光场满足的非线性Schr dinger方程(NLSE)。通过与梯度折射率下的光场满足的方程比较,发现高斯光束在对数型饱和非线性介质中可自诱导梯度折射率。利用数值计算,详细地讨论了自诱导梯度折射率对高斯光束传输特性的影响。发现高斯光束在其自诱导的梯度折射率的影响下,呈振荡形式的准稳定的传输。光束注入介质中的初始状态,直接影响着光束的振荡形式(先发散还是先聚焦)、振荡深度(幅度)、振荡周期。得到高斯光束形成孤子的条件,以及若使高斯光束在对数饱和非线性介质中保持小损耗、高稳定的传输,应该使光束在阈值(孤子条件)附近注入介质的结论。     

对数型折射率饱和非线性介质中光孤子高斯型呼吸模式

根据对数型折射率饱和非线性介质中光束尺寸和波阵面曲率变化所遵循的方程,详细描述了空间光孤子高斯型呼吸模式．采用势函数分析方法,对光束尺寸一阶导数的正、负号进行了正确的选择,并计算了呼吸模式的光束尺寸、波阵面曲率半径、呼吸周期等重要参量. 关键词：     

Annihilation of Vertical-Bloch-Line Chains in the Walls of the Second Kind of Dumbbell Domains Subjected to Joint Static Bias Field and In-Plane Field

Using equations governing the variation of the beam size and the curvature of wave front in the logarithmically saturable nonlinear media, the Gaussian-type breath mode of spatial soliton has been described in detail. With the aid of a potential method, the positive and negative signs can be assigned to the first order derivative of the beam size with respect to the propagation distance. Thus, important parameters of the breath mode, such as the beam size, curvatwre radius of the wave front, the period, etc., have been calculated.     

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.     

Numerical implementation of complex geometrical optics

We propose a numerical scheme for calculation of the wave field, based on the geometrical-optics method generalized for complex values. The main advantage of the complex-value method is a possibility to take into account diffraction effects using only the ordinary differential equations of the geometrical optics. This allows one to significantly reduce the amount of computations and, hence, computation time. The efficiency of this algorithm is illustrated by two numerical examples that allow comparison with the known analytical solutions: the plane-wave field behind the caustic in the linearly inhomogeneous layer and the field of a Gaussian beam in a homogeneous medium. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 7, pp. 630–637, July, 2000.     

对数饱和非线性介质中的自洽多模高斯孤子解

通过解对数饱和非线性介质中光场满足的非线性薛定谔方程,得到一组厄米-高斯型的自洽多模解.在借鉴了R.G.Glauber的相干态理论的基础上,合理假设这组解在非线性介质中呈泊松分布,进而得到了在对数饱和非线性介质中存在高斯孤子的结论,并获得高斯孤子解、非线性系数与泊松参量三者之间的关系.该关系说明,若在介质中存在高斯孤子解,其非线性系数必须满足条件a≥1.当α=1,在介质中仅存在单模高斯孤子,其光斑尺寸必须满足的条件W=1/k n0/n2.在该条件下,以"束腰"注入介质中的高斯光束才可以在保持其光斑尺寸不变的情况下传输,否则光斑尺寸会存在一定的振荡.而振荡方式、振荡范围(表示光斑尺寸展宽或压缩及大小)与输入光束光斑尺寸及其一次导数有直接关系.     

Propagation of Optical Beams in Active Media Inside Gaussian Cavities

The evolution of relevant beam parameters of a light beam propagating through an iterated sequence of spherical lenses and Gaussian apertures immersed in an active medium is investigated. This structure is a classical model for an optical resonator. The effective size of the field distribution, the beam quality factor and the radius of wave front curvature are calculated as functions of the number of transits. Steady-state values of these parameters are also determined and the dependence of the results on the gain of the medium, the aperture width and the focal length is illustrated. A comparison with the case without active medium is also discussed.     

高斯光束在克尔型非线性介质中的演化特性

由光束在克尔型吸收介质中传输的非线性薛定谔方程,推导了高斯光束注入介质后满足的耦合方程,并分别在不考虑吸收和高阶展开项的情况下,对脉冲的腰斑半径的演化进行了理论分析。发现当注入脉冲满足一定的条件时,脉冲可以以“孤波”的形式传播。当考虑吸收和高阶展开项时,脉冲不存在“孤波”形式,且存在一个阈值,低于阈值的输入,脉冲发生自聚焦;对高于阈值的输入,腰斑半径随着距离的增加而增加,聚焦趋势根本就不存在。     

Propagation of Gaussian beam in an absorbing waveguide

Propagation of a Gaussian beam in an absorbing waveguide is analyzed for cubic-quintic and saturable media taking into account both linear and nonlinear absorption. A “collective variable approach” technique, based on trial functions, is used to solve the general nonlinear Schrodinger equation. In the absence of losses, we construct a diagram which defines regions of oscillatory and diffractive beam propagation for both types of media, and also a diagram that compares bistable behavior in such media. We show that if the linear and nonlinear absorption coefficients are small, the behavior of the oscillations of the beam width on propagation allows one to distinguish between cubic-quintic and saturable media. By reversing the sign of the linear absorption, we analyze the behavior of the beam propagation in media with gain and nonlinear absorption. In cubic-quintic media, the energy reaches a plateau for certain ratios of gain to losses, whereas for saturable media, the energy increases throughout the beam propagation.     

Transformation of Gaussian beams by spherical and cylindrical lenses: the scalar diffraction approach

The transformation of a Gaussian beam by a lens has often been described in terms of geometrical optics by the formal application of the ABCD-matrix law of the lens to the complex beam parameter. In this paper we present as a wave optical method the scalar diffraction approach to the same problem. It is shown that the fresnel approximation yields results which are analytically identical to those obtained by the ABCD-law, if truncation effects of the lens can be neglected.     

Dynamics of one- and two-dimensional kinks in bistable reaction-diffusion equations with quasidiscrete sources of reaction

We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially inhomogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous works on homogeneous reaction terms, we derive asymptotically an equation governing the front motion, which is strongly nonlinear and, for the two-dimensional case, generalizes the classical mean curvature flow equation. We study the motion of one- and two-dimensional fronts, finding that the inhomogeneity acts as a "potential function" for the motion of the front; i.e., there is wave propagation failure and the steady state solution depends on the structure of the function describing the inhomogeneity. (c) 2001 American Institute of Physics.     

聚吡咯甲烯/聚乙烯醇薄膜对高斯光束的衍射行为

制备了一种新型有机聚合物（聚吡咯甲烯）与聚乙烯醇的非线性光学复合薄膜,在该样品的激光纵向扫描实验中发现,随着样品相对于高斯光束束腰位置的不同,产生了两种不同结构的同心衍射环,理论分析表明,该现象可以用光克尔效应和热光非线性效应共同作用下的附加相位孔对入射光束的衍射行为解释,从菲涅耳－基尔霍夫衍射积分公式出发,建立了非线性光学介质对高斯光束的衍射模型,通过数值积分,得到了与实验现象符合的计算结果。     

Propagation of ellipitic Gaussian laser beam in a higher order non-linear medium

Using a direct variational technique involving elliptic Gaussian laser beam trial function, the combined effect of nonlinearity and diffraction on wave propagation of optical beam in a homogeneous higher order nonlinear medium is presented. Particular emphasis is put to understand the variation of beam width and longitudinal phase delay with the distance of propagation in case of lossless and lossy medium. It is also observed that stationary self-trapping is possible in lossless medium at higher laser intensity where fifth order nonlinearity becomes comparable to third order nonlinearity. The phase is also seen to be always negative.