Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity:Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated.An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field,with linear absorption and due to saturation effects for arbitrary large intensity.The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters.Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode.Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence.The beam is more focussed at lower intensity in both cases viz.extraordinary and ordinary mode.     

Methods of measuring the nonlinear-optical coefficients of the refractive index of nonlinear media

A cousistent analysis of a method of measuring the coefficient n ₂ of the Kerr nonlinearity and the two-photon absorption coefficient in presented. The method is based on the study of the dependence of the nonlinear transmittance with respect to the far-field axial intensity of the laser beam on the position of the layer of the nonlinear medium on the z (longitudinal) coordinate of this beam (z scanning). The possibility for the measurement of n ₂ and the two-photon (multiphoton) absorption coefficient based on the study of the far-field variations in the spatial profile of the beam having passed through the nonlinear medium is also analyzed. The calculations prove the efficiency of the new method for measuring n ₂ and the two-photon (multiphoton) absorption coefficient.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity: Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode.     

平顶光束经表面有缺陷的厚非线性介质后的光强分布

基于非线性薛定谔方程和分步傅里叶算法, 研究了高功率平顶高斯光束经过厚非线性介质后在自由空间传输的光强演变过程, 详细分析了介质表面缺陷对光强演化规律的影响.研究结果表明, 平顶阶数越大, 光束的自聚焦效果越差, 最大光强点越靠近介质后表面.入射光束的初始场强越强, 介质的厚度和非线性系数越大, 光束的自聚焦越强, 且极值点越靠近介质后表面.介质表面的缺陷使得光束在靠近介质后表面有较大的光强. 并且相位调制型缺陷比振幅调制型缺陷对光强的影响更大. 关键词： 平顶光束 自聚焦 缺陷 光强分布     

数字重现无透镜傅里叶变换X射线全息的实验模拟研究

参照无透镜傅里叶变换（ＬＬＦＴ）Ｘ射线全息图的记录光路，采用可见光源模拟研究了无透镜傅里叶变换Ｘ射线全息从记录到数字重现的全过程，给出了实验结果，并对光学重现和数字重现结果作了比较，分析了该记录方式存在的一些问题，指出实际Ｘ射线全息记录中可直接使用波带板＋１级衍射而不必在物面加一滤波小孔。分析了利用数字重现消除记录过程中非线性效应的可行性。并着重指出波带板的多级衍射的互干涉对重现象的干扰，应设法消除。     

电磁感应透明介质中的弱光空间暗孤子环

利用多重尺度方法,解析地研究了Λ型三能级冷原子气及一束较强耦合光组成的电磁感应透明介质体系中的非线性动力学性质.结果表明：一束较弱的探测光能在电磁感应透明介质中形成弱光空间暗孤子,当弱光空间暗孤子沿轴向传播时,它会逐渐演化成一个稳定的弱光空间暗孤子环,这是衍射效应和自散焦效应相互平衡的结果. 关键词： 电磁感应透明 弱光空间暗孤子环 多重尺度方法     

Formation of elliptically polarized ring-shaped electric field structures on the self-focusing of light in an isotropic medium featuring a spatially disperse nonlinearity

The possibility is demonstrated that the self-focusing of an elliptically polarized beam in a medium featuring a spatially disperse cubic nonlinearity can give rise to several radially symmetric ring-shaped regions of the same sense of rotation (right or left) of the electric-field vector in the cross-section of the beam. The formation dynamics and propagation features of such electric field structures are studied for various parameters of the incident radiation and nonlinear medium.     

Effect of the interaction of spatial modes on the nonlinear dynamics of sound beams

Propagation of an acoustic beam in a medium with a combined second-and third-order nonlinearity is studied. The derivation of the dynamics equations and the determination of modes is performed using the orthogonal-projection operator technique. The problem on the beam evolution considered with allowance for weak nonlinearity, diffraction, and dissipation leads to a set of equations describing the interaction of directed waves and a quasi-stationary (thermal) mode. In the conditions of a directed beam, the inclusion of the interaction leads to a modified Khokhlov-Zabolotskaya-Kuznetsov equation with quadratic and cubic nonlinearities. The solutions to the problem are obtained in the region near the beam axis, in the form of series expansions in the transverse coordinate up to the focal point. The results of calculations are represented in graphical form for different nonlinearity combinations.     

Thermal nonlinearity in a photoacoustic cell

The effect of the thermal nonlinearity caused by the temperature dependence of the specific heat and thermal conductivity of a sample, substrate, and air on the temperature field in a photoacoustic cell is stud-ied theoretically. Exact solutions are obtained for a steady temperature field with allowance for thermal nonlin-earity and for a nonsteady field without allowance for this nonlinearity. The nonsteady nonlinear problem was solved numerically. It is shown that, due to thermal nonlinearity, the linear dependence of the temperature of the irradiated surface on the heating beam intensity gradually transforms into a power-law dependence as the beam intensity increases.     

多层介质中超声相控阵声场仿真*

由于良好的声束偏转与聚焦特性,超声相控阵已经广泛应用于多层固体介质的缺陷检测。当超声束经过多层介质时,由于反射、透射以及模式转换的存在,多种声束存在于这种结构中,使得声场分析变得复杂。为了提高多层介质检测的准确性,有必要对超声声场的分布规律进行深入地了解。该文结合高斯声束等效点源模型以及射线追踪法,给出了相控阵声源在多层固体介质中激发声场的仿真方法,并且模拟计算了一维线型相控阵在楔块-铝-黄铜-钢四层固体介质中的辐射声场。通过对不同延时法则的计算,实现了声波在这种复杂介质中的偏转与聚焦,进而研究了不同焦点处聚焦声场的分布。结果表明:相控阵方法能使聚焦点处的声场幅值增大,能量集中,提高了检测分辨率;不同聚焦点处声场聚焦效果不同,实际检测时应根据检测区域结构及位置特点,合理放置相控阵换能器。与瑞利积分法的比较表明,该文的仿真方法适用于多层介质相控阵声场的计算。     

Nonlinear Effects of a Gaussian Laser Beam on Megagauss Magnetic Field Generation in Laser Produced Plasma

The generation of megagauss magnetic field due to the time dependent part of the ponderomotive force of a self-focused Gaussian laser beam indicent on a plasma has been studied. Defocusing of the laser beam becomes possible due to diffraction divergence in the case of a weakly nonlinear medium. The influence of defocusing of a laser beam on magnetic field generation has also been investigated. It is found that the magnitude of the magnetic field due to self focusing of the beam is enhanced and is comparable with the observed values, while there is a reduction in the magnitude of the magnetic field when the beam defocuses due to diffraction divergence in the presence of weak nonlinearity.     

Wideband modulation instability at combination frequencies in wave beams

We study theoretically wideband modulation instability at combination frequencies in media having cubic nonlinearity of self-focusing type along with the higher-order defocusing nonlinearity. It is assumed that in a medium with a purely cubic nonlinearity, the medium dispersion does not permit modulation instability. In this case, a collapse of the wave field exists if the beam power is higher than the critical power of self-focusing. The higher-order nonlinearity limits the field at the nonlinear focus, and the instability at combination frequencies becomes possible. It turns out that the field at the nonlinear focus increases with increasing excess of the beam power over the critical power of self-focusing. The obtained values of the nonlinear dielectric permittivity are used for determination of the growth rates of instability at combination frequencies. These growth rates ensure an increase in the combination fields from noise levels up to values comparable with the field of the high-power beam. Such an increase takes place if the beam power is severalfold higher than the critical one. The developed theory can be used for explanation of spectrum superbroadening during self-focusing of sufficiently short laser pulses and high-harmonic generation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 522–532, June 2007.     

Nonlinear ultrasonic waves in bubbly liquids with nonhomogeneous bubble distribution: Numerical experiments

This paper deals with the nonlinear propagation of ultrasonic waves in mixtures of air bubbles in water, but for which the bubble distribution is nonhomogeneous. The problem is modelled by means of a set of differential equations which describes the coupling of the acoustic field and bubbles vibration, and solved in the time domain via the use and adaptation of the SNOW-BL code. The attenuation and nonlinear effects are assumed to be due to the bubbles exclusively. The nonhomogeneity of the bubble distribution is introduced by the presence of bubble layers (or clouds) which can act as acoustic screens, and alters the behaviour of the ultrasonic waves. The effect of the spatial distribution of bubbles on the nonlinearity of the acoustic field is analyzed. Depending on the bubble density, dimension, shape, and position of the layers, its effects on the acoustic field change. Effects such as shielding and resonance of the bubbly layers are especially studied. The numerical experiments are carried out in two configurations: linear and nonlinear, i.e. for low and high excitation pressure amplitude, respectively, and the features of the phenomenon are compared. The parameters of the medium are chosen such as to reproduce air bubbly water involved in the stable cavitation process.     

输入面纵向偏移诱导的强非局域非线性光传输特性变化

基于模式分解方法, 分析了输入面纵向偏移诱导的强非局域非线性光传输特性变化的普适性规律. 结果表明光束输入面移动后导致的影响包括: 光斑在每个周期内出现的位置和顺序的变化、 相同形状的光斑在输入面移动前后大小的差异以及波面曲率因子的演化. 这些性质可用一个简单的数学公式进行归纳; 利用这一公式可方便地由输入面移动前的任意光束解得到输入面纵向移动后的光束解. 关键词： 强非局域非线性 光束 输入面     

Nonlinear response of shear deformable beams on tensionless nonlinear viscoelastic foundation under moving loads

In this paper, a boundary element method is developed for the geometrically nonlinear response of shear deformable beams of simply or multiply connected constant cross-section, traversed by moving loads, resting on tensionless nonlinear three-parameter viscoelastic foundation, undergoing moderate large deflections under general boundary conditions. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse moving loading as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Three boundary value problems are formulated with respect to the transverse displacement, to the axial displacement and to a stress functions and solved using the Analog Equation Method, a Boundary Element based method. Application of the boundary element technique yields a system of nonlinear Differential-Algebraic Equations, which is solved using an efficient time discretization scheme, from which the transverse and axial displacements are computed. The evaluation of the shear deformation coefficient is accomplished from the aforementioned stress function using only boundary integration. Analyses are performed to illustrate, wherever possible, the accuracy of the developed method, to investigate the effects of various parameters, such as the load velocity, load frequency, shear deformation, foundation nonlinearity, damping, on the beam displacements and stress resultants and to examine how the consideration of shear and axial compression affects the response of the system.     

轴向加速运动黏弹性梁受迫振动中的混沌动力学

研究了黏弹性轴向运动梁在外部激励和参数激励共同作用下横向振动的混沌非线性动力学行为. 引入有限支撑刚度, 并考虑黏弹性本构关系取物质导数, 同时计入由梁轴向加速度引起的沿径向变化的轴力, 建立轴向运动黏弹性梁横向非线性振动的偏微分-积分模型. 通过Galerkin截断方法研究了外部激励的频率和因速度简谐脉动引起的参数激励的频率在不可通约关系时轴向运动连续体的非线性动力学行为, 并对不同截断阶数的数值预测进行了对比. 基于对控制方程的Galerkin截断, 得到离散化的常微分方程组, 使用四阶Runge-Kutta方法求解. 基于此数值解, 运用非线性动力学时间序列分析方法, 通过Poincaré 映射, 观察到轴向运动梁随扰动速度幅值的倍周期分岔现象, 并比较了有无外部激励对倍周期分岔的影响. 分别在低速以及近临界高速运动状态下, 从相平面图、Poincaré 映射以及频谱分析的角度识别了系统中存在的准周期运动形态. 关键词： 轴向运动梁 非线性 混沌 分岔     

New approaches to nonlinear diffractive field propagation

In many domains of acoustic field propagation, such as medical ultrasound imaging, lithotripsy shock treatment, and underwater sonar, a realistic calculation of beam patterns requires treatment of the effects of diffraction from finite sources. Also, the mechanisms of loss and nonlinear effects within the medium are typically nonnegligible. The combination of diffraction, attenuation, and nonlinear effects has been treated by a number of formulations and numerical techniques. A novel model that incrementally propagates the field of baffled planar sources with substeps that account for the physics of diffraction, attenuation, and nonlinearity is presented. The model accounts for the effect of refraction and reflection (but not multiple reflections) in the case of propagation through multiple, parallel layers of fluid medium. An implementation of the model for axis symmetric sources has been developed. In one substep of the implementation, a new discrete Hankel transform is used with spatial transform techniques to propagate the field over a short distance with diffraction and attenuation. In the other substep, the temporal frequency domain solution to Burgers' equation is implemented to account for the nonlinear accretion and depletion of harmonics. This approach yields a computationally efficient procedure for calculating beam patterns from a baffled planar, axially symmetric source under conditions ranging from quasilinear through shock. The model is not restricted by the usual parabolic wave approximation and the field's directionality is explicitly accounted for at each point. Useage of a harmonic-limiting scheme allows the model to propagate some previously intractable high-intensity nonlinear fields. Results of the model are shown to be in excellent agreement with measurements performed on the nonlinear field of an unfocused 2.25-MHz piston source, even in the near field where the established parabolic wave approximation model fails. Next, the model is used to compare the water path and in situ fields of a medical ultrasound device. Finally, the model is used to calculate the spatial heating rate associated with a nonlinear field and to simulate the phenomenon of saturation-induced beam broadening.     

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.     

The self-action of the electromagnetic field in a medium with considerable nonlinearity

The propagation of the electromagnetic wave field in a nonlinear medium is discussed in the framework of generalized nonlinear geometrical optics. In this approach the nonlinearity of the medium and the angles between the rays and the general orientation of the wave's beam are not assumed to be small. The exact analytical solutions of the equations of this generalized nonlinear geometrical optics are constructed. These solutions show the possibility of a peculiar mechanism of space stratification of the field.     

Nonlinear optical and magneto-optical effects in non-spherical magnetic granular composite

The magnetization-induced nonlinear optical and nonlinear magneto-optical properties in a magnetic metal-insulator composite are studied based on a tensor effective medium approximation with shape factor and Taylcr-expansion method. There is a weakly nonlinear relation between electric displacement D and elcctric field E in the composite. The results of our studies on the effective dielectric tensor and the nonlinear susceptibility tensor in a magnetic nanocomposite are surveyed. It is shown that such a metal-insulator composite exhibits the enhancements of optical and magneto-optical nonlinearity. The frequencies at which the enhancements occur, and the amplitude of the enhancement factors depend on the concentration and shape of the magnetic grains.