Instability of a light beam and its decomposition with thermal self-stress in a moving medium

On the basis of linearized equations for perturbations in a one-dimensional light beam propagating in a moving medium with thermal nonlinearity, the article shows the possibility of an exponential growth of these perturbations with an intensity above the critical in the beam. Numerical solutions were carried out for the nonlinear equations of the propagation of Gaussian beams, showing that small perturbations can lead to decomposition of the beams.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 11, pp. 1610–1617, November, 1978.     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

高功率超高斯光束传输的非线性补偿研究

 分析了高功率超高斯光束在非线性介质中传播的基本理论，用分步傅里叶变换方法计算了10阶超高斯光束在非线性介质内的传输过程，最后采用具有负折射率系数的非线性介质作为补偿材料，对不同的补偿方式进行了对比分析。研究表明，四种补偿方式均可以大大减小光束的B积分，有效防止超高斯光束边缘的非线性增长，降低光束的小尺度自聚焦，同时选用后补偿作为最佳补偿方式。     

Analytical propagation equation of astigmatic Hermite–Gaussian beams through a 4×4 paraxial optical system and their symmetrizing transformation

Starting from the Collins formula, a closed-form propagation equation of astigmatic Hermite–Gaussian (H–G) beams through a 4×4 paraxial optical system is derived, which permits us to calculate the irradiance distribution at any propagation plane and to study the symmetrization of astigmatic standard and elegant H–G beams. A detailed symmetrizing transformation of astigmatic H–G beams through a three-cylindrical-lens mode converter is illustrated both analytically and numerically. It is found that in accordance with the second-order moments characterization, there are two types of beam symmetrization. The transformation of standard H–G beams through the three-cylindrical-lens mode converter belongs to the perfect symmetrization, whereas the transformation of elegant H–G beams is the imperfect one.     

Correlation of the displacements of spatially bounded light beams in a turbulent medium

The correlation function of the displacement of the axes of spatially bounded beams in a turbulent medium is calculated in the general case when both the points of entry of the beam into the medium and the observation points are spaced. Specific estimates are carried out for a turbulent model of the medium. It is shown that even for beam separations that are considerably greater than their initial width the correlation of the displacements of the axes has a noticeable value.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 4, pp. 533–539, April, 1972.The author expresses his indebtedness to V. I. Tatarskii for his useful discussion.     

Persistence and breakdown of Airy beams driven by an initial nonlinearity

We study the behavior of Airy beams propagating from a nonlinear medium to a linear medium. We show that an Airy beam initially driven by a self-defocusing nonlinearity experiences anomalous diffraction and can maintain its shape in subsequent propagation, but its intensity pattern and acceleration cannot persist when driven by a self-focusing nonlinearity. The unusual behavior of Airy beams is examined from their energy flow as well as the Brillouin zone spectrum of self-induced chirped photonic lattices.     

Beam coupling and decoupling in degenerate two-wave mixing in a reflection geometry with photorefractive Bi2GeO20 crystals

The dependence of the effective gain on the incident angle of the beams and on the initial beam intensity ratio is studied in the experiment of degenerate two-wave mixing (TWM) in a reflection geometry with photorefractive Bi₁₂GeO₂₀ (BGO) crystals. A saturation value of the effective coupling constant ¦g¦-0.4 cm^–1 is obtained. In contrast to TWM operated in the drift mode (i.e. with a nonzero electric field applied to the crystal), for TWM operated in the diffusion mode (zero external electric field) as is our case, beam coupling is reduced by moving the crystal or the interference fringes at a constant speed. At high moving speeds, complete beam decoupling can be reached. A comparison between the theoretical and measured dependence of the effective gain on the moving speed is also made. Using this technique, complete isolation of two intersecting coherent beams inside a nonlinear medium can be achieved.     

Nonlinear dynamics of an electron beam with a virtual cathode in a finite drift space

Nonlinear oscillations of an electron beam with a virtual cathode in a finite-length drift tube region are examined by numerical simulation (the PIC method). The change in dynamics of the beam complex with decreasing radius of the drift tube is investigated. The dynamical nature of the stochastic oscillations produced by the virtual cathode is demonstrated by an attractor dimension analysis. Physical processes in the electron beam are studied. It is found that one mechanism responsible for the chaotic behavior of the electron beam is due to the nonlinear interaction between the autostructures organized in it.State University, Saratov. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 268–274, March–April, 1995.     

Feasibility of remote focusing of a curvilinearly scanning beam in a moving defocusing medium

The thermal blooming of a collimated parabolically scanning beam in a defocusing medium moving across the beam is modeled. It is shown by numerical analysis that the maximum intensity in the beam within a specified portion of the path can be increased significantly by proper selection of the parameters of the scanning trajectory.Preliminary results of the present study have been reported at the Thirteenth All-Union Conference on Radio Wave Propagation [1] and at the Sixth All-Union Symposium on the Propagation of Laser Radiation in the Atmosphere [2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 27, No. 1, pp. 41–47, January, 1984.The authors are indebted to the editors for useful comments, which have contributed greatly to the improvement of certain aspects of the article.     

Coupled tapering/uptapering of soliton pairs in nonlinear media

Phenomenon of coupled tapering/uptapring of two mutually incoherent beams coaxially co-propagating in a nonlinear medium with small gain or loss has been investigated in this paper using standard parabolic equation approach (PEA) and the results are compared with the results obtained by Beam Propagation Method (BPM), i.e., by direct simulations of the underlying Nonlinear Schrödinger Equation (NLSE). The PEA results are shown to be in excellent agreement with the BPM results. It is seen that both beams of the pair induce uptapering in each other in presence of losses and tapering in presence of gain. When the medium offers gain to the first beam and losses to the other, both beams taper. When the medium offers gain/absorption to only one of the two beams, the beam undergoes self-tapering/self-uptapering and induces a taperd/uptaperd waveguide. The other beam (for which the medium is lossless) uptapers/tapers due to the taperd/uptaperd waveguide created by the first beam.     

Fields of apertured polychromatic laser beams with Gaussian and Hermite–Gaussian transverse modes

Starting from the Huygens–Fresnel diffraction integral, the field expressions of apertured polychromatic laser beams with Gaussian and Hermite–Gaussian transverse modes are derived. Influence of the bandwidth on the intensity distributions of the laser beams is analyzed. It is found that when the bandwidth increases, the amplitudes and numbers of the intensity spikes decrease and beam uniformity is improved in the near field and the width of transverse intensity distribution of the apertured beams decreases in the far field. Thus, the smoothing and narrowing effects can be achieved by increasing the bandwidth. Also, these effects are found in the laser beams with Hermite–Gaussian transverse modes as the bandwidth increases.     

Mighty morphing spatial solitons and bullets

We give what we believe to be the first closed-form exact expression for the dynamic evolution of nonstationary beams of arbitrary intensity and width propagating in a uniform nonlinear medium and in both two and three dimensions. This shows that periodic and quasi-periodic (nonradiating) beams can exist in a non-Kerr nonlinear medium. The Schr?dinger equation is solved for Gaussian beams in a saturable medium. For one critical (initial) beam width, the Gaussian is a stable stationary soliton or bullet, independent of its intensity; otherwise, it breathes. New quasi-periodic beams (mighty morphing solitons) and bullets (mighty morphs) of elliptical cross section also exist whose ellipticity changes with propagation.     

Adaptive focusing of a high-intensity beam in an irregular medium

Conclusions These model studies show that the performance in adaptive focusing for high-intensity beams in randomly inhomogeneous media is restricted primarily by nonlinear phenomena. The power density at the object is increased by adaptive control and is only slightly dependent on the fluctuation variance for the modes considered and for the range of nonlinearity parameters.In thermal self-action, large-scale spatial distortions predominate, for which one can use adaptive suppression systems with small numbers of control coordinates. In the case of nonlinear refraction in a moving medium, a considerable improvement is obtained by control on the lower aberrations, i.e., by means of the wavefront tilt and curvatures.A current problem in optimizing adaptive-optics systems is evidently the determination of a sufficient set of control coordinates for focusing a high-intensity beam propagating under real conditions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 30–41, November, 1985.     

Airy光束在Kerr介质中的传输特性

通过对非线性薛定谔方程的研究,得出Airy光束在Kerr介质中的崩塌功率及有效束宽演化的解析表达式。经过数值计算发现,Airy光束在聚焦的Kerr介质中,其主瓣在开始传播时始终是会聚的;当输入功率小于临界崩塌功率时,Airy光束主瓣的中心部分出现局部崩塌。在不同的Kerr介质中, Airy光束的形状和传输轨道均能保持不变,如同在自由空间中传播,但光场大小的分布,随着不同的Kerr介质会发生改变:在Kerr的聚焦介质中,光场向中心聚焦;而在散焦的Kerr介质中,光场会发散。     

Nonlinear diffraction and total internal reflection in optical-beam interaction in defocusing media

We elaborate the theory of reflection of an optical signal beam from an inhomogeneous channel created by a high-power laser beam of different frequency in a nonlinear defocusing medium. We study the effects of total internal reflection and nonlinear diffraction in the interaction of these beams. We derive and analyze the equation for the trajectory of the reflected signal beam and obtain the expression for the critical value of beam-intersection angle below which the total internal reflection occurs. We discuss the results of numerical modeling of nonlinear Schr¨odinger equations for envelopes of the beams in media with quadratic, photorefractive, and thermal nonlinearities. We present experimental data on the interaction of beams of argon and helium–neon lasers in a cuvette with tinted alcohol.     

Excitation of nonlinear surface modes by wave beams

We consider the interaction of 2-D and 3-D wave beams with an interface between linear and nonlinear media. The range of parameters of Gaussian beams exciting nonlinear surface waves (NSW) with high efficiency is analytically determined. Different regimes of NSW excitation are numerically studied. Analytical data are in good agreement with numerical results.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 246–255, March–April, 1995.     

Steady-state self-focusing of Gaussian electromagnetic beams in an inhomogeneous nonlinear medium: Effect of absorption and initial curvature of the beam

The authors have investigated the effect of linear absorption and initial curvature of an electromagnetic Gaussian beam on focusing/defocusing in an inhomogeneous nonlinear medium. Numerical computations have been made for linear inhomogeneity and saturating nonlinearity, characteristic of dielectrics and collisional plasmas. The maximum and minimum of the beam width keep decreasing with increase in distance of propagation (or absorption), till the beam becomes very weak and diverges steeply; penetration in an overdense medium also decreases with increasing absorption. Converging beams initially converge and then go in: (i) the oscillatory divergence (ii) self-focusing or (iii) steady divergence mode, depending upon the initial values of beam width and axial irradiance. The maximum penetration in an overdense medium has the highest values for −0.7<(df/dξ)_ξ=0<0.4 and falls sharply, outside these limits.     

Comparison of SRS thresholds under pumping by Gaussian and Bessel beams

In the paraxial approximation, it has been shown that the quasi-stationary SRS amplification coefficient in the near-threshold region is determined by the product of the pump intensity in the beam center and the overlap integral of the transverse structure of the pump and the Stokes component. Expressions for the overlap integral and the scattering powers have been obtained and analyzed for the following cases: the pump and the Stokes field are Gaussian beams; the pump and the Stokes field are Bessel beams; the pump is a Bessel beam and the Stokes field is an axial Gaussian beam. Relations between the SRS excitation thresholds in different cases have been found.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 778–787, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

高斯光束通过非线性介质后的远场衍射图样的研究

 利用菲涅尔－基尔霍夫衍射积分公式，对发散和会聚高斯光束通过薄非线性介质时形成的远场衍射图样进行了研究。模拟计算结果表明：当发散高斯光束通过自散焦介质或会聚高斯光束通过自聚焦介质时，远场均会出现中央较暗、向外围逐渐增强、分布尺度较大的粗衍射环；当发散高斯光束通过自聚焦介质或会聚高斯光束通过自散焦介质时，远场均会出现中心强度最大、向外围逐渐减弱、分布尺度较小的细衍射环。不同远场衍射图样归根结底是入射高斯光束因介质折射率变化造成的空间自相位调制及其波前曲率共同作用的结果。     

Dechannelization of relativistic protons in an elastically deformed single crystal

Experimental results on the deflection of a beam of relativistic protons by a single crystal are compared with the results of a theoretical analysis of protons channeling in curved planar channels in the crystal. The effectiveness of using curved single crystals for controlling high-energy charged particle beams is analyzed. The effect of the divergence of the beam on the effectiveness of deflecting relativistic protons by the crystal is examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 8–11, June, 1981.