Ultranarrow optical beams in quadratically nonlinear media

The vector Maxwell equations for the first-and second-harmonic planar beams are solved with allowance made for the nonlinear diffraction that weakens quadratic nonlinearity. The structure of the transverse and longitudinal components of the electromagnetic field of a parametric soliton is calculated for different values of the wave vector and phase mismatch. Exact analytic expressions are obtained for the self-similar profiles of extremally narrow solitons, and it is shown that the width has a fundamental limit of the order of a wavelength in a linear medium.     

Propagation of optical beams in strongly nonlocal nonlinear media

The propagation of arbitrary laser beams in strongly nonlocal nonlinear media is investigated based on the ABCD matrix. The second-order moment beam width and the mean curvature radius are derived under the off-waist incident condition.     

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.     

Boundary-induced localized structures in a nonlinear optical feedback experiment

Experimental and numerical evidence of symmetry-breaking bifurcations of a circular dissipative soliton with additional boundary conditions in the feedback of a liquid crystal light valve are reported. By tuning the strength of the nonlinearity or the size of the additional boundaries, the circular structure breaks up into polygonal symmetries and the system exhibits multistability. The experimental results are confirmed by numerical simulations with different configurations of the polarizers thus demonstrating the universality of the phenomenon.     

Modulation instability of broad optical beams in nonlinear media with general nonlinearity

The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.     

Formation and control of localized structures in nonlinear optical systems

Diffractive effects in passive nonlinear optical resonators can lead to pattern-forming instabilities. When the pattern (in our case, a regular hexagonal lattice of intensity peaks) coexists with the homogeneous solution, soliton-like intensity peaks in the transverse plane can be excited. These solutions have the characteristics of localized structures and are highly degenerate with respect to the peak location. By injecting narrow laser pulses, it is possible to turn on such peaks at desired locations and to turn them off selectively. The conditions to ensure independence among the peaks are described as well. These features suggest the possibility of encoding optical information in the structure of the field profile. (c) 1996 American Institute of Physics.     

双光束在自散焦介质中对向共同传输时的诱导聚焦

对二维自散焦介质中双光束对向共同传输问题进行了系统研究.数值模拟结果表明：在适当的条件下，强的抽运光能通过交叉相位调制效应诱导弱的信号光聚焦.讨论了样品长度、抽运光初始振幅、信号光初始振幅及两光束中心初始横向间距4个参数对信号光聚焦过程的影响，发现存在最佳参数值，选择恰当的参数可提高光束聚焦的效率. 关键词： 自散焦介质 对向传输 诱导聚焦 交叉相位调制效应     

空间相位调制对强非局域空间光孤子的影响

利用空间相位调制技术和数值分析的方法，讨论了高斯光束在强非局域非线性平板波导中的传输问题，发现只要介质的响应具有对称性,光束就会有相同的演化规律，可控的空间相位调制参数不仅能让光束自偏转还能实现分束，其全新特性在全光开关及分光器上有潜在的应用价值. 关键词： 强非局域空间光孤子 空间相位调制 光偏转 光开关     

自散焦介质中光束聚焦的最佳参数选择

对自散焦介质中由交叉相位调制效应引发的光束聚焦过程进行了细致的系统研究,讨论了抽运光初始振幅、抽运光信号光初始间距和抽运光信号光波长比三个参量对信号光聚焦过程的影响.数值模拟结果表明:抽运光越强,信号光聚焦程度越大;抽运光信号光初始间距和抽运光信号光波长比均存在一个最佳值,使得光束聚焦达到最佳效果.通过参数最佳值的选择,可提高光束聚焦的效率 关键词： 非线性折射率系数 交叉相位调制效应 自散焦介质 光束聚焦     

Mechanism of formation of simple optical structures in nonlinear fizeau interferometry

Explanations are suggested for the specific shapes of simple structures, generated in nonlinear interferometry. This is done within the mathematical model of dynamics of nonlinear phase clamping, developed by A. S. Akhmanov and M. A. Vorontsov. The basis of the analysis is an estimate of the contributions of diffusion and relaxation effects, as well as that of the Kerr effect, to the rates of phase dynamics.Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 77–81, June, 1995.     

Excitability mediated by localized structures in a dissipative nonlinear optical cavity

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point there is a regime of excitable localized structures under the application of suitable perturbations. Excitability emerges from the spatial dependence since the system does not exhibit any excitable behavior locally. We show that the whole scenario is organized by a Takens-Bogdanov codimension-2 bifurcation point.     

Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures

The linear and nonlinear characteristics of optical slow-wave structures made of direct coupled Fabry–Pérot and Ring Resonators are discussed. The main properties of an infinitely long slow-wave structure are derived analytically with an approach based on the Bloch theory. The spectral behaviour is periodical and closed form expressions for the bandwidth, the group velocity, the dispersion and the linear and nonlinear induced phase shift are derived. For structures of finite length the results still hold providing that proper input/output matching sections are added. In slow-wave structures most of the propagation parameters are enhanced by a factor S called the slowing ratio. In particular nonlinearities result strongly enhanced by the resonant propagation, so that slow-wave structures are likely to become a key point for all-optical processing devices. A numerical simulator has been implemented and several numerical examples of propagation are discussed. It is also shown as soliton propagation is supported by slow-wave structures, demonstrating the flexibility and potentiality of these structures in the field of the all-optical processing.     

Correction of nonlinear distortions of light beams by an optical system with feedback

The operation of a phase-conjugate COAT system under conditions of thermal self-interaction is investigated. The analogy between the phase conjugation and optimal focusing algorithms is discussed. A method is proposed for raising the stability of the adaptive system under conditions of strong nonlinearity. The possibility of using an optical system with feedback to suppress thermal spreading of light beams is analyzed on the basis of the results of a numerical simulation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 15–20, October, 1980.     

Cavity light bullets: three-dimensional localized structures in a nonlinear optical resonator

We consider the paraxial model for a nonlinear resonator with a saturable absorber beyond the mean-field limit. For accessible parametric domains we observe total radiation confinement and the formation of 3D localized bright structures. Different from freely propagating light bullets, here the self-organization proceeds from the resonator feedback, combined with diffraction and nonlinearity. Such "cavity" light bullets can be independently excited and erased by appropriate pulses, and once created, they endlessly travel the cavity round-trip.     

Splitting of atomic beams by light for creation of high-resolution spatial structures in optical nanolithography

Diffraction of atomic wave packets from a standing laser wave with a Gaussian profile is studied theoretically and numerically in pursuing the aim of creating high-resolution spatial structures in optical nanolithography. To this end, we propose to use nonadiabatic transitions between two optical potentials which take place when square of the value of detuning off the resonance is approximately equal to the Doppler shift. In this case, atomic wave packets experience splitting at nodes of the standing wave, which allows creating atomic structures on a substrate with a period substantially smaller than the standard nanofabrication limit equal to half the wavelength of light. We propose a scheme of the experiment for the observation of nonadiabatic transitions and splitting of the wave of matter caused by them. A number of computer simulations with parameters corresponding to real atoms have been performed, which exhibit this effect in both momentum and coordinate spaces.     

Statistical mechanics of nonlinear hydrodynamic fluctuations

The paper studies nonlinear hydrodynamic fluctuations by the methods of nonequilibrium statistical mechanics. The generalized Fokker-Planck equation for the distribution function of coarse-grained densities of conserved quantities is derived from the Liouville equation and then is investigated by using the gradient expansions in the flux correlation matrix. We have obtained the functional-differential Fokker-Planck equation describing the nonlinear hydrodynamic fluctuations in spatially nonuniform systems to second order in gradients of coarse-grained fluctuating fields. An outline of the derivation of Fokker-Planck equations containing the Burnett terms is also given. The explicit coordinate representation for the hydrodynamic Fokker-Planck equation is discussed in the case of one-component simple fluid. The general scheme of a change of coarse-grained functional variables is developed for hydrodynamic Fokker-Planck equations. The corresponding transformation rules are found for “drift” terms, “diffusion coefficients” and thermodynamic forces. The dynamical equations and stationary conditions for averages of functions (functionals) of hydrodynamic fields are discussed by using the Fokker-Planck operators acting on such functions. The explicit form of these operators are found for various sets of fluctuating fields. As an application of the formalism the calculation of the stationary correlation functions is presented for a simple nonequilibrium steady state.