Solutions for the propagation of light in nonlinear optical media with spatially inhomogeneous nonlinearities

In this paper, we present solutions for the nonlinear Schrödinger (NLS) equation with spatially inhomogeneous nonlinearities describing propagation of light in nonlinear media, under two sets of transverse modulation forms of inhomogeneous nonlinearity. The bright soliton solution and Gaussian solution have been obtained for one set of inhomogeneous nonlinearity modulation. For the other, bright soliton solution, black soliton solution and the train solution have been presented. Stability of the solutions has been determined by exact soliton solutions under certain conditions.     

非均匀系统中非自治孤子的色散和非线性管理

基于包含自发拉曼散射和外电光调制效应的非自治非线性薛定谔方程,采用简单的变换方法,解析研究了三种非均匀系统中非自治孤子的管理和传输。结果发现,在非均匀的非线性渐增或色散渐减光纤系统中都存在精确的啁啾非自治孤子解,都可以实现孤子的放大和压缩,但具有不同的速度、频移和啁啾特性;而在非均匀的色散和非线性均渐减光纤系统中,可以支持无啁啾的非自治孤子,该孤子具有不变的脉宽和振幅以及振荡衰减的速度,孤子的频移仅由自发拉曼散射决定。同时,数值模拟结果进一步证实在三种非均匀管理系统中都可支持非自治孤子的传输。该研究结果为实际非均匀孤子管理系统中实现孤子的压缩和传输提供了理论依据。     

Trapping and fusion of solitons in a nonuniform toda lattice

In this paper we consider strongly localized solitons leading to high energy events in a Toda lattice with springs of distinct nonlinearity. The trapping and superposition of solitons at a single soft spring embedded in a hard host lattice is investigated numerically. We further show the generation of high energy solitons at an interface between a hard and a soft lattice. The behaviour of a soliton incident on an inhomogeneity is approached analytically. The interaction of solitons in an inhomogeneous Toda lattice is compared to that in a homogeneous one.     

EPR and NMR line shapes in disordered ferroelectric crystals

A theory is developed for the magnetic resonance line shape in disordered ferroelectric crystals. In a study of the random fields responsible for inhomogeneous line broadening, nonlinear and spatial correlation effects are taken into account. It is shown that homogeneous broadening depends on the temperature and on the magnitude and orientation of the external magnetic field, as well as on the nonlinearity parameters of the ferroelectric material. The resonance line shape is calculated as the envelope of homogeneously broadened Lorentzian spin packets. Analytic expressions for I ₂(ω) and I ₃(ω) are introduced to account for nonlinearity and correlation effects of second and third order, respectively. Calculations are done for centrally symmetric crystals, as well as for those without a center of symmetry. It is shown that homogeneous broadening is important near the line peak, while the wings are determined mainly by inhomogeneous broadening. Manifestations of the predicted effects in the spectrum lines of disordered ferroelectric crystals are discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 340–347 (February 1998)     

Dynamics of two-mode radiation in optical waveguides with strong mode coupling

Amplitude equations, as well as the effective dispersion and nonlinearity parameters, which define the dynamics of a wave packet formed by two strongly coupled modes, are derived with allowance for the frequency dependence of the linear mode coupling coefficient. These equations are used to study the onset of the modulation instability of the two-mode wave packet, soliton-like pulses, and compression modes. Unlike single-mode systems, the last two effects in optical waveguides may arise for both a negative and positive disper-sion of the waveguide material.     

Discrete diffraction on a cascade-induced periodic lattice

A method for cascade generation of a periodic lattice in a medium with quadratic nonlinearity is proposed. Such a lattice is induced as a result of interference of two or four crossed fundamental-frequency waves. Numerical simulation of the discrete diffraction of a signal beam coupled to one of the lattice waveguides is performed. With an increase in the modulation depth of the refractive index, the signal wave is trapped in the waveguide.     

The evolution of two-frequency solitons in an optical fiber with a longitudinally nonuniform nonlinearity

The evolution of two-frequency solitons in an optical fiber, as well as the practically important special case of absence of the second-harmonic wave, in the presence of a longitudinal nonuniformity of the coefficients characterizing the propagation nonlinearity are considered. The solitons found for media with constant values of the nonlinearity coefficients are used as initial distributions for media with a periodic dependence of the nonlinearity coefficients on the longitudinal coordinate. Modulation of the coefficient of cubic or quadratic nonlinearity is shown to result in oscillations of the peak intensity of the solitons (in both their components if two-color solitons are considered). In the case of a weak modulation of the nonlinearity coefficients, oscillations of the peak intensity occur at the frequency coinciding with the frequency of modulation of the nonlinearity coefficients. Under the weak influence of a periodically modulated cubic nonlinearity, parameters of quadratic solitons also oscillate upon the propagation. Regions of stability of solitons in the space of the modulation parameters are established.     

An Intense Wave in Defective Media Containing Both Quadratic and Modular Nonlinearities: Shock Waves,Harmonics, and Nondestructive Testing

The observed nonclassical power-law dependence of the amplitude of the second harmonic wave on the amplitude of a harmonic pump wave is explained as a phenomenon associated with two types of nonlinearity in a structurally inhomogeneous medium. An approach to solving the inverse problem of determining the nonlinearity parameters and the exponent in the above-mentioned dependence is demonstrated. To describe the effects of strongly pronounced nonlinearity, equations containing a double nonlinearity and generalizing the Hopf and Burgers equations are proposed. The possibility of their exact linearization is demonstrated. The profiles, spectral composition, and average wave intensity in such doubly nonlinear media are calculated. The shape of the shock front is found, and its width is estimated. The wave energy losses that depend on both nonlinearity parameters—quadratic and modular—are calculated.     

Local interaction simulation approach to modelling nonclassical,nonlinear elastic behavior in solids

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.     

非线性声波方程二次谐波高阶近似解及实验验证

非线性声波方程的传统二次谐波二阶近似解不够精确,对测量材料的非线性系数造成较大误差。利用摄动法展开非线性声波方程得到一系列非齐次偏微分方程,根据低阶解的性质拟定高阶特解的形式,通过符号计算求出高次谐波特解,对所有二次谐波成分求和最终获得二次谐波的高阶近似解。在水中开展非线性声学实验验证高阶近似解,结果表明:二次谐波相对幅度随传播距离和输入信号均呈现先增加后减小的趋势,高阶近似解即使在传播距离不太短和输入信号不太弱的宽泛条件下也能更好地吻合实验结果。得到的高阶近似解不仅弥补了现有二次谐波幅度理论公式的不足,进行非线性声学实验时还可扩展测量范围,充分利用实验数据也能提高非线性系数的测量精度。      

Calculation of nonlinear waves guided by optical fibers with an inhomogeneous nonlinear core

A circular optical fiber consisting of an inhomogeneous nonlinear core bounded by a linear cladding medium is considered here. In this case, the calculation of the nonlinear modes is of practical importance because of the joint effects of nonlinearity and inhomogeneity on the field concentration and the achievable optical confinement. Numerical results indicate that the combination of this type of inhomogeneity along with the characteristics of nonlinearity may play a significant role towards the optical confinement in the core.     

Theory of stimulated concentration scattering of light in a liquid suspension of transparent microspheres

A theory of stimulated light scattering in a nonlinear liquid suspension of transparent microspheres—an artificially created medium whose nonlinearity is caused by modulation of the concentration of microspheres by gradient forces in a field of spatially inhomogeneous laser radiation—is constructed. The threshold, angular, and spectral characteristics of the scattering are studied in the diffusion-limit approximation based on the solution of the system of wave equations in combination with the Planck-Nernst two-dimensional equation for the concentration of microspheres. The transient regime of scattering in the field of a specified step-like pump pulse is considered. A sharp angular dependence of the scattering efficiency on the microsphere radius is predicted and proposed for use in optical diagnostics of liquid suspensions of dielectric microspheres—highly efficient wideband nonlinear media.     

Two-frequency parametric generation of sound in acoustic resonator

Steady-state parametric generation of sound in an acoustic resonator with time modulation of the speed of sound in a resonator material was theoretically studied taking into account quadratic nonlinearity of a medium.     

Energy Squeeze of Ultrashort Light Pulse by Kerr Nonlinear Photonic Crystals

Self-phase modulation can efficiently shape the spectrum of an optical pulse propagating along an optical material with Kerr nonlinearity. In this work we show that a one-dimensional Kerr nonlinear photonic crystal can impose anomalous spectrum modulation to a high-power ultrashort light pulse. The spectrum component at the photonic band gap edge can be one order of magnitude enhanced in addition to the ordinary spectrum broadening due to self-phase modulation. The enhancement is strictly pinned at the band gap edge by changing the sample length, the intensity or central wavelength of the incident pulse. The phenomenon is attributed to band gap induced enhancement of light-matter interaction.     

Dark solitons in optical fiber with inhomogeneous effects

We study the nonlinear wave propagation in an inhomogeneous optical fiber core in the normal dispersive regime. In order to include the inhomogeneous physical effects, the nonlinear Schrödinger equation (NLSE), which governs the solitary pulse propagation in optical fiber, is modified by adding terms for phase modulation and power gain or loss. The modified NLSEs are bilinearized and exact dark soliton solutions are obtained. The results are discussed.     

Discrete solitons in inhomogeneous waveguide arrays

The existence and dynamical properties of discrete solitons in inhomogeneous waveguide arrays with a Kerr nonlinearity are studied in two different configurations. First we investigate the effect of a longitudinal periodic modulation of the coupling strength on the dynamics of discrete solitons. It is shown that resonances of internal modes of the soliton with the longitudinal structure may lead to soliton oscillations and decay. Second we study the existence and stability of discrete solitons in arrays exhibiting a linear variation of the waveguide effective index in the transverse direction. We find that resonant coupling between conventional discrete solitons and linear Wannier-Stark states leads to the formation of so-called hybrid discrete solitons.     

Observation of the "Luxemburg-Gorky effect" for elastic waves

An experimental observation of a new nonlinear-modulation effect for longitudinal elastic waves is reported. The phenomenon is a direct elastic wave analogy with the so-called Luxemburg-Gorky (L-G) effect known over 60 years for radio waves propagating in the ionosphere. The effect consists of the appearance of modulation of a weaker initially non-modulated wave propagating in a nonlinear medium in the presence of an amplitude-modulated stronger wave that produces perturbations in the medium properties on the scale of its modulation frequency. The reported transfer of modulation from one elastic wave to another was observed in a resonator cut of a glass rod containing a few small cracks. Presence of such a small damage drastically enhances the material nonlinearity compared to elastic atomic nonlinearity of homogeneous solids, so that the pronounced L-G type cross-modulation could be observed at strain magnitude in the stronger wave down to 10(-7) and smaller. Main features of the effect are pointed out and physical mechanism of the observed phenomena is discussed.     

Rogue wave management in an inhomogeneous Nonlinear Fibre with higher order effects

We consider an inhomogeneous Hirota equation with variable dispersion and nonlinearity. We introduce a novel transformation which maps this equation to a constant coefficient Hirota equation. By employing this transformation we construct the rogue wave solution of the inhomogeneous Hirota equation. Furthermore, we demonstrate that one can control the rogue wave dynamics by suitably choosing the dispersion and the nonlinearity. These results suggest an efficient approach for controlling the basic features of the relevant rogue wave and may have practical implications for the management of the rogue waves in nonlinear optical systems.     

Optical nonlinearities in lyotropic liquid crystals

Summary The existence of an optical nonlinearity of the Kerr-like type in a lyotropic liquid crystal is described in c.w. operation. The nonlinearity is found using the liquid crystal as a cladding material in a waveguide, or studying the interface properties between the liquid crystal and an ordinary glass. The used material is potassium caprillate and the nonlinearity is ascribed to thermal effects. Work performed with partial support from MPI-40% (Italian Education Ministry) and GNEQP-CNR (Italian National Research Council-Quantum Electronics Group).