Phasematching of frequency-conversion processes induced by additional selective pump

Possibility to induce phasematching in gaseous nonlinear media with the help of additional pumping of a proper energy level of atoms is shown.     

Localization of the femtosecond pulse train energy in a one-dimensional nonlinear photonic crystal

Computer simulation demonstrates the feasibility of pumping a one-dimensional nonlinear photonic crystal (layered one-dimensional periodic structure) by optical energy localizing in the crystal when it is irradiated by a femtosecond pulse train. Simulation is based of the recently suggested approach to similar problems. It is shown that the pumping effect can be employed in 3D optical storages.     

Kink with Allowance for the Energy Dissipation and Pumping

In the present work, the (1+1)-dimensional nonlinear equation of motion of ϕ⁴ scalar theory is examined with simultaneous allowance for the processes of energy dissipation and pumping in the system. The energy dissipation is described in the equation by a linear term, and the energy pumping is described by a squared time derivative of the field. A single-kink solution is constructed for the given problem. It is demonstrated that a scalar field expansion in the inflationary model can occur with balanced energy dissipation and pumping. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 40–42, May, 2005.     

Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device

This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free–free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.     

Experimental study of targeted energy transfer from an acoustic system to a nonlinear membrane absorber

This paper deals with the application of the concept of targeted energy transfer to the field of acoustics, providing a new approach to passive sound control in the low frequency domain, where no efficient dissipative mechanism exists. The targeted energy transfer, also called energy pumping, is a phenomenon that we observe by combining a pure nonlinear oscillator with a linear primary system. It corresponds to an almost irreversible transfer of vibration energy from the linear system to the auxiliary nonlinear one, where the energy is finally dissipated. In this study, an experimental set-up has been developed using the air inside a tube as the acoustic linear system, a thin circular visco-elastic membrane as an essentially cubic oscillator and the air inside a box as a weak coupling between those two elements. In this paper, which mainly deals with experimental results, it is shown that several regimes exist under sinusoidal forcing, corresponding to the different nonlinear normal modes of the system. One of these regimes is the quasi-periodic energy pumping regime. The targeted energy transfer phenomenon is also visible on the free oscillations of the system. Indeed, above an initial excitation threshold, the sound extinction in the tube follows a quasi-linear decrease that is much faster than the usual exponential one. During this linear decrease, the energy of the acoustic medium is irreversibly transferred to the membrane and then damped into this element called nonlinear energy sink. We present also the frequency responses of the system which shows a clipping of the original resonance peak of the acoustic medium and we finally demonstrate the ability of the nonlinear absorber to operate in a large frequency band, tuning itself to any linear system.     

Free vibrations of an uncertain energy pumping system

The aim of this paper is to study the energy pumping (the irreversible energy transfer from one structure, linear, to another structure, nonlinear) robustness considering the uncertainties of the parameters of a two DOF mass-spring-damper, composed of two subsystems, coupled by a linear spring: one linear subsystem, the primary structure, and one nonlinear subsystem, the so-called NES (nonlinear energy sink). Three parameters of the system will be considered as uncertain: the nonlinear stiffness and the two dampers. Random variables are associated to the uncertain parameters and probability density functions are constructed for the random variables applying the Maximum Entropy Principle. A sensitivity analysis is then performed, considering different levels of dispersion, and conclusions are obtained about the influence of the uncertain parameters in the robustness of the system.     

Nonequilibrium states of the soft mode anharmonic phonons

A theory of the nonequilibrium state of the soft mode optical phonons in ferroelectrics exposed to the pumping electromagnetic field has been developed. The self-consistent field equation, which determines the phase transition temperature shift and the dielectric permeability change due to a deviation of the system from the equilibrium state is derived. A two-temperature model describing the energy transport in the presence of pumping is suggested. Analytic solutions of this model both for evolving in time and for stationary states are obtained. Spatial oscillations of the soft mode temperature are predicted for the observation time approximately equal to the energy relaxation time. It is shown that nonlinear effects can be a reason of forming of the bottleneck in the energy relaxation process. An exactly solvable model of a breather: the breather with the one-site non-linearity has been constructed and investigated.     

Multi-scale energy exchanges between a nonlinear oscillator of Bouc-Wen type and another coupled nonlinear system

The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.     

染料激光抽运Nd:YCOB自倍频激光器

Ｎｄ：ＹＣａ４Ｏ（ＢＯ３）３（简称Ｎｄ：ＹＣＯＢ）是一种新型自倍频激光复合功能晶体,利用Ｄａｔａｃｈｒｏｍ－５０００型染料激光器作为抽运源,横向抽运钕离子原子比为８％的Ｎｄ：ＹＣＯＢ获得了５３０．２ｎｍ绿色自倍频激光输出。在样品未镀膜的情况下阈值抽运量小于２ｍＪ,绿光输出能量最大为１．０３ｍＪ,能量转换效率约为３．３％。     

Formation of a direct Kolmogorov-like cascade of second-sound waves in He II

Based on measurements of nonlinear second-sound resonances in a high-quality resonator, we have observed a steady-state wave energy cascade in He II involving a flux of energy through the spectral range towards high frequencies. We show that the energy balance in the wave system is nonlocal in K space and that the frequency scales of energy pumping and dissipation are widely separated. The wave amplitude distribution follows a power law over a wide range of frequencies. Numerical computations yield results in agreement with the experimental observations. We suggest that second-sound cascades of this kind may be useful for model studies of acoustic turbulence.     

Nonlinear seismics and the acoustic action on the oil recovery from an oil pool

At the first stage of seismic action, the attenuation of acoustic waves in real (porous, creviced) rocks is always related to the energy pumping to high-frequency (ultrasonic) modes, and only at the next stage are these waves converted into chaotic thermal oscillations, so that the entire phenomenon refers to a basic problem of nonlinear seismics. Several physical phenomena related to the excitation of ultrasound and the corresponding transformations of the wave spectrum (including the dry friction in contacts, the instability of viscoelastic oscillations, the seismic energy pumping to the rotational modes, and the resonance of gas bubbles in natural oil) are considered in relation to the development of vibroseismic methods of acting upon a producing oil pool. The results of experiments on the ultrasound-stimulated water displacement of natural (gas-saturated) oil from a porous medium are presented, in which the oil recovery reached up to 90%.     

Frequency intermittency and energy pumping by linear attachments

The present paper considers the problem of realizing an effective targeted energy pumping from a linear oscillator to a set of ungrounded linear resonators attached to it. Theoretical as well as numerical results demonstrate the efficacy of using a complex attachment as a passive absorber of broadband energy injected into the primary structure. The paper unveils also the existence of an instantaneous frequency associated with the master response characterized by intermittency: a rather surprising result for a linear autonomous system. Comparison with nonlinear energy sinks demonstrates that the two systems have some analogies in this respect and that the linear complex attachment is a very efficient energy trap.     

泵浦光强对激光相位共轭波非线性效应的影响

分析了泵浦光强对激光相位共轭谐振腔中探测光场的作用。基于稳定性定理,通过确定系统的Lyapunov指数,数值计算了在不同泵浦光强下的激光相位共轭波的非线性效应。结果显示,泵浦光强是系统的控制参量。调节泵浦光强的数值,系统的动力学性质发生了改变,可以呈现一周期、二周期、四周期以及倍周期分岔、周期并缩和混沌现象。     

Supercritical dynamics of magnetoelastic wave triad in a solid

Parametric coupling of three traveling waves is studied numerically on an example of magnetoelastic waves in a highly anharmonic antiferromagnetic crystal. The physical mechanism of coupling is explained as a result of modulation of the nonlinear elastic moduli of the crystal by RF electromagnetic pumping. Parametric interaction of a coupled wave triad with homogeneous pumping field results in an instability of explosive type. Above the threshold of instability, the amplitudes of waves increase to occurrence of singularity in finite time. Explosion is accompanied by spatial localization of wave envelopes. The supercritical dynamics of a wave triad is simulated numerically taking into account the third- and fourth-order magnetoelastic anharmonicity of the medium. Violation of the explosive scenario by nonlinear phase mismatch between the coupled waves and pumping field is demonstrated. Modulation of the pumping phase in time is considered as a tool to compensate for the nonlinear mismatch and recondition the explosive amplification and spatial localization of wave triads. A proper phase modulation law is found in a numerical experiment.     

Generation and detection of terahertz radiation by means of periodically and aperiodically poled crystals

The nonlinear optical methods for generating and detecting terahertz radiation using periodically and aperiodically poled crystals in the quasi-phase-matching mode are analyzed. Two radically different versions of optical pumping are considered: a quasi-continuous mode and pumping by Fourier-limited femto-second pulses. General relations are obtained, which determine the spectra of generated and detected waves through the optical pumping parameters and the crystal generator and crystal detector nonlinear transfer functions. It is shown that, by choosing the optimal spatial modulation of the crystal nonlinear susceptibility, one can control the shape of the generation and detection spectra. An optical scheme is proposed and the optimal parameters of domain structures for quasi-phase-matched generation and frequency-matched detection of forward and backward terahertz waves under quasi-continuous-wave optical pumping are reported.     

Formation of an energy cascade in a system of vortices on the surface of water

The formation of an energy cascade in a system of vortices generated by perpendicular standing waves with a frequency of 6 Hz on the water surface has been experimentally studied. It has been found that peaks appear on the energy distribution over wave vectors E(k) after switching on pumping. These peaks are transformed with time because of the energy redistribution over scales. The stationary distribution E(k) established 300 s after switching on pumping can be described by a power-law function of the wave vector E(k) ～ k^1.75. It has been shown that waves with frequencies of about 18, 15, 12, 9, and 3 Hz appear on the surface of water owing to the nonlinear interaction at the excitation of a 6-Hz wave. It is assumed that the energy cascade of the turbulent motion in the wave vector range of 0.3–5 cm^?1 is formed by the nonlinear interaction between vortices generated by all waves propagating on the surface and direct energy fluxes toward high wave vectors dominate.     

Picosecond stimulated Raman scattering in crystals

The comparative values of the peak and integral cross sections of spontaneous Raman scattering and the optical dephasing time of molecular vibrations were determined for several oxide crystals by spontaneous Raman spectroscopy. The spectral, time, and energy parameters of stimulated Raman scattering (SRS) were measured for ten crystals using picosecond YLF: Nd laser pumping with a radiation wavelength of 1047 nm. An analysis of the experimental dependence of the threshold energy of pumping SRS on the integral and peak cross sections of spontaneous Raman scattering showed that the SRS gain increment explicitly depended on the integral cross section and was independent of the peak cross section of spontaneous Raman scattering as the ratio between the pumping pulse width (11 ps) and the time of optical dephasing of molecular vibrations changed from 0.42 to 9.3. The gain coefficients of steady-state stimulated Raman scattering under threshold stimulated Raman scattering conditions were determined for all the crystals studied on the basis of the measured threshold SRS pumping energies, the duration and width of the spectrum of pulses, the nonlinear interaction length, the intensity of pumping, and the theoretical dependences that relate the steady-state and transient SRS gain increments. The steady-state SRS gain coefficients obtained in this work fitted well a linear dependence on the peak cross sections of spontaneous Raman scattering, which substantiated the correctness of our analysis and measurements.     

Large-Scale Coherent Vortex Formation in Two-Dimensional Turbulence

The evolution of a vortex flow excited by an electromagnetic technique in a thin layer of a conducting liquid was studied experimentally. Small-scale vortices, excited at the pumping scale, merge with time due to the nonlinear interaction and produce large-scale structures—the inverse energy cascade is formed. The dependence of the energy spectrum in the developed inverse cascade is well described by the Kraichnan law k^–5/3. At large scales, the inverse cascade is limited by cell sizes, and a large-scale coherent vortex flow is formed, which occupies almost the entire area of the experimental cell. The radial profile of the azimuthal velocity of the coherent vortex immediately after the pumping was switched off has been established for the first time. Inside the vortex core, the azimuthal velocity grows linearly along a radius and reaches a constant value outside the core, which agrees well with the theoretical prediction.     

Karhunen–Loeve analysis and order reduction of the transient dynamics of linear coupled oscillators with strongly nonlinear end attachments

The Karhunen–Loeve (K–L) decomposition method has become a popular technique to create low-dimensional, reduced-order models of dynamical systems. In this paper this technique is applied to a multi-degree-of-freedom chain of linear coupled oscillators with a strongly nonlinear (nonlinearizable), lightweight end attachment. By performing K–L decomposition we show that the lightweight nonlinear attachment (possessing 0.5% of the total mass of the chain) can affect the global dynamics of the linear chain, exhibiting nonlinear energy-pumping phenomena; that is, irreversible passive targeted energy transfers from the linear chain to the nonlinear end attachment, where this energy is locally confined and dissipated without ‘spreading back’ to the primary system. It is shown that the occurrence of energy pumping can be identified by studying the dominant K–L modes of the dynamics, as well as, the energy distribution among them. Moreover, by comparing the action of the strongly nonlinear attachment to the classical linear vibration absorber, we show robustness of passive nonlinear energy absorption over wide parameter ranges. On the other hand, the case-sensitive nature of K–L-based reduced-order models has always been a constraint for K–L decomposition, since one cannot quantify a priori the error bound of such low-dimensional reduced-order models when different initial conditions are applied to the system. To alleviate this constraint, the paper proposes a multiple correlation coefficient (MCC) as a quantitative measure to effectively assess the applicability of a K–L-based reduced-order model derived for a specific set of initial conditions to a small neighborhood of initial conditions containing that initial state. The derived reduced-order models are validated through reconstruction of the system responses and comparisons to direct numerical integrations.