Nonlinear optical interactions in dye-doped solids

We present a brief review of non-linear optical investigations on dye-doped solids using low-power CW lasers. After a brief introduction to the photophysics of the dye molecules, we discuss specific nonlinear processes such as self-diffraction, optical phase conjugation, two-beam coupling and polarization gratings in these systems. The application potential of dye-doped solid devices is discussed.     

Nonlinear electronic transport in TTF-TCNQ observed by microwave harmonic mixing

The field dependent electronic conductivity of single crystals of TTF-TCNQ has been studied in both the metallic and the semiconducting range by means of microwave harmonic mixing, a method which excludes a contribution to the non-linearity by lattice heating. Because of the small strength of the applied field, the deviations from Ohm's law are also small such that they are proportional to the square of the field strength. The results in the semiconducting range are explained by the assumption of pinned charge density waves which are depinned by means of the microwave electric field.     

Nonlinear solitary waves in nonlocal elastic solids

The possibility of new weakly nonlinear solitary waves in nonlocal elastic media is demonstrated. The properties of these waves are determined by the characteristic features of wave dispersion in the linear approximation, and their velocity and amplitude cannot exceed certain limiting values. In the case of small amplitudes and velocities close to the velocity of sound, the profile of the waves under consideration coincides with the profile of the soliton described by the Korteweg-de Vries equation. When the amplitude and velocity of the aforementioned waves reach their limiting values, the wave profile sharpens. It is concluded that the propagation of such waves in rocks and soils is possible.     

Nonlinear shear wave interaction in soft solids

This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.     

Nonlinear refraction spectroscopy in resonance with laser lines in solids

We report a simple extension of the Z-scan technique that permits a spectral line-shape measurement of the real and the imaginary parts of n(2) . In this technique the sample is placed at the peak position of the usual Z-scan curve while the laser frequency is scanned. We employed this method to investigate the nonlinear susceptibility of the R lines of ruby and alexandrite, using a cw dye laser. This susceptibility can be explained by the resonant interaction and by a nonresonant contribution that is due to the difference in polarizability between Cr(3+) excited and ground states. For ruby, the nonresonant contribution to the technique is 1 order of magnitude larger than the resonant contribution. However, for alexandrite both contributions are comparable, and their interference leads to a shift between n(2)(?) and n(2)(??) spectra that is not observed in ruby.     

Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.     

Nonlinear wave propagation in constrained solids subjected to thermal loads

The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such “residual” energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.     

Collective motion of microspheres in suspensions observed by phase-mode dynamic ultrasound scattering technique

Compared with a nano-sized particle, dynamics of a micron-sized particle in a liquid is often associated with sedimentation (or floating) due to its relatively large mass. The motion of more than two particles is dominated by the hydrodynamic interactions, which are known to persist over a fairly long range, e.g., several millimeters, in suspensions. The particle size may be obtained from the dynamic ultrasound scattering (DSS) technique by the analysis of velocity fluctuations, whose origin is believed to take root in the particle-number fluctuations among temporally formed domains involving collective motion of particles with a certain cut-off length. In this study, such collective particle motion in highly turbid solutions was visualized by means of the phase-mode DSS technique with a single element transducer. Quantitative agreement between the velocity fluctuations obtained by the phase- and conventional amplitude-mode analyses was confirmed, followed by examination of the concentration and the particle size dependences on the dynamic structures induced by the long-ranged interactions. It was found that the phase mode-DSS was a promising method to evaluate the time-dependent structures of the micro-particles in highly turbid suspensions.     

Nonlinear dynamic phenomena in macroscopic tunneling

Numerical simulations of the NLSE (or GPE) are presented demonstrating emission of short pulses of the matter (light) density formed in the course of tunneling in wave-guided light and/or trapped BEC. The phenomenon is observed under various conditions, for nonlinearities of different signs, zero nonlinearity included. We study, both numerically and analytically, pulsations of matter (light) remaining within the trap and use the results in order to induce emission of sequential pulses by properly narrowing the trap. This allows us to propose a mechanism for a realization of Atom Pulse Laser.     

光梯度力驱动纳谐振器的非线性动力学特性研究

光梯度力作为纳谐振器的一种新型驱动方式,得到了广泛关注.本文研究了光梯度力的固有非线性特性,建立了光梯度力驱动圆环与辐条谐振系统的动力学模型.揭示了入射光功率以及几何参数对系统的非线性动力学响应的影响规律.研究表明:光梯度力会引起系统呈现刚度软化效应,随着入射光功率增大,系统主共振峰值明显增大,且谐振频率随着振幅增大而产生较大偏移;两环初始间隙增大,系统振动幅值和谐振频率均下降;辐条厚度越大,系统主共振峰值和谐振频率均减小.因此,可以通过调节入射光功率来实现圆环辐条谐振器的频率调节,为光梯度力驱动纳谐振器动力学设计和性能预测提供理论参考.     

Evaluation of the dynamic characteristics of structures by transient testing

Transient methods of measuring the frequency response of structures may be used now that the digital computer is established as a means of analysing transient data. The spectral properties of the rapid frequency sweep are well defined and it is shown that this type of forcing function is extremely suitable for transient tests on structures. Methods of deriving the frequency response function from rapid frequency sweep tests are discussed and possible sources of error are investigated. Results from practical tests show how the method may be used to derive the frequency response characteristics of built-up structures.     

Nonlinear damping calculation in cylindrical gear dynamic modeling

The nonlinear dynamic problem posed by cylindrical gear systems has been extensively covered in the literature. Nonetheless, a significant proportion of the mechanisms involved in damping generation remains to be investigated and described. The main objective of this study is to contribute to this task. Overall, damping is assumed to consist of three sources: surrounding element contribution, hysteresis of the teeth, and oil squeeze damping. The first two contributions are considered to be commensurate with the supported load; for its part however, squeeze damping is formulated using expressions developed from the Reynolds equation. A lubricated impact analysis between the teeth is introduced in this study for the minimum film thickness calculation during contact losses. The dynamic transmission error (DTE) obtained from the final model showed close agreement with experimental measurements available in the literature. The nonlinear damping ratio calculated at different mesh frequencies and torque amplitudes presented average values between 5.3 percent and 8 percent, which is comparable to the constant 8 percent ratio used in published numerical simulations of an equivalent gear pair. A close analysis of the oil squeeze damping evidenced the inverse relationship between this damping effect and the applied load.     

Nonlinear absorption of femtosecond light pulses under conditions of multiphoton resonances in solids

A theory of nonlinear absorption of femtosecond light pulses by bulk crystals and nanostructures of differing dimensionality is developed. The pulse width is assumed to be small compared to the relaxation times of the electron and hole momenta. Expressions for the absorbed energy under conditions of multiphoton resonance are derived for transitions between discrete or band-related electron states and between sub-band states of size quantization in quantum wells and quantum wires. The dependence of the absorbed energy on the multiphoton resonance detuning and pulse width is analyzed.     

CONTRA: improving the performance of dynamic investigations in natural abundance organic solids by mirror-symmetric constant-time CODEX

We present a minor but essential modification to the CODEX 1D-MAS exchange experiment. The new CONTRA method, which requires minor changes of the original sequence only, has advantages over the previously introduced S-CODEX, since it is less sensitive to artefacts caused by finite pulse lengths. The performance of this variant, including the finite pulse effect, was confirmed by SIMPSON calculations and demonstrated on a number of dynamic systems.     

黏弹材料动力学参数的宽频测试

利用改进的波速法,对黏弹性材料连续宽频范围的动力学参数进行测试。利用有限元方法,对波速法的测试过程进行了仿真,验证了利用长短棒波速法测量宽频动力学参数的有效性。采用可控脉冲生成技术,在激振器上产生了用于宽频测试的短脉冲信号。黏弹性长短棒在上述宽带短脉冲激励下作纵向强迫振动,利用激光测振仪测量长短两棒自由端的纵向振动速度,从而可得两振动信号在连续宽频范围的幅值比和相位差,进而可根据波速法原理计算得到材料在连续宽频范围的储能模量和损耗因子。测试结果表明,该系统通过较少次数测试,可直接计算得到1~5 kHz连续宽频范围的动力学参数,测试结果与黏弹仪数据吻合。通过对幅值比和相位差进行线性最小二乘拟合,可以进一步拓展测量的频率范围。该方法准确可靠、简便快速,具有实际应用价值。     

黏弹材料动力学参数的宽频测试

利用改进的波速法,对黏弹性材料连续宽频范围的动力学参数进行测试。利用有限元方法,对波速法的测试过程进行了仿真,验证了利用长短棒波速法测量宽频动力学参数的有效性。采用可控脉冲生成技术,在激振器上产生了用于宽频测试的短脉冲信号。黏弹性长短棒在上述宽带短脉冲激励下作纵向强迫振动,利用激光测振仪测量长短两棒自由端的纵向振动速度,从而可得两振动信号在连续宽频范围的幅值比和相位差,进而可根据波速法原理计算得到材料在连续宽频范围的储能模量和损耗因子。测试结果表明,该系统通过较少次数测试,可直接计算得到1~5 kHz连续宽频范围的动力学参数,测试结果与黏弹仪数据吻合。通过对幅值比和相位差进行线性最小二乘拟合,可以进一步拓展测量的频率范围。该方法准确可靠、简便快速,具有实际应用价值。     

Classification of audiograms by sequential testing using a dynamic Bayesian procedure

A new method for estimating audiograms using behavioral responses is presented. The method is based upon a modification of the Bayesian probability formula in which an outcome is predicted from a static set of events. In the new method, classification of audiograms by sequential testing (CAST), the probabilities of occurrence of audiogram patterns are dynamically updated according to the outcome of each test trial. Computer simulation using an infant response model suggests that the procedure is efficient, sensitive, and specific.     

An investigation of cracking in brittle solids under dynamic compression using photoelasticity

Crack initiation in brittle materials was experimentally studied using photoelasticity under dynamic loading conditions with particular attention to the frictional characteristics of the microcracks. Two pieces of Homalite-100 were bonded except central region to prepare plate specimens with an inclined center crack. An edge of the specimen was impacted with and without lateral confinement. In situ photoelastic (isochromatic) fringes were obtained using a high-speed camera. Initial direction and profile of wing crack was the same as in static loading tests. Effect of crack surface roughness and lateral confinement on fringe pattern is discussed. Average speed of wing crack propagation was about 100 m/s and wing cracks from a crack with higher friction coefficient propagated faster than from a smooth crack.