Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics

A dual frequency mixing technique has been developed for measuring velocity changes caused by material nonlinearity. The technique is based on the parametric interaction between two surface acoustic waves (SAWs): The low frequency pump SAW generated by a transducer and the high frequency probe SAW generated and detected using laser ultrasonics. The pump SAW stresses the material under the probe SAW. The stress (typically <5 MPa) is controlled by varying the timing between the pump and probe waves. The nonlinear interaction is measured as a phase modulation of the probe SAW and equated to a velocity change. The velocity-stress relationship is used as a measure of material nonlinearity. Experiments were conducted to observe the pump-probe interaction by changing the pump frequency and compare the nonlinear response of aluminum and fused silica. Experiments showed these two materials had opposite nonlinear responses, consistent with previously published data. The technique could be applied to life-time predictions of engineered components by measuring changes in nonlinear response caused by fatigue.     

Profiles of initially sinusoidal waves propagating in nonlinear microinhomogeneous materials

The asymptotic analytical theory predicting acoustic wave profiles in microinhomogeneous materials with hysteretic quadratic nonlinearity and attenuation proportional to an even power of frequency is developed. The theory predicts that the influence on the nonlinear wave of the Rayleigh scattering of acoustic waves, which is proportional to the forth power of frequency, results in the net diminishing of wave attenuation. This is due to the suppression (diminishing) by scattering of the nonlinear hysteretic losses which is more important than direct increase in linear losses added by scattering.     

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.     

SRS generation of anti-Stokes radiation under phase quasi-matching conditions

New methods of generation of anti-Stokes radiation of stimulated Raman scattering in media with changeable parameters of the third-order nonlinearity χ⁽³⁾ along the longitudinal coordinate are proposed. The conditions of obtaining phase quasi-matching in different media and reaching the maximum efficiency of conversion into the anti-Stokes component of stimulated scattering are determined by numerical methods. The dependence of the efficiency of energy transfer from the pump wave to the anti-Stokes wave on the ratio of intensities of the pump and Stokes waves at the input of the medium is studied. The models of the media in which the efficiency of generation of anti-Stokes radiation exceeds 30% are obtained. The results of the investigation can be used for the development of new efficient nonlinear optical devices upconverting the laser radiation frequency.     

Quantum cascade structure for mid-IR four-wave mixing

The design and modeling of a quantum cascade optical amplifier (QCOA) using intra-cavity non-linear interactions to achieve wavelength conversion is proposed. The model is based on the nonlinear equation coupled with Maxwell wave equations for different emission modes. In the proposed structure, four wave mixing (FWM) output exhibits a peak as a function of pump and probe frequency if they are tuned to the energy levels of the QC structure subbands. Results demonstrate that the FWM output signal power significantly depends on how subbands are engineered and interact with optical pulses which propagate in multi layer medium. In addition, we show that by adjusting pump and probe signal frequencies, FWM output power can be tuned.     

微结构光纤近红外色散波产生的研究

采用有限元法对实验室自制的非线性微结构光纤进行理论分析, 表明该光纤具有良好的非线性和色散波产生的相位匹配特性. 为实现微结构光纤非线性的全光纤化, 本实验采用中心波长为1032 nm的光纤飞秒激光器作为抽运源, 获得了753–789 nm 的近红外色散波. 实验中发现色散波中心波长和带宽随着抽运功率的改变会产生明显变化, 并且在不同光纤长度时, 色散波的频移量不同, 脉冲展宽及频谱也会有明显的变化. 实验结果与理论分析一致. 这些结果对实现微结构光纤非线性的全光纤化具有良好的借鉴作用, 为生物医疗应用特别是非线性光学显微成像术的近红外光源研究打下基础.     

Circuit QED with a nonlinear resonator: ac-Stark shift and dephasing

We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier.     

Nonlinear elastic imaging using reciprocal time reversal and third order symmetry analysis

This paper presents a nonlinear imaging method for the detection of the nonlinear signature due to impact damage in complex anisotropic solids with diffuse field conditions. The proposed technique, based on a combination of an inverse filtering approach with phase symmetry analysis and frequency modulated excitation signals, is applied to a number of waveforms containing the nonlinear impulse responses of the medium. Phase symmetry analysis was used to characterize the third order nonlinearity of the structure by exploiting its invariant properties with the phase angle of the input waveforms. Then, a "virtual" reciprocal time reversal imaging process, using only one broadcasting transducer and one receiving transducer, was used to insonify the defect taking advantage of multiple linear scattering as mode conversion and boundary reflections. The robustness of this technique was experimentally demonstrated on a damaged sandwich panel, and the nonlinear source, induced by low-velocity impact loading, was retrieved with a high level of accuracy. Its minimal processing requirements make this method a valid alternative to the traditional nonlinear elastic wave spectroscopy techniques for materials showing either classical or non-classical nonlinear behavior.     

Effects of finite probe intensity on degenerate frequency mixing in saturable amplifiers

Phase conjugation by degenerate frequency mixing (DFM) in saturable amplifiers, including the effects of pump depletion, a non-zero incident probe wave intensity and saturated gain of all waves in the nonlinear medium, is analyzed numerically. Plane wave DFM reflectivities greater than unity are predicted, even in the presence of pump depletion, for sufficiently large amplifier gains. At a given level of incident probe-wave intensity the DFM reflectivity approaches its weak probe-wave value at sufficiently large incident pump intensities, but deviates from these values at lower pump intensities. Conditions are established under which the DFM reflectivity is effectively independent of the incident probe-wave intensity even when the incident pump intensity is smaller than that of the incident probe wave. Under these conditions the system holds the potential for faithful conjugation using pump waves that are considerably weaker than the probe waves being conjugated. The results also predict that under certain conditions, the intensity of the backward-generated wave can be larger than either the incident probe wave or the incident pump wave.     

等离子体中受激Raman效应引起的近简并四波混频

本文研究等离子体中由于受激Raman散射激发起来的电子等离子体波引起的近简并四波混频。文中解析地导出此情况下等离子体介质的三阶非线性极化率,并讨论其位相匹配条件。通过求解偶合波方程得到位相复共轭反射率,并详细研究该反射率与泵浦光和探针光的频率差以及与相互作用长度的关系。     

Non-linear optical properties and all optical switching of Congo red in solution

We present the results from investigations of the nonlinear properties of Congo red solutions using Z-scan technique with a continuous wave argon ion laser at 514 nm. The magnitude and sign of the third-order nonlinear refractive index n₂ of aqueous solution of Congo red were determined. The nonlinear refractive index was found to vary with concentration. Third-order nonlinearity is dominated by nonlinear refractive index, which leads to strong self-defocusing and self diffraction in the samples studied. A pump and probe technique was used to investigate the origin of nonlinearity. Furthermore the nonlinear refractive index effect was utilized to demonstrate all optical switching. The optical limiting behavior based on nonlinear refractive index was investigated.     

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.     

On the velocity of propagation of a signal in nonlinear optical media

The maximum velocity of propagation of a signal, which is defined as the velocity of propagation of the wave front, is considered for electromagnetic waves in nonlinear media. It is shown that the magnitude of velocity is determined to a considerable extent on the form of the constitutive equation defining the relation between the polarization of the medium with the radiation field strength. In the noninertial nonlinearity model, this velocity may be smaller (in media with self-focusing nonlinearity) or larger (defocusing nonlinearity) than the velocity of light in vacuum. For real nonlinear media, for which the inertia of their response is taken into account, the wave front velocity coincides with the velocity of light in vacuum.     

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.     

Enhanced Raman Scattering of Elliptical Laser beam in a Collisional Plasma

This paper presents the Enhanced Raman scattering of a elliptical laser beam in a collisional plasma. We have considered the mechanism of non‐uniform heating of carriers along the wave‐front, which is important in collisional plasma. The nonlinearity arising through non‐uniform heating leads to redistribution of carriers, which modifies the background plasma density profile in a direction transverse to pump beam axis. This modification in density effects the incident laser beam, plasma wave and back‐scattered beam. Non‐linear differential equations for the beam width parameters of pump laser beam, plasma wave and back‐scattered beam are set up and solved numerically. Numerical results predict the effect of self‐focusing of waves on the back‐scattered beam (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stationary and quasi-stationary waves in even-order dissipative systems

A new equation was recently suggested by Rudenko and Robsman [1] for describing the nonlinear wave propagation in scattering media that are characterized by weak sound signal attenuation proportional to the fourth power of frequency. General self-similar properties of the solutions to this equation were studied. It was shown that stationary solutions to this equation in the form of a shock wave exhibit unusual oscillations around the shock front, as distinct from the classical Burgers equation. Here, similar solutions are studied in detail for nonlinear waves in even-order dissipative media; namely, the solutions are compared for the media with absorption proportional to the second, fourth, and sixth powers of frequency. Based on the numerical results and the self-similar properties of the solutions, the fine structure of the shock front of stationary waves is studied for different absorption laws and magnitudes. It is shown that the amplitude and number of oscillations appearing in the stationary wave profile increase with increasing power of the frequency-dependent absorption term. For initial disturbances in the form of a harmonic wave and a pulse, quasi-stationary solutions are obtained at the stage of fully developed discontinuities and the evolution of the profile and width of the shock wave front is studied. It is shown that the smoothening of the shock front in the course of wave propagation is more pronounced when the absorption law is quadratic in frequency.     

较高阶非线性抽运-探测过程中的空间效应

在飞秒抽运一探测光谱技术中,空间分辨的探测光信号反映了在不同空间位置的材料的非线性效应。当抽运光强度增大时,探测光信号中会出现明显的高阶特别是五阶非线性效应。利用劈裂算子方法直接解决了一维非线性传播方程的问题。在数值模拟中,研究了在不同抽运强度和位置下的抽运一探测过程中的五阶非线性效应。在足够高的抽运场下,探测信号出现清晰的振荡,显示了三阶和五阶非线性效应之间的干涉。当空间位置离抽运场中心足够远时,五阶比三阶非线性效应的衰减快得多,对其物理机制和趋势进行了定性的讨论。     

Direct measurement of free carrier nonlinearity in semiconductor-doped glass with picosecond pump-probe Z-scan experiment

We report the direct measurement of free carrier nonlinearity in a semiconductor-doped glass with picosecond pump-probe Z-scan experiment. A strong Z-scan signal from a weak and time delayed probe beam is observed. The probe beam Z-scan signal is comparable in magnitude to the Z-scan signal of the intense pump beam, clearly showing the dominance of the effective fifth order nonlinearity due to the pump beam generated free carriers in the overall nonlinear response of semiconductor-doped glass. The estimated magnitude of the fifth order nonlinearity is consistent with that obtained from earlier reported experiments.     

Nonlinear shoaling of shallow water waves: perspective in terms of the inverse scattering transform

Summary We study nonlinear interactions in measured surface wave trains obtained in the Northern Adriatic Sea about 16 kilometres from Venice, Italy.Nonlinear Fourier analysis is discussed in terms of the exact spectral solution to the Korteweg-deVries (KdV) equation as given by theinverse scattering transform (IST). For the periodic and/or quasi-periodic boundary conditions assumed herein, the approach may be viewed as a nonlinear, broad-banded generalization of the ordinary, linear Fourier transform. In particular, we study solition interactions, their properties and the nonlinear dynamics of the radiation (or oscillation) modes as found from the inverse scattering transform analysis. We also conduct a number of computer experiments in which measured wave trains are numerically propagated forward in time toward shallow water and backward in time into deep water in order to assess how the nonlinear wave dynamics are influenced by propagation over variable bathymetry. On this basis we develop a scenario for the evolution of nonlinear wave trains, initially far offshore in deep water, as they propagate into shallow water regions. The deep-water waves have a small Ursell number and are hence not very nonlinear; as they propagate toward shallow water, the Ursell number gradually increases in the numerical experiments by about an order of magnitude. A useful parameterization of nonlinearity in these studies is the ?spectral modulus,? a number between 0 and 1, which is associated with each IST spectral frequency. Small values of the modulus mean that a particular spectral component is linear (a sine wave); large values of the modulus (≈1) indicate that the component is nonlinear (a soliton). There is a systematic increase of the modulus as the waves propagate into shallow water where nonlinear effects predominate; we describe how the modulus varies as a function of spectral frequency during this shoaling process. The results suggest that the effect of increasing nonlinearity ?saturates? the IST spectrum (i.e. the modulus ≈1 for all frequencies) to that virtually all spectral components become solitons in sufficiently shallow water.     

Parametric reversal of nonlinear acoustic waves

A mechanism of parametric reversal of the ultrasonic field from a quasi-monochromatic radiator situated in a nonlinear acoustic medium is proposed and analyzed. The mechanism is based on the phonon-plasmon interaction in semiconductors with a high concentration of electron traps, when a sample is irradiated by a periodic sequence of short laser pulses. The spectrum of output signal and, correspondingly, the temporal profile of the spatially reversed wave are investigated as functions of the intensity and duration of pumping pulses. It is shown that the choice of pumping parameters allows one to control the spectrum of reversed wave and, in particular, closely reproduce the spatiotemporal structure of the original wave. The frequency matching of the nonlinear ultrasonic wave harmonics and the pump Fourier frequencies occurs automatically at a certain pulse repetition rate in this scheme.