A Note on Second Harmonic Resonance of a Magneto-Acoustic Wave in Planar Plasma-Filled Waveguide

The second harmonic generated by non-linear self interaction of a magneto-acoustic wave in a planar plasma-filled waveguide is a freely propagating mode. Coupled-mode equations for resonant nonlinear interaction of this second harmonic mode with the fundamental mode are derived. Using these equations the possibility of generation of the second harmonic is analysed.     

PARAMETRIC SIMULTONS IN ONE-DIMENSIONAL NONLINEAR LATTICES

Parametric simultaneous solitary wave (simulton) excitations are shown to be possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example, we consider the nonlinear coupling between the upper cut-off mode of acoustic branch (as a fundamental wave) and the upper cut-off mode of optical branch (as a second harmonic wave). Based on a quasi-discreteness approach the Karamzin－Sukhorukov equations for two slowly varying amplitudes of the fundamental and the second harmonic waves in the lattice are derived when the condition of second harmonic generation is satisfied. The lattice simulton solutions are given explicitly and the results show that these lattice simultons can be nonpropagating when the wave vectors of the fundamental wave and the second harmonic waves are exactly at π/a (where a is the lattice constant) and zero, respectively.     

High space harmonic perturbations in travelling wave tubes

Stability properties of the free streaming mode in an electron beam propagating through a cylindrical waveguide loaded with a tape helix are investigated, including influence of high space harmonic perturbations. Closed algebraic dispersion relation of the free streaming mode are obtained. Properties of the high space harmonic perturbations are numerically investigated in connection with application on a high frequency microwave amplifier. One of the most important features in this analysis is that instability of high harmonic perturbations occurs at a very large value of microwave frequency. In this regard, millimeter microwave can be easily attainable by reducing the helix radius to a subcentimeter.     

q-Breathers and the Fermi-Pasta-Ulam problem

The Fermi-Pasta-Ulam (FPU) paradox consists of the non-equipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here q-breathers (QB). They are characterized by time periodicity, exponential localization in the q-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.     

Filtering of light fluctuations by multiple second harmonic generation

It is shown that the level of both quantum and classical light fluctuations can be considerably decreased by multiple second harmonic generation in thin nonlinear plates, when filtering out the generated second harmonic radiation behind each plate. As for the application, a second harmonic plate is proposed to be placed in the laser resonator in order to improve statistical and coherence properties of the lasing mode.     

Second Harmonic Generation of Lamb Wave in Numerical Perspective

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective.Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching,with and without group velocity matching,respectively.The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance.The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity.The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective,while group velocity matching is demonstrated to not be a necessary condition.     

Experimental study of nonlinear acoustic effects in a granular medium

Results of a series of experimental studies of nonlinear acoustic effects in a granular medium are presented. Different effects observed in the experiments simultaneously testify that the nonlinearity of granular media is governed by the weakest intergrain contacts. The behavior of the observed dependences suggests that the distribution function of contact forces strongly increases in the range of forces much smaller than the mean force value, which is inaccessible for conventional experimental measuring techniques. For shear waves in a granular medium, the effects of demodulation and second harmonic generation with conversion to longitudinal waves are studied. These effects are caused by the nonlinear dilatancy of the medium, i.e., by the nonlinear law of its volume variation in the shear stress field. With the use of shear waves of different polarizations, the anisotropy of the nonlinearity of the medium is demonstrated. The observation of the cross-modulation effect shows that the nonlinearity-induced modulation components of the probe wave are much more sensitive to weak nonstationary perturbations of the medium, as compared to the linearly propagating fundamental harmonic. The nonlinear effects under study offer promise for diagnostic applications in laboratory measurements and in seismic monitoring systems.     

高功率高重复频率多波长飞秒激光系统的研究

以大模场面积光子晶体光纤飞秒激光系统为基频光源,利用非线性频率上转换的方法,获得了高功率高重复频率多波长的飞秒激光脉冲.理论分析并实验验证了聚焦透镜的焦距对倍频光横向模场分布的影响,透镜焦距越长,模场质量越好.在基频光平均功率为218 W,脉冲宽度为110 fs,重复频率为50 MHz的条件下,经过二倍频、三倍频和四倍频获得波长分别为520,347和261 nm的飞秒激光,其平均功率分别达105,47和214 W.二倍频和三倍频的转换效率分别为482%和216%,二倍频到四倍频的转换效率为20 关键词： 超快光学 紫外飞秒激光 频率上转换 光子晶体光纤激光器     

Mode Competition and Self-Consistent Simulation of a Second Harmonic Gyrotron Oscillator

A nonlinear numerical simulation of a second harmonic gyrotron oscillator is presented in this paper. Mode competition from a competing fundamental mode is investigated. In addition, a self-consistent nonlinear theoretical model, including the effect of velocity spread, is applied to analyze the second harmonic gyrotron. A series of numerical calculations is carried out for different electron beam parameters. The results are compared with that of calculations using the cold-cavity, fixed field approximation and with experiments. Good agreement is found between our calculations and an experiment at Fukui University. The azimuthal polarization of the field and the choice of the electron beam radius are also discussed.     

Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis

The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scope of linear stability theory. Finger competition arises through enhanced growth of sub-harmonic perturbations, while spreading and splitting occur through the growth of harmonic modes. Nonlinear mode-coupling enhances the growth of these specific perturbations with appropriate relative phases, as we demonstrate through a symmetry analysis of the mode coupling equations. We contrast mode coupling in radial flow with rectangular flow geometry.     

Numerical Perspective of Second-Harmonic Generation of Circumferential Guided Wave Propagation in a Circular Tube

The effect of second-harmonic generation(SHG) by primary(fundamental) circumferential guided wave(CGW)propagation is investigated from a numerical standpoint.To enable that the second harmonic of the primary CGW mode can accumulate along the circumferential direction,an appropriate mode pair of primary and double frequency CGWs is chosen.Finite element simulations and evaluations of nonlinear CGW propagation are analyzed for the selected CGW mode pair.The numerical simulations performed directly demonstrate that the response of SHG is completely generated by the desired primary CGW mode that satisfies the condition of phase velocity matching at a specific driving frequency,and that the second harmonic of the primary CGW mode does have a cumulative effect with circumferential angles.The numerical perspective obtained yields an insight into the complicated physical process of SHG of primary CGW propagation unavailable previously.     

二维不可压缩流体Kelvin-Helmholtz不稳定性的二次谐波产生

推导了Kelvin-Helmholtz(KH)不稳定性二次谐波产生的理论公式,利用该公式得到的二次谐波增长的弱非线性结果与LARED-S程序的模拟结果符合.二维模拟定出了KH不稳定性单模非线性增长的阈值. 关键词： Kelvin-Helmholtz不稳定性 二次谐波产生 非线性阈值     

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.     

Coupled mode analysis to study cascading in the QPM Cerenkov regime in waveguides

In this paper we use the coupled mode analysis to study nonlinear phase shifts of the fundamental beam caused by cascaded second order nonlinear effects in the Quasi Phase Matched Cerenkov (QPMC) configuration in waveguides. Under the no-pump depletion approximation which is valid for low conversion efficiencies, we obtain the nonlinear phase shift as a function of length of interaction and grating period. It is observed that the nonlinear phase shift of the fundamental beam can be maximized by choosing a grating period for which the phase matched second harmonic radiation mode is radiated parallel to the film-substrate interface, i.e., for zero Cerenkov angle. Although the phase shifts are smaller than in the case of all guided geometry, QPM Cerenkov configuration is expected to have greater tolerance towards various waveguide parameters and the fundamental wavelength.     

OH− ions in Oxide Crystals

This article reviews the spectroscopic properties of hydrogen bound to a large variety of synthetic compounds like simple oxides, perovskites, the LiNbO₃ family, KTP, sillenites, eulytites, borates, garnets, spinels and some others. In almost all compounds the OH stretch mode is found in the range 3200-3700 cm^?1, with isotope replica of deuterium (2350-2750 cm^?1) and a few examples of tritium (2050-2250 cm^?1). The fundamental vibration, the isotope replica and the corresponding overtones are described with an anharmonic oscillator model. A nonlinear relation between the anharmonicity and the harmonic frequency is found and interpreted using recent second order perturbation calculations. An often pronounced temperature dependence of the stretch mode and phonon coupling is discussed. Data for the stretching vibration influenced by additional weak or strong doping are presented. Atomistic defect models are described and tested by means of light polarization, external perturbations like pressure and electric field, and Raman scattering analyzed with the behavior-type method. The last section briefly reviews applications profiting from doping with hydrogen and its easy detection by means of the OH stretch mode.     

Optical second harmonic generation with surface plasmons in piezoelectric crystals

We report the first observation of reflected optical second harmonic generation of light due to excitation of fundamental and harmonic surface plasmon modes at the interface between a metallic film and a piezoelectric crystal. Excitation of the fundamental surface plasmon mode produces a large enhancement of the piezoelectric generated reflected harmonic light whereas excitation of the nonlinear mode produces only a small minimum in the background surface generated harmonic light.     

Resonant interaction of a magneto-hydrodynamic wave with its second harmonic in a planar plasma filled waveguide

To describe the nonlinear interactions of a magneto-hydrodynamic wave with its second harmonic propagating in a planar waveguide filled with cold magnetized plasma, coupled mode equations have been derived. Solution of these equations shows the possibility of energy transfer between the fundamental and the second harmonic.     

Enhancement of the SHG efficiency in a doubly resonant 2D-photonic crystal microcavity

In this paper we discuss the conditions to obtain the enhancement of second harmonic generation in a two-dimensional circular photonic crystal AlGaAs cavity. The photonic crystal circular cavity offers the possibility of having high-Q resonance modes with respect to those obtained with other types of photonic crystal lattices. The crystallographic cut of the AlGaAs provides a strong nonlinear coupling between a transverse-magnetic (TM) polarized resonant mode at the fundamental wavelength and a transverse-electric (TE) polarized resonant mode at second harmonic wavelength. The double resonance condition leads to a strong improvement of the second harmonic generation process. A preliminary linear analysis has been performed by using the finite-difference time-domain method, which includes the dispersive response of the material, modeled using the well-known one-pole pair Lorentzian function.     

Observation of harmonic generation and nonlinear coupling in the collective dynamics of a bose-einstein condensate

We report the observation of harmonic generation and strong nonlinear coupling of two collective modes of a condensed gas of rubidium atoms. Using a modified time averaged orbiting potential trap we changed the trap anisotropy to a value where the frequency of the m = 0 high-lying mode corresponds to twice the frequency of the m = 0 low-lying mode, thus leading to strong nonlinear coupling between these modes. By changing the anisotropy of the trap and exciting the low-lying mode we observed significant frequency shifts of this fundamental mode and also the generation of its second harmonic.