Second-harmonic generation of the nth-order Bessel beam

We investigate the second-harmonic generation of the nth-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an nth-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam of the order 2n, and that the axial pressure amplitude is proportional to the square root of propagation distance. A variety of applications in many fields of nonlinear acoustics and nonlinear optics is expected.     

Higher-order harmonics of general limited diffraction Bessel beams

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-thorder Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov(KZK)equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example.     

小瓣数贝塞尔声束的二次谐波

采用高斯展开法,研究了具有三个瓣的小瓣数贝塞尔声束的基波和二次谐波的传播性质.根据准线性近似下Khokhlov-Zabolotskaya-Kuznetsov方程的积分形式解,分析了媒质的声吸收(声衰减)对波束形状的影响.结果表明:吸收参量对二次谐波径向分布有很大的影响.当瓣数较少时,实际的有限孔径贝塞尔声束二次谐波仍然具有理想无限大孔径贝塞尔声束的主要特征,在近场无衍射区,径向几乎无衍射. 关键词： 二次谐波 贝塞尔声束 声吸收 有限孔径声束     

一种含时贝塞尔光束的理论性质研究

本文从理论角度提出了一种"含时贝塞尔光束"的概念.在非傍轴和非时谐条件下,直接从麦克斯韦方程出发,借鉴半贝塞尔光束的处理方法,同时引入第四维虚数坐标,由此获得了完整的"含时贝塞尔光束"的解析表达式.并从无衍射性质和时空特性两个方面对其进行了探讨和研究,发现该光束具有如下性质:符合贝塞尔光束类型的无衍射特征;在时空双曲线上强度保持不变;光波时空特性的临界条件类似于相对论中的光锥."含时贝塞尔光束"的概念为无衍射自加速光束的研究开拓了新的思路和方向.     

非线性有限束光声效应理论

当一束受正弦调制的激光入射于光声腔中的固体样品上时,由于非线性的光声效应,在光声腔中不仅能接收到基频成份的声信号,还能接收到其二次谐波成份。本文提出一个非线性热波束方程及其相应的非线性边界条件。借助于逐步近似法在光源为高斯径向分布的情形下,求解这一方程。利用Hankel变换获得这一方程的一级与二级近似解。解析结果表明,二次谐波的热波束仍然维持高斯径向分布,而其高斯半径比基频成份小。分析还表明,二次谐波的振幅不仅与线性热参数,而且也与非线性热参数有关。后者或许能提供样品的更多的有意义的信息。综合其各种特点, 关键词：     

多注RKA束流调制的理论与模拟比较分析

采用非线性理论探索了同轴多注相对论速调管放大器(CMRKA)的束波互作用特性，并与PIC结果进行了验证分析。首先推导了实心电子束的几何因子，然后分别给出了归一化调制电流和电子束动能的积分微分方程，并给出了多注速调管放大器的同轴输入腔间隙耦合系数的公式。对于束压为600 kV、束流为5 kA的16注电子束，当输入腔间隙电压分别为4.6，32.7，189 kV时，采用一维非线性理论和三维粒子模拟程序分别计算了基波电流调制系数和距离的关系，理论和模拟结果比较一致。当间隙电压为4.6 kV时，理论计算了多注电子数的个数分别为8, 12, 16以及实心电子束的半径与单注电子束通道半径比6/15, 8/15, 10/15(通道半径不变)时基波电流调制系数随传输距离的变化。结果表明，随着多注电子数的个数和电子束半径的增加，基波电流调制系数有逐渐变大的趋势。此外还计算了当间隙电压为20 kV时，归一化电流和归一化电子束动能随时间的变化和归一化常数N(z)与调制电流的n次谐波的电流调制系数随传输距离的变化。     

Efficiency of the second-harmonic generation with the zeroth-order bessel-profile beams in uniaxial crystals

We study the efficiency of the second-harmonic generation with the zeroth-order Bessel beam (SHGzoBB) in uniaxial crystals. We show that the conversion efficiency is always less than that of the second-harmonic generation with the Gaussian beam (SHGGB). The fundamental reason relies on the fact that the advantage associated with the ??nondiffractive?? nature of the Bessel beam is not sufficient to compensate the disadvantage of its wave-vector distribution. We show that the zeroth-order Bessel beam is not the optimum beam for the second-harmonic generation in uniaxial crystals.     

Three-dimensional nonlinear theory of travelling wave tubes and simulation

A three-dimensional (3D) nonlinear theory of travelling wave tubes (TWTs) is developed, which includes a fundamental radio frequency (RF) and harmonics. When the instantaneous bandwidth exceeds an octave, the harmonic is generated and the mutual coupling between the harmonic and the fundamental RF can be observed in TWTs due to nonlinear interaction between the electron beam and the RF. At low frequencies the harmonic has an obvious effect.Based upon Tien‘‘s disc model, a plastic 3D super-particle model is proposed to improve the nonlinear analysis of TWTs.Numerical results employing a periodic magnetic focusing field are presented.     

Nonlinear computer-generated holograms

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.     

Nonlinear dynamics with higher-order modes in lithium niobate waveguide arrays

We present theoretical and experimental studies on nonlinear beam propagation in lithium niobate waveguide arrays utilizing higher-order second harmonic bands. We find that the implementation of the higher-order second harmonic bands leads to a number of new effects. The combined interaction of two second harmonic bands with a propagating fundamental beam can lead to a complete inhibition of nonlinear effects or to the formation of discrete spatial solitons, depending only on the wavelength of the fundamental wave. Furthermore we analyze the properties of discrete solitons, allowing for linear coupling of the second harmonic. Here we predict and demonstrate experimentally a power dependent phase transition of the soliton topology.     

上海深紫外自由电子激光的非线性谐波辐射研究

 自由电子激光中的非线性谐波辐射能达到较高的谐波功率,可以用来得到短波长辐射或者降低第4代先进光源对电子束团品质的严厉要求。基于3维自由电子激光软件,深入详细地研究了上海深紫外自由电子激光装置的非线性谐波辐射,并且提出了谐波辐射实验和测量建议。研究表明上海深紫外自由电子激光装置3次非线性谐波辐射的功率可以达到基波功率的2%水平。     

考虑谐波互作用的行波管欧拉非线性理论模型

基于拉格朗日体系的考虑谐波互作用的理论模型,将离散的粒子近似处理为流体,得到电子相位的连续分布函数.对电子相位连续分布函数进行傅里叶一阶展开,并结合贝塞尔母函数关系式,建立了考虑谐波互作用的欧拉非线性理论模型.应用考虑谐波互作用的欧拉非线性理论模型对一支L波段空间行波管和一支C波段空间行波管进行大信号分析,并与拉格朗日理论模型进行对比.结果表明:在增益1dB压缩点之前,考虑谐波互作用的欧拉非线性理论模型与拉格朗日理论模型十分符合,增益最大误差不超过4%.考虑谐波互作用的欧拉非线性理论模型能够有效的对增益1 dB压缩点之前的谐波进行分析.仿真结果验证了考虑谐波互作用的欧拉非线性理论模型的正确性和有效性.考虑谐波互作用的欧拉非线性理论不但提供了一个谐波快速计算模型,而且为后续研究行波管谐波的产生机理与抑制方法奠定了基础.     

贝塞尔光束的应用

本文对文献中提出的贝塞尔光束的可能应用作了较全面的分析和评述，包括在能量传输、激光打孔、精密准直、小物体的测量、非线性光学、导航和测距、条形码读出、带电粒子加速中的应用，我们的分析表明，贝塞尔光束的许多提议中的应用实际上是不成立的，如能量传输、激光打孔、非线性光学和导航等，对带电粒子的加速问题作了修正     

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.     

相对论速调管放大器两腔束流调制的理论与模拟比较分析

采用一维自洽束波互作用的非线性理论,探索了相对论速调管放大器(RKA)的束流调制特性,并与二维PIC结果进行了比较和分析。首先推导了环形电子束的几何因子,然后分别给出了两腔调制时归一化调制电流和电子束动能的积分微分方程。采用调制电子束激励中间腔的非线性理论估算了中间腔间隙电压的幅度和相位,幅度的相对误差为0.07%,相位误差为2.15°。给出了输入腔和中间腔的间隙耦合系数公式,对于束压为715.2 kV、束流为8 kA的电子束,当输入腔和中间腔间隙电压分别为14,315.2 kV,输入腔和中间腔相位差为90.59°时,采用一维非线性理论和二维粒子模拟程序分别计算了基波电流调制系数和距离的关系。对于基波电流调制系数,中间腔之前处于线性区,理论值与模拟值比较一致;在中间腔内部基波电流调制系数出现明显的下降,理论值与模拟值之间的差距较大;中间腔之后处于非线性区,对于基波电流调制系数的最大值和对应的纵向位置,理论值与模拟值基本一致。当束流传输距离为65.8 cm时,计算了归一化电流和归一化电子束动能随时间的变化和电荷守恒参量N(z)与调制电流的n次谐波的电流调制系数随传输距离的变化情况。     

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.     

无衍射光束的产生及其应用

近年来,随着激光技术的快速发展,相继产生了多种在远距离传输后中心光斑保持不变的无衍射光束,包括贝塞尔光束、高阶贝塞尔光束、马丢光束、高阶马丢光束、余弦光束、抛物线光束以及艾里光束.无衍射光束在激光打孔、激光精密准直、光学精密控制、光学微操控、光通信、等离子体导向、光子弹产生、光通信、自聚焦光束的合成以及非线性光学等领域中有着广泛的应用.本文介绍了各类无衍射光束的数学表达式、产生方法及对应的实验结果;就无衍射光束的特性和应用进行了归纳和讨论;并对其在未来的研究与应用前景中发挥的重要作用进行了简要总结与展望.     

Two-dimensional nonlinear beam shaping

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.     

基于Fourier-Bessel级数的Bessel型超声场二次谐波近场特性研究

将Fourier-Bessel级数引入KZK方程的求解，用于计算黏滞媒质中零阶Bessel型超声场的二次谐波声场，得到其级数形式的解析解，并由此得出二次谐波声场在近场分布的一个新结论.设声源表面声压分布为J₀(α₀r)，则二次谐波声压在近场的径向分布服从J²₀(α₀r)函数规律.这一结论合理解释了相关的实验结果，表明二次谐波声场在近场和远场有不同的径向分布，从而解决了非线性Bessel型超声场二次谐波的近场分布问题.研究还发现二次谐波声场具有类似基波声场的有限衍射特性.给出了一个数值计算和仿真实例.