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1.
Third‐order nonlinear and linear time‐dependent dynamical diffraction of X‐rays in crystals
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Minas K. Balyan 《Journal of synchrotron radiation》2016,23(4):919-928
For the first time the third‐order nonlinear time‐dependent Takagi's equations of X‐rays in crystals are obtained and investigated. The third‐order nonlinear and linear time‐dependent dynamical diffraction of X‐rays spatially restricted in the diffraction plane pulses in crystals is investigated theoretically. A method of solving the linear and the third‐order nonlinear time‐dependent Takagi's equations is proposed. Based on this method, results of analytical and numerical calculations for both linear and nonlinear diffraction cases are presented and compared. 相似文献
2.
We theoretically investigate the phase noise in quasi-linear optical transmission systems and study the mitigation of phase noise by properly choosing periodic dispersion compensation and amplification. Variational method is used to deduce the analytical formula for calculating the phase fluctuations of a Gaussian pulse. The analytical predictions are then checked against direct simulations by numerically solving the nonlinear Schrödinger equation. We find that stronger dispersion compensation maps can be used to reduce phase noise and it can be further mitigated by modifying the dispersion map appropriately. It is also found that shorter amplifier spacing yields lower phase noise. We also explore the effect of pre-, post- and bi-end dispersion compensation configurations on phase noise with full compensation and check the reduction of phase noise along the fiber link. 相似文献
3.
为提高传统光滑粒子动力学(SPH)方法求解高维非线性薛定谔(nonlinear Schr?dinger/Gross-Pitaevskii equation, NLS/GP)方程的数值精度和计算效率,本文首先基于高阶时间分裂思想将非线性薛定谔方程分解成线性导数项和非线性项,其次拓展一阶对称SPH方法对复数域上线性导数部分进行显式求解,最后引入MPI并行技术,结合边界施加虚粒子方法给出一种能够准确、高效地求解高维NLS/GP方程的高阶分裂修正并行SPH方法.数值模拟中,首先对带有周期性和Dirichlet边界条件的NLS方程进行求解,并与解析解做对比,准确地得到了周期边界下孤立波的奇异性,且对提出方法的数值精度、收敛速度和计算效率进行了分析;随后,运用给出的高阶分裂粒子方法对复杂二维和三维NLS/GP问题进行了数值预测,并与其他数值结果进行比较,准确地展现了非线性孤立波传播中的奇异现象和玻色-爱因斯坦凝聚态中带外旋转项的量子涡旋变化过程. 相似文献
4.
We investigate the phase jitter in long-haul optical transmission systems with periodic dispersion management and amplification. We compare different dispersion-managed soliton systems and a conventional soliton system having the same pulse width and path-averaged dispersion. Using the variational method, we derive the ordinary differential equations for the pulse parameters perturbed by amplifier noise and hence calculate the phase jitter. We verify the analytical results by numerically solving the nonlinear Schrödinger equation using split-step Fourier algorithm. The results suggest that the reduction of nonlinear phase noise in dispersion-managed soliton systems is possible compared to a conventional soliton system. It is also revealed that the phase noise is enhanced in stronger dispersion-managed systems. We also explore the phase noise effect in dispersion-managed quasi-linear systems and find that phase jitter is mitigated in highly dispersive fibers. 相似文献
5.
In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single field in a fiber medium with phase modulation and fibre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modified NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects. 相似文献
6.
ELECTROSTATIC POTENTIAL OF STRONGLY NONLINEAR COMPOSITES: HOMOTOPY CONTINUATION APPROACH 总被引:3,自引:0,他引:3
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The homotopy continuation method is used to solve the electrostatic boundary-value problems of strongly nonlinear composite media, which obey a current-field relation of J=σ E+χ|E|2E. With the mode expansion, the approximate analytical solutions of electric potential in host and inclusion regions are obtained by solving a set of nonlinear ordinary different equations, which are derived from the original equations with homotopy method. As an example in dimension two, we apply the method to deal with a nonlinear cylindrical inclusion embedded in a host. Comparing the approximate analytical solution of the potential obtained by homotopy method with that of numerical method, we can obverse that the homotopy method is valid for solving boundary-value problems of weakly and strongly nonlinear media. 相似文献
7.
JiaQi Mo 《中国科学G辑(英文版)》2009,52(7):1007-1010
The model for gain fluency of a laser pulse amplifier is studied. Using the homotopic mapping method, firstly, the system
of the original model is packed up standardization; secondly, introducing a homotopic mapping, taking the property of the
mapping, inducing a contrived parameter, the solving of a nonlinear problem translates into the solving of a linear problem.
Then the approximate expressions of the solution for the corresponding model are obtained. And the precision for the approximate
solution is compared. It illuminates that the obtained approximate solution using the homotopic mapping method possesses higher
approximate degree. At one time, the expansion of solution through the homotopic mapping method can be kept in the analytic
operation. Thus it also enables us through differential and integral operations to obtain other physics behavior for the gain
fluency of laser pulse amplifier. 相似文献
8.
In this research, we work on a specific class of nonlinear evolution equation which is the modify unstable nonlinear Schrödinger equation. This equation is used to describe a time evolution of disturbances in unstable media. Various solutions have been obtained. The results deduced are of varied types and include bright solution, dark solution, rational dark-bright solution, as well as cnoidal solutions. These solutions might be useful in engineering fields. Some conditions for the stability of these solutions are presented. The method used here is understandable and very powerful for solving the nonlinear problems. 相似文献
9.
V. I. Zubov 《Russian Physics Journal》1984,27(3):235-239
The nonlinear integral equations of the asymmetric self-consistent field method are applied to a semiinfinite, strongly anharmonic crystal bounded by a gaseous phase. These equations are used to obtain the self-consistent potential for crystal atoms close to the surface, and through this potential, the surface free energy is obtained. The nonlinear integral equation is reduced to a set of transcendental equations and a method is given for the solving the latter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 80–84, March, 1984. 相似文献
10.
首先介绍了模拟光参量啁啾脉冲放大(OPCPA)过程的多种计算模型,在此基础上提出了三步走逐步逼近算法,以确定OPCPA过程中最稳输出时所需的非线性晶体长度.这种算法综合利用了上述计算模型,随着计算模型越来越精确,非线性晶体长度的计算范围越来越小.因而利用这种算法能高效、精确地确定最佳非线性晶体长度.最后提出在OPCPA过程引入一定的相位失配量,来调谐最稳输出时所需晶体长度,从而能突破晶体加工精度不够的局限,在实际OPCPA过程中获得稳定输出. 相似文献
11.
首先介绍了模拟光参量啁啾脉冲放大(OPCPA)过程的多种计算模型,在此基础上提出了三步走逐步逼近算法,以确定OPCPA过程中最稳输出时所需的非线性晶体长度.这种算法综合利用了上述计算模型,随着计算模型越来越精确,非线性晶体长度的计算范围越来越小.因而利用这种算法能高效、精确地确定最佳非线性晶体长度.最后提出在OPCPA过程引入一定的相位失配量,来调谐最稳输出时所需晶体长度,从而能突破晶体加工精度不够的局限,在实际OPCPA过程中获得稳定输出.
关键词:
光参量啁啾脉冲放大
最稳输出
相位失配
非线性晶体长度 相似文献
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14.
单个波长到多个波长的变换实验 总被引:3,自引:1,他引:2
报道一种波长变换的新方法.采用此方法不需要任何泵浦光便能够直接将信号光变换成在特定谱宽内的任意多个任意波长的变换光,这对于将来的波分复用光网络提供了较大的方便.此波长变换的原理是利用色散位移光纤的非线性效应产生超连续光谱(SC)信号,由于这种SC信号携带有变换光信号,对这种连续谱进行滤波便能够得到所需要的任意频率的变换信号.此变换方式具有变换频带宽,偏振不敏感的优点。 相似文献
15.
根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH(Camassa-Holm)方程、五阶KdV-like 方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解.
关键词:
非线性波方程
尖峰孤子解
待定系数法 相似文献
16.
Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this Letter; one is He's variational iteration method (VIM) and the other is the homotopy–perturbation method (HPM). Nonlinear convective–radiative cooling equations are used as examples to illustrate the simple solution procedures. These methods are useful and practical for solving the nonlinear heat diffusion equation, which is associated with variable thermal conductivity condition. Comparison of the results obtained by both methods with exact solutions reveals that both methods are tremendously effective. 相似文献
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18.
To deal with the radiation from an axially symmetric pillbox resonator embedded in LiNbO3 substrate, an eigenvalue equation is derived from the expression of the finite-element beam propagation method in a cylindrical coordinate system. By solving the eigenvalue equation iteratively, the field distributions and the angular phase constants of the pillbox resonator are evaluated. The iterative scheme of solving the eigenvalue equation is an extension of our previous direct solution method which was described for a lossless case. The results obtained by this method are compared with those obtained analytically, and excellent agreement is found. 相似文献
19.
In this study we use the spectral relaxation method (SRM) for the solution of the steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation. The spectral relaxation method is a new Chebyshev spectral collocation based iteration method that is developed from the Gauss-Seidel idea of decoupling systems of equations. In this work, we investigate the applicability of the method in solving strongly nonlinear boundary value problems of von Kármán flow type. The SRM results are validated against previous results present in the literature and with those obtained using the bvp4c, a MATLAB inbuilt routine for solving boundary value problems. The study highlights the accuracy and efficiency of the proposed SRM method in solving highly nonlinear boundary layer type equations. 相似文献