高温超导薄膜微波非线性的全波分析研究
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摘要
高温超导薄膜的微波非线性性能具有重要的意义，国内外已在实验及理论等方面展开了广泛的研究，并随着该研究的深入向实用化发展。尽管如此，目前对该非线性的精确分析尚无可靠解决方法，因此如何建立有效的分析手段已成为一个迫切需要解决的问题。
本论文结合时域有限差分法（Finite Difference Time Domain，FDTD法）和Ginzburg-Landau方程（GL方程）的有限差分求解方法，对高温超导微波非线性进行全波分析，仿真计算了不同传输功率下超导的非线性传输特性和电流密度分布，预测了一定线宽时的超导转变功率点。主要完成了以下工作：
1.研究了适合于微带类型的FDTD算法，如色散吸收边界条件，非均匀网格剖分，以及导电良好材料里面场的差分形式以保证时间迭代上的稳定性，以便对高温超导进行电磁场仿真；
2.提出了计算实正规矩阵若干特征值问题的神经网络计算办法，并且通过矩阵范数降低技术推广到了任意实矩阵的特征值问题，建立了一个求解实反对称矩阵模最大特征值及其特征向量的模的复神经网络模型，并给出和证明了复神经网络模型的收敛性定理。这些算法可以被应用全波分析GL有限差分求解稳定性判断的问题研究中；
3.研究了GL方程的有限差分数值解法，包括对GL方程的有限差分离散近似，两个GL方程的有限差分时边界条件的处理，GL方程离散后求解非线性方程组的Newton迭代法，以及内部和边界处场的插值算法；
4.将FDTD法与GL方程结合，对超导薄膜传输线进行了全波仿真，分析了不同传输功率时电流密度的分布和变化情况，预估了一定线宽时低损耗超导态向高损耗态转变的功率点；
5.设计实验，测试了超导共面波导传输线的功率非线性传输特性，验证了全波仿真对功率转变点的预估，测试表明预估值与测试值一致，表明了全波分析的有效性。
Microwave nonlinear performance of the high-temperature superconductor thinfilm has an important significance, and extensive researches have been conducted inexperimental and theoretical aspects either at home and abroad. With the deepening ofthe study, the development of the nonlinearity research turns to practical application.Nevertheless, there is no accurate method for nonlinear analysis at present, how toestablish an effective technique for nonlinear study has become an urgent problem to besolved.
This dissertation combines the finite difference time domain method and finitedifference method for solving the Ginzburg-Landau equations for full-wave analysis ofhigh-temperature superconductor microwave nonlinearity. In this dissertation Thecurrent density distribution and nonlinear transmission characteristics of superconductorare simulated with different transmitted power. Also the transition point of power forsuperconducting transimission line with certain line width is predicted. Such contentsinvolved in this dissertation are as following:
1. The FDTD algorithm suitable for microstrip type is studied, such as dispersiveabsorbing boundary conditions, non-uniform mesh, as well as the differential forms forfields in a good conductor to ensure stability on the time iteration. All of these works isto smimulate the electromagnetic field in high-temperature superconductor.
2. some neural network models are proposed for computing some eigenvaluesproblems of normal matrices, and also extended to arbitary real matrices eigenvaluesproblems by matrix norm reducing technique, a complex nueral network model is setupto calculate the modulus largest eigenvector and the corresponding eigenvalue, in thesame time the convergency is improved also. these methods can be applied to the studyof stability problems from numerical computation of Ginzburg-Landau equations infull-wave analysis.
3. The finite difference numerical solution for the GL equations is studied,including finite difference discrete approximation of the GL equations, treatment ofboundary conditions of the two GL equations discretized by finite difference, the Newton iteration method for solving system of linear equations produced by GLequations' discretization, and internal and boundary field interpolation algorithm.
4. Full-wave simulation is conducted for superconducting thin film transmissionline by the combination of FDTD method and GL equations numerical solution. Thecurrent density distribution is analyzed when different power is transmitted. Thetransition point of power needed for the transition between low-loss superconductingstate to the high loss state is estimated in the situation of different linewidth.
5. Experiments are designed to mearsure the power nonlinear propagationproperties of high-temperature superconductor coplanar waveguide transmission line.The estimation for the power transition point is verifying by full-wave analysis. Themeasurements show that the estimation is close to the tested value, and this proves thatfull-wave analysis is effective, we also find that transmission line method for measuringsurface resistance is failure.
本论文结合时域有限差分法（Finite Difference Time Domain，FDTD法）和Ginzburg-Landau方程（GL方程）的有限差分求解方法，对高温超导微波非线性进行全波分析，仿真计算了不同传输功率下超导的非线性传输特性和电流密度分布，预测了一定线宽时的超导转变功率点。主要完成了以下工作：
1.研究了适合于微带类型的FDTD算法，如色散吸收边界条件，非均匀网格剖分，以及导电良好材料里面场的差分形式以保证时间迭代上的稳定性，以便对高温超导进行电磁场仿真；
2.提出了计算实正规矩阵若干特征值问题的神经网络计算办法，并且通过矩阵范数降低技术推广到了任意实矩阵的特征值问题，建立了一个求解实反对称矩阵模最大特征值及其特征向量的模的复神经网络模型，并给出和证明了复神经网络模型的收敛性定理。这些算法可以被应用全波分析GL有限差分求解稳定性判断的问题研究中；
3.研究了GL方程的有限差分数值解法，包括对GL方程的有限差分离散近似，两个GL方程的有限差分时边界条件的处理，GL方程离散后求解非线性方程组的Newton迭代法，以及内部和边界处场的插值算法；
4.将FDTD法与GL方程结合，对超导薄膜传输线进行了全波仿真，分析了不同传输功率时电流密度的分布和变化情况，预估了一定线宽时低损耗超导态向高损耗态转变的功率点；
5.设计实验，测试了超导共面波导传输线的功率非线性传输特性，验证了全波仿真对功率转变点的预估，测试表明预估值与测试值一致，表明了全波分析的有效性。
Microwave nonlinear performance of the high-temperature superconductor thinfilm has an important significance, and extensive researches have been conducted inexperimental and theoretical aspects either at home and abroad. With the deepening ofthe study, the development of the nonlinearity research turns to practical application.Nevertheless, there is no accurate method for nonlinear analysis at present, how toestablish an effective technique for nonlinear study has become an urgent problem to besolved.
This dissertation combines the finite difference time domain method and finitedifference method for solving the Ginzburg-Landau equations for full-wave analysis ofhigh-temperature superconductor microwave nonlinearity. In this dissertation Thecurrent density distribution and nonlinear transmission characteristics of superconductorare simulated with different transmitted power. Also the transition point of power forsuperconducting transimission line with certain line width is predicted. Such contentsinvolved in this dissertation are as following:
1. The FDTD algorithm suitable for microstrip type is studied, such as dispersiveabsorbing boundary conditions, non-uniform mesh, as well as the differential forms forfields in a good conductor to ensure stability on the time iteration. All of these works isto smimulate the electromagnetic field in high-temperature superconductor.
2. some neural network models are proposed for computing some eigenvaluesproblems of normal matrices, and also extended to arbitary real matrices eigenvaluesproblems by matrix norm reducing technique, a complex nueral network model is setupto calculate the modulus largest eigenvector and the corresponding eigenvalue, in thesame time the convergency is improved also. these methods can be applied to the studyof stability problems from numerical computation of Ginzburg-Landau equations infull-wave analysis.
3. The finite difference numerical solution for the GL equations is studied,including finite difference discrete approximation of the GL equations, treatment ofboundary conditions of the two GL equations discretized by finite difference, the Newton iteration method for solving system of linear equations produced by GLequations' discretization, and internal and boundary field interpolation algorithm.
4. Full-wave simulation is conducted for superconducting thin film transmissionline by the combination of FDTD method and GL equations numerical solution. Thecurrent density distribution is analyzed when different power is transmitted. Thetransition point of power needed for the transition between low-loss superconductingstate to the high loss state is estimated in the situation of different linewidth.
5. Experiments are designed to mearsure the power nonlinear propagationproperties of high-temperature superconductor coplanar waveguide transmission line.The estimation for the power transition point is verifying by full-wave analysis. Themeasurements show that the estimation is close to the tested value, and this proves thatfull-wave analysis is effective, we also find that transmission line method for measuringsurface resistance is failure.
引文
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