贴片型左手超材料的传输性能分析和构型设计优化
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摘要
本文在经典物理学框架下论述了左手超材料的起源、分类和特性应用,其研究凭借日新月异的材料制备技术获得了长足的发展,尤以基于谐振机理的贴片型左手超材料为最。负折射率是左手超材料最核心的特异属性,其表征的左手传输性能是诸多电磁器件应用的基本前提。控制左手传输衰减和拓大其带宽是左手超材料广阔应用前景的需求,同时也对当前飞速发展的射频段电磁器件具有特别重要的现实意义。基于此,本文分别从理论解析和数值仿真两种途径开展了贴片型左手超材料的传输性能分析及其在尺寸、形状和拓扑等三种层次的结构优化设计研究。主要的研究内容和成果如下：
现有贴片型左手超材料的传输性能分析。首先,给出了折射率完整的解析表达式,并介绍了磁性介质实现负折射率的三种情形。进而,研究了已有贴片构型左手超材料的左手传输性能,发现强磁谐振是开口环类构型具备大带宽优势的机理,但同时也造成其衰减高的不足；绘制了已有构型左手超材料传输性能的双轴分布图,点明了左手超材料的设计目标：低衰减的宽带传输性能。
细圆金属棒与开口谐振环列阵电磁性能分析的修正理论模型和尺寸优化设计。(1)推导了细圆金属棒和开口同心金属环周期性列阵电磁特性分析的理论模型,修正了Drude模型中电等离子体频率和阻尼因子表达式,改进了Pendry模型中磁谐振频率的表达式；数值算例表明改良的理论模型具有更高的预测准确度。(2)研究了谐振环构型的尺寸参数对带宽性能的影响,发现最敏感的参数是外径。研究了谐振环构型的材料参数对左手传输性能的影响,发现其在低衰减性能设计方面存在较大局限。(3)基于尺寸敏度分析的结果,借助参数化建模技术和有限差分求敏度的方法提出了正多边形谐振环构型相对带宽最大化的形状-尺寸协同设计,并采用了序列二次规划法和枚举归纳法对其进行分步式求解；通过改进的磁谐振理论模型定性讨论了最优结果大间距正方形谐振环的合理性。
超材料电磁性能仿真方法研究。(1)研究了有限元网格对超材料结构电磁性能仿真分析精度的影响,发现等效电磁参数的反演精度对散射参数准确度的依赖性非常大,特别是处在谐振频域的透射参数相位误差将导致反演的性态误差。基于该发现,提出了改进结构电磁有限元求解准确度的两步式分析方法,通过设置恰当的求解频率可获得高准确度的散射参数；数值算例表明新方法可有效且经济地提高仿真分析的准确度。(2)研究了不同周期数下结构胞元间的电磁耦合对其散射特性的影响,发现超材料胞元微结构的均匀度是其影响的关键。基于此建立了考虑结构胞元间电磁耦合影响的五层模型,通过解耦少量样本胞元结构的数值结果可以快速且较准确地预测任意有限周期胞元结构的散射参数；数值算例表明五层模型具有高性价比的求解优势。
贴片型左手超材料改进传输性能的微结构拓扑优化设计方法。以射频段左手传输的平均衰减与其绝对带宽的比值为目标函数,以磁谐振贴片的离散化方格子材料的有无为设计变量,建立了贴片型左手超材料的微结构构型设计的拓扑模型以及基于遗传算法的优化求解流程。根据拓扑优化结果给出了三种贴片新构型；重分析结果表明新构型具有更优良的左手传输性能,进一步的电磁场分析发现半高尺寸的类U型结构是其实现低衰减宽带传输性能的核心构型。表面电流密度分布的结果对比发现磁谐振贴片传导电流的强弱分布,亦即磁谐振贴片格子的合理布置对实现低衰减的宽带传输非常关键。提出了考虑可制备性的微结构拓扑优化设计方法,类似机器人头形的新构型算例结果表明周长约束法可有效地抑制棋盘格式结构的产生。
The left-handed metamaterial origin, classifications, novel features and their applications are reviewed in the framework of classical physics. Left-handed metamaterials have developed by leaps and bounds along with the ever-changing material preparation technology, especially for the patch-typed left-handed metamaterials based on resonance mechanism. Negative refractive index is the core character of left-handed metamaterials and decides the left-handed transmission performance, which is the basic premise of various electromagnetic device applications. Wide application requirements of left-handed metamaterials are to control left-handed transmission attenuation and broaden its bandwidth. And broadband transmission with low attenuation is particularly important and practical for electromagnetic devices of rapid development in the radio frequency band. Focusing on the left-handed transmission performance, structural size, shape and topology optimization design of patch-typed left-handed metamaterials are realized in this dissertation through theoretical analysis and numerical simulation. The main contents and conclusions of this dissertation are as follows:
Transmission performance for existing configurations of patch-typed left-handed metamaterials is analyzed. Firstly, a complete analytical expression of the refractive index is theoretically derived, and three different cases in magnetic media are introduced to generate a negative refractive index. Then left-handed transmission performance indicators for representing configurations of patch-typed left-handed metamaterials are numerically analyzed respectively. It is found that stronger magnetic resonance is internal mechanism for broader bandwidth and high attenuation of split-ring resonator-like structure configurations. Dual-axis distribution graphs of transmission performance indicators from the representing configurations are plotted, and the goal of left-handed metamaterial design is pointed out: broadband transmission with low attenuation performance.
Corrected theoretical models are presented for structural electromagnetic performance analysis of patch-typed left-handed metamaterials with thin circle metal rods and metal split-ring resonators. Size designs for the transmission performance are also proposed for the classic patch-typed configuration.(1) The prediction models about periodic array of thin circle metal rod and the split-ring resonators are theoretically derived. The electric plasma frequency expression and the damping factor expression of Drude model are corrected. The magnetic resonance frequency expression of Pendry model is also improved. The numerical examples show that these modified theoretical prediction models have higher accuracy.(2) The left-handed bandwidth with different structural size parameters of the square split-ring resonators configuration is numerically analyzed respectively, and their results show that the outer ring radius has an overwhelmingly greater effect than other parameters. The left-handed transmission performance with different material parameters of the square split-ring resonators configuration is also numerically analyzed respectively. It is found that to achieve the goal of low attenuation has been greatly restricted.(3) Based on the above sensitivity studies, a shape-size cooperative design is proposed to maximize relative bandwidth of regular polygon split-ring resonators through an automatic parametric modeling technology and the sensitivities from the finite difference method. Sequential quadratic programming method and induction by simple enumeration are applied to solve the optimization problem in two steps. The reasonability of the optimal results, that is, square split-ring resonator with a bigger radial distance is qualitatively discussed by the improved magnetic resonance theoretical model.
New analysis methods for structural electromagnetic performance of the metamaterials are presented.(1) Mesh-dependency in simulation results of metamaterial electromagnetic performance is analyzed based on finite element analysis. It is found that the retrieval metamaterial equivalent electromagnetic parameters have a strong dependence on the calculation accuracy of scattering parameters, especially in the resonant frequency-domain where the phase error of transmission parameters may be cause a qualitative error of the electromagnetic parameters. An improved electromagnetic simulation analysis two-step method is presented and used to obtain accurate S-parameters by determining a proper solution frequency. The numerical results show that the new method can effectively improve the accuracy of the simulation analysis through a reasonable cost.(2) The scattering performance with different periodic cells structure is numerically analyzed respectively, and their results show that a key of the electromagnetic coupling impact between those cells is the uniformity of metamaterial microstructure. So a five-layer model is established to quickly and accurately predict scattering parameters of any finite periodic cells structure by decoupling bits of numerical results of sample structure, and the electromagnetic coupling impact between structural cells is taken into consideration. The numerical examples show that the five-layer model is very cost-effective.
A topology optimization design method for improving the transmission performance of patch-typed microstructure configurations is presented. A topology optimization model of microstructure configuration design of patch-typed left-handed metamaterials is established, with the objective function defined by the ratio of the mean attenuation to the absolute left-handed bandwidth and the design variables defined by the presence or absence of discrete magnetic resonance patch lattices. Based on genetic algorithm, a flow chart for the optimization problem is also given. Three new patch-typed configurations are given according to the optimization results, and their excellent transmission performance indicators are analyzed by numerical simulation. Further analysis demonstrates that a U-shaped-like structure with half unit cell height is the core configuration of broadband transmission with low attenuation. Comparing their surface current density distributions, it is found that the distribution of conduction currents of magnetic resonance patch, that is, a reasonable arrangement of magnetic resonance patch lattices is the key to the broadband transmission with low attenuation. A new topology optimization design with the perimeter constraint is proposed to solve the problem in the manufacturing process for checkerboard-typed lattices from those configurations. The new optimum configuration of robot head-shaped-like structure shows that the new strategy is very effective.
现有贴片型左手超材料的传输性能分析。首先,给出了折射率完整的解析表达式,并介绍了磁性介质实现负折射率的三种情形。进而,研究了已有贴片构型左手超材料的左手传输性能,发现强磁谐振是开口环类构型具备大带宽优势的机理,但同时也造成其衰减高的不足；绘制了已有构型左手超材料传输性能的双轴分布图,点明了左手超材料的设计目标：低衰减的宽带传输性能。
细圆金属棒与开口谐振环列阵电磁性能分析的修正理论模型和尺寸优化设计。(1)推导了细圆金属棒和开口同心金属环周期性列阵电磁特性分析的理论模型,修正了Drude模型中电等离子体频率和阻尼因子表达式,改进了Pendry模型中磁谐振频率的表达式；数值算例表明改良的理论模型具有更高的预测准确度。(2)研究了谐振环构型的尺寸参数对带宽性能的影响,发现最敏感的参数是外径。研究了谐振环构型的材料参数对左手传输性能的影响,发现其在低衰减性能设计方面存在较大局限。(3)基于尺寸敏度分析的结果,借助参数化建模技术和有限差分求敏度的方法提出了正多边形谐振环构型相对带宽最大化的形状-尺寸协同设计,并采用了序列二次规划法和枚举归纳法对其进行分步式求解；通过改进的磁谐振理论模型定性讨论了最优结果大间距正方形谐振环的合理性。
超材料电磁性能仿真方法研究。(1)研究了有限元网格对超材料结构电磁性能仿真分析精度的影响,发现等效电磁参数的反演精度对散射参数准确度的依赖性非常大,特别是处在谐振频域的透射参数相位误差将导致反演的性态误差。基于该发现,提出了改进结构电磁有限元求解准确度的两步式分析方法,通过设置恰当的求解频率可获得高准确度的散射参数；数值算例表明新方法可有效且经济地提高仿真分析的准确度。(2)研究了不同周期数下结构胞元间的电磁耦合对其散射特性的影响,发现超材料胞元微结构的均匀度是其影响的关键。基于此建立了考虑结构胞元间电磁耦合影响的五层模型,通过解耦少量样本胞元结构的数值结果可以快速且较准确地预测任意有限周期胞元结构的散射参数；数值算例表明五层模型具有高性价比的求解优势。
贴片型左手超材料改进传输性能的微结构拓扑优化设计方法。以射频段左手传输的平均衰减与其绝对带宽的比值为目标函数,以磁谐振贴片的离散化方格子材料的有无为设计变量,建立了贴片型左手超材料的微结构构型设计的拓扑模型以及基于遗传算法的优化求解流程。根据拓扑优化结果给出了三种贴片新构型；重分析结果表明新构型具有更优良的左手传输性能,进一步的电磁场分析发现半高尺寸的类U型结构是其实现低衰减宽带传输性能的核心构型。表面电流密度分布的结果对比发现磁谐振贴片传导电流的强弱分布,亦即磁谐振贴片格子的合理布置对实现低衰减的宽带传输非常关键。提出了考虑可制备性的微结构拓扑优化设计方法,类似机器人头形的新构型算例结果表明周长约束法可有效地抑制棋盘格式结构的产生。
The left-handed metamaterial origin, classifications, novel features and their applications are reviewed in the framework of classical physics. Left-handed metamaterials have developed by leaps and bounds along with the ever-changing material preparation technology, especially for the patch-typed left-handed metamaterials based on resonance mechanism. Negative refractive index is the core character of left-handed metamaterials and decides the left-handed transmission performance, which is the basic premise of various electromagnetic device applications. Wide application requirements of left-handed metamaterials are to control left-handed transmission attenuation and broaden its bandwidth. And broadband transmission with low attenuation is particularly important and practical for electromagnetic devices of rapid development in the radio frequency band. Focusing on the left-handed transmission performance, structural size, shape and topology optimization design of patch-typed left-handed metamaterials are realized in this dissertation through theoretical analysis and numerical simulation. The main contents and conclusions of this dissertation are as follows:
Transmission performance for existing configurations of patch-typed left-handed metamaterials is analyzed. Firstly, a complete analytical expression of the refractive index is theoretically derived, and three different cases in magnetic media are introduced to generate a negative refractive index. Then left-handed transmission performance indicators for representing configurations of patch-typed left-handed metamaterials are numerically analyzed respectively. It is found that stronger magnetic resonance is internal mechanism for broader bandwidth and high attenuation of split-ring resonator-like structure configurations. Dual-axis distribution graphs of transmission performance indicators from the representing configurations are plotted, and the goal of left-handed metamaterial design is pointed out: broadband transmission with low attenuation performance.
Corrected theoretical models are presented for structural electromagnetic performance analysis of patch-typed left-handed metamaterials with thin circle metal rods and metal split-ring resonators. Size designs for the transmission performance are also proposed for the classic patch-typed configuration.(1) The prediction models about periodic array of thin circle metal rod and the split-ring resonators are theoretically derived. The electric plasma frequency expression and the damping factor expression of Drude model are corrected. The magnetic resonance frequency expression of Pendry model is also improved. The numerical examples show that these modified theoretical prediction models have higher accuracy.(2) The left-handed bandwidth with different structural size parameters of the square split-ring resonators configuration is numerically analyzed respectively, and their results show that the outer ring radius has an overwhelmingly greater effect than other parameters. The left-handed transmission performance with different material parameters of the square split-ring resonators configuration is also numerically analyzed respectively. It is found that to achieve the goal of low attenuation has been greatly restricted.(3) Based on the above sensitivity studies, a shape-size cooperative design is proposed to maximize relative bandwidth of regular polygon split-ring resonators through an automatic parametric modeling technology and the sensitivities from the finite difference method. Sequential quadratic programming method and induction by simple enumeration are applied to solve the optimization problem in two steps. The reasonability of the optimal results, that is, square split-ring resonator with a bigger radial distance is qualitatively discussed by the improved magnetic resonance theoretical model.
New analysis methods for structural electromagnetic performance of the metamaterials are presented.(1) Mesh-dependency in simulation results of metamaterial electromagnetic performance is analyzed based on finite element analysis. It is found that the retrieval metamaterial equivalent electromagnetic parameters have a strong dependence on the calculation accuracy of scattering parameters, especially in the resonant frequency-domain where the phase error of transmission parameters may be cause a qualitative error of the electromagnetic parameters. An improved electromagnetic simulation analysis two-step method is presented and used to obtain accurate S-parameters by determining a proper solution frequency. The numerical results show that the new method can effectively improve the accuracy of the simulation analysis through a reasonable cost.(2) The scattering performance with different periodic cells structure is numerically analyzed respectively, and their results show that a key of the electromagnetic coupling impact between those cells is the uniformity of metamaterial microstructure. So a five-layer model is established to quickly and accurately predict scattering parameters of any finite periodic cells structure by decoupling bits of numerical results of sample structure, and the electromagnetic coupling impact between structural cells is taken into consideration. The numerical examples show that the five-layer model is very cost-effective.
A topology optimization design method for improving the transmission performance of patch-typed microstructure configurations is presented. A topology optimization model of microstructure configuration design of patch-typed left-handed metamaterials is established, with the objective function defined by the ratio of the mean attenuation to the absolute left-handed bandwidth and the design variables defined by the presence or absence of discrete magnetic resonance patch lattices. Based on genetic algorithm, a flow chart for the optimization problem is also given. Three new patch-typed configurations are given according to the optimization results, and their excellent transmission performance indicators are analyzed by numerical simulation. Further analysis demonstrates that a U-shaped-like structure with half unit cell height is the core configuration of broadband transmission with low attenuation. Comparing their surface current density distributions, it is found that the distribution of conduction currents of magnetic resonance patch, that is, a reasonable arrangement of magnetic resonance patch lattices is the key to the broadband transmission with low attenuation. A new topology optimization design with the perimeter constraint is proposed to solve the problem in the manufacturing process for checkerboard-typed lattices from those configurations. The new optimum configuration of robot head-shaped-like structure shows that the new strategy is very effective.
引文
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