左手材料微结构构型设计优化
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摘要
社会的发展对新材料的设计提出了更高的要求。而某些属性要求超出了自然界所能提供的范围,研发具有新的特性的材料成为学术界和工程领域的非常重要的课题。作为一种新型材料,左手材料(LHM)以其独特的电磁性质引起了学术和工程领域的广泛关注。据此背景,本文主要研究左手材料的电磁传播特性及微结构构型优化设计问题,建立左手材料微结构构型设计的系统方法。研究了左手材料宏观等效电磁性能的预测方法,建立了准确表征材料宏观电磁性能与微结构之间关系的理论体系；研究了左手材料微结构构型设计的系统方法,以(拓扑)优化方法为手段,建立了特定性能要求的左手材料微结构设计优化模型及求解方法；基于设计技术和试验验证技术,发现并确认了几种左手材料微结构新构型。具体研究内容和结果包括：
1.电磁波在周期性开口谐振环(SRRs)型材料中传播的色散性能和透射特性分析。SRRs型左手材料是目前研究的焦点。分析和了解其电磁波传播规律以及色散性能和透射特性,将更利于其多功能化设计。本文以SRRs构型的左手材料为研究对象,系统分析了影响SRRs、Wires以及LHMs微波透射行为的因素。各种参数的敏度分析结果表明：不同形状的SRRs对左手材料的左手特性激发机理相同,其磁谐振频率主要和SRRs的外环所包含的面积有关；LHMs的谐振响应主要由SRRs引起,其谐振频率随介质基板的介电常数增大而降低,但介质基板的厚度对左手材料的透射特性影响非常小；细金属线的宽度对LHMs的左手性质影响较小,且当细金属线位于单胞的中心时,谐振频率最低；在SRRs的各项尺寸中,外环的边长对SRRs的透射特性影响最大；与典型的SRRs相比,单个的SRR也可以产生负的磁导率,且与SRRs没有本质区别。在此基础上,进一步将频率扩展到THz波段,研究了THz频率下SRR的谐振特性,并讨论了THz下实现左手材料的可能性。建立了SRR构型左手材料的尺寸参数优化问题的提法和求解方法,并给出了3种具有不同所需目标的左手材料微结构构型。
2.左手材料微结构新构型设计的系统理论和一般方法。左手材料的优异特性,激发了新型左手材料的设计需求。然而,目前的左手材料微结构构型的设计主要是基于SRRs-Wire这一基本构型,借助于简单的传输线模型的模拟分析,通过变形和尺寸调整方式获得新的微结构构型。这种设计方式主要是基于经验的积累和直觉灵感,缺乏一般性。研究建立左手材料微结构构型设计的系统方法意义重大。本文建立了基于拓扑优化技术的左手材料微结构构型描述及演化方法和具有所要求性能的左手材料微结构新构型设计的系统理论和一般方法。以最大带宽为目标,以金属材料的排布为设计变量进行拓扑优化设计,成功地设计了几种典型的左手材料微结构构型,并获得了金属丝和SRRs功能统一并集成的微结构构型。几种典型构型的左手材料性质的试验测试结果验证了所设计的左手材料微结构构型的正确性。
3.铁氧体类薄膜型左手材料设计。利用铁氧体在微波阶段的磁响应,可以设计铁氧体类型的左手材料。针对金属--铁氧体型左手薄膜材料,基于传输矩阵的等效层理论,研究了周期性多层薄膜系统的波传播性质,建立了对称单胞的薄膜材料与其等效折射率、介电常数和磁导率的关系,建立了特定频率下的最小折射率、特定常数折射率材料以及考虑单胞长度条件下的左手性质设计的方法。研究证明,通过调整单胞内材料的分布可以实现左手薄膜材料的拓扑优化设计。数值算例的结果说明,改变单胞内微结构的拓扑可极大地改变其负折射性质。
4.颗粒型左手材料的电磁性能分析。基于Wiener界限和Hashin-shtrikman界限,对包含具有负介电常数的相材料的情况进行讨论,拓展了Bruggeman理论的适用范围,建立了设计颗粒型左手材料的理论模型。研究发现,如果相材料分别具有单负(负介电常数或负磁导率)的性质,材料的整体性质可表现为两种：一种是负折射,但并不具备左手性,另一种则是典型的左手材料。颗粒材料均匀性好的优点,使得具有负折射性质的颗粒材料具有更广阔的应用前景。
本论文工作得到国家自然科学基金(编号：90605002,90816025,10721062),国家重点基础研究(973)计划(编号：2006CB601205)和科技部国家重点实验室专项经费(编号：S08102)的资助,在此表示感谢。
The materials are often required to exhibit prescribed/specific and excellent properties in advanced engineering. In some cases, these requirements may not be fulfilled by existed materials found in nature and developed in engineering. As a new material, the Left-handed material (LHM) with its unique electromagnetic properties has aroused widespread attention in the academic and engineering fields.In this dissertation, the electromagnetic propagation characteristics of left-handed materials and the design optimization program of micro-structural configuration are investigated, and a systematic approach for designing micro-structural configuration of left-handed materials is established. Furthermore, the retrieval method for macro effective electromagnetic parameters of LHMs is studied, and a theoretical system of characterizing the relationship between effective electromagnetic parameter and micro-structure is presented. Based on the idea of topology optimization, the mathematical formulations and the corresponding solving methods for design optimization of the micro-structural configuration of LHMs with specific electromagnetic properties are established. Finally, several left-handed materials with new configuration have been discovered and identified based on the numerical simulation techniques and experimental test verification technologies. The main content and results are given in the following paragraphs:
1. Analysis of the dispersion characteristics and transmission properties of meta-materials with split-ring resonators (SRRs). SRRs-type LHMs have been the focus of current research. It benefits the designs of multi-functional material to analyze the propagation, dispersion characteristics, and the transmission properties of electromagnetic wave in periodic SRRs structures.In this dissertation, we study the transmission properties of LHMs and SRRs, and analyze the dependence of the transmission on parameters of the system such as the size and shape of the SRRs, size of the wires, and the constants of the dielectric board. The results show that:there is no qualitative difference during the different shapes of the SRRs. The magnetic resonance frequency of the SRRs is mainly dependent on compassed area of the outer SRRs. The resonant response of the LHMs caused mainly by SRRs, and the increase of the dielectric constant of the background will bring about the decrease of the magnetic resonance frequencies. However, the dependence of the thickness of the background is quite small. The influence of the width of the metal wires relative to the LHMs is small, and the optimum position of the wires is that of median position, with a lowest magnetic resonance frequency. Of all the size of the SRRs, the outer ring radius has most effect on the transmission properties. Compared with the typical SRRs, a single SRR can also produce negative permeability, and there is no essential difference with the SRRs. Furthermore, the resonant characteristics of SRR in THz frequencies are studied, and the possibility of achieving terahertz LHMs is discussed. The formulation and the solving algorithm of size optimization for LHMs are achieved, and three micro-structural configurations with different objects are presented.
2. Systematic approach and general method for designing new micro-structural configuration of LHMs. The novel property of the LHMs induces many design requirements for new LHMs. However, most of existing configurations of LHMs were obtained by the typical SRRs-Wire structure, i.e., changing the shape and (or) the size of the billet topology (configuration) proposed by Pendry. This design approach is mainly based on the accumulation of experience and intuition inspiration, with a great disadvantage. Thus, an effective and systematic method for designing the micro-structural configurations of LHMs is quite desirable. In the dissertation, systematic approach and conventional method for designing new micro-structural configuration of LHMs with required properties base on topology optimization technique are established. By choosing the arrangements of the metal film pieces as design variables and the maximum width of negative refraction as objective, several typical micro-structural configurations of LHMs are designed, which include integrative LHM with simultaneous negative permittivity and permeability. Experimental results show good agreement with the transmission properties of the designed configuration using numerical method.
3. Design of multilayer Left-handed materials based on ferrite. Magnetic response of ferrite at GHz is useful to design ferrite-based LHMs. Based on the theory of equivalent layer, the propagation of electromagnetic wave in periodic multi-layer film system is analyzed. By using metal-ferrite film LHMs, the relationship between effective electromagnetic parameter and the symmetrical unit cell is presented, and the design method for several objectives, such as minimum refractive indices under specified frequency, material with prescribed negative refractive index, as well as the unit cell with a fixed length, is established. Our study have shown that the topology optimization design of one-dimensional film LHMs can be performed by controlling the layout and the ratio of the contrasting materials in the unit cell, and the nature of the negative refraction can be changed significantly.
4. Analysis of electromagnetic properties of granular LHMs. Based on the Wiener bounds and the Hashin-shtrikman bounds, we theoretically investigate the possible existence of granular LHMs using Bruggeman formalism. While the two component mediums have negative permittivity (permeability), the application scope of the Bruggeman theory is extended, and the theoretical model of designing granular LHMs is established. The results show that if the component material is single-negative (negative permittivity or permeability) material, there can be two types of composites:one is double-negative medium (but not LHMs), the other is a typical LHMs. Due to the advantage of the homogenization effect, this granular LHMs can be a more broad application prospects.
The work of this dissertation is supported by the National Natural Science Foundation of China through the Grant No.s (90605002,90816025,10721026), the National Key Basic Research Program of China (Grant No.2006CB601205), and the Special found for state key laboratory from ministry of science and technology of China (Grant No.S08102). The financial contributions are gratefully acknowledged.
1.电磁波在周期性开口谐振环(SRRs)型材料中传播的色散性能和透射特性分析。SRRs型左手材料是目前研究的焦点。分析和了解其电磁波传播规律以及色散性能和透射特性,将更利于其多功能化设计。本文以SRRs构型的左手材料为研究对象,系统分析了影响SRRs、Wires以及LHMs微波透射行为的因素。各种参数的敏度分析结果表明：不同形状的SRRs对左手材料的左手特性激发机理相同,其磁谐振频率主要和SRRs的外环所包含的面积有关；LHMs的谐振响应主要由SRRs引起,其谐振频率随介质基板的介电常数增大而降低,但介质基板的厚度对左手材料的透射特性影响非常小；细金属线的宽度对LHMs的左手性质影响较小,且当细金属线位于单胞的中心时,谐振频率最低；在SRRs的各项尺寸中,外环的边长对SRRs的透射特性影响最大；与典型的SRRs相比,单个的SRR也可以产生负的磁导率,且与SRRs没有本质区别。在此基础上,进一步将频率扩展到THz波段,研究了THz频率下SRR的谐振特性,并讨论了THz下实现左手材料的可能性。建立了SRR构型左手材料的尺寸参数优化问题的提法和求解方法,并给出了3种具有不同所需目标的左手材料微结构构型。
2.左手材料微结构新构型设计的系统理论和一般方法。左手材料的优异特性,激发了新型左手材料的设计需求。然而,目前的左手材料微结构构型的设计主要是基于SRRs-Wire这一基本构型,借助于简单的传输线模型的模拟分析,通过变形和尺寸调整方式获得新的微结构构型。这种设计方式主要是基于经验的积累和直觉灵感,缺乏一般性。研究建立左手材料微结构构型设计的系统方法意义重大。本文建立了基于拓扑优化技术的左手材料微结构构型描述及演化方法和具有所要求性能的左手材料微结构新构型设计的系统理论和一般方法。以最大带宽为目标,以金属材料的排布为设计变量进行拓扑优化设计,成功地设计了几种典型的左手材料微结构构型,并获得了金属丝和SRRs功能统一并集成的微结构构型。几种典型构型的左手材料性质的试验测试结果验证了所设计的左手材料微结构构型的正确性。
3.铁氧体类薄膜型左手材料设计。利用铁氧体在微波阶段的磁响应,可以设计铁氧体类型的左手材料。针对金属--铁氧体型左手薄膜材料,基于传输矩阵的等效层理论,研究了周期性多层薄膜系统的波传播性质,建立了对称单胞的薄膜材料与其等效折射率、介电常数和磁导率的关系,建立了特定频率下的最小折射率、特定常数折射率材料以及考虑单胞长度条件下的左手性质设计的方法。研究证明,通过调整单胞内材料的分布可以实现左手薄膜材料的拓扑优化设计。数值算例的结果说明,改变单胞内微结构的拓扑可极大地改变其负折射性质。
4.颗粒型左手材料的电磁性能分析。基于Wiener界限和Hashin-shtrikman界限,对包含具有负介电常数的相材料的情况进行讨论,拓展了Bruggeman理论的适用范围,建立了设计颗粒型左手材料的理论模型。研究发现,如果相材料分别具有单负(负介电常数或负磁导率)的性质,材料的整体性质可表现为两种：一种是负折射,但并不具备左手性,另一种则是典型的左手材料。颗粒材料均匀性好的优点,使得具有负折射性质的颗粒材料具有更广阔的应用前景。
本论文工作得到国家自然科学基金(编号：90605002,90816025,10721062),国家重点基础研究(973)计划(编号：2006CB601205)和科技部国家重点实验室专项经费(编号：S08102)的资助,在此表示感谢。
The materials are often required to exhibit prescribed/specific and excellent properties in advanced engineering. In some cases, these requirements may not be fulfilled by existed materials found in nature and developed in engineering. As a new material, the Left-handed material (LHM) with its unique electromagnetic properties has aroused widespread attention in the academic and engineering fields.In this dissertation, the electromagnetic propagation characteristics of left-handed materials and the design optimization program of micro-structural configuration are investigated, and a systematic approach for designing micro-structural configuration of left-handed materials is established. Furthermore, the retrieval method for macro effective electromagnetic parameters of LHMs is studied, and a theoretical system of characterizing the relationship between effective electromagnetic parameter and micro-structure is presented. Based on the idea of topology optimization, the mathematical formulations and the corresponding solving methods for design optimization of the micro-structural configuration of LHMs with specific electromagnetic properties are established. Finally, several left-handed materials with new configuration have been discovered and identified based on the numerical simulation techniques and experimental test verification technologies. The main content and results are given in the following paragraphs:
1. Analysis of the dispersion characteristics and transmission properties of meta-materials with split-ring resonators (SRRs). SRRs-type LHMs have been the focus of current research. It benefits the designs of multi-functional material to analyze the propagation, dispersion characteristics, and the transmission properties of electromagnetic wave in periodic SRRs structures.In this dissertation, we study the transmission properties of LHMs and SRRs, and analyze the dependence of the transmission on parameters of the system such as the size and shape of the SRRs, size of the wires, and the constants of the dielectric board. The results show that:there is no qualitative difference during the different shapes of the SRRs. The magnetic resonance frequency of the SRRs is mainly dependent on compassed area of the outer SRRs. The resonant response of the LHMs caused mainly by SRRs, and the increase of the dielectric constant of the background will bring about the decrease of the magnetic resonance frequencies. However, the dependence of the thickness of the background is quite small. The influence of the width of the metal wires relative to the LHMs is small, and the optimum position of the wires is that of median position, with a lowest magnetic resonance frequency. Of all the size of the SRRs, the outer ring radius has most effect on the transmission properties. Compared with the typical SRRs, a single SRR can also produce negative permeability, and there is no essential difference with the SRRs. Furthermore, the resonant characteristics of SRR in THz frequencies are studied, and the possibility of achieving terahertz LHMs is discussed. The formulation and the solving algorithm of size optimization for LHMs are achieved, and three micro-structural configurations with different objects are presented.
2. Systematic approach and general method for designing new micro-structural configuration of LHMs. The novel property of the LHMs induces many design requirements for new LHMs. However, most of existing configurations of LHMs were obtained by the typical SRRs-Wire structure, i.e., changing the shape and (or) the size of the billet topology (configuration) proposed by Pendry. This design approach is mainly based on the accumulation of experience and intuition inspiration, with a great disadvantage. Thus, an effective and systematic method for designing the micro-structural configurations of LHMs is quite desirable. In the dissertation, systematic approach and conventional method for designing new micro-structural configuration of LHMs with required properties base on topology optimization technique are established. By choosing the arrangements of the metal film pieces as design variables and the maximum width of negative refraction as objective, several typical micro-structural configurations of LHMs are designed, which include integrative LHM with simultaneous negative permittivity and permeability. Experimental results show good agreement with the transmission properties of the designed configuration using numerical method.
3. Design of multilayer Left-handed materials based on ferrite. Magnetic response of ferrite at GHz is useful to design ferrite-based LHMs. Based on the theory of equivalent layer, the propagation of electromagnetic wave in periodic multi-layer film system is analyzed. By using metal-ferrite film LHMs, the relationship between effective electromagnetic parameter and the symmetrical unit cell is presented, and the design method for several objectives, such as minimum refractive indices under specified frequency, material with prescribed negative refractive index, as well as the unit cell with a fixed length, is established. Our study have shown that the topology optimization design of one-dimensional film LHMs can be performed by controlling the layout and the ratio of the contrasting materials in the unit cell, and the nature of the negative refraction can be changed significantly.
4. Analysis of electromagnetic properties of granular LHMs. Based on the Wiener bounds and the Hashin-shtrikman bounds, we theoretically investigate the possible existence of granular LHMs using Bruggeman formalism. While the two component mediums have negative permittivity (permeability), the application scope of the Bruggeman theory is extended, and the theoretical model of designing granular LHMs is established. The results show that if the component material is single-negative (negative permittivity or permeability) material, there can be two types of composites:one is double-negative medium (but not LHMs), the other is a typical LHMs. Due to the advantage of the homogenization effect, this granular LHMs can be a more broad application prospects.
The work of this dissertation is supported by the National Natural Science Foundation of China through the Grant No.s (90605002,90816025,10721026), the National Key Basic Research Program of China (Grant No.2006CB601205), and the Special found for state key laboratory from ministry of science and technology of China (Grant No.S08102). The financial contributions are gratefully acknowledged.
引文
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