等效异向介质的特性与结构研究
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摘要
异向介质是当前科学研究的热点之一,它的发现被认为是2003年度十大科学突破之一,是当前物理与电磁学研究领域中的前沿与热点问题。异向介质是指等效的介电常数和磁导率同时为负值的人工合成电磁材料。电磁波在这种介质中传播时将显现与传统介质不同的各种逆向或反向效应,如负折射效应、逆多普勒效应、逆切仑科夫辐射等等。对于其特性的研究,在理论分析、数值计算和实际应用等方面还需要不断地完善和深入发展。
在经典电动力学中,介质的电磁性质是用介电常数和磁导率两个宏观参数来描述的,我们所讨论的异向介质模型通常是等效的双负或单负介质,所以在理论分析中应该强调“等效”的概念。
本文主要对不同等效异向介质模型的特性进行了研究,在理论上涉及了等效各向同性异向介质、等效单负介质、等效各向异性异向介质、等效非线性异向介质等近几年陆续提出的复杂模型,从而向实际结构靠近,以揭示异向介质的物理本质;而在异向介质结构方面,设计了以三角形开口环为基础的单环、对环结构,诣在简化传统内外嵌套式结构。论文的主要工作可以概括为:
(1)简要介绍了异向介质的研究现状和进展,分析了它的理论基础和实验基础及简单构造。其次研究了电磁波在几种等效各向同性异向介质模型中的传播特性,并结合常规介质作了比较,结果表明异向介质存在很多特殊的传播规律,深入研究将能挖掘出其巨大的意义;
(2)研究了沿等效单负介质平板波导传播表面波的特性,根据本征方程运用图解法得到沿单负介质平板传播的奇、偶对称TE极化表面波的色散曲线图和能流分布图,发现表面波在单负介质波导中传播的比传统介质波导中慢,场和能量集中于介质板的上下表面,一定频率范围内奇、偶表面波型能流反向,该慢波特性在发展微波器件的小型化方面有着潜在的应用价值;使用传输矩阵方法对等效负介电常数材料和负磁导率材料双层结构进行分析,发现某些角度的入射波存在零反射率、无衰减的完全隧穿、带通的特性,并得到数值结果对结论进行了验证;
(3)针对实际复合材料构成的异向介质都是各向异性的特点,提出了电磁波从各向同性右手介质斜入射到等效各向异性异向介质时发生负折射应满足的条件。根据理论分析结果,给出了满足条件的介电常数和磁导率组合;同时研究了不同参数条件下,等效各向异性异向介质界面出现的正、负、零Goos-H(a|¨)nchen位移的情况,数值结果验证了理论的正确性;
(4)详细研究了等效非线性异向介质中的二次非线性现象。推导了异向性材料非线性互相作用的电磁公式;发现非线性异向介质中的二次谐波过程、和频过程和差频过程具有与传统非线性介质完全不同的能流传播方向以及场分布;同样介质厚度的非线性参量放大过程,异向介质能够得到比传统介质大得多的信号波和闲频波能量输出;分析了等效非线性异向与等效非线性右手介质界面表面波的传播特性,运用图解法研究了表面波的频率范围和能流方向与右手材料参量的关系;
(5)针对现有的内外嵌套开口双环异向介质结构,其结构形式过于复杂,根据单开口环结构同样具有磁响应和负磁导率的性质,提出一种简化的三角形单环谐振结构,并引申出两种形式的三角形对环结构。通过参数提取、棱镜仿真、能量传输实验等三种方式验证其左手特性,结果吻合良好。
The newly discovery of left-handed material (LHM) has been regarded as one of the ten most significant discoveries in science community in 2003, and has been the front and focus area in physics and electromagnetics research. LHM is an electromagnetic artificial metamaterial with simultaneously negative equivalent permittivity and equivalent negative permeability. Compared with traditional materials, electromagnetic waves transmitted in such material will behave some fantastic phenomena, such as negative Snell refraction, reversed Dollper effect, reversed Cerenkov radiation, and so on. However, for the newly artificial electromagnetic materials, theories, numerical methods and applications of electromagnetic fields need to be developed.
In classical electrodynamics, electromagnetic properties of mediums are described by the two macroscopical parameters: permittivity and permeability. The metamaterial models we discussed are usually equivalent double-negative or single-negative. So the term of“equivalent”should be emphasized in the theoretical analysis of metamaterials.
This thesis mainly focuses on the research of properties of different equivalent metamaterial models. It involves complex models proposed in recent years, such as equivalent isotropy metamaterials, equivalent single-negative materials, equivalent anisotropy metamaterials and equivalent nonlinear metamaterials, so as to indicate the metamaterials’physical essence. To simplify the complex frame of the double open-loop resonators, single triangular open-loop resonators and symmetric triangular open-loop resonators are proposed. The author’s work mainly consists of:
(1) The present research status on metamaterials around the world and analysis of the theoretical and experimental basis of metamaterials are introduced. Comparing with the traditional material, detail description about the wave reflection and transmission in some equivalent isotropy metamaterial models are made. The results indicate that metamaterials represent lots of particular propagated properties, and the significance is to be seen by deep research.
(2) The properties of surface waves along the equivalent single-negative slab waveguide are analyzed. According to the eigen mode equations, the graphical-solution technique is used in order to get dispersion curves profiles and energy fluxes distribution profile of odd and even symmetric TE surface modes which propagate along the epsilon-negative slab. It is found that surface waves propagate along the single-negative slab more slower than that along the traditional slab waveguide; Field and energy is confined on the top and bottom surfaces; Energy fluxes of odd and even symmetric surface waves have the opposite directions in a certain frequency range. This slow wave property may be utilized to design novel compact RF/microwave devices. Propagation matrices method is used to analyze the wave propagation properties in a pair of equivalent single negative slabs. Phenomena of bandpass, zero reflection and complete tunneling without any phase delay perform at some incident angles. Simulation results validate the salient features of such paired slabs.
(3) The conditions that the negative refraction takes place when a plane wave passes from an equivalent isotropic right-handed material into another equivalent anisotropic metamaterial are presented in order to study the negative refraction of anisotropic metamaterials constituted by the practicable composite meta-materials. The conditions of the existence and the sign of the Goos-H(a|¨)nchen shift on this interface are also discussed. Simulation results are presented and used to prove the validities of the theoretical analysis.
(4) Quadratic nonlinear phenomena in equivalent nonlinear metamaterials are detailedly analyzed. General coupled-mode equations for quadratic coupling in nonlinear metamaterials are studied. It is found that energy flow directions and energy spatial distributions are absolutely different in nonlinear metamaterials and in nonlinear traditional materials. It is shown that through a parametric amplification process, bigger output power of signal wave and idle wave can be obtained in a metamaterial slab than a traditional slab of the same thickness. The frequency range and energy fluxes’direction of surface waves on the interface of equivalent nonlinear metamaterials are dependent on the parameters of traditional materials, and their relations are analyzed by the graphical method.
(5) Aiming at the complex frame of the double open-loop resonators, a simplified single triangular open-loop resonator is proposed, for simultaneously negative permittivity and negative permeability can be achieved by a single open-loop. Two kinds of symmetric triangular open-loop resonator combinations are designed. Parameter retrieval algorithms, refraction lens simulations and power transmission experiments are employed to validate the negative properties of these structures. The results are in well agreements.
在经典电动力学中,介质的电磁性质是用介电常数和磁导率两个宏观参数来描述的,我们所讨论的异向介质模型通常是等效的双负或单负介质,所以在理论分析中应该强调“等效”的概念。
本文主要对不同等效异向介质模型的特性进行了研究,在理论上涉及了等效各向同性异向介质、等效单负介质、等效各向异性异向介质、等效非线性异向介质等近几年陆续提出的复杂模型,从而向实际结构靠近,以揭示异向介质的物理本质;而在异向介质结构方面,设计了以三角形开口环为基础的单环、对环结构,诣在简化传统内外嵌套式结构。论文的主要工作可以概括为:
(1)简要介绍了异向介质的研究现状和进展,分析了它的理论基础和实验基础及简单构造。其次研究了电磁波在几种等效各向同性异向介质模型中的传播特性,并结合常规介质作了比较,结果表明异向介质存在很多特殊的传播规律,深入研究将能挖掘出其巨大的意义;
(2)研究了沿等效单负介质平板波导传播表面波的特性,根据本征方程运用图解法得到沿单负介质平板传播的奇、偶对称TE极化表面波的色散曲线图和能流分布图,发现表面波在单负介质波导中传播的比传统介质波导中慢,场和能量集中于介质板的上下表面,一定频率范围内奇、偶表面波型能流反向,该慢波特性在发展微波器件的小型化方面有着潜在的应用价值;使用传输矩阵方法对等效负介电常数材料和负磁导率材料双层结构进行分析,发现某些角度的入射波存在零反射率、无衰减的完全隧穿、带通的特性,并得到数值结果对结论进行了验证;
(3)针对实际复合材料构成的异向介质都是各向异性的特点,提出了电磁波从各向同性右手介质斜入射到等效各向异性异向介质时发生负折射应满足的条件。根据理论分析结果,给出了满足条件的介电常数和磁导率组合;同时研究了不同参数条件下,等效各向异性异向介质界面出现的正、负、零Goos-H(a|¨)nchen位移的情况,数值结果验证了理论的正确性;
(4)详细研究了等效非线性异向介质中的二次非线性现象。推导了异向性材料非线性互相作用的电磁公式;发现非线性异向介质中的二次谐波过程、和频过程和差频过程具有与传统非线性介质完全不同的能流传播方向以及场分布;同样介质厚度的非线性参量放大过程,异向介质能够得到比传统介质大得多的信号波和闲频波能量输出;分析了等效非线性异向与等效非线性右手介质界面表面波的传播特性,运用图解法研究了表面波的频率范围和能流方向与右手材料参量的关系;
(5)针对现有的内外嵌套开口双环异向介质结构,其结构形式过于复杂,根据单开口环结构同样具有磁响应和负磁导率的性质,提出一种简化的三角形单环谐振结构,并引申出两种形式的三角形对环结构。通过参数提取、棱镜仿真、能量传输实验等三种方式验证其左手特性,结果吻合良好。
The newly discovery of left-handed material (LHM) has been regarded as one of the ten most significant discoveries in science community in 2003, and has been the front and focus area in physics and electromagnetics research. LHM is an electromagnetic artificial metamaterial with simultaneously negative equivalent permittivity and equivalent negative permeability. Compared with traditional materials, electromagnetic waves transmitted in such material will behave some fantastic phenomena, such as negative Snell refraction, reversed Dollper effect, reversed Cerenkov radiation, and so on. However, for the newly artificial electromagnetic materials, theories, numerical methods and applications of electromagnetic fields need to be developed.
In classical electrodynamics, electromagnetic properties of mediums are described by the two macroscopical parameters: permittivity and permeability. The metamaterial models we discussed are usually equivalent double-negative or single-negative. So the term of“equivalent”should be emphasized in the theoretical analysis of metamaterials.
This thesis mainly focuses on the research of properties of different equivalent metamaterial models. It involves complex models proposed in recent years, such as equivalent isotropy metamaterials, equivalent single-negative materials, equivalent anisotropy metamaterials and equivalent nonlinear metamaterials, so as to indicate the metamaterials’physical essence. To simplify the complex frame of the double open-loop resonators, single triangular open-loop resonators and symmetric triangular open-loop resonators are proposed. The author’s work mainly consists of:
(1) The present research status on metamaterials around the world and analysis of the theoretical and experimental basis of metamaterials are introduced. Comparing with the traditional material, detail description about the wave reflection and transmission in some equivalent isotropy metamaterial models are made. The results indicate that metamaterials represent lots of particular propagated properties, and the significance is to be seen by deep research.
(2) The properties of surface waves along the equivalent single-negative slab waveguide are analyzed. According to the eigen mode equations, the graphical-solution technique is used in order to get dispersion curves profiles and energy fluxes distribution profile of odd and even symmetric TE surface modes which propagate along the epsilon-negative slab. It is found that surface waves propagate along the single-negative slab more slower than that along the traditional slab waveguide; Field and energy is confined on the top and bottom surfaces; Energy fluxes of odd and even symmetric surface waves have the opposite directions in a certain frequency range. This slow wave property may be utilized to design novel compact RF/microwave devices. Propagation matrices method is used to analyze the wave propagation properties in a pair of equivalent single negative slabs. Phenomena of bandpass, zero reflection and complete tunneling without any phase delay perform at some incident angles. Simulation results validate the salient features of such paired slabs.
(3) The conditions that the negative refraction takes place when a plane wave passes from an equivalent isotropic right-handed material into another equivalent anisotropic metamaterial are presented in order to study the negative refraction of anisotropic metamaterials constituted by the practicable composite meta-materials. The conditions of the existence and the sign of the Goos-H(a|¨)nchen shift on this interface are also discussed. Simulation results are presented and used to prove the validities of the theoretical analysis.
(4) Quadratic nonlinear phenomena in equivalent nonlinear metamaterials are detailedly analyzed. General coupled-mode equations for quadratic coupling in nonlinear metamaterials are studied. It is found that energy flow directions and energy spatial distributions are absolutely different in nonlinear metamaterials and in nonlinear traditional materials. It is shown that through a parametric amplification process, bigger output power of signal wave and idle wave can be obtained in a metamaterial slab than a traditional slab of the same thickness. The frequency range and energy fluxes’direction of surface waves on the interface of equivalent nonlinear metamaterials are dependent on the parameters of traditional materials, and their relations are analyzed by the graphical method.
(5) Aiming at the complex frame of the double open-loop resonators, a simplified single triangular open-loop resonator is proposed, for simultaneously negative permittivity and negative permeability can be achieved by a single open-loop. Two kinds of symmetric triangular open-loop resonator combinations are designed. Parameter retrieval algorithms, refraction lens simulations and power transmission experiments are employed to validate the negative properties of these structures. The results are in well agreements.
引文
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