异向介质与基于EBG的相控阵天线研究
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摘要
以异向介质和电磁带隙(EBG)结构为代表的新型人工电磁材料是当前物理学与电磁学研究领域的前沿和热点,相关研究成果在许多领域都有巨大的应用前景。对于其特性的研究,在理论分析、数值模拟和实际应用等方面还需要不断地发展和完善。本文主要讨论了非色散和色散异向介质导行结构中的导模,研究了主轴与界面存在旋转角的各向异性异向介质及双轴各向异性回旋介质中的负折射现象,采用矩量法(MoM)分析了EBG波导端头缝隙相控阵天线的扫描盲区。
本文的主要工作可以概括为:
1.详细研究了非色散的异向介质平板波导中的导模。给出了各向同性异向介质平板中为实、虚横波数时的模式导行条件。讨论了导行TE波的奇模和偶模特性,采用图解法分析了不同异向介质参数情况下虚横波数导模的存在性。由于实验上制备的异向介质均是各向异性的,因而本文还构造了接地的单轴各向异性异向介质平板波导,分类讨论了介电常数张量和磁导率张量中各分量符号不同组合时的模式特性。
2.讨论了各向同性色散异向介质界面及单轴各向异性色散异向介质平板波导的导行波传输特性。结果表明,这两种导行结构的模式特性与色散异向介质的工作频率密切相关。
3.深入研究了电磁波在各向同性常规媒质和主轴与界面不重合的各向异性异向介质界面的反射和透射特性。根据主轴系下张量分量符号的不同组合,将媒质分为四类。讨论了不同情况下发生负折射的条件及旋转角对全反射和全透射现象的影响。当旋转角为或时,这种各向异性媒质将退化为普通各向异性异向介质,这使得文中的结论更具有一般性。0 o90o
4.讨论了一种双轴各向异性回旋介质,这种材料中也可以发生负折射并且容易为目前的技术设计和制备。详细分析了TE极化波在各向同性常规介质和双轴各向异性回旋介质界面的传输特性。分类讨论了媒质参数正负号变化对全反射、垂直入射全透射和负折射的影响。得到的数值结果证实了理论分析的正确性。
5.采用MoM对矩形波导端头缝隙为辐射单元的三角形排布相控阵进行了扫描盲区分析。计算了与盲区现象相关的各参数,包括中心单元反射系数,单元的阵中方向图和耦合系数。由矩量法理论证明了全阵等幅激励且反射系数相位为零(谐振)是有限阵单元方向图与中心单元反射系数描述盲区问题统一的充分条件。得到的结论有助于通过加载EBG对相控阵天线扫描盲区进行有效抑制。
Presently, new artificial electromagnetic materials, such as metamaterials and electromagnetic bandgap (EBG) structures, become the foreland and hotspot field in Physics and Electromagnetism. The research results can be applied to many fields in the future. Thus, the investigation of the properties of the metamaterials and EBG structures needs developing and perfecting constantly in theoretical analysis, numerical simulations and actual applications. In this thesis, the guided modes in guiding structures containing non-dispersive and dispersive metamaterials are discussed, the negative refraction at the interface associated with anisotropic metamaterials cut along nonprincipal axes and biaxially anisotropic gyrotropic media is investigated, and a blind spot analysis is carried out in EBG waveguide end-slot phased array antennas by using the method of moments (MoM). The work of the author is mainly focused on:
1. The guided modes in a slab waveguide of non-dispersive metamaterial are investigated in detail. The guidance conditions of modes with both real and imaginary transverse wave numbers in an isotropic metamaterial slab are obtained. The odd and even mode properties for guided TE waves are discussed, and besides, the existence of guided modes with imaginary transverse wave numbers for different medium parameters is analyzed graphically. However, the metamaterials that have been prepared successfully in experiments are actually anisotropic. Thus, a grounded slab waveguide of uniaxially anisotropic metamaterial is constructed. In terms of the different sign combinations of the permittivity and permeability tensor components, the mode properties are discussed in different cases.
2. The guidance of waves at the interface associated with an isotropic dispersive metamaterial and in a slab waveguide of uniaxially anisotropic dispersive metamaterial is discussed. The results show that the mode properties of the two guiding structures are closely dependent on the operating frequency of the dispersive metamaterial.
3. The characteristics of reflection and refraction of electromagnetic waves at the interface between an isotropic regular media and an anisotropic metamaterial cut along nonprincipal axes are thoroughly investigated. In terms of the different sign combinations of the tensor components along principal axes, the anisotropic media is divided into four categories. The existence conditions of negative refraction and the influence of the rotation angle on the total reflection and total transmission phenomenon are discussed for each case. When the rotation angle is equal to 0o or 90o , this anisotropic media can be reduced to general anisotropic media, which makes the conclusions in this paper more general.
4. A biaxially anisotropic gyrotropic media, in which the negative refraction may occur, is discussed, and the use of such a medium offers flexibility in design and ease of fabrication. The propagation characteristics of TE-polarized waves at the interface between an isotropic regular medium and a biaxially anisotropic gyrotropic medium are analyzed. The effect of the different medium parameters on the total reflection, normally incident total transmission and negative refraction is discussed in different cases. Numerical results are given to validate the theoretical analysis.
5. A blind spot analysis is carried out in rectangular waveguide end-slot phased arrays of a triangular arrangement by using the MoM. The parameters associated with blind effect, such as the reflection coefficient of the center element, the active element pattern and the coupling coefficient are all computed. The sufficient condition of the unity of the active element pattern and reflection coefficient in describing blind effect is proved, which is the array should be equal scale excited and the phase of the reflection coefficient be zero (resonance). The conclusions will be helpful in effectively suppressing the scan blind spots by using EBG.
本文的主要工作可以概括为:
1.详细研究了非色散的异向介质平板波导中的导模。给出了各向同性异向介质平板中为实、虚横波数时的模式导行条件。讨论了导行TE波的奇模和偶模特性,采用图解法分析了不同异向介质参数情况下虚横波数导模的存在性。由于实验上制备的异向介质均是各向异性的,因而本文还构造了接地的单轴各向异性异向介质平板波导,分类讨论了介电常数张量和磁导率张量中各分量符号不同组合时的模式特性。
2.讨论了各向同性色散异向介质界面及单轴各向异性色散异向介质平板波导的导行波传输特性。结果表明,这两种导行结构的模式特性与色散异向介质的工作频率密切相关。
3.深入研究了电磁波在各向同性常规媒质和主轴与界面不重合的各向异性异向介质界面的反射和透射特性。根据主轴系下张量分量符号的不同组合,将媒质分为四类。讨论了不同情况下发生负折射的条件及旋转角对全反射和全透射现象的影响。当旋转角为或时,这种各向异性媒质将退化为普通各向异性异向介质,这使得文中的结论更具有一般性。0 o90o
4.讨论了一种双轴各向异性回旋介质,这种材料中也可以发生负折射并且容易为目前的技术设计和制备。详细分析了TE极化波在各向同性常规介质和双轴各向异性回旋介质界面的传输特性。分类讨论了媒质参数正负号变化对全反射、垂直入射全透射和负折射的影响。得到的数值结果证实了理论分析的正确性。
5.采用MoM对矩形波导端头缝隙为辐射单元的三角形排布相控阵进行了扫描盲区分析。计算了与盲区现象相关的各参数,包括中心单元反射系数,单元的阵中方向图和耦合系数。由矩量法理论证明了全阵等幅激励且反射系数相位为零(谐振)是有限阵单元方向图与中心单元反射系数描述盲区问题统一的充分条件。得到的结论有助于通过加载EBG对相控阵天线扫描盲区进行有效抑制。
Presently, new artificial electromagnetic materials, such as metamaterials and electromagnetic bandgap (EBG) structures, become the foreland and hotspot field in Physics and Electromagnetism. The research results can be applied to many fields in the future. Thus, the investigation of the properties of the metamaterials and EBG structures needs developing and perfecting constantly in theoretical analysis, numerical simulations and actual applications. In this thesis, the guided modes in guiding structures containing non-dispersive and dispersive metamaterials are discussed, the negative refraction at the interface associated with anisotropic metamaterials cut along nonprincipal axes and biaxially anisotropic gyrotropic media is investigated, and a blind spot analysis is carried out in EBG waveguide end-slot phased array antennas by using the method of moments (MoM). The work of the author is mainly focused on:
1. The guided modes in a slab waveguide of non-dispersive metamaterial are investigated in detail. The guidance conditions of modes with both real and imaginary transverse wave numbers in an isotropic metamaterial slab are obtained. The odd and even mode properties for guided TE waves are discussed, and besides, the existence of guided modes with imaginary transverse wave numbers for different medium parameters is analyzed graphically. However, the metamaterials that have been prepared successfully in experiments are actually anisotropic. Thus, a grounded slab waveguide of uniaxially anisotropic metamaterial is constructed. In terms of the different sign combinations of the permittivity and permeability tensor components, the mode properties are discussed in different cases.
2. The guidance of waves at the interface associated with an isotropic dispersive metamaterial and in a slab waveguide of uniaxially anisotropic dispersive metamaterial is discussed. The results show that the mode properties of the two guiding structures are closely dependent on the operating frequency of the dispersive metamaterial.
3. The characteristics of reflection and refraction of electromagnetic waves at the interface between an isotropic regular media and an anisotropic metamaterial cut along nonprincipal axes are thoroughly investigated. In terms of the different sign combinations of the tensor components along principal axes, the anisotropic media is divided into four categories. The existence conditions of negative refraction and the influence of the rotation angle on the total reflection and total transmission phenomenon are discussed for each case. When the rotation angle is equal to 0o or 90o , this anisotropic media can be reduced to general anisotropic media, which makes the conclusions in this paper more general.
4. A biaxially anisotropic gyrotropic media, in which the negative refraction may occur, is discussed, and the use of such a medium offers flexibility in design and ease of fabrication. The propagation characteristics of TE-polarized waves at the interface between an isotropic regular medium and a biaxially anisotropic gyrotropic medium are analyzed. The effect of the different medium parameters on the total reflection, normally incident total transmission and negative refraction is discussed in different cases. Numerical results are given to validate the theoretical analysis.
5. A blind spot analysis is carried out in rectangular waveguide end-slot phased arrays of a triangular arrangement by using the MoM. The parameters associated with blind effect, such as the reflection coefficient of the center element, the active element pattern and the coupling coefficient are all computed. The sufficient condition of the unity of the active element pattern and reflection coefficient in describing blind effect is proved, which is the array should be equal scale excited and the phase of the reflection coefficient be zero (resonance). The conclusions will be helpful in effectively suppressing the scan blind spots by using EBG.
引文
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