多维异向介质的实现及其在隐身衣与天线等电磁器件中的应用
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摘要
异向介质以其不同于传统材料的许多特殊电磁效应揭开了现代电磁学崭新的一页,成为近年来科学界的一个重要研究课题。本文以异向介质为研究背景,着重讨论了多维异向介质的设计,及其在隐身衣、天线等电磁器件中的应用。
本文首先深入分析了传统二维异向介质构造方法的局限性并提出了相应的解决方案。我们指出,通过交叉嵌入的方法构成的二维异向介质,其两个垂直方向谐振单元之间的耦合干扰效应大大的减小,因此与传统的方法相比可以实现更宽的带宽及更低的损耗。本文不仅从理论上给出了详细的阐述,还通过实验对交叉嵌入结构和传统结构二维异向介质的性能进行了比较和论证。
除了对多维异向介质结构设计的讨论之外,本文的另一个研究重点即为异向介质在各种电磁器件设计中的应用,其中最主要的是隐身衣和天线的设计。这些工作包括:
提出了当隐身衣的背景介质为非均匀介质的情况下隐身衣的设计方法。着重讨论了当隐身衣的背景介质为分层或渐变介质的情况。这种通用的方法可以被推广来处理各种环境下隐身衣的设计问题。
提出了基于分割法的任意形状隐身衣的设计方案。对于截面为任意不对称多边形的二维隐身衣,我们可以将其分割成多个三角形,然后对每个三角形进行独立的坐标变换来得到其参数。而通过无限逼近的方式,该方法可用来设计截面为任意形状的二维隐身衣,并且可以推广到任意形状三维隐身衣的设计。
提出了利用二维异向介质实现完美参数隐身衣的方案。与目前世界上已经报导的所有隐身衣实验方案相比(这些实验都基于简化的参数),基于完美参数设计的隐身衣可以满足内外边界与空气的较好匹配,能够在厚度很小的条件下明显的抑制散射,达到很好的隐身效果。我们提出了轴向分量为常数的二维完美隐身衣参数,该参数可以用二维异向介质实现,由此可以降低完美隐身衣的设计难度。
利用坐标变换法设计方向性可控的高指向性天线。只要将辐射源放置于平板异向介质天线的不同位置,就可以得到向不同方向辐射的高指向性波束,因此该方法还可以实现空分复用。通过选取合适的异向介质参数,并将几个辐射源置于天线中的不同特定位置,就可以使它们同时向不同的方向辐射而互不影响。由于该天线的参数随空间而变化,可以用分层异向介质来实现。
除了以上的几个主要应用之外,本文还包含了一些特殊异向介质导波器件的设计,以及异向介质宽带/多通带反向耦合器的实验验证等。
Artificially structured metamaterials, which open up new conceptual frontiers in electromagnetics, have generated enormous interest for their ability to display electromagnetic responses unavailable in conventional materials. This dissertation addresses the design of multi-dimensional metamaterials, and their applications in electromagnetic devices, including invisibility cloak and antennae.
In the first part of the dissertation, we investigated the limitation of the traditional method in two-dimensional (2D) metamaterial design, which is realized by repeating the resonant elements in two orthogonal directions. As a solution to this problem, we experimentally realize an isotropic left-handed material based on a cross-embedded S-ring resonator. Experimental results show that the 2D metamaterial with cross embedded arrangement exhibits much better performance than that with conventional arrangement. Theoretical interpretations are also proposed in the thesis, showing a reduced coupling between the rings that are located in the two orthogonal directions.
Apart from the discussion on metamaterial design, this dissertation also gives a thorough study on the main applications of metamterials, among which the applications in invisibility cloak and antenna are the most important. The corresponding work includes:
We consider the case where the background of the cloak is no longer a homogeneous medium and determine the relative constitutive parameters of the cloak according to the background. The parameters of cylindrical cloak structures working in multilayered and gradually changing media are proposed and the design scheme could also be applied in cases of arbitrary background.
A segmentation design approach for the cloak of arbitrary shape is suggested. We propose that polygonal 2D cloaks with any number of sides, which do not require geometrical symmetry, can be achieved by dividing the polygon into many triangular regions and applying a spatial transformation on each triangle. This segmentation-transformation method is free to deal with cloaks of arbitrary shapes, including 3D cases.
Ideal parameters, which can be realized with 2D metamaterials, are proposed to simplify the cloak design process. Compared with cloaks in all the reported experiments, which are all based on reduced parameters, the cloak with ideal parameters has several superiorities: The impedance of the cloak is well matched at the inner and outer boundaries, and good performance can be achieved even when the thickness of the cloak is very small. The parameters we proposed, the axial component of which is spatially invariant, provide the possibility of realizing 2D ideal cloak with 2D metamaterials, and therefore greatly reduce the difficulty of ideal cloak design.
Coordinate transformation approach is introduced to manipulate the directivity of antennas. We show that by embedding a dipole at different locations inside this substrate, the emitted rays can be directed to different orientations as required. As a result, spatial multiplexing can be realized by carefully selecting proper parameters of this substrate. Since the substrate of the antenna has spatially variant parameters, it can be realized with layered metamaterials.
Apart from the above applications, this dissertation also includes the experimental demonstration of a wideband/dual-band backward coupler, which can be realized by judiciously combining metamaterial slabs. Other interesting applications, such as guiding electromagnetic waves through a virtual tunnel in open space and bending beams without causing reflection are also discussed.
本文首先深入分析了传统二维异向介质构造方法的局限性并提出了相应的解决方案。我们指出,通过交叉嵌入的方法构成的二维异向介质,其两个垂直方向谐振单元之间的耦合干扰效应大大的减小,因此与传统的方法相比可以实现更宽的带宽及更低的损耗。本文不仅从理论上给出了详细的阐述,还通过实验对交叉嵌入结构和传统结构二维异向介质的性能进行了比较和论证。
除了对多维异向介质结构设计的讨论之外,本文的另一个研究重点即为异向介质在各种电磁器件设计中的应用,其中最主要的是隐身衣和天线的设计。这些工作包括:
提出了当隐身衣的背景介质为非均匀介质的情况下隐身衣的设计方法。着重讨论了当隐身衣的背景介质为分层或渐变介质的情况。这种通用的方法可以被推广来处理各种环境下隐身衣的设计问题。
提出了基于分割法的任意形状隐身衣的设计方案。对于截面为任意不对称多边形的二维隐身衣,我们可以将其分割成多个三角形,然后对每个三角形进行独立的坐标变换来得到其参数。而通过无限逼近的方式,该方法可用来设计截面为任意形状的二维隐身衣,并且可以推广到任意形状三维隐身衣的设计。
提出了利用二维异向介质实现完美参数隐身衣的方案。与目前世界上已经报导的所有隐身衣实验方案相比(这些实验都基于简化的参数),基于完美参数设计的隐身衣可以满足内外边界与空气的较好匹配,能够在厚度很小的条件下明显的抑制散射,达到很好的隐身效果。我们提出了轴向分量为常数的二维完美隐身衣参数,该参数可以用二维异向介质实现,由此可以降低完美隐身衣的设计难度。
利用坐标变换法设计方向性可控的高指向性天线。只要将辐射源放置于平板异向介质天线的不同位置,就可以得到向不同方向辐射的高指向性波束,因此该方法还可以实现空分复用。通过选取合适的异向介质参数,并将几个辐射源置于天线中的不同特定位置,就可以使它们同时向不同的方向辐射而互不影响。由于该天线的参数随空间而变化,可以用分层异向介质来实现。
除了以上的几个主要应用之外,本文还包含了一些特殊异向介质导波器件的设计,以及异向介质宽带/多通带反向耦合器的实验验证等。
Artificially structured metamaterials, which open up new conceptual frontiers in electromagnetics, have generated enormous interest for their ability to display electromagnetic responses unavailable in conventional materials. This dissertation addresses the design of multi-dimensional metamaterials, and their applications in electromagnetic devices, including invisibility cloak and antennae.
In the first part of the dissertation, we investigated the limitation of the traditional method in two-dimensional (2D) metamaterial design, which is realized by repeating the resonant elements in two orthogonal directions. As a solution to this problem, we experimentally realize an isotropic left-handed material based on a cross-embedded S-ring resonator. Experimental results show that the 2D metamaterial with cross embedded arrangement exhibits much better performance than that with conventional arrangement. Theoretical interpretations are also proposed in the thesis, showing a reduced coupling between the rings that are located in the two orthogonal directions.
Apart from the discussion on metamaterial design, this dissertation also gives a thorough study on the main applications of metamterials, among which the applications in invisibility cloak and antenna are the most important. The corresponding work includes:
We consider the case where the background of the cloak is no longer a homogeneous medium and determine the relative constitutive parameters of the cloak according to the background. The parameters of cylindrical cloak structures working in multilayered and gradually changing media are proposed and the design scheme could also be applied in cases of arbitrary background.
A segmentation design approach for the cloak of arbitrary shape is suggested. We propose that polygonal 2D cloaks with any number of sides, which do not require geometrical symmetry, can be achieved by dividing the polygon into many triangular regions and applying a spatial transformation on each triangle. This segmentation-transformation method is free to deal with cloaks of arbitrary shapes, including 3D cases.
Ideal parameters, which can be realized with 2D metamaterials, are proposed to simplify the cloak design process. Compared with cloaks in all the reported experiments, which are all based on reduced parameters, the cloak with ideal parameters has several superiorities: The impedance of the cloak is well matched at the inner and outer boundaries, and good performance can be achieved even when the thickness of the cloak is very small. The parameters we proposed, the axial component of which is spatially invariant, provide the possibility of realizing 2D ideal cloak with 2D metamaterials, and therefore greatly reduce the difficulty of ideal cloak design.
Coordinate transformation approach is introduced to manipulate the directivity of antennas. We show that by embedding a dipole at different locations inside this substrate, the emitted rays can be directed to different orientations as required. As a result, spatial multiplexing can be realized by carefully selecting proper parameters of this substrate. Since the substrate of the antenna has spatially variant parameters, it can be realized with layered metamaterials.
Apart from the above applications, this dissertation also includes the experimental demonstration of a wideband/dual-band backward coupler, which can be realized by judiciously combining metamaterial slabs. Other interesting applications, such as guiding electromagnetic waves through a virtual tunnel in open space and bending beams without causing reflection are also discussed.
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