非双盲超透镜声隐身结构的研究
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摘要
近年来,变换光学以及由此发展而来的变换声学的研究引起了人们的关注。变换声学的基础是声波方程在空间坐标变换下能够保持形式不变,所改变的只是空间中材料参数的分布。假设存在一个虚空间这个空间中材料的分布已知,并且声场在这个空间中的传播情况可以很容易的得到,通过一个映射关系将这个虚空间和实际物理空间联系起来。根据这个映射关系和虚空间中已知的材料参数分布推算出物理空间中材料参数的分布,声场就可以按照这个映射关系在物理空间中传播。但是按照这个方法设计出的结构中的材料往往会超出自然界中材料参数的范围,比如会出现负的质量密度或者各项异性的质量密度。幸运的是,最近兴起的“超常材料”正好可以为我们提供这样的材料。于是,可以通过改变空间中材料参数的分布来任意操控声波的传播路径。由此我们可以设计出许多拥有的奇特性质的结构装置,其中最有趣的莫过于著名的“隐身斗篷”。但是大多数隐身结构都是通过将被隐身的物体与外界入射场隔开达到隐身效果,在隐身物体的同时这个被隐身的物体也失去了与外界的联系。之后几种“非双盲”隐身结构被相继提出,这种结构可以在隐身一个物体的同时让这个物体接受到外界的信息。但是在这些设计中往往需要用到大量的“单负”材料(质量密度或者弹性模量为负数的材料)甚至“双负”材料(质量密度和弹性模量同时为负数的材料),这对实验提出了极大的技术挑战。为了降低实验重现的难度,我们要减少这种结构所需使用到的负材料的数量。
本文提出了一种由一对互补的单负材料构成的超透镜隐身结构,从而使所需材料的数量降到最低。本文分为以下几个部分。
第一章绪论部分,从Veselago透镜出发介绍了光学和声学超常材料的研究内容和进展。接着,我们讨论并比较了目前几种常见的隐身结构,并着重介绍基于变换光学和变换声学的隐身结构,以及变换声学的若干应用。
第二章介绍变换声学理论。在笛卡尔坐标下详细推导出了变换声学的公式,并在正交曲线坐标系中给出一种简便的公式。最后,通过变换声学设计出一种可以适应边界的完美匹配层。
第三章我们重点介绍本文计算中所用到的两种数值方法,有限元法和声散射理论,为之后的数值模拟做铺垫。
第四章首先简要介绍声隐身领域的发展过程,然后提出由一对互补的单负材料构成的“超透镜”声隐身结构的设计方法,并用数值方法进行验证。这种结构由一对互补的材料做成的薄层相互间隔层叠而成。研究表明,当每层材料的厚度远小于入射波波长时,这个多层结构可以有效的消除由被隐身物体造成的大部分散射,并且能让被隐身的物体探测到入射波的信号,故这个结构可以用来隐藏个声传感器。接着我们讨论了被隐身物体或者多层结构中的互补材料发生变化对结构的散射消除效果的影响。最后,我们将这个设计方法推广到三维,提出了一个类似的三维超透镜隐身结构的初步方案。
最后在第五章中,我们给出了本文的主要结论和对今后工作的展望。
1.提出了一种新型的“超透镜”声隐身斗篷的设计思路。与“双盲”隐身斗篷相比,这种结构可以在对外界观测者隐藏被隐身物体的同时使得这个物体仍然可以无失真的观测到周围环境的信息。该结构仅由需要一对互补的单负材料构成,与背景媒质和被隐身的物体无关,只要求每层材料的厚度远低于入射声波的波长。与之前的“非双盲”隐身结构相比,该结构可以显著降低在实验上实现的技术难度。
2.研究了被隐身物体材料参数的鲁棒性间题。当隐身物体的质量密度和弹性模量同时乘以一个鲁棒性因子时,本文指出如果这个鲁棒性因子控制在0.5到2之间,单负材料组成的多层结构仍然可以讲散射降低一个数量级。
3.研究了当多层结构中的单负材料层存在耗散的情况。提出当结构中的超常材料层的耗散在10%以内时,这种多层结构仍然可以有效的抑制掉由被隐身物体造成的绝大部分散射。
Recently, the investigations of transformation optics, as well as its derived counterpart transformation acoustics, have received more and more attention. Transformation acoustics is based on the fact that acoustic wave function can keep its form under coordinate transformation, expect for the distributions of the parameters of the materials. Suppose we know the materials distributions in a virtual space and the propagating of the acoustic wave can be easily obtained in that space. The virtual space can be mapped to the real physical space by a certain mapping relationship. The distributions of the materials in the physical world are determined by those in the virtual world and the mapping relationship. In that case, the propagating of acoustic field in the physical world will follow that mapping relationship. However, parameters of the materials in the physical space are often beyond those in the nature, such as a mass density with negative value or anisotropic mass density. Lucky, the recently popular topic "metamaterial" could provide such materials for us. Thus, the trajectory of acoustic waves can easily be manipulated by changing the distributions of materials. A large number of fascinate devices can be designed by this scheme.
Among all these, the most interesting one is the famous "invisibility cloak". However, most cloaking devices isolate the cloaked objects from incident fields to hide the objects. As a result, the cloaked objects lost the contact from outside world. Later, some "none-double-blind" cloaking schemes, in which the cloaked object can receive external information have been proposed. But those schemes always refer to plenty's of single-negative-index materials (materials with negative mass density or negative bulk modulus), or even double-negative-index materials (materials with simultaneously negative mass density and bulk modulus) which may bring a great challenge to experimental realizations. Consequently, the number of required negative materials of such a device shall be reduced to simplify the experimental realizations.
This dissertation proposes a new "superlens" cloaking strategy which only consists of a pair of complementary single-negative-index materials. This should be the minimal requirement to form such devices. The dissertation is divided into following sections:
In Chapter Ⅰ, we start from the Veselago lens and review the background as well as the developments of optical and acoustical metamaterial. Cloaking structures based on different theory are discussed and compared. Those cloaking structures and some other applications based on transformation optics and acoustics are briefly discussed.
In Chapter Ⅱ, the theory of transformation acoustics are introduced. The formulas are detailed deduced in the Cartesian coordinates and are convent to a reduced way in the orthogonal curvilinear coordinate. Finally, a perfectly matched layer which can adapt boundary is designed through transformation acoustics.
In Chapter III, two numerical methods used in this article, the finite element method and the acoustic scattering theory are introduced.
In Chapter IV, the development in the domain of acoustic cloaking is briefly introduced. Then, a new "superlens" cloaking strategy which only consists of a pair of complementary single-negative-index materials is proposed and is verified by numerical method. The proposed device is a multi-layered structure consists of a pair of complementary materials which are arranged alternately. Numerical results show the multi-layered structure can remarkably reduce the scattering of the cloaked object when the thickness of each layer is much smaller than the wavelength of the incident wave, while the cloaked object can receive outside information. Thus this structure can be used to hide an acoustic sensor. Then, we discuss the influences to the scattering-reducing effect when the parameters of the cloaked object and the complementary materials are changed. At last, the proposed scheme is extended to three dimensions; and a preliminary scheme for a similar three-dimensional superlens cloaking is proposed.
Finally, in Chapter V, the main conclusions of the dissertation and the prospect of the future work are presented.
The principal contribution of the present study is summarized as below:
1. A new strategy to design acoustic cloaking device is proposed. Compared to "double-blind" invisibility cloaks, this structure can hide the cloaked object from outside obverses while this object can receive undistorted external information. The proposed structure only requires a pair of complementary materials which are independent with the parameters of background medium as well as the cloaked object. The only need of the scheme is the thickness of each layer should be much smaller than the wavelength of incident wave. Therefore, compared to the previous "non-double-blind" cloaking structure, the proposed structure should notably reduce the technical difficulties in experimental realization.
2. The robustness of the parameters of the cloaked object has been studied. When the mass density and the bulk modulus are multiplied by the same robust factor simultaneously, it is shown the scatter wave can be reduced almost an order of magnitude by the proposed multi-layered structure, provided the robust factor is between0.5and2.
3. The situation when single-negative-index layers of the multi-layered structure exists dissipation has been studied. It is pointed that the scatter wave caused by the cloaked object can be remarkably reduced when the loss of the single-negative-index layers is less than10%.
本文提出了一种由一对互补的单负材料构成的超透镜隐身结构,从而使所需材料的数量降到最低。本文分为以下几个部分。
第一章绪论部分,从Veselago透镜出发介绍了光学和声学超常材料的研究内容和进展。接着,我们讨论并比较了目前几种常见的隐身结构,并着重介绍基于变换光学和变换声学的隐身结构,以及变换声学的若干应用。
第二章介绍变换声学理论。在笛卡尔坐标下详细推导出了变换声学的公式,并在正交曲线坐标系中给出一种简便的公式。最后,通过变换声学设计出一种可以适应边界的完美匹配层。
第三章我们重点介绍本文计算中所用到的两种数值方法,有限元法和声散射理论,为之后的数值模拟做铺垫。
第四章首先简要介绍声隐身领域的发展过程,然后提出由一对互补的单负材料构成的“超透镜”声隐身结构的设计方法,并用数值方法进行验证。这种结构由一对互补的材料做成的薄层相互间隔层叠而成。研究表明,当每层材料的厚度远小于入射波波长时,这个多层结构可以有效的消除由被隐身物体造成的大部分散射,并且能让被隐身的物体探测到入射波的信号,故这个结构可以用来隐藏个声传感器。接着我们讨论了被隐身物体或者多层结构中的互补材料发生变化对结构的散射消除效果的影响。最后,我们将这个设计方法推广到三维,提出了一个类似的三维超透镜隐身结构的初步方案。
最后在第五章中,我们给出了本文的主要结论和对今后工作的展望。
1.提出了一种新型的“超透镜”声隐身斗篷的设计思路。与“双盲”隐身斗篷相比,这种结构可以在对外界观测者隐藏被隐身物体的同时使得这个物体仍然可以无失真的观测到周围环境的信息。该结构仅由需要一对互补的单负材料构成,与背景媒质和被隐身的物体无关,只要求每层材料的厚度远低于入射声波的波长。与之前的“非双盲”隐身结构相比,该结构可以显著降低在实验上实现的技术难度。
2.研究了被隐身物体材料参数的鲁棒性间题。当隐身物体的质量密度和弹性模量同时乘以一个鲁棒性因子时,本文指出如果这个鲁棒性因子控制在0.5到2之间,单负材料组成的多层结构仍然可以讲散射降低一个数量级。
3.研究了当多层结构中的单负材料层存在耗散的情况。提出当结构中的超常材料层的耗散在10%以内时,这种多层结构仍然可以有效的抑制掉由被隐身物体造成的绝大部分散射。
Recently, the investigations of transformation optics, as well as its derived counterpart transformation acoustics, have received more and more attention. Transformation acoustics is based on the fact that acoustic wave function can keep its form under coordinate transformation, expect for the distributions of the parameters of the materials. Suppose we know the materials distributions in a virtual space and the propagating of the acoustic wave can be easily obtained in that space. The virtual space can be mapped to the real physical space by a certain mapping relationship. The distributions of the materials in the physical world are determined by those in the virtual world and the mapping relationship. In that case, the propagating of acoustic field in the physical world will follow that mapping relationship. However, parameters of the materials in the physical space are often beyond those in the nature, such as a mass density with negative value or anisotropic mass density. Lucky, the recently popular topic "metamaterial" could provide such materials for us. Thus, the trajectory of acoustic waves can easily be manipulated by changing the distributions of materials. A large number of fascinate devices can be designed by this scheme.
Among all these, the most interesting one is the famous "invisibility cloak". However, most cloaking devices isolate the cloaked objects from incident fields to hide the objects. As a result, the cloaked objects lost the contact from outside world. Later, some "none-double-blind" cloaking schemes, in which the cloaked object can receive external information have been proposed. But those schemes always refer to plenty's of single-negative-index materials (materials with negative mass density or negative bulk modulus), or even double-negative-index materials (materials with simultaneously negative mass density and bulk modulus) which may bring a great challenge to experimental realizations. Consequently, the number of required negative materials of such a device shall be reduced to simplify the experimental realizations.
This dissertation proposes a new "superlens" cloaking strategy which only consists of a pair of complementary single-negative-index materials. This should be the minimal requirement to form such devices. The dissertation is divided into following sections:
In Chapter Ⅰ, we start from the Veselago lens and review the background as well as the developments of optical and acoustical metamaterial. Cloaking structures based on different theory are discussed and compared. Those cloaking structures and some other applications based on transformation optics and acoustics are briefly discussed.
In Chapter Ⅱ, the theory of transformation acoustics are introduced. The formulas are detailed deduced in the Cartesian coordinates and are convent to a reduced way in the orthogonal curvilinear coordinate. Finally, a perfectly matched layer which can adapt boundary is designed through transformation acoustics.
In Chapter III, two numerical methods used in this article, the finite element method and the acoustic scattering theory are introduced.
In Chapter IV, the development in the domain of acoustic cloaking is briefly introduced. Then, a new "superlens" cloaking strategy which only consists of a pair of complementary single-negative-index materials is proposed and is verified by numerical method. The proposed device is a multi-layered structure consists of a pair of complementary materials which are arranged alternately. Numerical results show the multi-layered structure can remarkably reduce the scattering of the cloaked object when the thickness of each layer is much smaller than the wavelength of the incident wave, while the cloaked object can receive outside information. Thus this structure can be used to hide an acoustic sensor. Then, we discuss the influences to the scattering-reducing effect when the parameters of the cloaked object and the complementary materials are changed. At last, the proposed scheme is extended to three dimensions; and a preliminary scheme for a similar three-dimensional superlens cloaking is proposed.
Finally, in Chapter V, the main conclusions of the dissertation and the prospect of the future work are presented.
The principal contribution of the present study is summarized as below:
1. A new strategy to design acoustic cloaking device is proposed. Compared to "double-blind" invisibility cloaks, this structure can hide the cloaked object from outside obverses while this object can receive undistorted external information. The proposed structure only requires a pair of complementary materials which are independent with the parameters of background medium as well as the cloaked object. The only need of the scheme is the thickness of each layer should be much smaller than the wavelength of incident wave. Therefore, compared to the previous "non-double-blind" cloaking structure, the proposed structure should notably reduce the technical difficulties in experimental realization.
2. The robustness of the parameters of the cloaked object has been studied. When the mass density and the bulk modulus are multiplied by the same robust factor simultaneously, it is shown the scatter wave can be reduced almost an order of magnitude by the proposed multi-layered structure, provided the robust factor is between0.5and2.
3. The situation when single-negative-index layers of the multi-layered structure exists dissipation has been studied. It is pointed that the scatter wave caused by the cloaked object can be remarkably reduced when the loss of the single-negative-index layers is less than10%.
引文
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