电磁坐标变换及其应用研究
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摘要
2006年Pendry等人在Science杂志上发表基于电磁坐标变换实现电磁斗篷的方法,稍后这一理论结果被Schurig等人实验证实。此后,电磁坐标变换及其电磁斗篷现象成为科学研究的热点,并被Science杂志评为年度十大科技进展之一。除利用坐标变换方法设计电磁斗篷外,许多新型的电磁装置也被提了出来。
本文分析了电磁坐标变换的基本原理,导出了任意形状电磁透明体和电磁聚焦装置的材料电磁特性方程,并讨论了电磁特性参数对其性能的影响;导出了任意形状电磁外斗篷的材料电磁特性方程,并详细研究了不同坐标变换对斗篷性能的影响。同时,通过有限元软件COMSOL验证了上述结论,进一步证实了本文提出的方法的有效性和正确性。
论文的主要内容包括以下四部分:
第一部分首先介绍了电磁坐标变换的原理,随后重点讨论了如何利用电磁坐标变换设计各种形状的封闭式电磁斗篷。
第二部分导出了正多边形、共形和非共形任意形状电磁透明体的材料电磁特性方程,通过仿真证实了这些方程的有效性,并探讨了电磁透明体在天线保护中的应用。
第三部分导出了椭圆形、正多边形、共形和非共形任意形状电磁聚焦器的材料电磁特性方程,通过仿真证实了这些方程的有效性,探讨了电磁聚焦装置在太阳能利用及传感应用的可能性。
第四部分导出了椭圆形、正多边形以及任意形状电磁外斗篷的材料电磁特性方程,详细研究了不同坐标变换对斗篷特性的影响,发现通过坐标变换后物质和反物质的形状不一样,并且为了隐形相同的物质,基于非线性变换的反物质更小,这为设计小型隐形装置奠定了理论基础。
The design of electromagnetic cloak based on coordinate transformation theory was firstly proposed by Pendry et al in 2006. Later, this theory was experimentally demonstrated by Schurig, which made the coordinate transformation and the phenomenon of cloaking a hot spot of scientific research. It was evaluated by Science as one of the year’s top ten scientific and technology developments. Since then, many novel devices based coordination transformation were proposed to manipulate the propagation of electromagnetic wave.
Based on the theory of coordination transformation, this thesis developed the material parameter equations for electromagnetic transparent devices and concentrators with arbitrary geometries. The influence of the material parameters on the characteristics of the devices was analyzed. Besides, the material parameter equation for the arbitrary shaped external cloak was derived. The performance of the external cloak based on linear and nonlinear coordinate transformations are compared with each other and discussed in detail. All the theoretical results were validated by numerical simulation using the finite element software COMSOL. The main contents and conclusions obtained are as follows.
In the first part, the coordinate transformation theory was introduced, and its application
in the design of arbitrary shaped electromagnetic cloak which hidden an object by enclosing it in the cloaking shell was discussed in detail.
In the second part, material parameter equations for the transparent device with regular polygonal cross section as well as arbitrary cross section of conformal and non-conformal boundaries were developed, and validated by numerical simulation. The application of the transparent device in the protection of antenna was investigated.
In the third part, the electromagnetic concentrator was studied. Material parameter equations for the elliptical concentrator, the regular polygonal concentrators as well as the arbitrary shaped concentrators with conformal and non-conformal inner and outer boundaries were developed and validated by numerical simulation. The phenomenon of field concentration of light plays an important role in the harnessing of light in solar cells similar devices. It is expected that this work is helpful for the designing concentrators in electromagnetic and optical fields, where high field intensities are required.
In the fourth part, material parameter equations for the elliptical external cloak, regular polygonal external cloak, as well as the external cloak with arbitrary geometries were developed. The performance of the cloak based linear coordination transformation was studied and compared with that based on non linear transformation. It’s found that the shape and size of the“antiobject”is dependent on the contour of the cloak and the coordination transformation. Interestingly, the object with much larger size can be hidden by the cloak based on non-linear transformation, which shows some advantages in open up an avenue for miniaturization in future cloak design.
本文分析了电磁坐标变换的基本原理,导出了任意形状电磁透明体和电磁聚焦装置的材料电磁特性方程,并讨论了电磁特性参数对其性能的影响;导出了任意形状电磁外斗篷的材料电磁特性方程,并详细研究了不同坐标变换对斗篷性能的影响。同时,通过有限元软件COMSOL验证了上述结论,进一步证实了本文提出的方法的有效性和正确性。
论文的主要内容包括以下四部分:
第一部分首先介绍了电磁坐标变换的原理,随后重点讨论了如何利用电磁坐标变换设计各种形状的封闭式电磁斗篷。
第二部分导出了正多边形、共形和非共形任意形状电磁透明体的材料电磁特性方程,通过仿真证实了这些方程的有效性,并探讨了电磁透明体在天线保护中的应用。
第三部分导出了椭圆形、正多边形、共形和非共形任意形状电磁聚焦器的材料电磁特性方程,通过仿真证实了这些方程的有效性,探讨了电磁聚焦装置在太阳能利用及传感应用的可能性。
第四部分导出了椭圆形、正多边形以及任意形状电磁外斗篷的材料电磁特性方程,详细研究了不同坐标变换对斗篷特性的影响,发现通过坐标变换后物质和反物质的形状不一样,并且为了隐形相同的物质,基于非线性变换的反物质更小,这为设计小型隐形装置奠定了理论基础。
The design of electromagnetic cloak based on coordinate transformation theory was firstly proposed by Pendry et al in 2006. Later, this theory was experimentally demonstrated by Schurig, which made the coordinate transformation and the phenomenon of cloaking a hot spot of scientific research. It was evaluated by Science as one of the year’s top ten scientific and technology developments. Since then, many novel devices based coordination transformation were proposed to manipulate the propagation of electromagnetic wave.
Based on the theory of coordination transformation, this thesis developed the material parameter equations for electromagnetic transparent devices and concentrators with arbitrary geometries. The influence of the material parameters on the characteristics of the devices was analyzed. Besides, the material parameter equation for the arbitrary shaped external cloak was derived. The performance of the external cloak based on linear and nonlinear coordinate transformations are compared with each other and discussed in detail. All the theoretical results were validated by numerical simulation using the finite element software COMSOL. The main contents and conclusions obtained are as follows.
In the first part, the coordinate transformation theory was introduced, and its application
in the design of arbitrary shaped electromagnetic cloak which hidden an object by enclosing it in the cloaking shell was discussed in detail.
In the second part, material parameter equations for the transparent device with regular polygonal cross section as well as arbitrary cross section of conformal and non-conformal boundaries were developed, and validated by numerical simulation. The application of the transparent device in the protection of antenna was investigated.
In the third part, the electromagnetic concentrator was studied. Material parameter equations for the elliptical concentrator, the regular polygonal concentrators as well as the arbitrary shaped concentrators with conformal and non-conformal inner and outer boundaries were developed and validated by numerical simulation. The phenomenon of field concentration of light plays an important role in the harnessing of light in solar cells similar devices. It is expected that this work is helpful for the designing concentrators in electromagnetic and optical fields, where high field intensities are required.
In the fourth part, material parameter equations for the elliptical external cloak, regular polygonal external cloak, as well as the external cloak with arbitrary geometries were developed. The performance of the cloak based linear coordination transformation was studied and compared with that based on non linear transformation. It’s found that the shape and size of the“antiobject”is dependent on the contour of the cloak and the coordination transformation. Interestingly, the object with much larger size can be hidden by the cloak based on non-linear transformation, which shows some advantages in open up an avenue for miniaturization in future cloak design.
引文
[1] Veselago Vg. The electrodynamics of substances with simultaneously negative values of |? and |ì[J]. Physics-Uspekhi, 1968, 10(4):509.
[2] Pendry Jb, Aj Holden, Wj Stewart, I Youngs. Extremely low frequency plasmons in metallic mesostructures [J]. Physical review letters, 1996, 76(25):4773-4776.
[3] Pendry Jb, Aj Holden, Dj Robbins, Wj Stewart. Magnetism from conductors and enhanced nonlinear phenomena [J]. IEEE transactions on microwave theory and techniques, 1999, 47(11):2075-2084.
[4] Smith Dr, Wj Padilla, Dc Vier, Sc Nemat-Nasser, S Schultz. Composite medium with simultaneously negative permeability and permittivity [J]. Physical review letters, 2000, 84(18):4184-4187.
[5] Shelby Ra, Dr Smith, Sc Nemat-Nasser, S Schultz. Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial [J]. Applied Physics Letters, 2001, 78:489.
[6] Shelby Ra, Dr Smith, S Schultz. Experimental verification of a negative index of refraction [J]. Science, 2001, 292(5514):77.
[7] Pacheco Jr J, Tm Grzegorczyk, Bi Wu, Y Zhang, Ja Kong. Power propagation in homogeneous isotropic frequency-dispersive left-handed media [J]. Physical review letters, 2002, 89(25):257401.
[8] Kong Ja. Electromagnetic wave interaction with stratified negative isotropic media [J]. Progress In Electromagnetics Research, 2002, 35:1-52.
[9] Houck Aa, Jb Brock, Il Chuang. Experimental observations of a left-handed material that obeys Snell?ˉs law [J]. Physical review letters, 2003, 90(13):137401.
[10] Kong Ja, Bi Wu, Y Zhang. Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability [J]. Applied Physics Letters, 2002, 80:2084.
[11] Schurig D, Jj Mock, Bj Justice, Sa Cummer, Jb Pendry, Af Starr, Dr Smith. Metamaterial electromagnetic cloak at microwave frequencies [J]. Science, 2006, 314(5801):977.
[12] Pendry Jb, D Schurig, Dr Smith. Controlling electromagnetic fields [J]. Science, 2006, 312(5781):1780.
[13] Cummer Sa, Bi Popa, D Schurig, Dr Smith, J Pendry. Full-wave simulations of electromagnetic cloaking structures [J]. Physical Review E, 2006, 74(3):36621.
[14] Cai W, Uk Chettiar, Av Kildishev, Vm Shalaev. Optical cloaking with metamaterials [J]. Nature Photonics, 2007, 1(4):224-227.
[15] Chen H, Bi Wu, B Zhang, Ja Kong. Electromagnetic wave interactions with a metamaterial cloak [J]. Physical review letters, 2007, 99(6):63903.
[16] Gaillot Dp, C Cro Nne, F Zhang, D Lippens. Transformation optics for the full dielectric electromagnetic cloak and metal¨Cdielectric planar hyperlens [J]. New Journal of Physics, 2008, 10:115039.
[17] Han T, X Tang, F Xiao. External cloak with homogeneous material [J]. Journal of Physics D: Applied Physics, 2009, 42(23):235403-235407.
[18] Hu J, X Zhou, G Hu. Design method for electromagnetic cloak with arbitrary shapesbased on Laplace?ˉs equation [J]. Opt. Express, 2009, 17:1308-1320.
[19] Hu J, X Zhou, G Hu. Nonsingular two dimensional cloak of arbitrary shape [J]. Applied Physics Letters, 2009, 95:011107.
[20] Kan Y, L Chao, L Fang. Electromagnetic Invisibility of Elliptic Cylinder Cloaks [J]. Chinese Physics Letters, 2008, 25:1657-1660.
[21] Kwon Dh, Dh Werner. Two-dimensional eccentric elliptic electromagnetic cloaks [J]. Applied Physics Letters, 2008, 92:013505.
[22] Kwon Dh, Dh Werner. Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions [J]. Applied Physics Letters, 2008, 92:113502.
[23] Li Clf. Two-dimensional electromagnetic cloaks with arbitrary geometries [J]. Opt. Express, 2008, 16:13414-13420.
[24] Luo Y, H Chen, J Zhang, L Ran, Ja Kong. Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations [J]. Physical Review B, 2008, 77(12):125127.
[25] Ma H, S Qu, Z Xu, J Wang. Approximation approach of designing practical cloaks with arbitrary shapes [J]. Opt. Express, 2008, 16:15449-15454.
[26] Ma H, S Qu, Z Xu, J Wang. Numerical method for designing approximate cloaks with arbitrary shapes [J]. Physical Review E, 2008, 78(3):36608.
[27] Ma H, S Qu, Z Xu, J Wang. The open cloak [J]. Applied Physics Letters, 2009, 94:103501.
[28] Ma H, S Qu, Z Xu, J Zhang, B Chen, J Wang. Material parameter equation for elliptical cylindrical cloaks [J]. Physical Review A, 2008, 77(1):13825.
[29] Nicolet A, F Zolla, S Guenneau. Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section [J]. Optics letters, 2008, 33(14):1584-1586.
[30] Rahm M, D Schurig, Da Roberts, Sa Cummer, Dr Smith, Jb Pendry. Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations [J]. Photonics and Nanostructures-Fundamentals and Applications, 2008, 6(1):87-95.
[31] Zharova Na, Iv Shadrivov, Aa Zharov, Y Kivshar. Ideal and nonideal invisibility cloaks [J]. Opt. Express, 2008, 16:21369-21374.
[32] Zhang J, Y Luo, H Chen, Bi Wu. Cloak of arbitrary shape [J]. Journal of the Optical Society of America B, 2008, 25(11):1776-1779.
[33] Zhang B, H Chen, Bi Wu, Y Luo, L Ran, Ja Kong. Response of a cylindrical invisibility cloak to electromagnetic waves [J]. Physical Review B, 2007, 76(12):121101.
[34] Yu Gx, Wx Jiang, Xy Zhou, Tj Cui. Non-rotationally invariant invisibility cloaks and concentrators of EM Waves [J]. The European Physical Journal Applied Physics, 2008, 44(2):181-185.
[35] Yu Gx, Wx Jiang, Tj Cui. Invisible slab cloaks via embedded optical transformation [J]. Applied Physics Letters, 2009, 94:041904.
[36] You Y, Gw Kattawar, Pw Zhai, P Yang. Invisibility cloaks for irregular particles using coordinate transformations [J]. Phys. Rev. Lett, 2007, 99:063903.
[37] Yan W, M Yan, Z Ruan, M Qiu. Coordinate transformations make perfect invisibility cloaks with arbitrary shape [J]. New Journal of Physics, 2008, 10:043040.
[38] Wu Q, K Zhang, F Meng, Lw Li. Material parameters characterization for arbitraryN-sided regular polygonal invisible cloak [J]. Journal of Physics D: Applied Physics, 2009, 42:035408.
[39] Li C, K Yao, F Li. Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries [J]. Opt. Express, 2008, 16:19366-19374.
[40] Chao L, Y Kan, L Fang. Two-Dimensional (2D) Polygonal Electromagnetic Cloaks [J]. Chinese Physics Letters, 2009, 26:064206.
[41] Chen H, Z Liang, P Yao, X Jiang, H Ma, Ct Chan. Extending the bandwidth of electromagnetic cloaks [J]. Physical Review B, 2007, 76(24):241104.
[42] Cummer Sa, Bi Popa, D Schurig, Dr Smith, J Pendry, M Rahm, A Starr. Scattering theory derivation of a 3D acoustic cloaking shell [J]. Physical review letters, 2008, 100(2):24301.
[43] Chen H, Ct Chan. Acoustic cloaking in three dimensions using acoustic metamaterials [J]. Applied Physics Letters, 2007, 91:183518.
[44] Gabrielli Lh, J Cardenas, Cb Poitras, M Lipson. Cloaking at optical frequencies [J]. Preprint at< http://arxiv. org/abs/0904.3508, 2009.
[45] Kildishev Av, W Cai, Uk Chettiar, Vm Shalaev. Transformation optics: approaching broadband electromagnetic cloaking [J]. New Journal of Physics, 2008, 10:115029.
[46] Smolyaninov Ii, Yj Hung, Cc Davis. Electromagnetic cloaking in the visible frequency range [J]. arXiv, 2007, 709.
[47] Yu Gx, Tj Cui, W Jiang. Design of Transparent Structure Using Matamaterial [J]. Journal of Infrared, Millimeter and Terahertz Waves, 2009, 30(6):633-641.
[48] Lai Y, J Ng, Hy Chen, Dz Han, Jj Xiao, Zq Zhang, Ct Chan. Illusion optics: the optical transformation of an object into another object [J]. Physical review letters, 2009, 102(25):253902.
[49] Lai Y, H Chen, Zq Zhang, Ct Chan. Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell [J]. Physical review letters, 2009, 102(9):93901.
[50] Chen H, B Hou, S Chen, X Ao, W Wen, Ct Chan. Design and experimental realization of a broadband transformation media field rotator at microwave frequencies [J]. Physical review letters, 2009, 102(18):183903.
[51] Luo Y, J Zhang, Bi Wu, H Chen. Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator [J]. Physical Review B, 2008, 78(12):125108.
[52] Chen H, Ct Chan. Transformation media that rotate electromagnetic fields [J]. Applied Physics Letters, 2007, 90:241105.
[53] Chen H, Ct Chan. Electromagnetic wave manipulation by layered systems using the transformation media concept [J]. Physical Review B, 2008, 78(5):54204.
[54] Gan Q, B Guo, G Song, L Chen, Z Fu, Yj Ding, Fj Bartoli. Plasmonic surface-wave splitter [J]. Applied Physics Letters, 2007, 90:161130.
[55] Yamazaki T, J Yamauchi, H Nakano. A branch-type TE/TM wave splitter using a light-guiding metal line [J]. Journal of Lightwave Technology, 2007, 25(3):922-928.
[56] Bord¨| Cj. Quantum theory of atom-wave beam splitters and application to multidimensional atomic gravito-inertial sensors [J]. General Relativity and Gravitation, 2004, 36(3):475-502.
[57] Rahm M, Sa Cummer, D Schurig, Jb Pendry, Dr Smith. Optical design of reflectionless complex media by finite embedded coordinate transformations [J]. Physical review letters, 2008, 100(6):63903.
[58] Luo X, T Yang, Y Gu, H Chen, H Ma. Conceal an entrance by means of superscatterer [J]. Applied Physics Letters, 2009, 94:223513.
[59] Yang T, H Chen, X Luo, H Ma. Superscatterer: Enhancement of scattering with complementary media [J]. Opt. Express, 2008, 16:18545-18550.
[60] Jiang Xzc. Two-dimensional elliptical electromagnetic superscatterer and superabsorber [J]. Opt. Express, 2010, 18:6891-6899.
[61] Ng J, H Chen, Ct Chan. A metamaterial frequency-selective super-absorber that has absorbing cross section significantly bigger than the geometric cross section [J]. Arxiv preprint arXiv:0811.0657, 2008.
[62] Post Ej. Formal structure of electromagnetics: general covariance and electromagnetics [M]. Dover Pubns. 1997.
[63] Jackson Jd. Classical electromagnetics [J]. Wiley, 1975.
[64] Schurig D, Jb Pendry, Dr Smith. Calculation of material properties and ray tracing in transformation media [J]. Opt. Express, 2006, 14:9794-9804.
[65] Milton Gw, M Briane, Jr Willis. On cloaking for elasticity and physical equations with a transformation invariant form [J]. New Journal of Physics, 2006, 8:248.
[66] Greenleaf A, M Lassas, G Uhlmann. Anisotropic conductivities that cannot be detected by EIT [J]. Physiological measurement, 2003, 24:413-419.
[67] Yang C, M Huang, J Yang, Z Xiao, J Peng. An external cloak with arbitrary cross section based on complementary medium [J]. Progress In Electromagnetics Research M, 2009, 10:13-24.
[68] Cummer Sa, D Schurig. One path to acoustic cloaking [J]. New Journal of Physics, 2007, 9:45.
[69] Hu J, X Zhou, G Hu. A numerical method for designing acoustic cloak with arbitrary shapes [J]. Computational Materials Science, 2009, 46(3):708-712.
[70] Chen H, Ct Chan. Acoustic cloaking and transformation acoustics [J]. Journal of Physics D: Applied Physics, 2010, 43:113001.
[71] Liu B, Jp Huang. Acoustically conceal an object with hearing [J]. The European Physical Journal Applied Physics, 2009, 48(2):20501-20501.
[2] Pendry Jb, Aj Holden, Wj Stewart, I Youngs. Extremely low frequency plasmons in metallic mesostructures [J]. Physical review letters, 1996, 76(25):4773-4776.
[3] Pendry Jb, Aj Holden, Dj Robbins, Wj Stewart. Magnetism from conductors and enhanced nonlinear phenomena [J]. IEEE transactions on microwave theory and techniques, 1999, 47(11):2075-2084.
[4] Smith Dr, Wj Padilla, Dc Vier, Sc Nemat-Nasser, S Schultz. Composite medium with simultaneously negative permeability and permittivity [J]. Physical review letters, 2000, 84(18):4184-4187.
[5] Shelby Ra, Dr Smith, Sc Nemat-Nasser, S Schultz. Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial [J]. Applied Physics Letters, 2001, 78:489.
[6] Shelby Ra, Dr Smith, S Schultz. Experimental verification of a negative index of refraction [J]. Science, 2001, 292(5514):77.
[7] Pacheco Jr J, Tm Grzegorczyk, Bi Wu, Y Zhang, Ja Kong. Power propagation in homogeneous isotropic frequency-dispersive left-handed media [J]. Physical review letters, 2002, 89(25):257401.
[8] Kong Ja. Electromagnetic wave interaction with stratified negative isotropic media [J]. Progress In Electromagnetics Research, 2002, 35:1-52.
[9] Houck Aa, Jb Brock, Il Chuang. Experimental observations of a left-handed material that obeys Snell?ˉs law [J]. Physical review letters, 2003, 90(13):137401.
[10] Kong Ja, Bi Wu, Y Zhang. Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability [J]. Applied Physics Letters, 2002, 80:2084.
[11] Schurig D, Jj Mock, Bj Justice, Sa Cummer, Jb Pendry, Af Starr, Dr Smith. Metamaterial electromagnetic cloak at microwave frequencies [J]. Science, 2006, 314(5801):977.
[12] Pendry Jb, D Schurig, Dr Smith. Controlling electromagnetic fields [J]. Science, 2006, 312(5781):1780.
[13] Cummer Sa, Bi Popa, D Schurig, Dr Smith, J Pendry. Full-wave simulations of electromagnetic cloaking structures [J]. Physical Review E, 2006, 74(3):36621.
[14] Cai W, Uk Chettiar, Av Kildishev, Vm Shalaev. Optical cloaking with metamaterials [J]. Nature Photonics, 2007, 1(4):224-227.
[15] Chen H, Bi Wu, B Zhang, Ja Kong. Electromagnetic wave interactions with a metamaterial cloak [J]. Physical review letters, 2007, 99(6):63903.
[16] Gaillot Dp, C Cro Nne, F Zhang, D Lippens. Transformation optics for the full dielectric electromagnetic cloak and metal¨Cdielectric planar hyperlens [J]. New Journal of Physics, 2008, 10:115039.
[17] Han T, X Tang, F Xiao. External cloak with homogeneous material [J]. Journal of Physics D: Applied Physics, 2009, 42(23):235403-235407.
[18] Hu J, X Zhou, G Hu. Design method for electromagnetic cloak with arbitrary shapesbased on Laplace?ˉs equation [J]. Opt. Express, 2009, 17:1308-1320.
[19] Hu J, X Zhou, G Hu. Nonsingular two dimensional cloak of arbitrary shape [J]. Applied Physics Letters, 2009, 95:011107.
[20] Kan Y, L Chao, L Fang. Electromagnetic Invisibility of Elliptic Cylinder Cloaks [J]. Chinese Physics Letters, 2008, 25:1657-1660.
[21] Kwon Dh, Dh Werner. Two-dimensional eccentric elliptic electromagnetic cloaks [J]. Applied Physics Letters, 2008, 92:013505.
[22] Kwon Dh, Dh Werner. Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions [J]. Applied Physics Letters, 2008, 92:113502.
[23] Li Clf. Two-dimensional electromagnetic cloaks with arbitrary geometries [J]. Opt. Express, 2008, 16:13414-13420.
[24] Luo Y, H Chen, J Zhang, L Ran, Ja Kong. Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations [J]. Physical Review B, 2008, 77(12):125127.
[25] Ma H, S Qu, Z Xu, J Wang. Approximation approach of designing practical cloaks with arbitrary shapes [J]. Opt. Express, 2008, 16:15449-15454.
[26] Ma H, S Qu, Z Xu, J Wang. Numerical method for designing approximate cloaks with arbitrary shapes [J]. Physical Review E, 2008, 78(3):36608.
[27] Ma H, S Qu, Z Xu, J Wang. The open cloak [J]. Applied Physics Letters, 2009, 94:103501.
[28] Ma H, S Qu, Z Xu, J Zhang, B Chen, J Wang. Material parameter equation for elliptical cylindrical cloaks [J]. Physical Review A, 2008, 77(1):13825.
[29] Nicolet A, F Zolla, S Guenneau. Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section [J]. Optics letters, 2008, 33(14):1584-1586.
[30] Rahm M, D Schurig, Da Roberts, Sa Cummer, Dr Smith, Jb Pendry. Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations [J]. Photonics and Nanostructures-Fundamentals and Applications, 2008, 6(1):87-95.
[31] Zharova Na, Iv Shadrivov, Aa Zharov, Y Kivshar. Ideal and nonideal invisibility cloaks [J]. Opt. Express, 2008, 16:21369-21374.
[32] Zhang J, Y Luo, H Chen, Bi Wu. Cloak of arbitrary shape [J]. Journal of the Optical Society of America B, 2008, 25(11):1776-1779.
[33] Zhang B, H Chen, Bi Wu, Y Luo, L Ran, Ja Kong. Response of a cylindrical invisibility cloak to electromagnetic waves [J]. Physical Review B, 2007, 76(12):121101.
[34] Yu Gx, Wx Jiang, Xy Zhou, Tj Cui. Non-rotationally invariant invisibility cloaks and concentrators of EM Waves [J]. The European Physical Journal Applied Physics, 2008, 44(2):181-185.
[35] Yu Gx, Wx Jiang, Tj Cui. Invisible slab cloaks via embedded optical transformation [J]. Applied Physics Letters, 2009, 94:041904.
[36] You Y, Gw Kattawar, Pw Zhai, P Yang. Invisibility cloaks for irregular particles using coordinate transformations [J]. Phys. Rev. Lett, 2007, 99:063903.
[37] Yan W, M Yan, Z Ruan, M Qiu. Coordinate transformations make perfect invisibility cloaks with arbitrary shape [J]. New Journal of Physics, 2008, 10:043040.
[38] Wu Q, K Zhang, F Meng, Lw Li. Material parameters characterization for arbitraryN-sided regular polygonal invisible cloak [J]. Journal of Physics D: Applied Physics, 2009, 42:035408.
[39] Li C, K Yao, F Li. Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries [J]. Opt. Express, 2008, 16:19366-19374.
[40] Chao L, Y Kan, L Fang. Two-Dimensional (2D) Polygonal Electromagnetic Cloaks [J]. Chinese Physics Letters, 2009, 26:064206.
[41] Chen H, Z Liang, P Yao, X Jiang, H Ma, Ct Chan. Extending the bandwidth of electromagnetic cloaks [J]. Physical Review B, 2007, 76(24):241104.
[42] Cummer Sa, Bi Popa, D Schurig, Dr Smith, J Pendry, M Rahm, A Starr. Scattering theory derivation of a 3D acoustic cloaking shell [J]. Physical review letters, 2008, 100(2):24301.
[43] Chen H, Ct Chan. Acoustic cloaking in three dimensions using acoustic metamaterials [J]. Applied Physics Letters, 2007, 91:183518.
[44] Gabrielli Lh, J Cardenas, Cb Poitras, M Lipson. Cloaking at optical frequencies [J]. Preprint at< http://arxiv. org/abs/0904.3508, 2009.
[45] Kildishev Av, W Cai, Uk Chettiar, Vm Shalaev. Transformation optics: approaching broadband electromagnetic cloaking [J]. New Journal of Physics, 2008, 10:115029.
[46] Smolyaninov Ii, Yj Hung, Cc Davis. Electromagnetic cloaking in the visible frequency range [J]. arXiv, 2007, 709.
[47] Yu Gx, Tj Cui, W Jiang. Design of Transparent Structure Using Matamaterial [J]. Journal of Infrared, Millimeter and Terahertz Waves, 2009, 30(6):633-641.
[48] Lai Y, J Ng, Hy Chen, Dz Han, Jj Xiao, Zq Zhang, Ct Chan. Illusion optics: the optical transformation of an object into another object [J]. Physical review letters, 2009, 102(25):253902.
[49] Lai Y, H Chen, Zq Zhang, Ct Chan. Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell [J]. Physical review letters, 2009, 102(9):93901.
[50] Chen H, B Hou, S Chen, X Ao, W Wen, Ct Chan. Design and experimental realization of a broadband transformation media field rotator at microwave frequencies [J]. Physical review letters, 2009, 102(18):183903.
[51] Luo Y, J Zhang, Bi Wu, H Chen. Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator [J]. Physical Review B, 2008, 78(12):125108.
[52] Chen H, Ct Chan. Transformation media that rotate electromagnetic fields [J]. Applied Physics Letters, 2007, 90:241105.
[53] Chen H, Ct Chan. Electromagnetic wave manipulation by layered systems using the transformation media concept [J]. Physical Review B, 2008, 78(5):54204.
[54] Gan Q, B Guo, G Song, L Chen, Z Fu, Yj Ding, Fj Bartoli. Plasmonic surface-wave splitter [J]. Applied Physics Letters, 2007, 90:161130.
[55] Yamazaki T, J Yamauchi, H Nakano. A branch-type TE/TM wave splitter using a light-guiding metal line [J]. Journal of Lightwave Technology, 2007, 25(3):922-928.
[56] Bord¨| Cj. Quantum theory of atom-wave beam splitters and application to multidimensional atomic gravito-inertial sensors [J]. General Relativity and Gravitation, 2004, 36(3):475-502.
[57] Rahm M, Sa Cummer, D Schurig, Jb Pendry, Dr Smith. Optical design of reflectionless complex media by finite embedded coordinate transformations [J]. Physical review letters, 2008, 100(6):63903.
[58] Luo X, T Yang, Y Gu, H Chen, H Ma. Conceal an entrance by means of superscatterer [J]. Applied Physics Letters, 2009, 94:223513.
[59] Yang T, H Chen, X Luo, H Ma. Superscatterer: Enhancement of scattering with complementary media [J]. Opt. Express, 2008, 16:18545-18550.
[60] Jiang Xzc. Two-dimensional elliptical electromagnetic superscatterer and superabsorber [J]. Opt. Express, 2010, 18:6891-6899.
[61] Ng J, H Chen, Ct Chan. A metamaterial frequency-selective super-absorber that has absorbing cross section significantly bigger than the geometric cross section [J]. Arxiv preprint arXiv:0811.0657, 2008.
[62] Post Ej. Formal structure of electromagnetics: general covariance and electromagnetics [M]. Dover Pubns. 1997.
[63] Jackson Jd. Classical electromagnetics [J]. Wiley, 1975.
[64] Schurig D, Jb Pendry, Dr Smith. Calculation of material properties and ray tracing in transformation media [J]. Opt. Express, 2006, 14:9794-9804.
[65] Milton Gw, M Briane, Jr Willis. On cloaking for elasticity and physical equations with a transformation invariant form [J]. New Journal of Physics, 2006, 8:248.
[66] Greenleaf A, M Lassas, G Uhlmann. Anisotropic conductivities that cannot be detected by EIT [J]. Physiological measurement, 2003, 24:413-419.
[67] Yang C, M Huang, J Yang, Z Xiao, J Peng. An external cloak with arbitrary cross section based on complementary medium [J]. Progress In Electromagnetics Research M, 2009, 10:13-24.
[68] Cummer Sa, D Schurig. One path to acoustic cloaking [J]. New Journal of Physics, 2007, 9:45.
[69] Hu J, X Zhou, G Hu. A numerical method for designing acoustic cloak with arbitrary shapes [J]. Computational Materials Science, 2009, 46(3):708-712.
[70] Chen H, Ct Chan. Acoustic cloaking and transformation acoustics [J]. Journal of Physics D: Applied Physics, 2010, 43:113001.
[71] Liu B, Jp Huang. Acoustically conceal an object with hearing [J]. The European Physical Journal Applied Physics, 2009, 48(2):20501-20501.