电磁超材料的电磁特性及其基于光学变换理论的应用
|
摘要
电磁超材料作为一个新兴、多学科交叉领域,具备潜在的发展前景,因此近十年来受到广泛关注。本论文从研究电磁超材料对入射电磁波的电磁响应特性出发,构造设计了新型的单面左手材料、以及可以减小对电磁波极化方向依赖性的高维四重C-形状平面左手材料；研究了不同开口数单环谐振环之间的耦合效应以及由于耦合产生的磁分裂现象；另外,我们还基于光学变换理论、研究了电磁超材料在控制电磁波场分布中的应用(如波束偏转器、隐身斗篷)。
本论文第一部分内容主要是研究新型电磁超材料的构造,及其在入射电磁波作用下的电磁响应特性。首先,我们详细分析了金属长细线(Rods)(或金属短线),与开口谐振环(SRRs)在不同相对排列情况下,电磁左手材料的负折射特性,经过模拟验证发现,当金属短线和谐振环共面、且彼此相连对称分布时,可以同时拥有宽通带、低损耗的优点。其次,我们设计了单面、结构简单、易于加工的双L形状的左手材料,并从理论和实验上对其负折射特性进行了验证,两种结果吻合,证实了设计的正确性；同时还详细分析了其负折射产生的机制,以及两种不同磁谐振模式的起因。然后,我们又设计了高维四重C-形状平面电磁左手材料,该设计减小了超材料对入射电磁波极化方向的依赖性,具有使不同方向入射、不同极化方式的电磁波均产生负折射率的特性；同时,对不同方向入射情况下,超材料的电磁响应特性及负折射产生的机制进行了详细分析和验证。最后,我们对同样极化方式下、不同开口数(1-开口、2-开口和4-开口)单环谐振环的电磁响应特性进行了详细研究,发现随着单环谐振环开口数量的增加,相邻谐振环之间的电磁耦合效应增强,4-开口时将会导致磁谐振模的分裂,形成两个不同起因的磁谐振模式；另外,通过调整4-开口谐振环的几何尺寸,我们构造了拥有超宽负磁禁带的单负电磁超材料。
本论文第二部分主要是基于光学变换理论、研究了电磁超材料在控制电磁波场分布中的应用。首先,我们设计了基于有限嵌入坐标变换的多分支波束偏转器,使入射电磁波可以同时向不同方向、以不同角度无反射的偏转；同时还研究设计了两分支、交叉情况下的波束偏转器,虽然分支之间存在着耦合并使波形稍微变形,但依然可以使入射电磁波按预定角度无反射的偏转。其次,我们还研究了关于组合隐身斗篷、不规则隐身斗篷的边界阻抗的匹配性问题,通过合理设计隐身斗篷的电磁参数,大大降低了斗篷对入射电磁波的散射,并对其隐身效果进行了仿真验证。
Electromagnetic metamaterial, a new and interdisciplinary field, has been received more and more attentions in the past ten years, for its potential development prospects. In this thesis, based on the electromagnetic response characteristics of the metamaterials, we construct new types single-sided structure left-handed metamaterials, and design a high dimensional four-fold C-shaped planar left-handed metamaterial, which can be reduce the effect of EM wave propagation direction on the metamaterial's response; then we discuss the electromagnetic coupling between the single-ring SRRs (split-ring resonators) with different gaps (1-gap,2-gaps, and 4-gaps), and the splitting of the magnetic resonance caused by the electromagnetic coupling. Furthermore, based on the optical transformations, we discuss the applications of electromagnetic metamaterials in the controlling of electromagnetic wave, such as wave bender and invisible cloak.
In the first part of this thesis, we investigate numerically the constructions of new types electromagnetic metamaterials, and their's electromagnetic responses to the incident EM wave. Firstly, we detail analyze the negative refraction properties of different left-handed metamaterials (LHMs), of which the Rods (or cut wire) are printed in-plane, off-plane, and connected with respect to the symmetric paried split-ring resonator, respectively. With the simulation results, we conclude that the conncected case single-sided LHM can exhibit a simultaneous low-loss and broad left-handed pass-band, compared with the in-plane and off-plane cases.
Secondly, we design a single-sided, easy fabricated left-handed metamaterial with double L-shaped resonator inclusions. In order to verify our design, both the numerical and experimental demonstrations are carried out, and the results agree well to each other. Then, the mechanism of negative refraction and the cause of two magnetic resonances of the double L-shaped resonator are detail explained and analyzed.
Thirdly, we design and investigate a high dimensional four-fold C-shaped planar left-handed metamaterial, it can exhibits negative refraction with electromagnetic wave incidence in three different directions and with different polarizations. So it can reduces the effect of electromagnetic wave paopagation direction on the metamaterial's response. Furthermore, the mechanism of the negative refraction and the electromagnetic responses of the four-fold C-shaped planar metamaterial to EM wave are discussed under the normal and parallel incidence case, respectively; and the left-handed property of this metamaterial is also demonstrated numerically.
Lastly, we investigate the electromagnetic response of the single ring resonator with 1-gap,2-gaps, and 4-gaps, respectively. From the simulation results, we conclude that the electromagnetic coupling between the rings becoming stronger with the gaps increase; and the magnetic resonace mode will be splitted into two modes, due to the strong coupling between the neighbor rings for the 4-gaps case. Also, we construct a negative meganetic metamaterial with super-wide band-gap by asjusting the geometric parameters of the 4-gaps split-ring resonator.
In the second part of this thesis, based on the optical transformations, we discuss numerically the application of electromagnetic metamaterials in controlling the EM wave. Firstly, we design a multi-branch wave bender by using finite embedded optical transformations, which can bents the electromagnetic wave simultaneously to different directions with different angles without reflection. Furthermore, we extend this wave bener, and design a crossed two branches wave bender, it can also bent the electromagnetic wave to the desired directions without reflection, though there exists coupling between two branches, and the wave shape is a little destroyed. Secondly, we investigate the impedance-matched problem between the boundaries of the combined cloaks, and the scattering of the electromagnetic cloak is substantially reduced after we have reasonably designed and modified the electromagnetic constitutive parameters of the cloak. Then, the full wave simulations are also carried out to demonstrate our designs and calculations.
本论文第一部分内容主要是研究新型电磁超材料的构造,及其在入射电磁波作用下的电磁响应特性。首先,我们详细分析了金属长细线(Rods)(或金属短线),与开口谐振环(SRRs)在不同相对排列情况下,电磁左手材料的负折射特性,经过模拟验证发现,当金属短线和谐振环共面、且彼此相连对称分布时,可以同时拥有宽通带、低损耗的优点。其次,我们设计了单面、结构简单、易于加工的双L形状的左手材料,并从理论和实验上对其负折射特性进行了验证,两种结果吻合,证实了设计的正确性；同时还详细分析了其负折射产生的机制,以及两种不同磁谐振模式的起因。然后,我们又设计了高维四重C-形状平面电磁左手材料,该设计减小了超材料对入射电磁波极化方向的依赖性,具有使不同方向入射、不同极化方式的电磁波均产生负折射率的特性；同时,对不同方向入射情况下,超材料的电磁响应特性及负折射产生的机制进行了详细分析和验证。最后,我们对同样极化方式下、不同开口数(1-开口、2-开口和4-开口)单环谐振环的电磁响应特性进行了详细研究,发现随着单环谐振环开口数量的增加,相邻谐振环之间的电磁耦合效应增强,4-开口时将会导致磁谐振模的分裂,形成两个不同起因的磁谐振模式；另外,通过调整4-开口谐振环的几何尺寸,我们构造了拥有超宽负磁禁带的单负电磁超材料。
本论文第二部分主要是基于光学变换理论、研究了电磁超材料在控制电磁波场分布中的应用。首先,我们设计了基于有限嵌入坐标变换的多分支波束偏转器,使入射电磁波可以同时向不同方向、以不同角度无反射的偏转；同时还研究设计了两分支、交叉情况下的波束偏转器,虽然分支之间存在着耦合并使波形稍微变形,但依然可以使入射电磁波按预定角度无反射的偏转。其次,我们还研究了关于组合隐身斗篷、不规则隐身斗篷的边界阻抗的匹配性问题,通过合理设计隐身斗篷的电磁参数,大大降低了斗篷对入射电磁波的散射,并对其隐身效果进行了仿真验证。
Electromagnetic metamaterial, a new and interdisciplinary field, has been received more and more attentions in the past ten years, for its potential development prospects. In this thesis, based on the electromagnetic response characteristics of the metamaterials, we construct new types single-sided structure left-handed metamaterials, and design a high dimensional four-fold C-shaped planar left-handed metamaterial, which can be reduce the effect of EM wave propagation direction on the metamaterial's response; then we discuss the electromagnetic coupling between the single-ring SRRs (split-ring resonators) with different gaps (1-gap,2-gaps, and 4-gaps), and the splitting of the magnetic resonance caused by the electromagnetic coupling. Furthermore, based on the optical transformations, we discuss the applications of electromagnetic metamaterials in the controlling of electromagnetic wave, such as wave bender and invisible cloak.
In the first part of this thesis, we investigate numerically the constructions of new types electromagnetic metamaterials, and their's electromagnetic responses to the incident EM wave. Firstly, we detail analyze the negative refraction properties of different left-handed metamaterials (LHMs), of which the Rods (or cut wire) are printed in-plane, off-plane, and connected with respect to the symmetric paried split-ring resonator, respectively. With the simulation results, we conclude that the conncected case single-sided LHM can exhibit a simultaneous low-loss and broad left-handed pass-band, compared with the in-plane and off-plane cases.
Secondly, we design a single-sided, easy fabricated left-handed metamaterial with double L-shaped resonator inclusions. In order to verify our design, both the numerical and experimental demonstrations are carried out, and the results agree well to each other. Then, the mechanism of negative refraction and the cause of two magnetic resonances of the double L-shaped resonator are detail explained and analyzed.
Thirdly, we design and investigate a high dimensional four-fold C-shaped planar left-handed metamaterial, it can exhibits negative refraction with electromagnetic wave incidence in three different directions and with different polarizations. So it can reduces the effect of electromagnetic wave paopagation direction on the metamaterial's response. Furthermore, the mechanism of the negative refraction and the electromagnetic responses of the four-fold C-shaped planar metamaterial to EM wave are discussed under the normal and parallel incidence case, respectively; and the left-handed property of this metamaterial is also demonstrated numerically.
Lastly, we investigate the electromagnetic response of the single ring resonator with 1-gap,2-gaps, and 4-gaps, respectively. From the simulation results, we conclude that the electromagnetic coupling between the rings becoming stronger with the gaps increase; and the magnetic resonace mode will be splitted into two modes, due to the strong coupling between the neighbor rings for the 4-gaps case. Also, we construct a negative meganetic metamaterial with super-wide band-gap by asjusting the geometric parameters of the 4-gaps split-ring resonator.
In the second part of this thesis, based on the optical transformations, we discuss numerically the application of electromagnetic metamaterials in controlling the EM wave. Firstly, we design a multi-branch wave bender by using finite embedded optical transformations, which can bents the electromagnetic wave simultaneously to different directions with different angles without reflection. Furthermore, we extend this wave bener, and design a crossed two branches wave bender, it can also bent the electromagnetic wave to the desired directions without reflection, though there exists coupling between two branches, and the wave shape is a little destroyed. Secondly, we investigate the impedance-matched problem between the boundaries of the combined cloaks, and the scattering of the electromagnetic cloak is substantially reduced after we have reasonably designed and modified the electromagnetic constitutive parameters of the cloak. Then, the full wave simulations are also carried out to demonstrate our designs and calculations.
引文
[1]Veselago V G. The electrodynamics of substance with simultaneously negative values of ε and μ. Sov. Phys. Usp.,1968,10(4):509-514.
[2]Lamb H. On group-velocity. Proc. London Math. Soc.,1904,1:473-479.
[3]Mandelshtam L I. Lectures on some problems of the theory of oscillations, in Complete Collection of Works, vol.5, Moscow:Academy of Science,1950,5: 428-467.
[4]Sivukhin D V. The energy of electromagnetic fields in dispersive. Opt. Spektrosk, 1957,3:308-312.
[5]Pendry J B, Holden A J, Robbins D J, Stewart W J. Megnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech.1999,47(11): 2075-2084.
[6]Smith D R, Padilla W J, Vier D C, Nemat-Nasser S C and Schultz S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett, 2000,84(18):4184-4187.
[7]Pendry J B, Holden A J, Stewart W J, Youngs I. Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett.,1996,76(25):4773-4776.
[8]Shelby R A, Smith D R, and Schultz S. Experimental verification of a negative index of refraction. Science,2001,292(5514):77-79.
[9]Marques R, Medina F, and Rafii-El-Idrissi R. Role of bianisotropy in negative permeability and left-handed metamaterials. Phys. Rev. B,2002,65(14):144440(6).
[10]Katsarakis N, Kafesaki M, and Tsiapa I, et al. High transmittance left-handed materials involving symmetric split-ring resonators. Photonics Nanostruct. Fundam. Appl,2007,5(2):149-155.
[11]Valanju P M, Walser R M, and Valanju A P. Wave refraction in negative index media: always positive and very inhomogeneous. Phys. Rev. Lett.,2002,88(18):187401(4).
[12]Garcia N, and Nieto-Vesperinas M. Is there an experimental verification of a negative index of refraction yet?. Opt. Lett.,2002,27(11):885-887.
[13]Pacheco Jr J, Grzegorczyk T M, and Kong J A, et al. Power propagation in homogeneous isotropic frequency dispersive left-handed media. Phys. Rev. Lett., 2002,89(25):257401(4).
[14]Pendry J B, Smith D R. Comment on "Wave refraction in negative index media: always positive and very inhomogeneous". Phys. Rev. Lett.,2003,90(2):029303.
[15]Ziolkouski R W. Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs. Opt. Express,2003,11(7):662-681.
[16]Houck A A, Brock J B, and Chuang I L. Experimental observation of a left-handed material that obeys Snell's law. Phys. Rev. Lett.,2003,90(13):137401(4).
[17]Parazzoli C G, Greegor R B, and Li K et al. Experimental verification and simulation of negative index of refraction using Snell's law. Phys. Rev. Lett.,2003,90(10): 107401(4).
[18]Ran Lixin, Huangfu Jiangtao, and Cheng Hongsheng, et al. Beam shifting experiment for the characterization of left-handed properties. J Appl. Phys.,2004, 95(5):2238-2241.
[19]皇甫江涛.微波异向介质的实验研究：[博士学位论文].杭州：浙江大学,2004.
[20]Chen Hongsheng, Ran Lixin, and Huangfu Jiangtao, et al. T-junction waveguide experiment to characterize left-handed properties of metamaterials. J Appl. Phys., 2003,94(7):3712-3716.
[21]陈红胜.异向介质等效电路理论及实验的研究：[博士学位论文].杭州：浙江大学,2005.
[22]Ramakrishna S A, Grzegorczyk T M. Physics and applications of negative refractive index materials. 2008 SPIE Press.
[23]Eleftheriades G V, Balmain K G Negative refraction metamaterials-Fundamental Principles and Applications.2005 IEEE Press.
[24]Engheta N, and Ziolkowski R W. Metamaterials-Physics and Engineering Explorations.2006 IEEE Press.
[25]Caloz C, Itoh T. Electromagnetic metamaterials:Transmission line theory and microwave applications.2006 IEEE Press.
[26]Hao Yang, and Mittra Raj. FDTD modeling of metamaterials:Theory and applications.2009, Artech House Press.
[27]崔万照,马伟,邱乐德,张洪太。电磁超介质及其应用。2008,国防工业出版社。北京
[28]Shvets G Photonic approach to making a material with a negative index of refraction. Phys. Rev. B,2003,67(3):035109(8).
[29]Eleftheriades G V, Omar S, and Iyer A K. Transmission line models for negative refractive index media and associated implementations without excess resonators. IEEE Micro. Wire. Component Lett.,2003,13(2):51-53.
[30]Ruan Zhichao, and Qiu Min. Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces. Opt. Express,2006, 14(13):6172-6177.
[31]Fan Xiebin, Wang Guoping, and Chan C T, et al. All-angle broadband negative refraction of metal waveguide arrays in the visible range:theoretical analysis and numerical demonstration. Phys. Rev. Lett.,2006,97(7):073901(4).
[32]Yablonovitch Eli. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett.,1987,58(20):2059-2062.
[33]John S. Strong localization of photons in certain disordered dielectric superlattice. Phys. Rev. Lett.,1987,58(23):2486-2489.
[34]Lakhtakia A. Positive and negative Goos-Hanchen shift and negative phase velocity mediums effect. Int. J Electron. Commun.,2004,58(3):229-231.
[35]Seddon N, and Bearpark T, Observation of the inverse Doppler effect. Science,2003, 302(5650):1537-1540.
[36]Moss C D, Grzegorczyk T M, and Zhang Y, et al. Numerical studies of left-handed metamaterials. Progress in Electromagnetic Research,2002,35:315-334.
[37]Ziolkowski R W, and Heyman E. Wave propagation in media having negative permittivity and permeability. Phys. Rev. E,2001,64(5):056625(15).
[38]Pendry J B. Negative refraction makes a perfect lens. Phys. Rev. Lett.,2000,85(18): 3966-3969.
[39]Smith D R. How to build a superlens. Science,2005,308(5721):502-503.
[40]Parimi P V, Lu W T, Vodo P, and Sridha S. Imaging by flat lens using negative refraction. Nature,2003,426(6965):404.
[41]Aydin K, Bulu I, and Ozbay E, Subwavelength resolution with a negative index metamaterial superlens. Appl. Phys. Lett.,2007,90(25):254102(3).
[42]Smith D R, Gollub J, and Mock J J, et al. Calculation and measurement of bianisotropy in a split ring resonator metamaterial. J. Appl. Phys.,2006,100(2): 024507(9).
[43]Aydin K, Li Zhaofeng, and Hudlicka M, et al. Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions. New J. Phys.,2007,9(7):326(11).
[44]Dong Zhenggao, Lei Shuangying, and Li Qi, et al. Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial. Phys. Rev. B,2007,75(7): 075117(5).
[45]Chen Xudong, Wu Bae-Ian, Kong Jin Au, et al. Retrieval of the effective constitutive parameters of bianisotropic metamaterials. Phys. Rev. E,2005,71(4): 046610(9).
[46]Cheng Xiangxiang, Chen Hongsheng, Jiang Tao, et al. Free space measurement of the cross-polarized transmission band of a bianisotropic left-handed metamaterial. Appl. Phys. Lett.,2008,92(17):174103(3).
[47]Xu Xinlong, Quan Baogang, and Gu Zhangzhi et al. Bianisotropic response of micro-fabricated metamaterials in the Terahertz region. J. Opt. Soc. Am. B,2006, 23(6):1174-1180.
[48]Ku Zahyun, Dani K M, and Upadhya P C, et al. Bianisotropic negative-index metamaterial embedded in a symmetric medium. J. Opt. Soc. Am. B,2009,26(12): B34-B38.
[49]Ku Zahyun, Zhang Jingyu, and Brueck S R J. Bi-anisotropy of multiple-layer fishnet negative-index metamaterials due to angled sidewalls. Optics Express,2009,17(8): 6782-6789.
[50]Koschny Th, Kafesaki M, Economou E N, and Soukoulis C M. Effective medium theory of left-handed materials. Phys. Rev. Lett.,2004,93(10):107402(4).
[51]Kafesaki M, Koschny Th, Penciu R S, Gundogdu T F, Economou E N, and Soukoulis C M. Left-handed metamaterials:detailed numerical studies of the transmission properties J. Opt. A:Pure Appl. Opt.2005,7(2):S12-S22.
[52]Aydin K, and Ozbay E. Negative refraction through an impedance matched left-handed metamaterial slab. J. Opt. Soc. Am B,2006,23(3):415-418.
[53]Zhou J, Koschny Th, Kafesaki M, et al. Saturation of the magnetic response of split-ring resonators at optical frequencies. Phys. Rev. Lett.,2005,95(22): 223902(4).
[54]Urzhumov Y A, and Shvets G. Optical magnetism and negative refraction in plasmonic metamaterial. Solid State Commun.,2008,146(5):208-220.
[55]Reynet O, and Acher O. Voltage controlled metamaterial. Appl. Phys. Lett.,2004, 84(7):1198-1200.
[56]Wang Dongxing, Ran Lixin, and Chen Hongsheng, et al. Active left-handed material collaborated with microwave varactors. Appl. Phys. Lett.,2007,91(16):164101(3).
[57]Chen Hou-Tong, Padilla W J, and Zide J M O, et al. Active terahertz metamaterial devices. Nature,2006,444(7119):597-600.
[58]Kang Lei, Zhao Qian, Li Bo, et al. Experimental verification of a tunable optical negative refraction in nematic liquid crystal. Appl. Phys. Lett.,2007,90(18): 181931(3).
[59]Aydin K, and Ozbay E. Capacitor-loaded split ring resonators as tunable metamaterial components. J. Appl. Phys.,2007,101(2):024911(5).
[60]Hand T H, and Cummer S A. Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings. Appl. Phys. Lett.,2008,103(6):066105(3).
[61]Zharov A A, Shadrivov I V, and Kivshar Y S. Nonlinear properties of left-handed metamaterial. Phys. Rev. Lett.,2003,91(3):037401(4).
[62]Shadrivov I V, Kozyrev A B, Van der Weide D W, et al. Nonlinear magnetic metamaterial. Optics Express,2008,16(25):20266-20271.
[63]Shadrivov I V, Kozyrev A B, Van der Weide D W, et al. Tunable transmission and harmonic generation in nonlinear metamaterial. Appl. Phys. Lett.,2008,93(16): 161903(3).
[64]Koschny Th, Markos P, Smith D R, and Coukoulis C M. Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. Phys. Rev. E, 2003,68(6):065602(4).
[65]Zhu W, Zhao X and Ji N. Double bands of negative refractive index in the left-handed metamaterials with asymmetric defects. Appl. Phys. Lett.,2007,90(1): 011911(3).
[66]Gollub Jonah, Hand Thomas, Sajuyigbe Doji et al. Characterizing the effects of disorder in metamaterial structures. Appl. Phys. Lett.,2007,91(16):162907(3).
[67]Zhao Xiaopeng, Zhao Qian, Kang Lei, et al. Defect effects of split ring resonators in left-handed metamaterials. Phys. Lett. A,2005,346(1):87-91.
[68]Aydin K, Guven K, Katsarakis N, et al. Effect of disorder on magnetic resonance band gap of split-ring resonator structures. Optics Express,2004,12(24): 5896-5901.
[69]Grzegoczyk T M, Moss C D, and Lu J, et al. Properties of left-handed metamaterials: transmission, backward phase, negative refraction, and focusing. IEEE Trans. On Microwave Theory and Tech.,2005,53(9):2956-2967.
[70]Lv J, Yan B, Liu M and Hu X. Numerical studies of low loss and broad pass-band single side structure left-handed metamaterial. Phys. Rev. E,2009,79(1): 017601(4).
[71]Huangfu J, Ran L, and Chen H, et al. Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns. Appl. Phys. Lett.,2004,84(9):1537-1539.
[72]Chen H, Ran L, and Huangfu J, et al. Left-handed materials composed of only S-shaped resonators. Phys. Rev. E,2004,70(5):057605(4).
[73]Ran Lixin, Huangfu Jiangtao, and Chen H, et al. Microwave solid-state left-handed material with a broad bandwidth and an ultra-low loss. Phys. Rev. B,2004,70(7): 073102(3).
[74]Chen H, Ran L, and Huangfu J, et al. Negative refraction of a combined double S-shaped metamaterial. Appl. Phys. Lett.,2005,86(15):151909(3).
[75]Chen H, Ran L, and Huangfu J, et al. Metamaterial exhibiting left-handed properties over multiple frequency bands. J Appl. Phys.,2004,96(9):5338-5340.
[76]Bayindir M, Aydin K, and Ozbay E. Transmission properties of composite metamaterials in free space. Appl. Phys. Lett.,2002,81(1):120-122.
[77]Ziolkouski R W. Design, fabrication, and testing of double negative metamaterials. IEEE Trans. Antennas Propag.2003,51(7):1516-1529.
[78]Wang Dongxing, Ran Lixin, Chen Hongsheng, et al. Experimental validation of negative refraction of metamaterial composed of single side paired S-ring resonators. Appl. Phys. Lett.,2007,90(25):254103(3).
[79]Lv Jianhong, Hu Xiwei, and Liu Minghai, et al. Negative refraction a double L-shaped metamaterial. J Opt. A:Pure Appl. Opt.,2009,11(8):085101(5).
[80]Zhou J, Zhang L, and Tuttle G, et al. Negative index materials using simple short wire pairs. Phys. Rev. B,2006,73(4):041101(4).
[81]Zhou J, Koschny Th, and Zhang L, et al. Experimental demonstration of negative index of refraction. Appl. Phys. Lett.,2006,88(22):221103(3).
[82]Kafesaki M, Tsiapa I, and Katsarakis N, et al. Left-handed metamaterials:the fishnet structure and its variations. Phys. Rev. B,2007,75(23):235114(9).
[83]Yen T J, Padilla W J, and Fang N, et al. Terahertz magnetic response from artificial materials. Science,2004,303(5663):1494-1496.
[84]Linden S, Enkrich C, and Wegener M, et al. Magnetic response of metamaterials at 100 Terahertz. Science,2005,306(5700):1351-1353.
[85]Dolling G, Enkrich C, and Wegener M, et al. Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials. Opt. Lett.,2005,30(23):3198-3140.
[86]Zhang Shuang, Fan Wenjun, and Panoiu N C, et al. Experimental demonstration of near-infrared negative index metamaterial. Phys. Rev. Lett.,2005,95(13): 137404(4).
[87]Shalaev V M, Cai Wenshan, and Chettiar U K, et al. Negative index of refraction in optical metamaterials. Opt. Lett.,2005,30(24):3356-3358.
[88]Dolling G, Wegener M, and Soukoulis C M, et al. Negative-index metamaterial at 780 nm wavelength. Opt. Lett.,2007,32(1):53-55.
[89]Valentine Jason, Zhang Shuang, and Zentgraf Thomas, et al. Three dimensional optical metamaterial with a negative refractive index. Nature,2009, 455(7211):376-379.
[90]Koschny Th, Zhang L, and Soukoulis C M, et al. Isotropic three-dimensional left-handed metamaterials. Phys. Rev. B,2005,71(12):121103(4).
[91]Gay-Balmaz P, and Martin O J F. Efficient isotropic magnetic resonator. Appl. Phys. Lett.,2002,81(5):939-941.
[92]Baena J D, Jelinek L, and Marques R, et al. Electrically small isotropic three-dimensional magnetic resonators for metamaterials design. Appl. Phys. Lett., 2006,88(13):134108(3).
[93]Vier D C, Schultz S, and Greegor R B, et al. Three-dimensional double-negative metamaterials resonating at 13.5 GHz. IET Microw. Antennas Propag.2009,3(5): 723-727.
[94]Zhang Jingjing, Chen Hongsheng, and Ran Lixin, et al. Experimental characterization and cell interactions of a two-dimensional isotropic left-handed metamaterial. Appl. Phys. Lett.,2008,92(8):084108(3).
[95]Alu A, Salandrino A, and Engheta N. Negative effective permeability and left-handed materials at optical frequencies. Optics Express,2006,14(4): 1557-1567.
[96]Liu Hui, and Zhao Xiaopeng. Metamaterials with dendriticlike structure at infrared frequencies. Appl. Phys. Lett.,2007,90(19):191904(3).
[97]Pimenov. A, Loidl. A, and Gehrke. K, et al. Negative refraction observed in a metallic ferromagnet in the Gigahertz frequency range. Phys. Rev. Lett.,2007, 98(19):197401(4).
[98]Peng Liang, Ran Lixin, and Chen Hongsheng, et al. Experimental observation of left-handed behavior in an array of standard dielectric resonators. Phys. Rev. Lett., 2007,98(15):157403(4).
[99]Zhao Qian, Kang Lei, Du B, et al. Experimental demonstration of isotropic negative permeability in a three dimensional dielectric composite. Phys. Rev. Lett.,2008, 101(2):027402(4).
[100]Pendry J B, Schurig D, and Smith D R. Controlling electromagnetic field. Science, 2006,312(5781):1780-1782.
[101]Schurig D, Mock J J, and Justice B J, et al. Metamaterial electromagnetic cloak at microwave frequencies. Science,2006,314(5801):977-980.
[102]Valentine J, Li J, and Zentgraf T, et al. An optical cloak made of dielectrics. Nature Mater.,2009,8(7):568-571.
[103]Enoch S, Tayeb G, and Sabouroux P, et al. A metamaterial for directive emission. Phys. Rev. Lett.,2002,89(21):213902(4).
[104]Landy N I, Sajuyigbe S, and Mock J J, et al. Perfect metamaterial absorber. Phys. Rev. Lett.,2008,100(20):207402(4).
[105]Tao Hu, Landy N I, and Bingham C M, et al. A metamaterial absorber for the Terahertz regime:Design, fabrication and characterization. Optics Express,2008, 16(10):7181-7188.
[106]Tao Hu, Bingham C M, and Strikwerda A C, et al. High flexible wide angle of incidence terahertz metamaterial absorber:Design, fabrication and characterization. Phys. Rev. B,2008,78(24):241103(4).
[107]Yuan Yu, Ran Lixin, and Chen Hongsheng, et al. Backward coupling waveguide coupler using left-handed material. Appl. Phys. Lett.,2006,88(21):211903(3).
[108]Liu Kaiyu, Li Chao, and Li Fang. A new type of microstrip coupler with complementary split-ring resonator. PIERS Online.2007,3(5):603-606.
[109]Aydin K, Cakmak A O, and Sahin L, et al. Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture. Phys. Rev. Lett.,2009, 102(1):013904(4).
[110]Gil M, Bonache J, and Martin F. Metamaterial filter:A review. Metamaterial,2008, 2(4):186-197.
[111]Wu Hung-Wei, Weng Min-Hang, and Su Yan-Kuin, et al. Propagation characteristics of complementary split-ring resonator for wide band-gap enhancement in microstrip bandpass filter. Microwave Opt. Tech. Lett.,2007,49(2): 292-295.
[112]Li Chao, and Li Fang. Microstrip bandpass filter based on zeroth-order resonator with complementary split-ring resonators. IET Microw. Antenna Propag.2009,3(2): 276-280.
[113]Freire M J, Marques R, and Medina F, et al. Planar magnetoinductive wave transducer:Theory and applications. Appl. Phys. Lett.,2004,85(19):4439-4441.
[114]Beruete M, Falcone F, and Freire M J, et al. Electroinductive wave in chains of complementary metamaterial elements. Appl. Phys. Lett.,2006,88(8):083503(3).
[115]Liu H, Genov D A, Wu D, Liu Y, Steele J M, Sun C, Zhu S, and Zhang X. Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies. Phys. Rev. Lett.,2006,97(24):243902(4).
[116]Cui Tiejun, and Kong J A. Time-domain electromagnetic energy in a frequency-dispersive left-handed medium. Phys. Rev. B,2004,70(20):205106(7).
[117]Ruppin P. Electromagnetic energy density in a dispersive and absorptive material. Phys. Lett. A,2002,299(2):309-312.
[118]Markos P, and Soukoulis C M. Numerical studies of left-handed materials and arrays of split-ring resonators. Phys. Rev. E,2002,65(3):036622(8).
[119]Markos P, Rousochatzakis I, and Soukoulis C M. Transmission losses in left-handed materials. Phys. Rev. E,2002,66(4):045601(4).
[120]Smith D R, Schultz S, and Markos P, et al. Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Phys. Rev. B,2002,65(19):195104(5).
[121]Smith D R, Vier D C, Koschny Th, and Soukoulis C M. Electromagnetic parameter retrieval from inhomogeneous metamaterials. Phys. Rev. E,2005,71(3): 036617(11).
[122]Chen X, Grzegoczyk T M, Wu B-I, Pacheco J, and Kong J A. Robust method to retrieve the constitutive effective parameters of metamaterials. Phys. Rev. E,2004 70(1):016608(7).
[123]隋强.微波异向介质的实验研究及理论研究：[博士学位论文].北京：中国科学院电子研究所,2004.
[124]Kolinko P. and Smith D R. Numerical study of electromagnetic waves interacting with negative index materials. Opt. Express,2003,11(7):640-648。
[125]Dong Z, Zhu S, Liu H, Zhu J, and Cao W. Numerical simulations of negative-index refraction in wedge-shaped metamaterials. Phys. Rev. E,2005,72(1):016607(4)。
[126]Hou Ling Li, Chin Jessie Yao, and Cui Tie Jun et al. Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model. J. Appl. Phys.,2008,103(6): 064904(6).
[127]Koschny Th, Markos P, Economou E N, et al. Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials. Phys. Rev. B,2005,71(24):245105(22).
[128]Li Zhaofeng, Aydin K, and Ozbay E. Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients. Phys. Rev. E,2009,79(2):026610(7).
[129]Chen Xudong, Wu B-I, and Kong J A, et al. Retrieval of the effective constitutive parameters of bianisotropic metamaterials. Phys. Rev. E,2005,71(4):046610(9).
[130]Aydin K, and Ozbay E. Experimental investigation of reflection characteristics of left-handed metamaterials in free space. IET Microw. Antennas Propag.2007,1(1): 89-93.
[131]Marques R, Martel J, and Mesa F, et al. Left-handed-media simulation and transmission of EM waves in the subwavelength split-ring-resonator-loaded metallic waveguides. Phys. Rev. Lett.,2002,89(18):183901(4).
[132]Chen Hongsheng, Zhang Jingjing, Bai Yang, et al. Experimental retrieval of the effective parameters of metamaterials based on waveguide methods. Optics Express, 2006,14(26):12944-12949.
[133]Ziolkowski R W. Design, Fabrication, and testing of double negative metamaterials. IEEE Trans. Antennas Propag.,2003,51(7):1516-1529.
[134]Zhang Fuli, Gregory Houzet, and Eric Lheurette, et al. Negative zero positive metamaterial with omega-type metal inclusions. J Appl. Phys.,2008,103(8): 084312(8).
[135]Wu W, Yu Z, and Zhang Xiang, et al. Midinfrared metamaterials fabricated by nanoimprint lithography. Appl. Phys. Lett.,2007,90(6):063107(3).
[136]Katsarakis N, Koschony T, and Kafesaki, et al. Electric coupling to the magnetic resonance of split ring resonators. Appl. Phys. Lett.,2004,84(15):2943-2945.
[137]Ozbay E, Guven K and Aydin K. Metamaterials with negative permeability and negative refractive index:experiments and simulations. J. Opt. A:Pure Appl. Opt., 2007,9(9) S301-S307.
[138]Zhou Jiangfeng, Koschny Th, and Soukoulis C M. An efficient way to reduce losses of left-handed metamaterials. Optics Express,2008,16(15):11147-11152.
[139]Gay-Balmaz P, and Martin O J F. Electromagnetic resonances in individual and coupled split-ring resonators. J Appl. Phys.,2002,92(5):2929-2936.
[140]Garcia-Garcia J. Bonache J, and Gil I, et al. Miniaturized microstrip and CPW filters using coupled metamaterial resonator. IEEE Trans Microw. Theory. Tech.,2006, 54(6):2628-2635.
[141]Liu Y, Fang N, and Wu D, et al. Symmetric and antisymmetric modes of electromagnetic resonators. Appl. Phys. A:Mater. Sci. Prog.,2007,87(2):171-174.
[142]Penciu R S, Aydin K, and Kafesaki M, et al. Multi-gap individual and coupled split-ring resonators structure. Opt. Express,2008,16(22):18131-18144.
[143]Schurig D, Pendry J B, and Smith D R. Calculation of material properties and ray tracing in transformation media. Optics Express,2006,14(21):9794-9804.
[144]Cummer S A, Popa B-I, and Schurig D, et al. Full-wave simulations of electromagnetic cloaking structures. Phys. Rev. E,2006,74(3):036621(5).
[145]Chen Hongsheng, Wu B-I, Zhang Baile, and Kong Jin Au. Electromagnetic wave interactions with a metamaterial cloak. Phys. Rev. Lett.,2007,99(6):063903(4).
[146]Huang Ying, Feng Yijun, and Jiang Tian. Electromagnetic cloaking by layered structure of homogeneous isotropic materials. Optics Express,2007,15(18): 11133-11141.
[147]Cai Wenshan, Chettiar U K, and Kildishev A V, et al. Nonmagnetic cloak with minimized scattering. Appl. Phys. Lett.,2007,91(11):111105(3).
[148]Ruan Zhichao, Yan Min, and Neff C W, et al. Ideal cylindrical cloak:Perfect but sensitive to tiny perturbations. Phys. Rev. Lett.,2007,99(11):113903(4).
[149]Yan Min, Ruan Zhichao, and Qiu Min. Cylindrical invisibility cloak with simplified material parameters is inherently visible. Phys. Rev. Lett.,2007,99(23):233901(4).
[150]Zhang Jingjing, Huangfu Jiangtao, and Luo Yu, et al. Cloak for multilayered and gradually changing media. Phys. Rev. B,2008,77(3):035116(5).
[151]Cummer S A, Liu Ruopeng, and Cui Tie Jun. A rigorous and nonsingular two dimensional cloaking coordination transformation. J. Appl. Phys.2009,105(5): 056102(3).
[152]Jiang Weixiang, Cui Tiejun, and Yang Xinmi, et al. Invisible cloak without singularity. Appl. Phys. Lett.,2008,93(19):194102(3).
[153]Zhang Pu, Jin Yi, and He Sailing. Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak. Appl. Phys. Lett.,2008, 93(24):243502(3).
[154]Ma Hua, Qu Shaobo, and Xu Zhou, et al. Material parameter equation for elliptical cylindrical cloaks. Phys. Rev. A,2008,77(1):013825(4).
[155]Jiang W X, Cui T J, and Yu G X, et al. Arbitrary elliptical-cylindrical invisible cloaking. J. Phys. D:Appl. Phys.,2008,41(8):085504(5).
[156]Cojocaru E. Exact analytical approaches for elliptic cylindrical invisibility cloaks. J. Opt. Soc. Am. B,2009,26(5):1119-1128.
[157]Rahm M, Schurig D, and Roberts D A, et al. Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations. Photonics Nanostruct. Fundam. Appl.2008,6(1):87-95.
[158]Wu Qun, Zhang Kuang, and Meng Fanyi, et al. Material parameters characterization for arbitrary N-shaped regular polygonal invisible cloak. J. Phys. D:Appl. Phys., 2009,42(3):035408(7).
[159]Zhang Jingjing, Luo Yu, and Chen Hongsheng, et al. Cloaking for arbitrary shape. J. Opt. Soc. B,2008,25(11):1776-1779.
[160]Jiang Weixiang, Chin J Y, and Li Zhou, et al. Analytical design of conformally invisible cloaks for arbitrarily shaped objects. Phys. Rev. E,2008,77(6):066607(6).
[161]Ma Hua, Qu Shaobo, and Xu Zhou, et al. Approximation approach of designing practical cloaks with arbitrary shapes. Optics Express,2008,16(20):15449-15454.
[162]Li Chao, and Li Fang. Two-dimensional electromagnetic cloaks with arbitrary geometries. Optics Express,2008,16(17):13414-13420.
[163]Li Jensen, and Pendry J B. Hiding under the carpet:A new strategy for cloaking. Phys. Rev. Lett.,2008,101(20):203901(4).
[164]Vasquez F G, Milton G W, and Onofrei D. Active exterior cloaking for the 2D Laplace and Helmholtz equations. Phys. Rev. Lett.,2009,103(7):073901(4).
[165]Hu Jin, Zhou Xiaoming, and Hu Gengkai. Design method for electromagnetic cloak with arbitrary shapes based on Laplace's equations. Optics Express,2009,17(3): 1308-1320.
[166]Cai Wenshan, Chettiar U K, and Kildishev A V, et al. Optical cloaking with metamaterials. Nature Photonics,2007,1(4):224-227.
[167]Chen Huanyang, Luo Xudong, and Ma Hongru, et al. The anti-cloak. Optics Express, 2008,16(19):14603-14608.
[168]Liu R, Ji C, and Mock J J, et al. Broadband ground-plane cloak. Science,2009, 323(5912):366-369.
[169]Chen Huanyang, and Chan C T. Transformation media that rotate electromagnetic fields. Appl. Phys. Lett.,2007,90(24):241105(3).
[170]陈焕阳.各向异性材料中的波：隐身衣,旋转衣和声子晶体：[博士学位论文].上海：上海交通大学.2008.
[171]Chen Huanyang, Hou Bo, and Chen Shuyu, et al. Design and Experimental realization of a broadband transformation media field rotator at microwave frequencies. Phys. Rev. Lett.,2009,102(18):183903(4).
[172]Luo Yu, Chen Hongsheng, and Zhang Jingjing, et al. Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations. Phys. Rev. B,2008,77(12): 125127(8).
[173]Jiang Weixiang, Cui Tiejun, and Cheng Qiang, et al. Design of arbitrary shaped concentrators based on conformal optical transformation of uniform rational B-spline surface. Appl. Phys. Lett.,2008,92(26):264101(3).
[174]Narimanov E E, and Kildishev A V. Optical black hole:Broadband omnidirectional light absorber. Appl. Phys. Lett.,2009,95(4):041106(3).
[175]Cheng Qiang, and Cui Tiejun. An electromagnetic black hole made of metamaterials. arXiv:0910.2159v1,2009.
[176]Tsang M, and Psaltis D. Magnifying perfect lens and superlens design by coordinate transformation. Phys. Rev. B,2008,77(3):035122(9).
[177]Kong Fanmin, Wu B-I, and Kong Jin Au, et al. Planar focusing antenna design by using coordinate transformation technology. Appl. Phys. Lett.,2007,91(25): 253509(3).
[178]Roberts D A, Rahm M, and Pendry J B, et al. Transformation-optical design of sharp waveguide bends and corners. Appl. Phys. Lett.,2008,93(25):251111(3).
[179]Rahm M, Roberts D A, and Pendry J B, et al. Transformation-optical design of adaptive beam bends and beam expenders. Optics Express,2008,16(15): 11555-11567.
[180]Jiang W X, Cui T J, and Zhou X Y, et al. Arbitrary bending of electromagnetic waves using realizable inhomogenoues and anisotropic materials. Phys. Rev. E, 2008,78(6):066607(4).
[181]Mei Z L, and Cui T J. Arbitrary bending of electromagnetic wave using isotropic materials. J. Appl. Phys.,2009,105(10):104913(5).
[182]Huangfu Jiangtao, Xi Sheng, and Kong Fanmin et al. Application of coordinate transformation in bent waveguides. J. Appl. Phys.,2008,104(1):014502(4).
[183]Wang M Y, Zhang J J, and Chen H S, et al. Designing and application of a beam shifter by transformation media. PIER,2008,83,147-155.
[184]Chen Huanyang, and Chan C T. Electromagnetic wave manipulation by layered systems using the transformation media concepts. Phys. Rev. B,2008,78(5): 054204(9).
[185]Rahm M, Cummer S A, and Schurig D, et al. Optical design of reflectionless complex media by finite embedded coordinate transformations. Phys. Rev. Lett., 2008,100(6):063903(4).
[186]Jiang Weixiang, Cui Tie Jun, and Ma Huifeng, et al. Cylindrical-to-plane-wave conversion via embedded optical transformation. Appl. Phys. Lett.,2008,92(26): 261903(3).
[187]Zhang Jingjing, Luo Yu, and Xi Sheng, et al. Directive emission obtained by coordination transformation. PIER,2008,81,437-446.
[188]Yan Min, Ruan Zhichao, and Qiu Min. Scattering characteristics of simplified cylindrical invisibility cloaks. Opt. Express,2007,15(26):17772-17782.
[189]Zhang Jingjing, Luo Yu, and Chen Hongsheng et al. Sensitivity of transformation cloak in engineering. PIER,2008,84,93-104.
[190]Nicolet A, Zolla F, and Guenneau S. Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section. Opt. Lett.,2008,33(14):1584-1586.
[2]Lamb H. On group-velocity. Proc. London Math. Soc.,1904,1:473-479.
[3]Mandelshtam L I. Lectures on some problems of the theory of oscillations, in Complete Collection of Works, vol.5, Moscow:Academy of Science,1950,5: 428-467.
[4]Sivukhin D V. The energy of electromagnetic fields in dispersive. Opt. Spektrosk, 1957,3:308-312.
[5]Pendry J B, Holden A J, Robbins D J, Stewart W J. Megnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech.1999,47(11): 2075-2084.
[6]Smith D R, Padilla W J, Vier D C, Nemat-Nasser S C and Schultz S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett, 2000,84(18):4184-4187.
[7]Pendry J B, Holden A J, Stewart W J, Youngs I. Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett.,1996,76(25):4773-4776.
[8]Shelby R A, Smith D R, and Schultz S. Experimental verification of a negative index of refraction. Science,2001,292(5514):77-79.
[9]Marques R, Medina F, and Rafii-El-Idrissi R. Role of bianisotropy in negative permeability and left-handed metamaterials. Phys. Rev. B,2002,65(14):144440(6).
[10]Katsarakis N, Kafesaki M, and Tsiapa I, et al. High transmittance left-handed materials involving symmetric split-ring resonators. Photonics Nanostruct. Fundam. Appl,2007,5(2):149-155.
[11]Valanju P M, Walser R M, and Valanju A P. Wave refraction in negative index media: always positive and very inhomogeneous. Phys. Rev. Lett.,2002,88(18):187401(4).
[12]Garcia N, and Nieto-Vesperinas M. Is there an experimental verification of a negative index of refraction yet?. Opt. Lett.,2002,27(11):885-887.
[13]Pacheco Jr J, Grzegorczyk T M, and Kong J A, et al. Power propagation in homogeneous isotropic frequency dispersive left-handed media. Phys. Rev. Lett., 2002,89(25):257401(4).
[14]Pendry J B, Smith D R. Comment on "Wave refraction in negative index media: always positive and very inhomogeneous". Phys. Rev. Lett.,2003,90(2):029303.
[15]Ziolkouski R W. Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs. Opt. Express,2003,11(7):662-681.
[16]Houck A A, Brock J B, and Chuang I L. Experimental observation of a left-handed material that obeys Snell's law. Phys. Rev. Lett.,2003,90(13):137401(4).
[17]Parazzoli C G, Greegor R B, and Li K et al. Experimental verification and simulation of negative index of refraction using Snell's law. Phys. Rev. Lett.,2003,90(10): 107401(4).
[18]Ran Lixin, Huangfu Jiangtao, and Cheng Hongsheng, et al. Beam shifting experiment for the characterization of left-handed properties. J Appl. Phys.,2004, 95(5):2238-2241.
[19]皇甫江涛.微波异向介质的实验研究：[博士学位论文].杭州：浙江大学,2004.
[20]Chen Hongsheng, Ran Lixin, and Huangfu Jiangtao, et al. T-junction waveguide experiment to characterize left-handed properties of metamaterials. J Appl. Phys., 2003,94(7):3712-3716.
[21]陈红胜.异向介质等效电路理论及实验的研究：[博士学位论文].杭州：浙江大学,2005.
[22]Ramakrishna S A, Grzegorczyk T M. Physics and applications of negative refractive index materials. 2008 SPIE Press.
[23]Eleftheriades G V, Balmain K G Negative refraction metamaterials-Fundamental Principles and Applications.2005 IEEE Press.
[24]Engheta N, and Ziolkowski R W. Metamaterials-Physics and Engineering Explorations.2006 IEEE Press.
[25]Caloz C, Itoh T. Electromagnetic metamaterials:Transmission line theory and microwave applications.2006 IEEE Press.
[26]Hao Yang, and Mittra Raj. FDTD modeling of metamaterials:Theory and applications.2009, Artech House Press.
[27]崔万照,马伟,邱乐德,张洪太。电磁超介质及其应用。2008,国防工业出版社。北京
[28]Shvets G Photonic approach to making a material with a negative index of refraction. Phys. Rev. B,2003,67(3):035109(8).
[29]Eleftheriades G V, Omar S, and Iyer A K. Transmission line models for negative refractive index media and associated implementations without excess resonators. IEEE Micro. Wire. Component Lett.,2003,13(2):51-53.
[30]Ruan Zhichao, and Qiu Min. Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces. Opt. Express,2006, 14(13):6172-6177.
[31]Fan Xiebin, Wang Guoping, and Chan C T, et al. All-angle broadband negative refraction of metal waveguide arrays in the visible range:theoretical analysis and numerical demonstration. Phys. Rev. Lett.,2006,97(7):073901(4).
[32]Yablonovitch Eli. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett.,1987,58(20):2059-2062.
[33]John S. Strong localization of photons in certain disordered dielectric superlattice. Phys. Rev. Lett.,1987,58(23):2486-2489.
[34]Lakhtakia A. Positive and negative Goos-Hanchen shift and negative phase velocity mediums effect. Int. J Electron. Commun.,2004,58(3):229-231.
[35]Seddon N, and Bearpark T, Observation of the inverse Doppler effect. Science,2003, 302(5650):1537-1540.
[36]Moss C D, Grzegorczyk T M, and Zhang Y, et al. Numerical studies of left-handed metamaterials. Progress in Electromagnetic Research,2002,35:315-334.
[37]Ziolkowski R W, and Heyman E. Wave propagation in media having negative permittivity and permeability. Phys. Rev. E,2001,64(5):056625(15).
[38]Pendry J B. Negative refraction makes a perfect lens. Phys. Rev. Lett.,2000,85(18): 3966-3969.
[39]Smith D R. How to build a superlens. Science,2005,308(5721):502-503.
[40]Parimi P V, Lu W T, Vodo P, and Sridha S. Imaging by flat lens using negative refraction. Nature,2003,426(6965):404.
[41]Aydin K, Bulu I, and Ozbay E, Subwavelength resolution with a negative index metamaterial superlens. Appl. Phys. Lett.,2007,90(25):254102(3).
[42]Smith D R, Gollub J, and Mock J J, et al. Calculation and measurement of bianisotropy in a split ring resonator metamaterial. J. Appl. Phys.,2006,100(2): 024507(9).
[43]Aydin K, Li Zhaofeng, and Hudlicka M, et al. Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions. New J. Phys.,2007,9(7):326(11).
[44]Dong Zhenggao, Lei Shuangying, and Li Qi, et al. Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial. Phys. Rev. B,2007,75(7): 075117(5).
[45]Chen Xudong, Wu Bae-Ian, Kong Jin Au, et al. Retrieval of the effective constitutive parameters of bianisotropic metamaterials. Phys. Rev. E,2005,71(4): 046610(9).
[46]Cheng Xiangxiang, Chen Hongsheng, Jiang Tao, et al. Free space measurement of the cross-polarized transmission band of a bianisotropic left-handed metamaterial. Appl. Phys. Lett.,2008,92(17):174103(3).
[47]Xu Xinlong, Quan Baogang, and Gu Zhangzhi et al. Bianisotropic response of micro-fabricated metamaterials in the Terahertz region. J. Opt. Soc. Am. B,2006, 23(6):1174-1180.
[48]Ku Zahyun, Dani K M, and Upadhya P C, et al. Bianisotropic negative-index metamaterial embedded in a symmetric medium. J. Opt. Soc. Am. B,2009,26(12): B34-B38.
[49]Ku Zahyun, Zhang Jingyu, and Brueck S R J. Bi-anisotropy of multiple-layer fishnet negative-index metamaterials due to angled sidewalls. Optics Express,2009,17(8): 6782-6789.
[50]Koschny Th, Kafesaki M, Economou E N, and Soukoulis C M. Effective medium theory of left-handed materials. Phys. Rev. Lett.,2004,93(10):107402(4).
[51]Kafesaki M, Koschny Th, Penciu R S, Gundogdu T F, Economou E N, and Soukoulis C M. Left-handed metamaterials:detailed numerical studies of the transmission properties J. Opt. A:Pure Appl. Opt.2005,7(2):S12-S22.
[52]Aydin K, and Ozbay E. Negative refraction through an impedance matched left-handed metamaterial slab. J. Opt. Soc. Am B,2006,23(3):415-418.
[53]Zhou J, Koschny Th, Kafesaki M, et al. Saturation of the magnetic response of split-ring resonators at optical frequencies. Phys. Rev. Lett.,2005,95(22): 223902(4).
[54]Urzhumov Y A, and Shvets G. Optical magnetism and negative refraction in plasmonic metamaterial. Solid State Commun.,2008,146(5):208-220.
[55]Reynet O, and Acher O. Voltage controlled metamaterial. Appl. Phys. Lett.,2004, 84(7):1198-1200.
[56]Wang Dongxing, Ran Lixin, and Chen Hongsheng, et al. Active left-handed material collaborated with microwave varactors. Appl. Phys. Lett.,2007,91(16):164101(3).
[57]Chen Hou-Tong, Padilla W J, and Zide J M O, et al. Active terahertz metamaterial devices. Nature,2006,444(7119):597-600.
[58]Kang Lei, Zhao Qian, Li Bo, et al. Experimental verification of a tunable optical negative refraction in nematic liquid crystal. Appl. Phys. Lett.,2007,90(18): 181931(3).
[59]Aydin K, and Ozbay E. Capacitor-loaded split ring resonators as tunable metamaterial components. J. Appl. Phys.,2007,101(2):024911(5).
[60]Hand T H, and Cummer S A. Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings. Appl. Phys. Lett.,2008,103(6):066105(3).
[61]Zharov A A, Shadrivov I V, and Kivshar Y S. Nonlinear properties of left-handed metamaterial. Phys. Rev. Lett.,2003,91(3):037401(4).
[62]Shadrivov I V, Kozyrev A B, Van der Weide D W, et al. Nonlinear magnetic metamaterial. Optics Express,2008,16(25):20266-20271.
[63]Shadrivov I V, Kozyrev A B, Van der Weide D W, et al. Tunable transmission and harmonic generation in nonlinear metamaterial. Appl. Phys. Lett.,2008,93(16): 161903(3).
[64]Koschny Th, Markos P, Smith D R, and Coukoulis C M. Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. Phys. Rev. E, 2003,68(6):065602(4).
[65]Zhu W, Zhao X and Ji N. Double bands of negative refractive index in the left-handed metamaterials with asymmetric defects. Appl. Phys. Lett.,2007,90(1): 011911(3).
[66]Gollub Jonah, Hand Thomas, Sajuyigbe Doji et al. Characterizing the effects of disorder in metamaterial structures. Appl. Phys. Lett.,2007,91(16):162907(3).
[67]Zhao Xiaopeng, Zhao Qian, Kang Lei, et al. Defect effects of split ring resonators in left-handed metamaterials. Phys. Lett. A,2005,346(1):87-91.
[68]Aydin K, Guven K, Katsarakis N, et al. Effect of disorder on magnetic resonance band gap of split-ring resonator structures. Optics Express,2004,12(24): 5896-5901.
[69]Grzegoczyk T M, Moss C D, and Lu J, et al. Properties of left-handed metamaterials: transmission, backward phase, negative refraction, and focusing. IEEE Trans. On Microwave Theory and Tech.,2005,53(9):2956-2967.
[70]Lv J, Yan B, Liu M and Hu X. Numerical studies of low loss and broad pass-band single side structure left-handed metamaterial. Phys. Rev. E,2009,79(1): 017601(4).
[71]Huangfu J, Ran L, and Chen H, et al. Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns. Appl. Phys. Lett.,2004,84(9):1537-1539.
[72]Chen H, Ran L, and Huangfu J, et al. Left-handed materials composed of only S-shaped resonators. Phys. Rev. E,2004,70(5):057605(4).
[73]Ran Lixin, Huangfu Jiangtao, and Chen H, et al. Microwave solid-state left-handed material with a broad bandwidth and an ultra-low loss. Phys. Rev. B,2004,70(7): 073102(3).
[74]Chen H, Ran L, and Huangfu J, et al. Negative refraction of a combined double S-shaped metamaterial. Appl. Phys. Lett.,2005,86(15):151909(3).
[75]Chen H, Ran L, and Huangfu J, et al. Metamaterial exhibiting left-handed properties over multiple frequency bands. J Appl. Phys.,2004,96(9):5338-5340.
[76]Bayindir M, Aydin K, and Ozbay E. Transmission properties of composite metamaterials in free space. Appl. Phys. Lett.,2002,81(1):120-122.
[77]Ziolkouski R W. Design, fabrication, and testing of double negative metamaterials. IEEE Trans. Antennas Propag.2003,51(7):1516-1529.
[78]Wang Dongxing, Ran Lixin, Chen Hongsheng, et al. Experimental validation of negative refraction of metamaterial composed of single side paired S-ring resonators. Appl. Phys. Lett.,2007,90(25):254103(3).
[79]Lv Jianhong, Hu Xiwei, and Liu Minghai, et al. Negative refraction a double L-shaped metamaterial. J Opt. A:Pure Appl. Opt.,2009,11(8):085101(5).
[80]Zhou J, Zhang L, and Tuttle G, et al. Negative index materials using simple short wire pairs. Phys. Rev. B,2006,73(4):041101(4).
[81]Zhou J, Koschny Th, and Zhang L, et al. Experimental demonstration of negative index of refraction. Appl. Phys. Lett.,2006,88(22):221103(3).
[82]Kafesaki M, Tsiapa I, and Katsarakis N, et al. Left-handed metamaterials:the fishnet structure and its variations. Phys. Rev. B,2007,75(23):235114(9).
[83]Yen T J, Padilla W J, and Fang N, et al. Terahertz magnetic response from artificial materials. Science,2004,303(5663):1494-1496.
[84]Linden S, Enkrich C, and Wegener M, et al. Magnetic response of metamaterials at 100 Terahertz. Science,2005,306(5700):1351-1353.
[85]Dolling G, Enkrich C, and Wegener M, et al. Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials. Opt. Lett.,2005,30(23):3198-3140.
[86]Zhang Shuang, Fan Wenjun, and Panoiu N C, et al. Experimental demonstration of near-infrared negative index metamaterial. Phys. Rev. Lett.,2005,95(13): 137404(4).
[87]Shalaev V M, Cai Wenshan, and Chettiar U K, et al. Negative index of refraction in optical metamaterials. Opt. Lett.,2005,30(24):3356-3358.
[88]Dolling G, Wegener M, and Soukoulis C M, et al. Negative-index metamaterial at 780 nm wavelength. Opt. Lett.,2007,32(1):53-55.
[89]Valentine Jason, Zhang Shuang, and Zentgraf Thomas, et al. Three dimensional optical metamaterial with a negative refractive index. Nature,2009, 455(7211):376-379.
[90]Koschny Th, Zhang L, and Soukoulis C M, et al. Isotropic three-dimensional left-handed metamaterials. Phys. Rev. B,2005,71(12):121103(4).
[91]Gay-Balmaz P, and Martin O J F. Efficient isotropic magnetic resonator. Appl. Phys. Lett.,2002,81(5):939-941.
[92]Baena J D, Jelinek L, and Marques R, et al. Electrically small isotropic three-dimensional magnetic resonators for metamaterials design. Appl. Phys. Lett., 2006,88(13):134108(3).
[93]Vier D C, Schultz S, and Greegor R B, et al. Three-dimensional double-negative metamaterials resonating at 13.5 GHz. IET Microw. Antennas Propag.2009,3(5): 723-727.
[94]Zhang Jingjing, Chen Hongsheng, and Ran Lixin, et al. Experimental characterization and cell interactions of a two-dimensional isotropic left-handed metamaterial. Appl. Phys. Lett.,2008,92(8):084108(3).
[95]Alu A, Salandrino A, and Engheta N. Negative effective permeability and left-handed materials at optical frequencies. Optics Express,2006,14(4): 1557-1567.
[96]Liu Hui, and Zhao Xiaopeng. Metamaterials with dendriticlike structure at infrared frequencies. Appl. Phys. Lett.,2007,90(19):191904(3).
[97]Pimenov. A, Loidl. A, and Gehrke. K, et al. Negative refraction observed in a metallic ferromagnet in the Gigahertz frequency range. Phys. Rev. Lett.,2007, 98(19):197401(4).
[98]Peng Liang, Ran Lixin, and Chen Hongsheng, et al. Experimental observation of left-handed behavior in an array of standard dielectric resonators. Phys. Rev. Lett., 2007,98(15):157403(4).
[99]Zhao Qian, Kang Lei, Du B, et al. Experimental demonstration of isotropic negative permeability in a three dimensional dielectric composite. Phys. Rev. Lett.,2008, 101(2):027402(4).
[100]Pendry J B, Schurig D, and Smith D R. Controlling electromagnetic field. Science, 2006,312(5781):1780-1782.
[101]Schurig D, Mock J J, and Justice B J, et al. Metamaterial electromagnetic cloak at microwave frequencies. Science,2006,314(5801):977-980.
[102]Valentine J, Li J, and Zentgraf T, et al. An optical cloak made of dielectrics. Nature Mater.,2009,8(7):568-571.
[103]Enoch S, Tayeb G, and Sabouroux P, et al. A metamaterial for directive emission. Phys. Rev. Lett.,2002,89(21):213902(4).
[104]Landy N I, Sajuyigbe S, and Mock J J, et al. Perfect metamaterial absorber. Phys. Rev. Lett.,2008,100(20):207402(4).
[105]Tao Hu, Landy N I, and Bingham C M, et al. A metamaterial absorber for the Terahertz regime:Design, fabrication and characterization. Optics Express,2008, 16(10):7181-7188.
[106]Tao Hu, Bingham C M, and Strikwerda A C, et al. High flexible wide angle of incidence terahertz metamaterial absorber:Design, fabrication and characterization. Phys. Rev. B,2008,78(24):241103(4).
[107]Yuan Yu, Ran Lixin, and Chen Hongsheng, et al. Backward coupling waveguide coupler using left-handed material. Appl. Phys. Lett.,2006,88(21):211903(3).
[108]Liu Kaiyu, Li Chao, and Li Fang. A new type of microstrip coupler with complementary split-ring resonator. PIERS Online.2007,3(5):603-606.
[109]Aydin K, Cakmak A O, and Sahin L, et al. Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture. Phys. Rev. Lett.,2009, 102(1):013904(4).
[110]Gil M, Bonache J, and Martin F. Metamaterial filter:A review. Metamaterial,2008, 2(4):186-197.
[111]Wu Hung-Wei, Weng Min-Hang, and Su Yan-Kuin, et al. Propagation characteristics of complementary split-ring resonator for wide band-gap enhancement in microstrip bandpass filter. Microwave Opt. Tech. Lett.,2007,49(2): 292-295.
[112]Li Chao, and Li Fang. Microstrip bandpass filter based on zeroth-order resonator with complementary split-ring resonators. IET Microw. Antenna Propag.2009,3(2): 276-280.
[113]Freire M J, Marques R, and Medina F, et al. Planar magnetoinductive wave transducer:Theory and applications. Appl. Phys. Lett.,2004,85(19):4439-4441.
[114]Beruete M, Falcone F, and Freire M J, et al. Electroinductive wave in chains of complementary metamaterial elements. Appl. Phys. Lett.,2006,88(8):083503(3).
[115]Liu H, Genov D A, Wu D, Liu Y, Steele J M, Sun C, Zhu S, and Zhang X. Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies. Phys. Rev. Lett.,2006,97(24):243902(4).
[116]Cui Tiejun, and Kong J A. Time-domain electromagnetic energy in a frequency-dispersive left-handed medium. Phys. Rev. B,2004,70(20):205106(7).
[117]Ruppin P. Electromagnetic energy density in a dispersive and absorptive material. Phys. Lett. A,2002,299(2):309-312.
[118]Markos P, and Soukoulis C M. Numerical studies of left-handed materials and arrays of split-ring resonators. Phys. Rev. E,2002,65(3):036622(8).
[119]Markos P, Rousochatzakis I, and Soukoulis C M. Transmission losses in left-handed materials. Phys. Rev. E,2002,66(4):045601(4).
[120]Smith D R, Schultz S, and Markos P, et al. Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Phys. Rev. B,2002,65(19):195104(5).
[121]Smith D R, Vier D C, Koschny Th, and Soukoulis C M. Electromagnetic parameter retrieval from inhomogeneous metamaterials. Phys. Rev. E,2005,71(3): 036617(11).
[122]Chen X, Grzegoczyk T M, Wu B-I, Pacheco J, and Kong J A. Robust method to retrieve the constitutive effective parameters of metamaterials. Phys. Rev. E,2004 70(1):016608(7).
[123]隋强.微波异向介质的实验研究及理论研究：[博士学位论文].北京：中国科学院电子研究所,2004.
[124]Kolinko P. and Smith D R. Numerical study of electromagnetic waves interacting with negative index materials. Opt. Express,2003,11(7):640-648。
[125]Dong Z, Zhu S, Liu H, Zhu J, and Cao W. Numerical simulations of negative-index refraction in wedge-shaped metamaterials. Phys. Rev. E,2005,72(1):016607(4)。
[126]Hou Ling Li, Chin Jessie Yao, and Cui Tie Jun et al. Advanced parameter retrievals for metamaterial slabs using an inhomogeneous model. J. Appl. Phys.,2008,103(6): 064904(6).
[127]Koschny Th, Markos P, Economou E N, et al. Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials. Phys. Rev. B,2005,71(24):245105(22).
[128]Li Zhaofeng, Aydin K, and Ozbay E. Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients. Phys. Rev. E,2009,79(2):026610(7).
[129]Chen Xudong, Wu B-I, and Kong J A, et al. Retrieval of the effective constitutive parameters of bianisotropic metamaterials. Phys. Rev. E,2005,71(4):046610(9).
[130]Aydin K, and Ozbay E. Experimental investigation of reflection characteristics of left-handed metamaterials in free space. IET Microw. Antennas Propag.2007,1(1): 89-93.
[131]Marques R, Martel J, and Mesa F, et al. Left-handed-media simulation and transmission of EM waves in the subwavelength split-ring-resonator-loaded metallic waveguides. Phys. Rev. Lett.,2002,89(18):183901(4).
[132]Chen Hongsheng, Zhang Jingjing, Bai Yang, et al. Experimental retrieval of the effective parameters of metamaterials based on waveguide methods. Optics Express, 2006,14(26):12944-12949.
[133]Ziolkowski R W. Design, Fabrication, and testing of double negative metamaterials. IEEE Trans. Antennas Propag.,2003,51(7):1516-1529.
[134]Zhang Fuli, Gregory Houzet, and Eric Lheurette, et al. Negative zero positive metamaterial with omega-type metal inclusions. J Appl. Phys.,2008,103(8): 084312(8).
[135]Wu W, Yu Z, and Zhang Xiang, et al. Midinfrared metamaterials fabricated by nanoimprint lithography. Appl. Phys. Lett.,2007,90(6):063107(3).
[136]Katsarakis N, Koschony T, and Kafesaki, et al. Electric coupling to the magnetic resonance of split ring resonators. Appl. Phys. Lett.,2004,84(15):2943-2945.
[137]Ozbay E, Guven K and Aydin K. Metamaterials with negative permeability and negative refractive index:experiments and simulations. J. Opt. A:Pure Appl. Opt., 2007,9(9) S301-S307.
[138]Zhou Jiangfeng, Koschny Th, and Soukoulis C M. An efficient way to reduce losses of left-handed metamaterials. Optics Express,2008,16(15):11147-11152.
[139]Gay-Balmaz P, and Martin O J F. Electromagnetic resonances in individual and coupled split-ring resonators. J Appl. Phys.,2002,92(5):2929-2936.
[140]Garcia-Garcia J. Bonache J, and Gil I, et al. Miniaturized microstrip and CPW filters using coupled metamaterial resonator. IEEE Trans Microw. Theory. Tech.,2006, 54(6):2628-2635.
[141]Liu Y, Fang N, and Wu D, et al. Symmetric and antisymmetric modes of electromagnetic resonators. Appl. Phys. A:Mater. Sci. Prog.,2007,87(2):171-174.
[142]Penciu R S, Aydin K, and Kafesaki M, et al. Multi-gap individual and coupled split-ring resonators structure. Opt. Express,2008,16(22):18131-18144.
[143]Schurig D, Pendry J B, and Smith D R. Calculation of material properties and ray tracing in transformation media. Optics Express,2006,14(21):9794-9804.
[144]Cummer S A, Popa B-I, and Schurig D, et al. Full-wave simulations of electromagnetic cloaking structures. Phys. Rev. E,2006,74(3):036621(5).
[145]Chen Hongsheng, Wu B-I, Zhang Baile, and Kong Jin Au. Electromagnetic wave interactions with a metamaterial cloak. Phys. Rev. Lett.,2007,99(6):063903(4).
[146]Huang Ying, Feng Yijun, and Jiang Tian. Electromagnetic cloaking by layered structure of homogeneous isotropic materials. Optics Express,2007,15(18): 11133-11141.
[147]Cai Wenshan, Chettiar U K, and Kildishev A V, et al. Nonmagnetic cloak with minimized scattering. Appl. Phys. Lett.,2007,91(11):111105(3).
[148]Ruan Zhichao, Yan Min, and Neff C W, et al. Ideal cylindrical cloak:Perfect but sensitive to tiny perturbations. Phys. Rev. Lett.,2007,99(11):113903(4).
[149]Yan Min, Ruan Zhichao, and Qiu Min. Cylindrical invisibility cloak with simplified material parameters is inherently visible. Phys. Rev. Lett.,2007,99(23):233901(4).
[150]Zhang Jingjing, Huangfu Jiangtao, and Luo Yu, et al. Cloak for multilayered and gradually changing media. Phys. Rev. B,2008,77(3):035116(5).
[151]Cummer S A, Liu Ruopeng, and Cui Tie Jun. A rigorous and nonsingular two dimensional cloaking coordination transformation. J. Appl. Phys.2009,105(5): 056102(3).
[152]Jiang Weixiang, Cui Tiejun, and Yang Xinmi, et al. Invisible cloak without singularity. Appl. Phys. Lett.,2008,93(19):194102(3).
[153]Zhang Pu, Jin Yi, and He Sailing. Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak. Appl. Phys. Lett.,2008, 93(24):243502(3).
[154]Ma Hua, Qu Shaobo, and Xu Zhou, et al. Material parameter equation for elliptical cylindrical cloaks. Phys. Rev. A,2008,77(1):013825(4).
[155]Jiang W X, Cui T J, and Yu G X, et al. Arbitrary elliptical-cylindrical invisible cloaking. J. Phys. D:Appl. Phys.,2008,41(8):085504(5).
[156]Cojocaru E. Exact analytical approaches for elliptic cylindrical invisibility cloaks. J. Opt. Soc. Am. B,2009,26(5):1119-1128.
[157]Rahm M, Schurig D, and Roberts D A, et al. Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations. Photonics Nanostruct. Fundam. Appl.2008,6(1):87-95.
[158]Wu Qun, Zhang Kuang, and Meng Fanyi, et al. Material parameters characterization for arbitrary N-shaped regular polygonal invisible cloak. J. Phys. D:Appl. Phys., 2009,42(3):035408(7).
[159]Zhang Jingjing, Luo Yu, and Chen Hongsheng, et al. Cloaking for arbitrary shape. J. Opt. Soc. B,2008,25(11):1776-1779.
[160]Jiang Weixiang, Chin J Y, and Li Zhou, et al. Analytical design of conformally invisible cloaks for arbitrarily shaped objects. Phys. Rev. E,2008,77(6):066607(6).
[161]Ma Hua, Qu Shaobo, and Xu Zhou, et al. Approximation approach of designing practical cloaks with arbitrary shapes. Optics Express,2008,16(20):15449-15454.
[162]Li Chao, and Li Fang. Two-dimensional electromagnetic cloaks with arbitrary geometries. Optics Express,2008,16(17):13414-13420.
[163]Li Jensen, and Pendry J B. Hiding under the carpet:A new strategy for cloaking. Phys. Rev. Lett.,2008,101(20):203901(4).
[164]Vasquez F G, Milton G W, and Onofrei D. Active exterior cloaking for the 2D Laplace and Helmholtz equations. Phys. Rev. Lett.,2009,103(7):073901(4).
[165]Hu Jin, Zhou Xiaoming, and Hu Gengkai. Design method for electromagnetic cloak with arbitrary shapes based on Laplace's equations. Optics Express,2009,17(3): 1308-1320.
[166]Cai Wenshan, Chettiar U K, and Kildishev A V, et al. Optical cloaking with metamaterials. Nature Photonics,2007,1(4):224-227.
[167]Chen Huanyang, Luo Xudong, and Ma Hongru, et al. The anti-cloak. Optics Express, 2008,16(19):14603-14608.
[168]Liu R, Ji C, and Mock J J, et al. Broadband ground-plane cloak. Science,2009, 323(5912):366-369.
[169]Chen Huanyang, and Chan C T. Transformation media that rotate electromagnetic fields. Appl. Phys. Lett.,2007,90(24):241105(3).
[170]陈焕阳.各向异性材料中的波：隐身衣,旋转衣和声子晶体：[博士学位论文].上海：上海交通大学.2008.
[171]Chen Huanyang, Hou Bo, and Chen Shuyu, et al. Design and Experimental realization of a broadband transformation media field rotator at microwave frequencies. Phys. Rev. Lett.,2009,102(18):183903(4).
[172]Luo Yu, Chen Hongsheng, and Zhang Jingjing, et al. Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations. Phys. Rev. B,2008,77(12): 125127(8).
[173]Jiang Weixiang, Cui Tiejun, and Cheng Qiang, et al. Design of arbitrary shaped concentrators based on conformal optical transformation of uniform rational B-spline surface. Appl. Phys. Lett.,2008,92(26):264101(3).
[174]Narimanov E E, and Kildishev A V. Optical black hole:Broadband omnidirectional light absorber. Appl. Phys. Lett.,2009,95(4):041106(3).
[175]Cheng Qiang, and Cui Tiejun. An electromagnetic black hole made of metamaterials. arXiv:0910.2159v1,2009.
[176]Tsang M, and Psaltis D. Magnifying perfect lens and superlens design by coordinate transformation. Phys. Rev. B,2008,77(3):035122(9).
[177]Kong Fanmin, Wu B-I, and Kong Jin Au, et al. Planar focusing antenna design by using coordinate transformation technology. Appl. Phys. Lett.,2007,91(25): 253509(3).
[178]Roberts D A, Rahm M, and Pendry J B, et al. Transformation-optical design of sharp waveguide bends and corners. Appl. Phys. Lett.,2008,93(25):251111(3).
[179]Rahm M, Roberts D A, and Pendry J B, et al. Transformation-optical design of adaptive beam bends and beam expenders. Optics Express,2008,16(15): 11555-11567.
[180]Jiang W X, Cui T J, and Zhou X Y, et al. Arbitrary bending of electromagnetic waves using realizable inhomogenoues and anisotropic materials. Phys. Rev. E, 2008,78(6):066607(4).
[181]Mei Z L, and Cui T J. Arbitrary bending of electromagnetic wave using isotropic materials. J. Appl. Phys.,2009,105(10):104913(5).
[182]Huangfu Jiangtao, Xi Sheng, and Kong Fanmin et al. Application of coordinate transformation in bent waveguides. J. Appl. Phys.,2008,104(1):014502(4).
[183]Wang M Y, Zhang J J, and Chen H S, et al. Designing and application of a beam shifter by transformation media. PIER,2008,83,147-155.
[184]Chen Huanyang, and Chan C T. Electromagnetic wave manipulation by layered systems using the transformation media concepts. Phys. Rev. B,2008,78(5): 054204(9).
[185]Rahm M, Cummer S A, and Schurig D, et al. Optical design of reflectionless complex media by finite embedded coordinate transformations. Phys. Rev. Lett., 2008,100(6):063903(4).
[186]Jiang Weixiang, Cui Tie Jun, and Ma Huifeng, et al. Cylindrical-to-plane-wave conversion via embedded optical transformation. Appl. Phys. Lett.,2008,92(26): 261903(3).
[187]Zhang Jingjing, Luo Yu, and Xi Sheng, et al. Directive emission obtained by coordination transformation. PIER,2008,81,437-446.
[188]Yan Min, Ruan Zhichao, and Qiu Min. Scattering characteristics of simplified cylindrical invisibility cloaks. Opt. Express,2007,15(26):17772-17782.
[189]Zhang Jingjing, Luo Yu, and Chen Hongsheng et al. Sensitivity of transformation cloak in engineering. PIER,2008,84,93-104.
[190]Nicolet A, Zolla F, and Guenneau S. Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section. Opt. Lett.,2008,33(14):1584-1586.