含特异材料平面结构中的Casimir效应研究
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摘要
Casimir效应是由边界的存在引起的真空零点能变化产生的宏观量子现象。随着近年来纳米技术的发展,这种由量子真空起伏效应而产生的力对系统的影响愈发明显,而其重要的潜在实际应用如致动器也引起广泛兴趣。最近,一些具有奇异电磁特性的特异材料,包括左手性材料以及单负材料近来被实验构造合成。特异材料的介电常数、磁导率在某些频段上同时为负或其中一个为负,但仍满足Maxwell方程,进而引发了人们对这些新型材料的关注,更多可能的特殊应用也被提出。实际的特异材料都是色散的,其色散关系中的特征频率参量取值影响着材料的电磁性质以及反射特性,所以特异材料的Casimir作用力强弱和方向也将受到影响。本论文对于包含特异材料的真空中平面结构,研究了其Casimir效应的强弱调制以及吸引作用与排斥作用的产生与转化,具体的研究工作如下:
将介质材料板间Casimir作用力的计算拓展到涉及特异材料的情况。通过考察分析复频率空间内的含特异材料的介质平面板间Casimir力被积函数的解析性质,根据实际的介质平板间Casimir作用力的计算理论,推导得到包含特异材料的平面板间Casimir作用力的计算公式。
研究了左手性材料介质板间的Casimir吸引效应。因果律要求左手性材料必须是色散的,即材料在一段频带上具有负的折射率。对于左手性材料中由Drude-Lorentz型色散关系描述的介电常数和磁导率,色散曲线中负值频带的曲线结构由等离子体频率、共振频率和阻尼系数等各色散吸收参数所决定,其负值频带宽度和深度等性质对应着介质材料板的反射特性,进而对两板间的Casimir效应强弱起着重要的作用。在以不同因素影响反射特性的角度来解释Casimir效应强弱的同时,可以将左手性材料介质的折射率色散曲线的负值区域结构特点与Casimir效应联系起来,即折射率负值区域的宽度与深度越大所对应的是Casimir效应越强。而当材料的介电常数色散的负值区域与磁导率色散的负值区域逐渐错开时,不易仅仅单纯把负折射率频带区域的结构与介质板间Casimir效应相联系,而要考虑到左手性材料到单负材料的转变和禁带的影响。对左手性材料的板间Casimir效应与正常材料板间Casimir效应做出了比较研究。相对于正常材料的板间Casimir效应,具有足够宽的负折射频带的左手性材料其板间Casimir效应会更强。
在涉及特异材料的情况下,研究了Casimir排斥效应的产生。随着实验技术的发展,Casimir吸引作用对微机械系统器件及设备产生限制,因而对Casimir排斥效应的研究愈发引起人们的注意。排斥的Casimir作用力只可能出现在两不同平板的情况中,而通过考察正常材料与特异材料介质的不同组合情况,我们发现板间媒质阻抗的值介于两板的阻抗之间且两板阻抗比与板间媒质的差异越大,Casimir排斥力越容易产生。进而可调节特异材料的色散参数以得到排斥的Casimir作用力。
对Casimir作用力的方向随板间距的变化进行了研究,而且着重考察了一种排斥力与吸引力的转化情况即Casimir平衡回复力的产生。在讨论含特异材料的板间Casimir效应的长距和短距近似之后,我们研究了由特异材料板组成的平板结构中,在两板间距改变时Casimir力方向的变化。一般来讲,在短距下Casimir力为吸引力,随着板间距逐渐增大,Casimir吸引力可以在达到某一板间距时变成排斥力。而若将其中一个材料板取为理想导体板,Casimir效应则可表现为随板间距的增大从排斥力转变为吸引力即平衡回复力,这种力可用来产生板间振荡或稳定真空中的力学系统。
Casimir effect is a macroscopic quantum effect that results from the change of zero-point energy due to the existence of the boundaries. In recent years, with the development of micro- and nanoelectromechanical systems and nanotechnology, Casimir forces that raise from quantum vacuum fluctuation have more influences on the system, and significant potential applications of the Casimir force, such as the actuator, have drawn extensive attention. Recently some composite materials namely metamaterials with special electromagnetic properties, including left-handed materials and single-negative materials, have been fabricated experimentally. The metamaterials have simultaneously negative permittivity and permeability , or negative permeability (permittivity) but positive permittivity (permeability) over a band of frequencies, and they still satisfy the Maxwell equations. Therefore these new types of materials attract a great deal of attention, and more possible applications have been proposed. Real metamaterials must exhibit frequency dispersion, and the values of material characteristic frequencies influence the material reflection property, and it is expected that the magnitude and the directions of Casimir force will be accordingly influenced. In this dissertation, we study the Casimir effect for the planar structures containing metamaterials, including the adjusting of the magnitude of the Casimir forces, the formation of attraction and repulsion and the transformation between them. The main work is summarized in detail as follows.
The extension of the calculation for the Casimir force between the parallel slabs to the metamaterial system is discussed. We have considered the analytic property of the integrand in the complex plane for the calculation of the Casimir force when the metamaterials are concerned, and based on the theory of the Casimir effect for real media situation, we obtained the formula of the Casimir force for the planar structures containing metamaterials.
We discussed the attraction effect between the left-handed material slabs which have simultaneously negative permittivity and permeability and thereby the refractive index is negative. The medium with negative refractive index in which the solutions to the wave equation satisfy causality must exhibit frequency dispersion, that is, the medium has negative refractive index within a frequency band. For the left-handed materials characterized by dispersive permittivity and permeability of the Drude-Lorentz type, the structure of dispersion curve over the negative refraction frequency band is determined by the plasma frequency, the resonant frequency and the damping frequency. The different widths and depths of the negative refraction frequency band correspond to different medium reflection properties, and thus influences the magnitude of Casimir effect between the slabs. We analyzed the strength of the Casimir effect from the point of view of the dependence of material reflection on different factors, and obtained the relationship between the structure characters of the dispersion curve over the negative refraction band and the Casimir effect. Generally, the greater width and depth of the negative refraction region may correspond to the larger forces. In addition, it is no longer easy to relate the structure characters of dispersion curve over the negative refraction frequency band to the Casimir effect when the frequency regions of negative permittivity and negative permeability of left-handed materials are not the same, since left-handed materials turns into single-negative material, and more stop band replacing the propagation band makes the case quite complicated. A comparison is shown between the Casimir forces for left-handed material and for ordinary dielectric slabs, which have the opposite values of refractive indices for the chosen frequency. The force between two left-handed material slabs having sufficiently wide negative refraction frequency band is generally stronger than the force between two ordinary dielectric slabs.
The formation of the repulsive Casimir effect between two parallel slabs has been studied when the metamaterials are concerned. With the development of the experimental techniques, the attractive Casimir forces could lead to restriction in micro- and nanoelectromechanical systems, and therefore, the repulsive forces may avoid that limits and are of possible practical significance. The repulsion is to be expected when the two parallel slabs have different electromagnetic properties. By studying different cases containing ordinary materials and metamaterials, we found that the repulsive behavior may possibly appear when the wave impedances, which are used to demonstrate the difference of electric and magnetic properties between two slabs, are smaller and larger than the impedance of vacuum, respectively, and moreover, the greater the difference between two wave impedances, the more easily the repulsive force is obtained. Therefore, one can adjust the values of the characteristic frequencies of the metamaterials to obtain the repulsive Casimir forces.
The dependence of directions of the Casimir forces on the distance between the slabs has been investigated, and special emphasis is put on a case of the transformation between the attraction and the repulsion, i.e., the restoring Casimir force. We discussed the asymptotic long- and short-distance laws of Casimir forces, and then studied the sign change of the forces between metamaterial slabs with the changing slab separation. In general, the Casimir force is always attractive at short distances, and as the slabs get further away from each other, the attractive force may become repulsive at certain distance. The restoring Casimir force, which is the force that changes from repulsion to attraction with the increasing slab separation, may be found to exist between perfectly conducting material and metamaterial slabs. This restoring force is a natural power for the system oscillation in vacuum and also can be used for system stabilization.
将介质材料板间Casimir作用力的计算拓展到涉及特异材料的情况。通过考察分析复频率空间内的含特异材料的介质平面板间Casimir力被积函数的解析性质,根据实际的介质平板间Casimir作用力的计算理论,推导得到包含特异材料的平面板间Casimir作用力的计算公式。
研究了左手性材料介质板间的Casimir吸引效应。因果律要求左手性材料必须是色散的,即材料在一段频带上具有负的折射率。对于左手性材料中由Drude-Lorentz型色散关系描述的介电常数和磁导率,色散曲线中负值频带的曲线结构由等离子体频率、共振频率和阻尼系数等各色散吸收参数所决定,其负值频带宽度和深度等性质对应着介质材料板的反射特性,进而对两板间的Casimir效应强弱起着重要的作用。在以不同因素影响反射特性的角度来解释Casimir效应强弱的同时,可以将左手性材料介质的折射率色散曲线的负值区域结构特点与Casimir效应联系起来,即折射率负值区域的宽度与深度越大所对应的是Casimir效应越强。而当材料的介电常数色散的负值区域与磁导率色散的负值区域逐渐错开时,不易仅仅单纯把负折射率频带区域的结构与介质板间Casimir效应相联系,而要考虑到左手性材料到单负材料的转变和禁带的影响。对左手性材料的板间Casimir效应与正常材料板间Casimir效应做出了比较研究。相对于正常材料的板间Casimir效应,具有足够宽的负折射频带的左手性材料其板间Casimir效应会更强。
在涉及特异材料的情况下,研究了Casimir排斥效应的产生。随着实验技术的发展,Casimir吸引作用对微机械系统器件及设备产生限制,因而对Casimir排斥效应的研究愈发引起人们的注意。排斥的Casimir作用力只可能出现在两不同平板的情况中,而通过考察正常材料与特异材料介质的不同组合情况,我们发现板间媒质阻抗的值介于两板的阻抗之间且两板阻抗比与板间媒质的差异越大,Casimir排斥力越容易产生。进而可调节特异材料的色散参数以得到排斥的Casimir作用力。
对Casimir作用力的方向随板间距的变化进行了研究,而且着重考察了一种排斥力与吸引力的转化情况即Casimir平衡回复力的产生。在讨论含特异材料的板间Casimir效应的长距和短距近似之后,我们研究了由特异材料板组成的平板结构中,在两板间距改变时Casimir力方向的变化。一般来讲,在短距下Casimir力为吸引力,随着板间距逐渐增大,Casimir吸引力可以在达到某一板间距时变成排斥力。而若将其中一个材料板取为理想导体板,Casimir效应则可表现为随板间距的增大从排斥力转变为吸引力即平衡回复力,这种力可用来产生板间振荡或稳定真空中的力学系统。
Casimir effect is a macroscopic quantum effect that results from the change of zero-point energy due to the existence of the boundaries. In recent years, with the development of micro- and nanoelectromechanical systems and nanotechnology, Casimir forces that raise from quantum vacuum fluctuation have more influences on the system, and significant potential applications of the Casimir force, such as the actuator, have drawn extensive attention. Recently some composite materials namely metamaterials with special electromagnetic properties, including left-handed materials and single-negative materials, have been fabricated experimentally. The metamaterials have simultaneously negative permittivity and permeability , or negative permeability (permittivity) but positive permittivity (permeability) over a band of frequencies, and they still satisfy the Maxwell equations. Therefore these new types of materials attract a great deal of attention, and more possible applications have been proposed. Real metamaterials must exhibit frequency dispersion, and the values of material characteristic frequencies influence the material reflection property, and it is expected that the magnitude and the directions of Casimir force will be accordingly influenced. In this dissertation, we study the Casimir effect for the planar structures containing metamaterials, including the adjusting of the magnitude of the Casimir forces, the formation of attraction and repulsion and the transformation between them. The main work is summarized in detail as follows.
The extension of the calculation for the Casimir force between the parallel slabs to the metamaterial system is discussed. We have considered the analytic property of the integrand in the complex plane for the calculation of the Casimir force when the metamaterials are concerned, and based on the theory of the Casimir effect for real media situation, we obtained the formula of the Casimir force for the planar structures containing metamaterials.
We discussed the attraction effect between the left-handed material slabs which have simultaneously negative permittivity and permeability and thereby the refractive index is negative. The medium with negative refractive index in which the solutions to the wave equation satisfy causality must exhibit frequency dispersion, that is, the medium has negative refractive index within a frequency band. For the left-handed materials characterized by dispersive permittivity and permeability of the Drude-Lorentz type, the structure of dispersion curve over the negative refraction frequency band is determined by the plasma frequency, the resonant frequency and the damping frequency. The different widths and depths of the negative refraction frequency band correspond to different medium reflection properties, and thus influences the magnitude of Casimir effect between the slabs. We analyzed the strength of the Casimir effect from the point of view of the dependence of material reflection on different factors, and obtained the relationship between the structure characters of the dispersion curve over the negative refraction band and the Casimir effect. Generally, the greater width and depth of the negative refraction region may correspond to the larger forces. In addition, it is no longer easy to relate the structure characters of dispersion curve over the negative refraction frequency band to the Casimir effect when the frequency regions of negative permittivity and negative permeability of left-handed materials are not the same, since left-handed materials turns into single-negative material, and more stop band replacing the propagation band makes the case quite complicated. A comparison is shown between the Casimir forces for left-handed material and for ordinary dielectric slabs, which have the opposite values of refractive indices for the chosen frequency. The force between two left-handed material slabs having sufficiently wide negative refraction frequency band is generally stronger than the force between two ordinary dielectric slabs.
The formation of the repulsive Casimir effect between two parallel slabs has been studied when the metamaterials are concerned. With the development of the experimental techniques, the attractive Casimir forces could lead to restriction in micro- and nanoelectromechanical systems, and therefore, the repulsive forces may avoid that limits and are of possible practical significance. The repulsion is to be expected when the two parallel slabs have different electromagnetic properties. By studying different cases containing ordinary materials and metamaterials, we found that the repulsive behavior may possibly appear when the wave impedances, which are used to demonstrate the difference of electric and magnetic properties between two slabs, are smaller and larger than the impedance of vacuum, respectively, and moreover, the greater the difference between two wave impedances, the more easily the repulsive force is obtained. Therefore, one can adjust the values of the characteristic frequencies of the metamaterials to obtain the repulsive Casimir forces.
The dependence of directions of the Casimir forces on the distance between the slabs has been investigated, and special emphasis is put on a case of the transformation between the attraction and the repulsion, i.e., the restoring Casimir force. We discussed the asymptotic long- and short-distance laws of Casimir forces, and then studied the sign change of the forces between metamaterial slabs with the changing slab separation. In general, the Casimir force is always attractive at short distances, and as the slabs get further away from each other, the attractive force may become repulsive at certain distance. The restoring Casimir force, which is the force that changes from repulsion to attraction with the increasing slab separation, may be found to exist between perfectly conducting material and metamaterial slabs. This restoring force is a natural power for the system oscillation in vacuum and also can be used for system stabilization.
引文
1 H. B. G. Casimir. The Energy between Two Large Uncharged Conducting Plates. Proc. K. Ned. Akad. Wet. 1948:793-797
2 E. M. Lifshitz. The Theory of Molecular Attractive Forces between Solids. Sov.Phys. JETP. 1956, 2:73-83
3 M. J. Sparnaay. Measurements of Attractive Forces between Flat Plates. Physica. 1958,24:751-764
4 S. K. Lamoreaux. Demonstration of the Casimir Force in the 0.6 to 6 μm Range.Phys. Rev. Lett. 1997, 78:5-8
5 U. Mohideen, A. Roy. Precision Measurement of the Casimir Force from 0.1 to 0.9μm. Phys. Rev. Lett. 1998, 81:4549-4552
6 A. Roy, U. Mohideen. Demonstration of the Nontrivial Boundary Dependence of the Casimir Force. Phys. Rev. Lett. 1999, 82:4380-4383
7 A. Roy, C. -Y. Lin, U. Mohideen. Improved Precision Measurement of the Casimir Force. Phys. Rev. D. 1999, 60:111101
8 B. W. Harris, F. Chen, U. Mohideen. Precision Measurement of the Casimir Force Using Gold Surfaces. Phys. Rev. A. 2000, 62:052109
9 M. Bostrom, Bo E. Sernelius. Thermal Effects on the Casimir Force in the 0.1- 5 μm Range. Phys. Rev. Lett. 2000, 84:4757-4760
10 H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, F. Capasso. Nonlinear Micromechanical Casimir Oscillator. Phys. Rev. Lett. 2001, 87:211801
11 R. S. Decca, D. Lopez, E. Fischbach, D. E. Krause. Measurement of the Casimir Force between Dissimilar Metals. Phys. Rev. Lett. 2003, 91:050402
12 G. Bressi, G. Carugno, R. Onofrio, G. Ruoso. Measurement of the Casimir Force between Parallel Metallic Surfaces. Phys. Rev. Lett. 2002, 88:041804
13 M. Bordag, U. Mohideen, V. M. Mostepanenko. New Developments in the Casimir Effect. Phys. Rep. 2001, 353:1-205
14 G. Plunien, B. Muller, W. Greiner. The Casimir Effect. Phys. Rep. 1986,134:87-193
15 V. M. Mostepanenko, N. N. Trunov. The Casimir Effect and Its Applications.Clarendon Press, Oxford. 1997:100-191
16 M. Bordag, B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko. Constraints for Hypothetical Interactions from a Recent Demonstration of the Casimir Force and some Possible Improvements. Phys. Rev. D. 1998, 58:075003
17 M. Bordag, B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko. Stronger Constraints for Nanometer Scale Yukawa-type Hypothetical Interactions from the New Measurement of the Casimir Force. Phys. Rev. D. 1999, 60:055004
18 M. Bordag, B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko. New Constraints for Non-newtonian Gravity in the Nanometer Range from the Improved Precision Measurement of the Casimir Force. Phys. Rev. D. 2000, 62:011701
19 M. Kardar, R. Golestanian. The "Friction" of Vacuum, and Other Fluctuation- induced Forces. Rev. Mod. Phys. 1999, 71:1233-1245
20 S. K. Lamoreaux. Resource Letter Cf-1: Casimir Force. Am. J. Phys. 1999,67:850-861
21 R. M. Cavalcanti. Casimir Force on a Piston. Phys. Rev. D. 2004, 69:065015
22 O. Kenneth, I. Klich. Opposites Attract: A Theorem about the Casimir Force.Phys. Rev. Lett. 2006, 97:160401
23 J. Wang, X. Zhang, S. -Y. Pei, and D. -H. Liu. Tunable Casimir Forces by Means of the External Magnetic Field. Phys. Rev. A. 2006, 73:042103
24 D. Kupiszewska, J. Mostowski. Casimir Effect for Dielectric Plates. Phys. Rev.A. 1990,41:4636-4644
25 M. S. Tomas. Casimir Force in Absorbing Multilayers. Phys. Rev. A. 2002,66:052103
26 C. Raabe, L. Knoll, D. -G. Welsch. Three-dimensional Casimir Force between Absorbing Multiplayer Dielectrics. Phys. Rev. A. 2003, 68:033810
27 M. Bordag, G. L. Klimchitskaya, V. M. Mostepanenko. The Casimir Force between Plates with Small Deviation from Plane Parallel Geometry. Int. J. Mod.Phys. A. 1995, 10(8):2661-2682
28 I. Brevik, V. N. Marachevsky, K. A. Milton. Identity of the Van Der Waals Force and the Casimir Effect and the Irrelevance of These Phenomena to Sono-luminescence. Phys. Rev. Lett. 1999, 82:3948-3951
29 T. H. Boyer. Quantum Electromagnetic Zero-point Energy of a Conducting Spherical Shell and the Casimir Model for a Charged Particle. Phys. Rev. 1968,174:1764-1776
30 M. Bordag, E. Elizalde, K. Kirsten, S. Leseduarte. Casimir Energies for Massive Scalar Fields in a Spherical Geometry. Phys. Rev. D. 1997, 56:4896-4904
31 R. L. Jaffe, A. Scardicchio. Casimir Effect and Geometric Optics. Phys. Rev.Lett. 2004, 92:070402
32 M. P. Hertzberg, R. L. Jaffe, M. Kardar, A. Scardicchio. Attractive Casimir Forces in a Closed Geometry. Phys. Rev. Lett. 2005, 95:250402
33 R. Golestanian. Lifshitz Interaction between Dielectric Bodies of Arbitrary Geometry. Phys. Rev. Lett. 2005, 95:230601
34 M. S. Tomas. Casimir Force between Dispersive Magnetodielectrics. Phys.Lett. A. 2005,342:381-388
35 G. L. Klimchitskaya, U. Mohideen, V. M. Mostepanenko. Casimir and Van Der Waals Forces between Two Plates Or a Sphere (lens) Above a Plate Made of Real Metals. Phys. Rev. A. 2000, 61:062107
36 M. Bordag, B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko. Casimir Force at Both Nonzero Temperature and Finite Conductivity. Phys. Rev. Lett. 2000,85:503-506
37 G. L. Klimchitskaya, A. Roy, U. Mohideen, V. M. Mostepanenko. Complete Roughness and Conductivity Corrections for Casimir Force Measurement.Phys. Rev. A. 1999, 60:3487-3495
38 A. Lambrecht,S. Reynaud. Casimir Force between Metallic Mirrors. Eur. Phys.J. D. 2000,8:309-318
39 V. B. Bezerra, G. L. Klimchitskaya, V. M. Mostepanenko. Higher-order Conductivity Corrections to the Casimir Force. Phys. Rev. A. 2000, 62:014102
40 C. Genet, A. Lambrecht, S. Reynaud. Temperature Dependence of the Casimir Effect between Metallic Mirrors. Phys. Rev. A. 2000, 62:012110
41 S. Y. Buhmann, L. Knoll, D. -G. Welsch. Casimir-polder Forces: A Nonpertur-bative Approach. Phys. Rev. A. 2004, 70:052117
42 R. Messina, R. Passante. Fluctuations of the Casimir-polder Force between an Atom and a Conducting Wall. Phys. Rev. A. 2007, 76:032107
43 M. S. Tomas. Medium Effects on the Van Der Waals Force. Phys. Rev. A. 2007,75:012109
44 M. Schaden, L. Spruch. Infinity-free Semiclassical Evaluation of Casimir Effects. Phys. Rev. A. 1998, 58:935-953
45 Y. Imry. Casimir Zero-point Radiation Pressure. Phys. Rev. Lett. 2005,95:080404
46 V. Hushwater. Repulsive Casimir Force as a Result of Vacuum Radiation Pressure. Am. J. Phys. 1997, 65(5):381-384
47 O. Kenneth, I. Klich, A. Mann, M. Revzen. Repulsive Casimir Forces. Phys.Rev. Lett. 2002, 89:033001
48 E. Buks, M. L. Rouke. Casimir Force Changes Sign. Nature. 2002, 419:119-120
49 U. Leonhardt, T. G. Philbin. Quantum Levitation by Left-handed Metamateri-als. New. J. Phys. 2007, 9:254
50 D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz. Composite Medium with Simultaneously Negative Permeability and Permittivity. Phys.Rev. Lett. 2000, 84:4184-4187
51 C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian. Experimental Verification and Simulation of Negative Index of Refraction Using Snell's Law. Phys. Rev. Lett. 2003, 90:107401
52 D. R. Smith, S. Schultz. Determination of Effective Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients. Phys. Rev.B. 2002,65:195104
53 V. M. Shalaev, W. Cai, U. K. Chettiar, H. -K. Yuan, A. K. Sarychev, V. P.Drachev, A. V. Kildishev. Negative Index of Refraction in Optical Metamaterials. Opt. Lett. 2005, 30(24):3356-3358
54 G. Dolling, M. Wegener, C. M. Soukoulis, S. Linden. Negative-index Metama-terial at 780 Nm Wavelength. Opt. Lett. 2007, 32(1):53-55
55 G. Dolling, M. Wegener, S. Linden. Realization of a Three-functional-layer Negative-index Photonic Metamaterial. Opt. Lett. 2007, 32(5):551-553
56 S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, S. R. J. Brueck.Experimental Demonstration of Near-infrared Negative-index Metamaterials.Phys. Rev. Lett. 2005, 95:137404
57 G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, S. Linden. Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial. Science. 2006,312:892-894
58 J. Zhou, E. N. Economon, T. Koschny, C. M. Soukoulis. Unifying Approach to Left-handed Material Design. Opt. Lett. 2006, 31(24):3620-3622
59 C. M. Soukoulis, M. Kafesaki, E. N. Economou. Negative Index Materials: New Frontiers in Optics. Adv. Mater. 2006, 18:1941-1952
60 N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu,M. Kafesaki, E. N. Economou, Th. Koschny, C. M. Soukoulis. Magnetic Response of Split-ring Resonators in the Far-infrared Frequency Regime. Opt.Lett. 2005, 30(11): 1348-1350
61 S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, S. R. J. Brueck.Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability. Phys. Rev. Lett. 2005, 94:037402
62 C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F.Zhou, Th. Koschny, C. M. Soukoulis. Magnetic Metamaterials at Telecommunication and Visible Frequencies. Phys. Rev. Lett. 2005, 95:203901
63 G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, S. Linden.Cut-wire Pairs and Plate Pairs as Magnetic Atoms for Optical Metamaterials.Opt. Lett. 2005, 30(23):3198-3200
64 G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, S. Linden. Low-loss Negative-index Metamaterial at Telecommunication Wavelengths. Opt. Lett 2006, 31(12):1800-1802
65 A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y.Khrushchev, J. Petrovic. Nanofabricated Media with Negative Permeability at Visible Frequencies. Nature. 2005, 438:355-338
66 A. N. Grigorenko. Negative Refractive Index in Artificial Metamaterials. Opt.Lett. 2006, 31(16):2483-2485
67 A. V. Kildishev, V. P. Drachev, U. K. Chettiar, D. Werner, D. -H. Kwon, V. M.Shalaev. Comment on "Negative Refractive Index in Artificial Metamaterials" . http://arxiv.org/abs/physics/0609234. 2006
68 V. G. Veselago. The Electrodynamics of Substances with Simultaneously Negative Values of ∈ and μ. Sov. Phys. Usp. 1968, 10:509-514
69 J. B. Pendry. Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett. 2000,85:3966-3969
70 J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs. Extremely Low Frequency Plasmons in Metallic Me so structures. Phys. Rev. Lett. 1996,76:4773-4776
71 J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart. Low Frequency Plasmons in Thin-wire Structures. J. Phys. Condens. Matter. 1998, 10:4785-4808
72 J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart. Magnetism from Conductors and Enhanced Nonlinear Phenomena. IEEE Trans. Microwave Theory Tech. 1999, 47:2075-2084
73 D. R. Smith, N. Kroll. Negative Refractive Index in Left-handed Matierials.Phys. Rev. Lett. 2000, 85:2933-2936
74 Y. Srivastava, A. Widom, M. H. Friedman. Microchips as Precision Quantum-electrodynamic Probes. Phys. Rev. Lett. 1985, 55:2246-2248
75 R. Castillo-Garza, C.-C. Chang, D. Jimenez, G. L. Klimchitskaya, V. M.Mostepanenko, U. Mohideen. Experimental Approaches to the Difference in the Casimir Force Due to Modifications in the Optical Properties of the Boundary Surface. Phys. Rev. A. 2007, 75:062114
76 T. Emig, A. Hanke, R. Golestanian, M. Kardar. Normal and Lateral Casimir Forces between Deformed Plates. Phys. Rev. A. 2003, 67:022114
77 E. Buks, M. L. Roukes. Stiction, Adhesion Energy, and the Casimir Effect in Micromechanical Systems. Phys. Rev. B. 2001, 63:033402
78 F. Serry, D. Walliser, G. J. Maclay. The Role of the Casimir Effect in the Static Deflection and Stiction of Membrane Strips in Microelectromechanical Systems (mems). J. Appl. Phys. 1998, 84:2501-2506
79 H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, F. Capasso. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force. Science. 2001,291:1941-1944
80 P. W. Milonni. Casimir Forces without the Vacuum Radiation Field. Phys. Rev.A. 1982,25:1315-1327
81 P. W. Milonni, R. J. Cook, M. E. Goggin. Radiation Pressure from the Vacuum:Physical Interpretation of the Casimir Force. Phys. Rev. A. 1988, 38:1621-1623
82 T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff. Extraordinary Optical Transmission Through Sub-wavelength Hole Arrays. Nature. 1998,391:667-669
83 W. L. Barnes, A. Dereux, T. W. Ebbesen. Surface Plasmon Subwavelength Optics. Nature. 2003, 424:824-830
84 J. B. Pendry, L. Martin-Moreno, F. J. Garcia-Vidal. Mimicking Surface Plas-mons with Structured Surfaces. Science. 2004, 305:847-848
85 T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis. Effective Medium Theory of Left-handed Materials. Phys. Rev. Lett. 2004, 93:107402
86 R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz. Microwave Transmission Through a Two-dimensional, Isotropic, Left-handed Metamate-rial. Appl. Phys. Lett. 2001, 78:489-491
87 R. A. Shelby, D. R. Smith, S. Schultz. Experimental Verification of a Negative Index of Refraction. Science. 2001,292:77-79
88 P. M. Valanju, R. M. Walser, A. P. Valanju. Wave Refraction in Negative-index Media: Always Positive and Very Inhomogeneous. Phys. Rev. Lett. 2002,88:187401
89 A. A. Houck, J. B. Brock, and I. L. Chuang. Experimental Obervations of a Left-handed Material That Obeys Snell's Law. Phys. Rev. Lett. 2003, 90:137401
90 G. V. Eleftheriades, A. K. Iyer, P. C. Kremer. Planar Negative Refractive Index Media Using Periodically L-c Loaded Transmission Lines. IEEE Trans.Microwave Theory Tech. 2002, 50:2702-2712
91 A. Grbic, G. V. Eleftheriades. Experimental Verification of Backward-wave Radiation from a Negative Refractive Index Metamaterial. J. Appl. Phys. 2002,92:5930-5935
92 L. Liu, C. Caloz, C. C. Chang, T. Itoh. Forward Coupling Phenomena between Artificial Left Handed Transmission Lines. J. Appl. Phys. 2002, 92:5560-5565
93 T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N.Basov, X. Zhang. Thz Magnetic Response from Artificial Materials. Science.2004,303:1494-1496
94 S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, C. M. Soukoulis. Magnetic Response of Metamaterials at 100 Terahertz. Science. 2004,306:1351-1353
95 H. O. Moser, B. D. F. Casse, O. Wilhelmi, B. T. Saw. Terahertz Response of a Microfabricated Rod-split-ring-resonator Electromagnetic Metamaterial. Phys.Rev. Lett. 2005, 94:063901
96 C. M. Soukoulis, S. Linden, M. Wegener. Negative Refractive Index at Optical Wavelengths. Science. 2007,315:47-49
97 H. J. Lezec, J. A. Dionne, H. A. Atwater. Negative Refraction at Visible Frequencies. Science. 2007, 316:430-432
98 X. S. Rao, C. K. Ong. Amplification of Evanescent Waves in a Lossy Left-handed Material Slab. Phys. Rev. B. 2003, 68:113103
99 S. A. Ramakrishna. Physics of Negative Refractive Index Materials. Rep. Prog.Phys. 2005, 68:449-521
100 G. W. 't Hooft. Comment on "Negative Refraction Makes a Perfect Lens" .Phys. Rev. Lett. 2001, 87:249701
101 N. Garcia, M. Nieto-Vesperinas. Left-handed Materials Do Not Make a Perfect Lens. Phys. Rev. Lett. 2002, 88:207403
102 J. B. Pendry. Pendry Replies:. Phys. Rev. Lett. 2001, 87:249702
103 J. B. Pendry. Pendry Replies:. Phys. Rev. Lett. 2001, 87:249704
104 J. B. Pendry. Comment on "left-handed Materials Do Not Make a Perfect Lens" . Phys. Rev. Lett. 2003, 91:099701
105 G. G. Santos. Universal Features of the Time Evolution of Evanescent Modes in a Left-handed Perfect Lens. Phys. Rev. Lett. 2003, 90:077401
106 L. Chen, S. L. He, L. F. Shen. Finite-size Effects of a Left-handed Material Slab on the Image Quality. Phys. Rev. Lett. 2004, 92:107404
107 A. N. Lagarkov, V. N. Kissel. Near-perfect Imaging in a Focusing System Based on a Left-handed-material Plate. Phys. Rev. Lett. 2004, 92:077401
108 L. Zhou, C. T. Chan. Vortex-like Surface Wave and Its Role in the Transient Phenomena of Meta-material Focusing. Appl. Phys. Lett. 2005, 86:101104
109 A. Grbic, G. V. Eleftheriades. Overcoming the Diffraction Limit with a Planar Left-handed Transmission-line Lens. Phys. Rev. Lett. 2004, 92:117403
110 N. Fang, H. Lee, C. Sun, X. Zhang. Sub-diffraction-limited Optical Imaging with a Silver Superlens. Science. 2005, 308:534-537
111 R. Marques, J. Martel, F. Mesa, F. Medina. Left-handed-media Simulation and Transmission of Em Waves in Subwavelength Split-ring-resonator-loaded Metallic Waveguides. Phys. Rev. Lett. 2002, 89:183901
112 S. Hrabar, J. Bartolic, Z. Sipus. Waveguide Miniaturization Using Uniaxial Negative Permeability Metamaterial. IEEE Trans. Antennas Propagat. 2005,53:110-119
113 N. Engheta. An Idea for Thin Subwavelength Cavity Resonators Using Meta-materials with Negative Permittivity and Permeability. IEEE Trans. Antennas Propagat. 2002, 1:10-13
114 L. F. Shen, S. L. He, S. S. Xiao. Mstability and Quality Factor of a One-dimensional Subwavelength Cavity Resonator Containing a Left-handed Material. Phys. Rev. B. 2004, 69:115111
115 L. Zhou, H. Q. Li, Y. Q. Qin, Z. Y. Wei, C. T. Chan. Directive Emissions from Subwavelength Metamaterial-based Cavities. Appl. Phys. Lett. 2005,86:101101
116 H. Q. Li, Z. H. Hang, Y. Q. Qin, Z. Y. Wei, L. Zhou, Y. W. Zhang, H. Chen,C. T. Chan. Quasi-periodic Planar Metamaterial Substrates. Appl. Phys. Lett.2005,86:121108
117 D. R. Fredkin, A. Ron. Effectively Left-handed (negative Index) Composite Material. Appl. Phys. Lett. 2002, 81:1753-1755
118 A. Alu, N. Engheta. Pairing an Epsilon-negative Slab with a Mu-negative Slab:Resonance, Tunneling and Transparency. IEEE Trans. Antennas Propag. 2003,51:2558-2570
119 H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, S. Zhu. Properties of One-dimensional Photonic Crystals Containing Single-negative Materials. Phys. Rev. E. 2004,69(6):066607
120 H. Jiang, H. Chen, H. Li, Y. Zhang. Compact High-q Filters Based on One-dimensional Photonic Crystals Containing Single-negative Materials. J. Appl.Phys. 2005,98:013101
121 L. S. Brown, G. J. Maclay. Vacuum Stress between Conducting Plates: An Image Solution. Phys. Rev. 1969, 184:1272-1279
122 J. S. Dowker, R. Critchley. Effective Lagrangian and Energy-momentum Tensor in De Sitter Space. Phys. Rev. D. 1976, 13:3224-3232
123 B. S. DeWitt. Quantum Field Theory in Curved Space-time. Phys. Rep. 1975,19:297-357
124 S. K. Blau, M. Visser, A. Wipf. Zeta Functions and the Casimir Energy. Nucl.Phys. B. 1988,310:163-180
125 J. Schwinger. Casimir Effect in Source Theory. Lett. Math. Phys. 1975, 1:43—47
126 R. Matloob, A. Keshavarz, D. Sedighi. Casimir Effect for Two Lossy Dispersive Dielectric Slabs. Phys. Rev. A. 1999, 60:3410-3420
127 M. S. Tomas. Green Function for Multilayers: Light Scattering in Planar Cavities. Phys. Rev. A. 1995, 51:2545-2559
128 T.H.Boyer.Van Der Waals Forces and Zero-point Energy for Dielectric and Permeable Materials.Phys.Rev.A.1974,9:2078-2084
129 S.Haroche.Fundamental Systems in Quantum Optics.Elsevier,Amsterdam.1992,9:809
2 E. M. Lifshitz. The Theory of Molecular Attractive Forces between Solids. Sov.Phys. JETP. 1956, 2:73-83
3 M. J. Sparnaay. Measurements of Attractive Forces between Flat Plates. Physica. 1958,24:751-764
4 S. K. Lamoreaux. Demonstration of the Casimir Force in the 0.6 to 6 μm Range.Phys. Rev. Lett. 1997, 78:5-8
5 U. Mohideen, A. Roy. Precision Measurement of the Casimir Force from 0.1 to 0.9μm. Phys. Rev. Lett. 1998, 81:4549-4552
6 A. Roy, U. Mohideen. Demonstration of the Nontrivial Boundary Dependence of the Casimir Force. Phys. Rev. Lett. 1999, 82:4380-4383
7 A. Roy, C. -Y. Lin, U. Mohideen. Improved Precision Measurement of the Casimir Force. Phys. Rev. D. 1999, 60:111101
8 B. W. Harris, F. Chen, U. Mohideen. Precision Measurement of the Casimir Force Using Gold Surfaces. Phys. Rev. A. 2000, 62:052109
9 M. Bostrom, Bo E. Sernelius. Thermal Effects on the Casimir Force in the 0.1- 5 μm Range. Phys. Rev. Lett. 2000, 84:4757-4760
10 H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, F. Capasso. Nonlinear Micromechanical Casimir Oscillator. Phys. Rev. Lett. 2001, 87:211801
11 R. S. Decca, D. Lopez, E. Fischbach, D. E. Krause. Measurement of the Casimir Force between Dissimilar Metals. Phys. Rev. Lett. 2003, 91:050402
12 G. Bressi, G. Carugno, R. Onofrio, G. Ruoso. Measurement of the Casimir Force between Parallel Metallic Surfaces. Phys. Rev. Lett. 2002, 88:041804
13 M. Bordag, U. Mohideen, V. M. Mostepanenko. New Developments in the Casimir Effect. Phys. Rep. 2001, 353:1-205
14 G. Plunien, B. Muller, W. Greiner. The Casimir Effect. Phys. Rep. 1986,134:87-193
15 V. M. Mostepanenko, N. N. Trunov. The Casimir Effect and Its Applications.Clarendon Press, Oxford. 1997:100-191
16 M. Bordag, B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko. Constraints for Hypothetical Interactions from a Recent Demonstration of the Casimir Force and some Possible Improvements. Phys. Rev. D. 1998, 58:075003
17 M. Bordag, B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko. Stronger Constraints for Nanometer Scale Yukawa-type Hypothetical Interactions from the New Measurement of the Casimir Force. Phys. Rev. D. 1999, 60:055004
18 M. Bordag, B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko. New Constraints for Non-newtonian Gravity in the Nanometer Range from the Improved Precision Measurement of the Casimir Force. Phys. Rev. D. 2000, 62:011701
19 M. Kardar, R. Golestanian. The "Friction" of Vacuum, and Other Fluctuation- induced Forces. Rev. Mod. Phys. 1999, 71:1233-1245
20 S. K. Lamoreaux. Resource Letter Cf-1: Casimir Force. Am. J. Phys. 1999,67:850-861
21 R. M. Cavalcanti. Casimir Force on a Piston. Phys. Rev. D. 2004, 69:065015
22 O. Kenneth, I. Klich. Opposites Attract: A Theorem about the Casimir Force.Phys. Rev. Lett. 2006, 97:160401
23 J. Wang, X. Zhang, S. -Y. Pei, and D. -H. Liu. Tunable Casimir Forces by Means of the External Magnetic Field. Phys. Rev. A. 2006, 73:042103
24 D. Kupiszewska, J. Mostowski. Casimir Effect for Dielectric Plates. Phys. Rev.A. 1990,41:4636-4644
25 M. S. Tomas. Casimir Force in Absorbing Multilayers. Phys. Rev. A. 2002,66:052103
26 C. Raabe, L. Knoll, D. -G. Welsch. Three-dimensional Casimir Force between Absorbing Multiplayer Dielectrics. Phys. Rev. A. 2003, 68:033810
27 M. Bordag, G. L. Klimchitskaya, V. M. Mostepanenko. The Casimir Force between Plates with Small Deviation from Plane Parallel Geometry. Int. J. Mod.Phys. A. 1995, 10(8):2661-2682
28 I. Brevik, V. N. Marachevsky, K. A. Milton. Identity of the Van Der Waals Force and the Casimir Effect and the Irrelevance of These Phenomena to Sono-luminescence. Phys. Rev. Lett. 1999, 82:3948-3951
29 T. H. Boyer. Quantum Electromagnetic Zero-point Energy of a Conducting Spherical Shell and the Casimir Model for a Charged Particle. Phys. Rev. 1968,174:1764-1776
30 M. Bordag, E. Elizalde, K. Kirsten, S. Leseduarte. Casimir Energies for Massive Scalar Fields in a Spherical Geometry. Phys. Rev. D. 1997, 56:4896-4904
31 R. L. Jaffe, A. Scardicchio. Casimir Effect and Geometric Optics. Phys. Rev.Lett. 2004, 92:070402
32 M. P. Hertzberg, R. L. Jaffe, M. Kardar, A. Scardicchio. Attractive Casimir Forces in a Closed Geometry. Phys. Rev. Lett. 2005, 95:250402
33 R. Golestanian. Lifshitz Interaction between Dielectric Bodies of Arbitrary Geometry. Phys. Rev. Lett. 2005, 95:230601
34 M. S. Tomas. Casimir Force between Dispersive Magnetodielectrics. Phys.Lett. A. 2005,342:381-388
35 G. L. Klimchitskaya, U. Mohideen, V. M. Mostepanenko. Casimir and Van Der Waals Forces between Two Plates Or a Sphere (lens) Above a Plate Made of Real Metals. Phys. Rev. A. 2000, 61:062107
36 M. Bordag, B. Geyer, G. L. Klimchitskaya, V. M. Mostepanenko. Casimir Force at Both Nonzero Temperature and Finite Conductivity. Phys. Rev. Lett. 2000,85:503-506
37 G. L. Klimchitskaya, A. Roy, U. Mohideen, V. M. Mostepanenko. Complete Roughness and Conductivity Corrections for Casimir Force Measurement.Phys. Rev. A. 1999, 60:3487-3495
38 A. Lambrecht,S. Reynaud. Casimir Force between Metallic Mirrors. Eur. Phys.J. D. 2000,8:309-318
39 V. B. Bezerra, G. L. Klimchitskaya, V. M. Mostepanenko. Higher-order Conductivity Corrections to the Casimir Force. Phys. Rev. A. 2000, 62:014102
40 C. Genet, A. Lambrecht, S. Reynaud. Temperature Dependence of the Casimir Effect between Metallic Mirrors. Phys. Rev. A. 2000, 62:012110
41 S. Y. Buhmann, L. Knoll, D. -G. Welsch. Casimir-polder Forces: A Nonpertur-bative Approach. Phys. Rev. A. 2004, 70:052117
42 R. Messina, R. Passante. Fluctuations of the Casimir-polder Force between an Atom and a Conducting Wall. Phys. Rev. A. 2007, 76:032107
43 M. S. Tomas. Medium Effects on the Van Der Waals Force. Phys. Rev. A. 2007,75:012109
44 M. Schaden, L. Spruch. Infinity-free Semiclassical Evaluation of Casimir Effects. Phys. Rev. A. 1998, 58:935-953
45 Y. Imry. Casimir Zero-point Radiation Pressure. Phys. Rev. Lett. 2005,95:080404
46 V. Hushwater. Repulsive Casimir Force as a Result of Vacuum Radiation Pressure. Am. J. Phys. 1997, 65(5):381-384
47 O. Kenneth, I. Klich, A. Mann, M. Revzen. Repulsive Casimir Forces. Phys.Rev. Lett. 2002, 89:033001
48 E. Buks, M. L. Rouke. Casimir Force Changes Sign. Nature. 2002, 419:119-120
49 U. Leonhardt, T. G. Philbin. Quantum Levitation by Left-handed Metamateri-als. New. J. Phys. 2007, 9:254
50 D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz. Composite Medium with Simultaneously Negative Permeability and Permittivity. Phys.Rev. Lett. 2000, 84:4184-4187
51 C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian. Experimental Verification and Simulation of Negative Index of Refraction Using Snell's Law. Phys. Rev. Lett. 2003, 90:107401
52 D. R. Smith, S. Schultz. Determination of Effective Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients. Phys. Rev.B. 2002,65:195104
53 V. M. Shalaev, W. Cai, U. K. Chettiar, H. -K. Yuan, A. K. Sarychev, V. P.Drachev, A. V. Kildishev. Negative Index of Refraction in Optical Metamaterials. Opt. Lett. 2005, 30(24):3356-3358
54 G. Dolling, M. Wegener, C. M. Soukoulis, S. Linden. Negative-index Metama-terial at 780 Nm Wavelength. Opt. Lett. 2007, 32(1):53-55
55 G. Dolling, M. Wegener, S. Linden. Realization of a Three-functional-layer Negative-index Photonic Metamaterial. Opt. Lett. 2007, 32(5):551-553
56 S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, S. R. J. Brueck.Experimental Demonstration of Near-infrared Negative-index Metamaterials.Phys. Rev. Lett. 2005, 95:137404
57 G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, S. Linden. Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial. Science. 2006,312:892-894
58 J. Zhou, E. N. Economon, T. Koschny, C. M. Soukoulis. Unifying Approach to Left-handed Material Design. Opt. Lett. 2006, 31(24):3620-3622
59 C. M. Soukoulis, M. Kafesaki, E. N. Economou. Negative Index Materials: New Frontiers in Optics. Adv. Mater. 2006, 18:1941-1952
60 N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu,M. Kafesaki, E. N. Economou, Th. Koschny, C. M. Soukoulis. Magnetic Response of Split-ring Resonators in the Far-infrared Frequency Regime. Opt.Lett. 2005, 30(11): 1348-1350
61 S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, S. R. J. Brueck.Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability. Phys. Rev. Lett. 2005, 94:037402
62 C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F.Zhou, Th. Koschny, C. M. Soukoulis. Magnetic Metamaterials at Telecommunication and Visible Frequencies. Phys. Rev. Lett. 2005, 95:203901
63 G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, S. Linden.Cut-wire Pairs and Plate Pairs as Magnetic Atoms for Optical Metamaterials.Opt. Lett. 2005, 30(23):3198-3200
64 G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, S. Linden. Low-loss Negative-index Metamaterial at Telecommunication Wavelengths. Opt. Lett 2006, 31(12):1800-1802
65 A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y.Khrushchev, J. Petrovic. Nanofabricated Media with Negative Permeability at Visible Frequencies. Nature. 2005, 438:355-338
66 A. N. Grigorenko. Negative Refractive Index in Artificial Metamaterials. Opt.Lett. 2006, 31(16):2483-2485
67 A. V. Kildishev, V. P. Drachev, U. K. Chettiar, D. Werner, D. -H. Kwon, V. M.Shalaev. Comment on "Negative Refractive Index in Artificial Metamaterials" . http://arxiv.org/abs/physics/0609234. 2006
68 V. G. Veselago. The Electrodynamics of Substances with Simultaneously Negative Values of ∈ and μ. Sov. Phys. Usp. 1968, 10:509-514
69 J. B. Pendry. Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett. 2000,85:3966-3969
70 J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs. Extremely Low Frequency Plasmons in Metallic Me so structures. Phys. Rev. Lett. 1996,76:4773-4776
71 J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart. Low Frequency Plasmons in Thin-wire Structures. J. Phys. Condens. Matter. 1998, 10:4785-4808
72 J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart. Magnetism from Conductors and Enhanced Nonlinear Phenomena. IEEE Trans. Microwave Theory Tech. 1999, 47:2075-2084
73 D. R. Smith, N. Kroll. Negative Refractive Index in Left-handed Matierials.Phys. Rev. Lett. 2000, 85:2933-2936
74 Y. Srivastava, A. Widom, M. H. Friedman. Microchips as Precision Quantum-electrodynamic Probes. Phys. Rev. Lett. 1985, 55:2246-2248
75 R. Castillo-Garza, C.-C. Chang, D. Jimenez, G. L. Klimchitskaya, V. M.Mostepanenko, U. Mohideen. Experimental Approaches to the Difference in the Casimir Force Due to Modifications in the Optical Properties of the Boundary Surface. Phys. Rev. A. 2007, 75:062114
76 T. Emig, A. Hanke, R. Golestanian, M. Kardar. Normal and Lateral Casimir Forces between Deformed Plates. Phys. Rev. A. 2003, 67:022114
77 E. Buks, M. L. Roukes. Stiction, Adhesion Energy, and the Casimir Effect in Micromechanical Systems. Phys. Rev. B. 2001, 63:033402
78 F. Serry, D. Walliser, G. J. Maclay. The Role of the Casimir Effect in the Static Deflection and Stiction of Membrane Strips in Microelectromechanical Systems (mems). J. Appl. Phys. 1998, 84:2501-2506
79 H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, F. Capasso. Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force. Science. 2001,291:1941-1944
80 P. W. Milonni. Casimir Forces without the Vacuum Radiation Field. Phys. Rev.A. 1982,25:1315-1327
81 P. W. Milonni, R. J. Cook, M. E. Goggin. Radiation Pressure from the Vacuum:Physical Interpretation of the Casimir Force. Phys. Rev. A. 1988, 38:1621-1623
82 T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff. Extraordinary Optical Transmission Through Sub-wavelength Hole Arrays. Nature. 1998,391:667-669
83 W. L. Barnes, A. Dereux, T. W. Ebbesen. Surface Plasmon Subwavelength Optics. Nature. 2003, 424:824-830
84 J. B. Pendry, L. Martin-Moreno, F. J. Garcia-Vidal. Mimicking Surface Plas-mons with Structured Surfaces. Science. 2004, 305:847-848
85 T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis. Effective Medium Theory of Left-handed Materials. Phys. Rev. Lett. 2004, 93:107402
86 R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz. Microwave Transmission Through a Two-dimensional, Isotropic, Left-handed Metamate-rial. Appl. Phys. Lett. 2001, 78:489-491
87 R. A. Shelby, D. R. Smith, S. Schultz. Experimental Verification of a Negative Index of Refraction. Science. 2001,292:77-79
88 P. M. Valanju, R. M. Walser, A. P. Valanju. Wave Refraction in Negative-index Media: Always Positive and Very Inhomogeneous. Phys. Rev. Lett. 2002,88:187401
89 A. A. Houck, J. B. Brock, and I. L. Chuang. Experimental Obervations of a Left-handed Material That Obeys Snell's Law. Phys. Rev. Lett. 2003, 90:137401
90 G. V. Eleftheriades, A. K. Iyer, P. C. Kremer. Planar Negative Refractive Index Media Using Periodically L-c Loaded Transmission Lines. IEEE Trans.Microwave Theory Tech. 2002, 50:2702-2712
91 A. Grbic, G. V. Eleftheriades. Experimental Verification of Backward-wave Radiation from a Negative Refractive Index Metamaterial. J. Appl. Phys. 2002,92:5930-5935
92 L. Liu, C. Caloz, C. C. Chang, T. Itoh. Forward Coupling Phenomena between Artificial Left Handed Transmission Lines. J. Appl. Phys. 2002, 92:5560-5565
93 T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N.Basov, X. Zhang. Thz Magnetic Response from Artificial Materials. Science.2004,303:1494-1496
94 S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, C. M. Soukoulis. Magnetic Response of Metamaterials at 100 Terahertz. Science. 2004,306:1351-1353
95 H. O. Moser, B. D. F. Casse, O. Wilhelmi, B. T. Saw. Terahertz Response of a Microfabricated Rod-split-ring-resonator Electromagnetic Metamaterial. Phys.Rev. Lett. 2005, 94:063901
96 C. M. Soukoulis, S. Linden, M. Wegener. Negative Refractive Index at Optical Wavelengths. Science. 2007,315:47-49
97 H. J. Lezec, J. A. Dionne, H. A. Atwater. Negative Refraction at Visible Frequencies. Science. 2007, 316:430-432
98 X. S. Rao, C. K. Ong. Amplification of Evanescent Waves in a Lossy Left-handed Material Slab. Phys. Rev. B. 2003, 68:113103
99 S. A. Ramakrishna. Physics of Negative Refractive Index Materials. Rep. Prog.Phys. 2005, 68:449-521
100 G. W. 't Hooft. Comment on "Negative Refraction Makes a Perfect Lens" .Phys. Rev. Lett. 2001, 87:249701
101 N. Garcia, M. Nieto-Vesperinas. Left-handed Materials Do Not Make a Perfect Lens. Phys. Rev. Lett. 2002, 88:207403
102 J. B. Pendry. Pendry Replies:. Phys. Rev. Lett. 2001, 87:249702
103 J. B. Pendry. Pendry Replies:. Phys. Rev. Lett. 2001, 87:249704
104 J. B. Pendry. Comment on "left-handed Materials Do Not Make a Perfect Lens" . Phys. Rev. Lett. 2003, 91:099701
105 G. G. Santos. Universal Features of the Time Evolution of Evanescent Modes in a Left-handed Perfect Lens. Phys. Rev. Lett. 2003, 90:077401
106 L. Chen, S. L. He, L. F. Shen. Finite-size Effects of a Left-handed Material Slab on the Image Quality. Phys. Rev. Lett. 2004, 92:107404
107 A. N. Lagarkov, V. N. Kissel. Near-perfect Imaging in a Focusing System Based on a Left-handed-material Plate. Phys. Rev. Lett. 2004, 92:077401
108 L. Zhou, C. T. Chan. Vortex-like Surface Wave and Its Role in the Transient Phenomena of Meta-material Focusing. Appl. Phys. Lett. 2005, 86:101104
109 A. Grbic, G. V. Eleftheriades. Overcoming the Diffraction Limit with a Planar Left-handed Transmission-line Lens. Phys. Rev. Lett. 2004, 92:117403
110 N. Fang, H. Lee, C. Sun, X. Zhang. Sub-diffraction-limited Optical Imaging with a Silver Superlens. Science. 2005, 308:534-537
111 R. Marques, J. Martel, F. Mesa, F. Medina. Left-handed-media Simulation and Transmission of Em Waves in Subwavelength Split-ring-resonator-loaded Metallic Waveguides. Phys. Rev. Lett. 2002, 89:183901
112 S. Hrabar, J. Bartolic, Z. Sipus. Waveguide Miniaturization Using Uniaxial Negative Permeability Metamaterial. IEEE Trans. Antennas Propagat. 2005,53:110-119
113 N. Engheta. An Idea for Thin Subwavelength Cavity Resonators Using Meta-materials with Negative Permittivity and Permeability. IEEE Trans. Antennas Propagat. 2002, 1:10-13
114 L. F. Shen, S. L. He, S. S. Xiao. Mstability and Quality Factor of a One-dimensional Subwavelength Cavity Resonator Containing a Left-handed Material. Phys. Rev. B. 2004, 69:115111
115 L. Zhou, H. Q. Li, Y. Q. Qin, Z. Y. Wei, C. T. Chan. Directive Emissions from Subwavelength Metamaterial-based Cavities. Appl. Phys. Lett. 2005,86:101101
116 H. Q. Li, Z. H. Hang, Y. Q. Qin, Z. Y. Wei, L. Zhou, Y. W. Zhang, H. Chen,C. T. Chan. Quasi-periodic Planar Metamaterial Substrates. Appl. Phys. Lett.2005,86:121108
117 D. R. Fredkin, A. Ron. Effectively Left-handed (negative Index) Composite Material. Appl. Phys. Lett. 2002, 81:1753-1755
118 A. Alu, N. Engheta. Pairing an Epsilon-negative Slab with a Mu-negative Slab:Resonance, Tunneling and Transparency. IEEE Trans. Antennas Propag. 2003,51:2558-2570
119 H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, S. Zhu. Properties of One-dimensional Photonic Crystals Containing Single-negative Materials. Phys. Rev. E. 2004,69(6):066607
120 H. Jiang, H. Chen, H. Li, Y. Zhang. Compact High-q Filters Based on One-dimensional Photonic Crystals Containing Single-negative Materials. J. Appl.Phys. 2005,98:013101
121 L. S. Brown, G. J. Maclay. Vacuum Stress between Conducting Plates: An Image Solution. Phys. Rev. 1969, 184:1272-1279
122 J. S. Dowker, R. Critchley. Effective Lagrangian and Energy-momentum Tensor in De Sitter Space. Phys. Rev. D. 1976, 13:3224-3232
123 B. S. DeWitt. Quantum Field Theory in Curved Space-time. Phys. Rep. 1975,19:297-357
124 S. K. Blau, M. Visser, A. Wipf. Zeta Functions and the Casimir Energy. Nucl.Phys. B. 1988,310:163-180
125 J. Schwinger. Casimir Effect in Source Theory. Lett. Math. Phys. 1975, 1:43—47
126 R. Matloob, A. Keshavarz, D. Sedighi. Casimir Effect for Two Lossy Dispersive Dielectric Slabs. Phys. Rev. A. 1999, 60:3410-3420
127 M. S. Tomas. Green Function for Multilayers: Light Scattering in Planar Cavities. Phys. Rev. A. 1995, 51:2545-2559
128 T.H.Boyer.Van Der Waals Forces and Zero-point Energy for Dielectric and Permeable Materials.Phys.Rev.A.1974,9:2078-2084
129 S.Haroche.Fundamental Systems in Quantum Optics.Elsevier,Amsterdam.1992,9:809