负折射率物质的理论和数值模拟研究
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摘要
负折射率材料是指介电常数ε和磁导率μ都小于零的介质材料,在这种介质中折射率n为负数。当电磁波在这种介质中传播时,电场矢量E、磁场矢量H和波矢k之间遵从左手系法则,所以负折射率材料又被称为“左手系材料”(LHM)。在负折射率材料中波矢k与能流密度S传播方向平行相反,由此导致了光的负折射、负Doppler效应和负Cherenkov辐射等一些反常的物理现象。2001年,Smith,et al.在微波波段首次发现利用特殊结构周期排列的复合介质能同时得到负介电常量ε和负磁导率μ,从而在试验上验证了制备这种材料的可行性。由于负折射率材料所表现出的众多物理特性,因此受到学术界极大的关注。
本论文通过理论分析和数值模拟,重点研究了负折射率材料的相关物理性质和应用。研究内容包括用时域有限差分法(FDTD)数值模拟了电磁波在负折射率材料平板透镜中的传播,验证了负折射率材料平板透镜的完美成像现象。用传输矩阵法(Transfer-Matrix Method)分析了由正负折射率材料平板构成的一维光子晶体的带隙特性和传输参数。最后还用时域有限差分法仿真模拟了电磁波在二维光子晶体中传播时具有的负折射现象。
本论文的研究工作和成果如下:
1.将时域有限差分(FDTD)法引入了对负折射率材料的物理现象的仿真研究。为了避免仿真程序在迭代过程中由于直接定义介电常量和磁导率为负数而出现的不稳定现象,引入了色散Drude模型间接定义介电常量和磁导率的值。并将色散Drude模型带入Maxwell方程组,推导出了TM电磁波在负折射率材料中传播的时域差分方程以及其在PML吸收边界中的指数差分方程。根据推导出的时域差分方程,我们仿真了由负折射率介质构成的平板透镜的完美成像现象,从仿真结果可以发现只有在ε_r=μ_r=-1的情况下,并且不考虑负折射率介质色散的情况下,由负折射率材料构成的平板透镜才会出现完美透镜的现象,当ε_r≠-1和μ_r≠-1时或者色散不为零时,完美成像现象就不会出现。但负折射率平板透镜仍然对电磁波有着近轴聚焦效应,这类似于光子隧道的效果。另外通过与电磁波在正折射率介质构成的平板透镜中传播特性相比较,可以验证电磁波在负折射率材料中传播时,其波矢方向和坡印廷矢量方向是平行相反的。这和理论分析的结果是一致的。从而证明了我们仿真结果的正确性。
2.研究了一维光子晶体中加入了负折射率材料后对光子禁带谱的影响。采用传输矩阵法(TMM,Transfer Matrix Method),计算了由正折射率材料和负折射率材料平板构成的一维光子晶体结构的色散曲线即光子禁带谱。通过计算发现,由正负折射率介质构成的一维光子晶体结构除了存在Bragg禁带以外,在其平均折射率为零时也存在禁带,即零折射率禁带((?)=0禁带)。我们分别计算了由正折射率介质和负折射率介质构成的周期为d和周期为d×2/3的一维光子晶体的透射率,通过比较二者的透过率图,我们可以发现zero-(?)禁带对应的频率没有改变,而Bragg禁带对应的频率向较高的频率区间偏移了。这说明Bragg禁带一维光子晶体的本身周期性有较强的依赖性,而zero-(?)禁带则对一维光子晶体的本身周期性没有什么依赖性。最后我们还计算了改变正负折射率介质构成的一维光子晶体的介质层的厚度对zero-(?)禁带和Bragg禁带的影响,通过比较我们发现改变介质层的厚度时,zero-(?)禁带没有什么明显的改变,而Bragg禁带则被破坏了。
3.结合光子晶体带隙图和等频率线(面)图分析了二维光子晶体中出现负折射现象的条件,推导出了负折射现象出现的频率范围。采用平面波展开法计算三角晶格空气柱二维光子晶体的光子晶体带隙图和等频率线(EFS)图,验证了在以上理论所给出的负折射出现的频段。采用有限时域差分法模拟了光在光子晶体界面和内部的传输行为,模拟了光在空气柱楔型二维光子晶体中的负折射现象,在等频率图给出的归一化频率范围内观察到比较明显的负折射现象。另外,还模拟了光在二维介质柱三角晶格光子晶体平板中的负折射现象,在能带图和等频率图给出的频率范围内,同样观察到比较明显的负折射现象。通过上面的模拟分析可以看到,由能带图和等频率面图得到的二维光子晶体的负折射频率范围是正确的,在以上理论所给出的负折射出现的频率范围内,能够观察到明显的负折射现象。
The negative refractive index materials are characterized by simultaneous negative permittivity and permeability, so the refractive index of this materials are negative. When the electromagnetic wave propagate in this materials, the electric field vector E, magnetic field vector H and wave vector k form a left-handed set, so we called this materials "left-handed materials"(LHM). In this materials the wave vector k (phase velocity) and Poynting vector S are anti-parallel, so there are novel electromagnetic properties, for example, the negative Snell's law, negative Doppler effect, negative Cherenkov radiation, et al. In 2001, Smith, et al. proposed and tested that the new meta-materials consisting of periodic structure can simultaneous have negative permittivity and permeability in the microwave range, so the feasibility of manufacturing this meta-materials is proved. Because the left-handed materials have many unique physics characteristics, there are much interesting in the academe.
In this paper, our research stress on the physics properties and application of the left-handed materials by the theoretic analysis and numerical simulation. In the second section, the propagation of the electromagnetic in the slab lens consisting of negative refractive materials is simulated by finite-difference time-domain method (FDTD). The perfect lens phenomenon is analyzed and approved by the FDTD. In the third section, the band structure and the transmittance of the one dimensional photonic crystals consisting of negative and positive refractive index materials are analyzed by the transfer matrix method (TMM). In the fourth section, the negative refraction phenomena of light propagation in the two dimensional photonic crystals are simulated by FDTD.
The main research works and conclusion are as following:
1. The finite-difference time-domain (FDTD) method was introduced into the simulation of the physics phenomena of the negative refractive index materials (NIM). The Drude model was introduced to indirectly defining the permittivityεand permeabilityμ, in order to avoid instability of the leapfrog in time domain caused by directly defining the negative values of the permittivityεand permeabilityμ. By introducing the Drude model to the Maxwell equations, the time-domain difference equations in the NIMs and the exponential difference equations in the PML absorbing boundary of TM model EW were induced. Based on these time-domain difference equations, the perfect lens phenomenon of the slab lens consisting of the NIMs was simulated. The simulation results show the perfect lens phenomenon only occur when theε_r =μ_r =-1 and ignoring the dispersion of the materials.When theε_r≠-1 andμ_r≠-1 or take the dispersion into account, theperfect lens phenomenon was disappear, but the paraxial focusing of the wave energy occurs. In addition, it was proved that the wave vector k and Poynting vector S are anti-parallel in the NIMs by comparing with the EW wave propagation phenomenon in the normal materials. These results were consistent with the theoretically analyzing, so proved the correctness of our simulation results.
2. The influences of the one dimensional photonic crystals consisting of the negative and positive refractive index materials on the action spectrum were studied in this section. The dispersive relation (i.e. the photonic band gap structure) of this one dimensional photonic crystals consisting of the negative and positive refractive index materials were calculated by the TMM. From the calculation results, it wasfound that there was the zero-n|- gap, besides the Bragg gap. The transmittances of the period d and the period d×2/3 of the one dimensional photonic crystals consisting of the negative and positive refractive index materials were calculated respectively. It can be found that the zero-n|- gap didn't changed but the Bragg gap shifted to higher frequency range by comparing two transmittances of the period d and the period d×2/3. It can be proved that the Bragg gap is an intrinsic consequence of periodicity and the gap frequency is tied with the size of period, but the zero-n|- gap is independent of the size of periodicity. Lastly, the influences of the thickness changing on the transmittance were calculated. From the calculation results, it canbe found that the zero - n|- gap didn't changed but the Bragg gap is destroyed, when the thickness of the negative and positive materials randomly changed.
3. In the fourth chapter, the negative refraction phenomenon in two-dimension (2D) photonic crystals (PCs) is investigated with the band structure calculation and equal frequency surface (EFS) of PCs. The frequency range of negative refraction phenomenon appearing is gained. The band structure and equal frequency surface (EFS) of triangle air-hole two dimensional PCs were calculated by the plane wave expansion method (PWE). The FDTD was used to simulate the propagation of light at the interface and inside of the photonic crystals. It is concluded that the negative refraction phenomena in two-dimension photonic crystals were real observed in the specific frequency range. Based on above analyzing, the negative refractive phenomenon of the prism-lens consisting of 2D air-column PCs was simulating and the obvious negative refractive phenomenon was observed. Furthermore, the negative refractive phenomenon of the slab-lens consisting of 2D triangle column PCs was simulating and the obvious negative refractive phenomenon was observed in the frequency range obtained from the band structure and the EFS method.
本论文通过理论分析和数值模拟,重点研究了负折射率材料的相关物理性质和应用。研究内容包括用时域有限差分法(FDTD)数值模拟了电磁波在负折射率材料平板透镜中的传播,验证了负折射率材料平板透镜的完美成像现象。用传输矩阵法(Transfer-Matrix Method)分析了由正负折射率材料平板构成的一维光子晶体的带隙特性和传输参数。最后还用时域有限差分法仿真模拟了电磁波在二维光子晶体中传播时具有的负折射现象。
本论文的研究工作和成果如下:
1.将时域有限差分(FDTD)法引入了对负折射率材料的物理现象的仿真研究。为了避免仿真程序在迭代过程中由于直接定义介电常量和磁导率为负数而出现的不稳定现象,引入了色散Drude模型间接定义介电常量和磁导率的值。并将色散Drude模型带入Maxwell方程组,推导出了TM电磁波在负折射率材料中传播的时域差分方程以及其在PML吸收边界中的指数差分方程。根据推导出的时域差分方程,我们仿真了由负折射率介质构成的平板透镜的完美成像现象,从仿真结果可以发现只有在ε_r=μ_r=-1的情况下,并且不考虑负折射率介质色散的情况下,由负折射率材料构成的平板透镜才会出现完美透镜的现象,当ε_r≠-1和μ_r≠-1时或者色散不为零时,完美成像现象就不会出现。但负折射率平板透镜仍然对电磁波有着近轴聚焦效应,这类似于光子隧道的效果。另外通过与电磁波在正折射率介质构成的平板透镜中传播特性相比较,可以验证电磁波在负折射率材料中传播时,其波矢方向和坡印廷矢量方向是平行相反的。这和理论分析的结果是一致的。从而证明了我们仿真结果的正确性。
2.研究了一维光子晶体中加入了负折射率材料后对光子禁带谱的影响。采用传输矩阵法(TMM,Transfer Matrix Method),计算了由正折射率材料和负折射率材料平板构成的一维光子晶体结构的色散曲线即光子禁带谱。通过计算发现,由正负折射率介质构成的一维光子晶体结构除了存在Bragg禁带以外,在其平均折射率为零时也存在禁带,即零折射率禁带((?)=0禁带)。我们分别计算了由正折射率介质和负折射率介质构成的周期为d和周期为d×2/3的一维光子晶体的透射率,通过比较二者的透过率图,我们可以发现zero-(?)禁带对应的频率没有改变,而Bragg禁带对应的频率向较高的频率区间偏移了。这说明Bragg禁带一维光子晶体的本身周期性有较强的依赖性,而zero-(?)禁带则对一维光子晶体的本身周期性没有什么依赖性。最后我们还计算了改变正负折射率介质构成的一维光子晶体的介质层的厚度对zero-(?)禁带和Bragg禁带的影响,通过比较我们发现改变介质层的厚度时,zero-(?)禁带没有什么明显的改变,而Bragg禁带则被破坏了。
3.结合光子晶体带隙图和等频率线(面)图分析了二维光子晶体中出现负折射现象的条件,推导出了负折射现象出现的频率范围。采用平面波展开法计算三角晶格空气柱二维光子晶体的光子晶体带隙图和等频率线(EFS)图,验证了在以上理论所给出的负折射出现的频段。采用有限时域差分法模拟了光在光子晶体界面和内部的传输行为,模拟了光在空气柱楔型二维光子晶体中的负折射现象,在等频率图给出的归一化频率范围内观察到比较明显的负折射现象。另外,还模拟了光在二维介质柱三角晶格光子晶体平板中的负折射现象,在能带图和等频率图给出的频率范围内,同样观察到比较明显的负折射现象。通过上面的模拟分析可以看到,由能带图和等频率面图得到的二维光子晶体的负折射频率范围是正确的,在以上理论所给出的负折射出现的频率范围内,能够观察到明显的负折射现象。
The negative refractive index materials are characterized by simultaneous negative permittivity and permeability, so the refractive index of this materials are negative. When the electromagnetic wave propagate in this materials, the electric field vector E, magnetic field vector H and wave vector k form a left-handed set, so we called this materials "left-handed materials"(LHM). In this materials the wave vector k (phase velocity) and Poynting vector S are anti-parallel, so there are novel electromagnetic properties, for example, the negative Snell's law, negative Doppler effect, negative Cherenkov radiation, et al. In 2001, Smith, et al. proposed and tested that the new meta-materials consisting of periodic structure can simultaneous have negative permittivity and permeability in the microwave range, so the feasibility of manufacturing this meta-materials is proved. Because the left-handed materials have many unique physics characteristics, there are much interesting in the academe.
In this paper, our research stress on the physics properties and application of the left-handed materials by the theoretic analysis and numerical simulation. In the second section, the propagation of the electromagnetic in the slab lens consisting of negative refractive materials is simulated by finite-difference time-domain method (FDTD). The perfect lens phenomenon is analyzed and approved by the FDTD. In the third section, the band structure and the transmittance of the one dimensional photonic crystals consisting of negative and positive refractive index materials are analyzed by the transfer matrix method (TMM). In the fourth section, the negative refraction phenomena of light propagation in the two dimensional photonic crystals are simulated by FDTD.
The main research works and conclusion are as following:
1. The finite-difference time-domain (FDTD) method was introduced into the simulation of the physics phenomena of the negative refractive index materials (NIM). The Drude model was introduced to indirectly defining the permittivityεand permeabilityμ, in order to avoid instability of the leapfrog in time domain caused by directly defining the negative values of the permittivityεand permeabilityμ. By introducing the Drude model to the Maxwell equations, the time-domain difference equations in the NIMs and the exponential difference equations in the PML absorbing boundary of TM model EW were induced. Based on these time-domain difference equations, the perfect lens phenomenon of the slab lens consisting of the NIMs was simulated. The simulation results show the perfect lens phenomenon only occur when theε_r =μ_r =-1 and ignoring the dispersion of the materials.When theε_r≠-1 andμ_r≠-1 or take the dispersion into account, theperfect lens phenomenon was disappear, but the paraxial focusing of the wave energy occurs. In addition, it was proved that the wave vector k and Poynting vector S are anti-parallel in the NIMs by comparing with the EW wave propagation phenomenon in the normal materials. These results were consistent with the theoretically analyzing, so proved the correctness of our simulation results.
2. The influences of the one dimensional photonic crystals consisting of the negative and positive refractive index materials on the action spectrum were studied in this section. The dispersive relation (i.e. the photonic band gap structure) of this one dimensional photonic crystals consisting of the negative and positive refractive index materials were calculated by the TMM. From the calculation results, it wasfound that there was the zero-n|- gap, besides the Bragg gap. The transmittances of the period d and the period d×2/3 of the one dimensional photonic crystals consisting of the negative and positive refractive index materials were calculated respectively. It can be found that the zero-n|- gap didn't changed but the Bragg gap shifted to higher frequency range by comparing two transmittances of the period d and the period d×2/3. It can be proved that the Bragg gap is an intrinsic consequence of periodicity and the gap frequency is tied with the size of period, but the zero-n|- gap is independent of the size of periodicity. Lastly, the influences of the thickness changing on the transmittance were calculated. From the calculation results, it canbe found that the zero - n|- gap didn't changed but the Bragg gap is destroyed, when the thickness of the negative and positive materials randomly changed.
3. In the fourth chapter, the negative refraction phenomenon in two-dimension (2D) photonic crystals (PCs) is investigated with the band structure calculation and equal frequency surface (EFS) of PCs. The frequency range of negative refraction phenomenon appearing is gained. The band structure and equal frequency surface (EFS) of triangle air-hole two dimensional PCs were calculated by the plane wave expansion method (PWE). The FDTD was used to simulate the propagation of light at the interface and inside of the photonic crystals. It is concluded that the negative refraction phenomena in two-dimension photonic crystals were real observed in the specific frequency range. Based on above analyzing, the negative refractive phenomenon of the prism-lens consisting of 2D air-column PCs was simulating and the obvious negative refractive phenomenon was observed. Furthermore, the negative refractive phenomenon of the slab-lens consisting of 2D triangle column PCs was simulating and the obvious negative refractive phenomenon was observed in the frequency range obtained from the band structure and the EFS method.
引文
[1]V G Veselago.The electrodynamics of substances with simultaneously negative values of ε and μ.Soy Phys Usp,1968,10(4):509-514.
[2]J B Pendry.Negative refraction makes a perfect lens.Phys Lett,2000,85:3966-3969.
[3]J B Pendry.Extremely Low Frequency Plasmons in Metallic Mesosotructures.Phys.Rev.Lett.,1966,76:4773-4776.
[4]J B Pendry,A J Holden,D J Robbins and W J Stewart.Low frequency plasmons in thin-wire structures.J.Phys:Condens.Matter,1998,10:4785-4808.
[5]J B Pendry,A J Holden,Robbins D J.Magnetism from conductors and enhanced nonlinear phenomena.IEEE Trans.Microwave Theory Tech,1999,47(11):2075-2084.
[6]J B Pendry.Negative Refractive Makes a Perfect Lens.Phys.Rev.Lett.,2000,85(18):3966-3969.
[7]Anthony Grbic.Disperison Analysis of a Microstrip-Based Negative Refractive Index Periodic Structure.IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS,2003,13(4):155-157.
[8]X H Hu,Y F Shen,X H Liu,et al.Superlensing effect in liquid surface waves.Phys.Rev.E,2004,69:030201-1-030201-4.
[9]X D Zhang,Z Y Liu.Negative refractive of acoustic waves in two-dimensional phononic crystals.Appl.Phys.Lett.,2004,85(2):341-343.
[10]S X Yang,J H Page and Z Y Liu,et al.Focusing of Sound in a 3D Photonic Crystal.Phys.Rev.Lett.,2004,93(2):034301-1-034301-4.
[11]K Imamura and S Tamura.Negative refraction of phonons and acoustic lensing effect of a crystalline slab.Phys.Rev.B,2004,70:174308-1-174308-7.
[12] J Li and C T Chan. Double-negative acoustic metamaterial. Phys. Rev. E, 2004, 70:055602-1-055602-4.
[13] Yi Jin and Sailing He. Focusing by a slab of chiral medium. Opt. Expr., 2005, 13(13): 4974-4979.
[14] C Monzon and D W Forester. Negative Refraction and Focusing of Circularly Polarizecd Waves in Optically Active Media. Phys. Rev. Lett., 2005, 95: 123904-1-123904-4.
[15] R Ruppin, Electromagnetic energy density in a dispersive and absorptive material, Phys. Lett. A, 299: 309-312.
[16] J Canning, D Moss and M Aslund, et al. Negative index gratings in germanosilicate planar waveguides. Electronics Letters, 1998, 34(4):366-367.
[17] A L Pokrovsky and A L Efros. Sign of refractive index and group velocity in left-handed media. Solid State Communications, 2002, 124: 283-287.
[18] P M Valanju, R M Walser and A P Valanju. Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous. Phys. Rev. Lett., 2002, 88(18):187401-l-187401-4.
[19] J B Pendry and D R Smith. Commnet on "Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogenous". Phys. Rev. Lett., 2003, 90(2):029703.
[20] D R Smith and D Schuring. Negative refraction of modulated electromagnetic waves. Appl. Phys. Lett., 2002, 81(15):2713-2715.
[21] D R Smith and Norman Kroll. Negative Refractive Index in Left-handed Materials. Phys. Rev. Lett., 2000,85(14):2933-2936.
[22] W T Lu, J B Sokoloff and S Sridhar. Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative. Phys. Rev. E, 2004, 69:026604-1-026604-5.
[23] Richard W Ziolkowski. Wave propagation in media having negative permittivity and permeability. Phys. Rev. E, 2001, 64: 056625-1-4356625-15.
[24]F J Rachford,D L Smith and P E Loschialpo.Calcultions and measurements of wire and/or split-ring negative index media.Phys.Rev.E,2002,66:036613-1-036613-5.
[25]A Grbic and G V Eleftheriades.Experimental verification of backward-wave radiation from a negative refractive index metamaterial.J.Appl.Phys.,92(10):5930-5935.
[26]A K Iyer and G V Eleftheriades.Negativd Refractive Index Metamaterials Supporting 2-D Waves.IEEE MTT-S CDROM,2002,1067-1070.
[27]R Ruppin.Surface polaritons of a left-handed material slab.J.Phys:Condens.Matter,2001,13:1811-1819.
[28]J N Gollub,D R Simth,et al.Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability.Phys.Rev.B,2005,71:195402-1-195402-7.
[29]Lei Zhou and C T Chan.Vortex-like surface wave and its role in the transient phenomena of meta-material focusing.Appl.Phys.Lett.,2005,86:101104-1-101104-3.
[30]J Yoon,S H Song,C H Oh and P S Kim.Backpropagating modes of sureface polaritons on a cross-negative interfave.Opt.Expr.,2005,13(2):417-427.
[31]Z M Zhang and C J Fu.Unusual photon tunneling in the presence of a layer with a negative refractive index.Appl.Phys.Lett.,2002,80(6):1097-1099.
[32]Chiyan Luo,S G Johnson and J D Joannopoulos.All-angle negative refraction without negative effective index.Phys.Rev.B,2002,65:201104-1-201104-4.
[33]Kyoung-Youm Kim.Photon tunneling in composite layers of negativeand positive-index media.Phys.Rev.E,2004,70:047603-1-047603-4.
[34]Kyoung-Youm Kim.Properties of photon tunneling through single-negative materials. Opt. Lett, 2005, 30(4): 430-432.
[35] P R Berman. Goos-Hanchen shift in negatively refractive media. Phys. Rev. E, 2002, 66: 067603-1-067603-3.
[36] A D Scher, C T Rodenbeck and K Chang. Compact gap coupled resonator using negative refractive index microstrip line. Electronics Letters, 2004, 40(2).
[37] J Hult, I S Burns and C F Kaminski. Measurements of the indium hyperfine structure in an atmospheric-pressure flame by use of diode-laser-induced fluorescence. Opt. Lett., 2004, 29(8): 827-829.
[38] X L Hu, Y D Huang and Wei Zhang. Opposite Goos-Hanchen shifts for transverse-electric and transverse-magnetic beams at the interface associated with single-negative materials. Opt. Lett., 2005, 30(8): 899-901.
[39] L V Shadrivov, A A Zharov and Y S Kivshar. Giant Goos-Hanchen effect at the reflection from left-handed metamaterials. Appl. Phys. Lett., 2003, 83(13): 2713-2715.
[40] C Fu, Z M Zhang and P N First. Brewster angle with a negative-index material. Appl. Opt., 2005, 44(18): 3716-3724.
[41] T M Grzegorczyk, Z M Thomas and J A Kong. Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials. Appl. Phys. Lett., 2005, 86: 251909-1-251909-3.
[42] D R Simth and D Schuring. Negative refraction of modulated electromagnetic waves. Appl. Phys. Lett., 2002, 81(15): 2713-2715.
[43] I V Shadrivov, A A Sukhorukov and Y S Kivshar. Guided modes in negative-refractive-index waveguides. Phys. Rev. E, 2003, 67: 057602-1-057602-4.
[44] B I Wu, T M Grzegorczyk and et al. Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability. J. Appl. Phys., 2003, 93(11): 9386-9388.
[45] G W Hoofit. Comment on "Negative Refraction Makes a Perfect Lens". Phys. Rev. Lett., 2001, 87(24): 249701-1-249701.
[46] J M Williams, P O Box. Some Problems with Negative Refraction. Phys. Rev.Lett., 2001, 87(24): 249703.
[47] N Garcia and M N Vesperinas. Left-Handed Materials Do Not Make a Perfect Lens. Phys. Rev. Lett., 2002, 88(20): 207403-1-207403-4.
[48] John Pendry. Pendry Replies. Phys. Rev. Lett. 2001, 87(24): 249702.
[49] John Pendry. Pendry Replies. Phys. Rev. Lett. 2001, 87(24): 249704.
[50] J B Pendry. Comment on "Left-Handed Materials Do Not Make a Perfect Lens". Phys. Rev. Lett., 2003, 91(9): 099701.
[51] J T Shen and P M Platzman. Near field imaging with negative dielectric constant lenses. Appl. Phys. Lett., 2002, 80(18): 3286-3288.
[52] Zhen Ye. Optical transmission and reflection of perfect lenses by left handed materials. Phys. Rev. B, 2003, 67: 193106-1-193106-4.
[53] K J Webb, M Yang, D W Ward and K A Nelson. Metrics for negative-refractive-index materials. Phys. Rev. E, 2004, 70: 035602-1-035602-4.
[54] V A Podolskiy and E E Narimanov. Near-sighted superlens. Opt. Lett., 2005, 30(1): 75-77.
[55] Daniel Maystre and Stefan Enoch. Perfect lenses made with left-handed materials Alice's mirror?, J. Opt. Soc. Am. A, 2001, 21(1): 122-131.
[56] S A Ramakrishna. Physics of negative refractive index materials. Rep. Prog. Phys., 2005, 68: 449-521.
[57] D R Smith, D Schurig and et al. Limitations on subdiffraction imaging with a negative refractive index slab. Appl. Phys. Lett., 2003, 82(10): 1506-1508.
[58] S A Cummer and B I Popa. Wave fields measured inside a negative refractive index metamaterial. Appl. Phys. Lett., 2004, 85(20): 4564-4566.
[59]J B Pendry and D R Smith.Reversing Light:Negative Refraction.Physics Today,2003,1-8.
[60]M Maksimovic and Zoran Jaksic.Modification of thermal radiation by periodical structures containing negative refractive index metamaterials.Phys.Lett.A,2005,342:497-503.
[61]L Chen,S He and L Shen.Finite-Size Effects of a Left-Handed Material Slab on the Image Quality.Phys.Rev.Lett.,2004,92(10):107404-1-107404-4.
[62]M W Feise,P J Bevelacqua and J B Schneider.Effects of sureface wave on the behavior of perfect lense.Phys.Rev.B,2002,66:035113-1-035113-5.
[63]P G Kik,S A Maier and H A Atwater.Image resolution of sureface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources.Phys.Rev.B,2004,69:045418-1-045418-5.
[64]Jian Qi Shen.Optical refractive index of massive particles and physical meanings of left-handed media.Phys.Lett.A,2005,344:144-148.
[65]N Fang and X Zhang.Imaging properties of a metamaterial superlens.Appl.Phys.Lett.,2003,82(2):161-163.
[66]Z Liu,N Fang,T J Yen,and Xiang Zhang.A pathway to subwavelength imaging using a metamaterial superlens.Proceedings of SPIE,2003,5221:116-123.
[67]O F Siddiqui,S J Erickson and et al.Time-Domain Measurement of Negative Group Delay in Negative-Refractive-Index Transmission-Line Metamaterials.IEEE Transactions on Microwave Theory and Techniques.2004,52(5):1449-1454.
[68]E Cubukcu,K Aydin and E Ozbay.Subwavelength Resolution in a Two-Dimensional Photonic-Crystal-Based Superlens.Phys.Rev.Lett.,2003,91(20):207401-1-207401-4,
[69]Z W Liu,N Fang and et al.Rapid growth of evanescent wave by a silver superlens. Appl. Phys. Lett., 2003, 83(25): 5184-5186.
[70] O S David, J B Richard and W O Conrad. Submicron imaging with a planar silver lens. Appl. Phys. Lett., 2004, 84(22): 4403-4405.
[71] O S M David and J B Richard. Super-resolution imaging through a planar silver layer. Opt. Expr., 2005, 13(6): 2127-2134.
[72] D F Sievenpiper, M E Sickmiller and E Yablonovitch. 3D Wire Mesh Photonic Crystals. Phys. Rev. Lett., 1996, 76(14): 2480-2483.
[73] D R Smith, W J Padilla and et al. Composite Medium with Simultaneously Negative Permeability and Permittivity. Phys. Rev. Lett., 2000, 84(18): 4184-4187.
[74] R A Shelby, D R Smith and et al. Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial. Appl. Phys. Lett., 2001, 78(4): 489-491.
[75] C Caloz, C C Chang and T Itoh. Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations. J Appl. Phys., 2001, 90(11): 5483-5486.
[76] Koray Aydin and Kaan Guven. Experimental observation of true left-handed transmission peaks in metamaterials. Opt. Lett., 2004, 29(22): 2623-2625.
[77] Koray Aydin and Kaan Guven. Observation of negative refraction and negative phase velocity in left-handed metamaterials. Appl. Phys. Lett., 2005, 86: 124102-1-124102-3.
[78] C G Parazzoli, R B Greegor, and et al. Experimental verification and Simulation of Negative Index of Refraction Using Snell's Law. Phys. Rev. Lett., 2003, 90(10): 107401-1-107401-4.
[79] A A Houck, J B Brock and I L Chuang. Experimental Observations of a Left-Handed Material That Obeys Snell's Law. Phys. Rev. Lett., 2003, 90(13): 137401-1-137401-4.
[80] Jensen Li, Lei Zhou and et al. Photonic Band Gap from a Stack of Positive and Negative Index Materials. Phys. Rev. Lett., 2003, 90(8): 083901-1-083901-4.
[81] L X Ran, J Huangfu and et al. Beam shifting experiment for thecharacterization of left-handed properties. J. Appl. Phys., 2004, 95(5): 2238-2241.
[82] P Markos and C M Soukoulis. Transmission studies of left-handed materials. Phys. Rev. B, 2001, 65: 033401-1-033401-4.
[83] A L Pokrovsky and A L Efros. Sign of refractive index and group velocity in left-handed media. Solid State Communications, 2002, 124:283-287.
[84] X Gao, W D Xu and F X Gan. The tunable negative refractive index in granular composite. Phys. Lett. A, 2005,339: 123-130.
[85] P G Balmza and O J F Martin. Efficient isotropic magnetic resonators. Appl. Phys. Lett. 2002, 81(5): 939-941.
[86] T Weiland and R Schuhmann. Ab initio numerical simulation of eft-handed metamaterials: Comparison of calculations and experiments. J Appl. Phys., 2001, 90(10): 5419-5424.
[87] J Gerardin and A Lakhtakia. Spectral response of Cantor multilayers made of materials with negative refractive index. Phys. Lett. A, 2002. 301: 377-381.
[88] G Burmell, D J Kang and D A Ansell. Directly coupled superconducting quantum interference device magnetometer fabricated in magnesium diboride by focused ion beam. Appl. Phys. Lett., 2002, 81(1): 102-104.
[89] C R Simovski and Sailing He. Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Ω particles. Phys. Lett. A, 311: 254-263.
[90] P M Poman, H L Du and J R Wolfgang. Modeling of Metamaterials With Negative Refractive Index Using 2-D Shunt and 3-D SCN TLM Networks. IEEE Transactions on Microwave Theory and Techniques, 2005, 53(4): 1496-1505.
[91] E Verney, B Sauviac and C R Simovski. Isotropic metamaterial electromagnetic lens. Phys. Lett. A, 2004, 331: 244-247.
[92] H S Chen, L X Ran and et al. Left-handed materials composed of only S-shaped resonators. Phys. Rev. E, 2004, 70: 057605-1-057605-4.
[93] G V Eleftheriades, A K Iyer and P C Kremer. Planar Negative Refractive Index Media Using Periodically L-C Loaded Transmission Lines. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(12): 2702-2712.
[94] O F Siddiqui, G V Eleftheriades. Periodically Loaded Transmission Line With Effective Negative Refractive Index and Negative Group Velocity. IEEE Transactions on Antennas and Propagation, 2003, 51(10): 2619-2625.
[95] Lei Liu, C Caloz and et al. Forward coupling phenomena between artificial left-handed transmission lines. J. Appl. Phys., 2002, 92(9): 5560-5565.
[96] A Gribic and G V Eleftheriades. Negative Refraction, Growing Evanescent Waves, and Sub-Diffraction Imaging in Loaded Transmission-Line Metamaterials. IEEE Transactions on Microwave Theory and Techniques, 2003, 51(12): 2297-2304.
[97] A Grbic and G V Eleftheriades. Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens. Phys. Rev. Lett., 2004, 92(11): 117403-1-117403-4.
[98] L Gao, C J Tang and S M Wang. Photonic band gap from a stack of single-negative materials. J. Magnetism and Magnetic Materials, 2006, 301:371-377.
[99] H Kosaka, T Kawashima and et al. Superprism phenomena in photonic crystals. Phys. Rev. B, 1998, 58(16): 10096-10099.
[100] C Luo, S G Johnson and J D Joannopoulos. All-angel negative refraction without negative effective index. Phys. Rev. B, 2002, 65: 201104-1-201104-4.
[101] W J Padilla, D N Basov and D R Smith. Negative refractive index metamaterials. Materials Today, 2006, 9: 28-35.
[102] Ulf Leonhardt. Notes on Waves With Negative Phase Velocity. IEEE Journal of Selected Topics in Quantum Electronics, 2003, 9(1): 102-105.
[103] S O Brien and J B Pendry. Photonic band-gap effects and magnetic activity in dielectric composites. J. Phys.: Condens. Matter, 2002, 14: 4035-4044.
[104] S O Brien and J B Pendry. Magnetic activity at infrared frequencies in structured metallic photonic crystals. J. Phys.: Condens. Matter, 2002, 14: 6383-6394.
[105] S Foteinopoulou, E N Economou and C M soukoulis. Refraction in Media with a Negative Refractive Index. Phys. Rev. Lett., 2003, 90(10): 107402-1-107402-4.
[106] Z L Lu, S Y Shi and et al. Experimental demonstration of negative refraction imageing in both amplitude and phase. Opt. Expr., 2005, 13(6): 2007-2008.
[107] L V Panina, A N Grigorenko and D P Makhnovskiy. Optomagnetic composite medium with conducting nanoelements. Phys. Rev. B, 2002, 66: 155411-1-155411-17.
[108] S A Ramakrishna. Physics of negative refractive index materials. Rep. Prog. Phys., 2005, 68: 449-521.
[109] P V Parimi, W T Lu and et al. Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals. Phys. Rev. Lett., 2004, 92(12): 127401-1-127401-4.
[110] S T Chui and L B Hu. Theoretical investigation on the possibility of preparing left-handed materials in metallic magnetic granular composites. Phys. Rev. B, 2002, 65: 144407-1-144407-6.
[111] P W Milonni and G J Maclay. Quantized-field description of light in negative-index media. Opt. Comm., 2003, 228: 161-165.
[112] I S Nefedov and S A Tretyakov. Photonic band gap structure containing metamaterial with negative permittivity and permeability. Phys. Rev. E, 2002, 66: 036611-1-036611-4.
[113] H X Zheng and D Y Yu. Transient Propagation in Meida with a Negative Refractive Index Simulated by ADI-FDTD Method. Progress In Electromagnetics Research Symposium, 2005.
[114] H Liu, S N Zhu and et al. Coupling of electromagnetic waves and superlattice vibrations in a piezomagnetic superlattice: Creation of a polariton through the piezomagnetic effect. Phys. Rev. B, 2005, 71: 125106-1-125106-5.
[115] V A Podolskiy and E E Narimanov. Strongly anisotropic waveguide as a nonmagnetic left-handed system. Phys. Rev. B, 2005, 71: 201101-1-201101-4.
[116] D R Smith and D Schuring. Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors, Phys. Rev. Lett., 2003, 90(7): 077405-1-077405-4
[117] L B Hu and Z F Lin. Imaging properties of uniaxially anisotropic negative refractive index materials, Phys. Lett. A, 2003, 313: 316-324
[118] M K Karkkainen. Numerical study of wave propagation in uniaxially anisotropic Lorentzian backward-wave slabs, Phys. Rev. E, 2003, 68: 026602-r026602-6
[119] D R Smith, D Schurig, J J Mock et al. Partial focusing of radiation by a slab of indefinite media, Appl. Phys. Lett., 2004, 84(13): 2244-2246
[120] Zheng Liu, J J Xu, Z F Lin. Omnidirectional reflection from a slab of uniaxially anisotropic negative refractive index materials, Opt. Comm., 2004, 240: 19-27
[121] D R Smith, P Kolinko and D Schurig. Negative refraction in indefinite media, J. Opt. Soc. Am. B, 2004, 21(5): 1032-1043
[122] A L Pokrovsky and A L Efros. Sign of refractive index and group velocity in left-handed media, Solid State Communications, 2002, 124: 283-287
[123] C D Moss, T M Grzegorczyk et al. Numerical Studies of Left Handed Metamaterials, Progress In Electromagnetics Research, 2002, 35: 315-334
[124] P Markos and C M Soukoulis. Numerical studies of left-handed materials and arrays of split ring resonators, Phys. Rev. E, 2002, 65: 036622-1-036622-8
[125] I V Shadrivov A A Sukhorukov and Y S Kivshar. Beam shaping by a periodic structure with negative refraction, Appl. Phys. Lett., 2003, 82(22): 3820-3822
[126] H X Da, C Xu and Z Y Li. Negative refractive index of layered nonmagnetic/magnetic composites, Journal of Magnetism and Magnetic Materials, 2005, 285: 155-163
[127] L F Shen, S L He and S S Xiao. Stability and quality factor of a one-dimensional subwavelength cavity resonator containing a left-handed material, Phys. Rev. B, 2004, 69: 115111-1 - 115111-6
[128] S Guenneau, B Gralak and J B Pendry. Perfect corner reflector, Opt. Lett., 2005, 30(10): 1204-1206
[129] Liu Liu and S L He. Near-field optical storage system using a solid immersion lens with a left-handed materials slab, Opt. Exp., 2004, 12 (20): 4835-4840
[130] Z C Ruan and S L He. Open cavity formed by a photonic crystal with negative effective index of refraction, Opt. Lett., 2005, 30(17): 2308-2310
[131] Jian Qi Shen. Optical refractive index of massive particles and physical meanings of left-handed media, Phys. Lett. A, 2005, 344: 144-148
[132] Q Cheng, T J Cui and W B Lu. A compact structure for energy localization using a thin grounded left-handed medium slab, Opt. Exp., 2005, 13(3): 770-775
[133] Qiang Cheng and T J Cui. Structure for localizing electromagnetic waves with a left-handed-medium slab and a conducting plane, Opt. Lett., 30(10): 1216-1218
[134] Q Cheng, T J Cui and W B Lu. Lossy and retardation effects on the localization of EM waves using a left-handed medium slab, Phys. Lett., A, 2005, 336:235-244
[1]Yee K S.Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media,IEEE Trans.Antennas Propagat.,1966,14(3):302-307
[2]Tallove A,Umashankar K R,Beker B,Harfoush F and Yee K S.Detailed FDTD analysis of EM fields penetrating narrow slots and lapped joints in thick conducting screens,IEEE Trans.Antennas Propagat.,1988,36(2):247-257
[3]Shlager K L and Schneider J B.A selective survey of the finite-difference time-domain literature,IEEE Antennas Propagate.Magazine,1995,37(4):39-7
[4]Davi Correia and Jian-Ming Jin.3D-FDTD-PML Analysis of Left-Handed Metamaterials,Microwave and Opticl Technology Letters,2004,40(3):201-205
[5]R W Ziolkowski and E Heyman,Wave Propagation in meida having negative permittivity and permeability,Phys.Rev.E,2001,64:056625
[6]Richard W.Ziolkowski.Superluminal transmission of information through an electromagnetic metamaterial.Phys.Rev.E 63:046604
[7]S C Winton,P Kosmas and C M Rappaport.FDTD Simulation of TE and TM Plane Waves at Nonzero Incidence in Arbitrary Layered Media,IEEE Trans.Antennas Propagat.,2005,53(5):1721-1728
[8]M K Karkkainen and S I Maslovski.Wave Propagation,Refraction,and Focusing Phenomena in Lorentzian Double-Negative Materials: A Theoretical and Numerical Study, Microwave and Opticl Technology Letters, 2003, 37(1): 4-7
[9] Michael W F, Yuri S K. Sub-wavelength imaging with a left-handed material flat, Phys. Lett. A, 2005, 334: 326-330
[10]Berenger J P. A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 1994, 114(2): 185- 200
[11] Berenger J P. Three-dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 1996, 127(2): 363-379
[12] Berenger J P. Perfectly matched layer for the FDTD solution of wave-structure interaction problem, IEEE Trans. Antennas Propagat., 1996, 44(1): 110-117
[13] Pendry J B. Negative refraction makes a perfect lens[J]. Phys. Lett., 2000, 85: 3966-3969.
[14] Zhang Z M and Fu C J. Unusual photon tunneling in the presence of a layer with a negative refractive index[J] . Appl. Phys. Lett. , 2002, 80: 1097-1099
[1]Yablonovitch E.Inhibited spontaneous emission in solid-state physics and electronics,Phys.Rev.Lett.,1987,58:2059-2062
[2]John S.Strong localization of photons in certain disordered dielectric superlattices,Phys.Rev.Lett.,1987,58:2486-2489
[3]RosenBerg A,Tonucci R J,Lin H Bet al.Near-infrared two-dimmensional photonic band-gap materials,Opt.Lett.,1996,21:830-832
[4]Robertson W et al.Measurement of photonic band structure in a two-dimensional periodic dielectric array,Phys.Rev.Lett.,1992,68:2023-2036
[5]Meade R,Brommer K,Rappe A et al.Nature of the photonic band gap:some insights from a field analysis,J.Opt.Soc.Am,1993,B10:328-332
[6]Cassague D,Jouanin C,Bertho D.Hexagonal photonic-band-gap structure,Phys.Rev.,1996,B53:7134-7142
[7]Fan Shanhui,Villencuve P R,Meade R D et al.Design of three-dimensional photonic crystals at submicron lengthscales,Appl.Phys.Lett.,1994,65:1466-1468
[8]Joannopoulos J D,Villencuve P R,Fan Shanhui.Photonic crystals:putting a new twist on light,Nature,1997,386
[9] A Suryanto. Transmission Characteristics of one-dimensional photonic bandgap structures with some defects, Journal of Nonlinear Optical Physics & Materials, 2006, 15(3): 331-343
[10] Y Zhang, B Y Gu and C P Liu. Investigation of properties of the confined states in photonic quantum-well structures, Int. J. Modern Phys. B, 2005, 19(24): 3705-3712
[11] S Z Han, Jie Tian et al. Y-type photonic crystal waveguide with minimum branches space, Int. J. Nanoscience, 2006, 5(6): 743- 746
[12] C P Liu, C J Wu et al. Flat pass-bands of one-dimensional photonic crystal composed of multiple quantum wells with gaussian-distributed refractive indices, 2006, 20(24): 1497- 1506
[13] Xu B S, Dang S H, Han P D et al. Band gaps of two-dimensional photonic crystal structure using conjugated polymer (3-octythiophenes), Opt. Comm., 2006, 267(2): 362-366
[14] Li Z Y, Lin L L et al. Light coupling with multimode photonic crystal waveguides, Appl. Phys. Lett., 2004, 84(23): 4699-4701
[15] Rung Andreas, Ribbing C G. Polaritonic and photonic gap interactions in a tow-dimensional photonic crystal, Phys. Rev. Lett., 2004, 92(12): 123901-1-123901-4
[16] Chen Chao, Li X C, Xu Kun et al. Photonic crystal waveguide sampled gratings, Opt. Comm., 2007, 276(2): 237-241
[17] Li Z Y, Ho K M. Anomalous Propagation Loss in Photonic Crystal Waveguides, Phys. Rev. Lett., 2004, 92(6): 63904-1-63904-4
[18] Lu X D, Han P D et al. Optical response of high-order band gap in one-dimensional photonic crystal applying in-plane integration, Opt. Comm., 2007, 277(2): 315-321
[17] Jensen Li, Lei Zhou. Photonic Band Gap from a Stack of Positive and Negative refractive index materials, Phys. Rev. Lett., 2003, 90(8): 083901
[18] Jing Li, Degang Zhao and Zhengyou Liu. Zero-n photonic band gap in a quasiperiodic stacking of positive and negative refractive index materials, Phys. Lett. A, 2004, 332: 461-468
[19]National Bureau of Standards Washington(Applied Mathematics Series 9 1952)
[20]Max Born and Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Seventh (Expanded) Edition [M], Publishing House of Electronics Industry, 2005, 46-63
[1]H Kosaka,T Kawashima and et al.Superprism phenomena in photonic crystals.Phys.Rev.B,1998,58(16):10096-10099.
[2]Daniel Maystre and Stefan Enoch.Perfect lenses made with left-handed materials Alice' s mirror?, J. Opt. Soc. Am. A, 2001, 21(1): 122-131.
[3] M Notomi. Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap, Phys. Rev. B, 2000, 62(16): 10696-10705
[4] S Foteinopoulou, E N Economou and C M soukoulis. Refraction in Media with a Negative Refractive Index. Phys. Rev. Lett., 2003, 90(10): 107402-1-107402-4.
[5] B.Gralak, S. Enoch, and G. Tayeb, Anomalous refractive properties of photonic crystals [J]. Opt. Soc. Am. A. 2000,17(6): 1012-1020.
[6] H .T. Chien, H .T .Tang.C .H .Kuo, C .C .Chen, and Z .Ye .Directed difraction without negativer efraction [J]. Phys. Rev. B. 2004. 70: 113101-1-113101-4.
[7] P. V Parimi, W. T. Lu, P. Vodo, J. Sokolof, J. S. Derov, and S. Sridhar Negative refraction and left handed electromagnetism crystals [J]. Phys. Rev. Lett. 2004, 92(12): 127401-1-127401-4.
[8] X . H . Hu and CT, " Chan, Photonic crystals with silver nanowires as a near infrared superlens[J]. Appl Phys. Lett. 2004, 85 (9.): 1520-1522.
[9] C. Luo, S. G . Johnson, J. D . Jo annopoulos, and J . B . Pendry. Negativere fraction without negative index in metallic photonic crystals [J]. Opt. Express. 2003, 11 (7) :746-754.
[10] C .Luo, S. G .Johnson, and J .D . Joannopoulos .All-angle negative refraction in a three dimensionally periodic photonic crystal [J]. Appl. Phys. Lett. 2002, 81(13) :2352-2354.
[11] X. D. Zhang, Tunable non-near-field focus and imaging of an unpolarized electromagnetic wave [J]. Phys. Rev. B, 2005,71: 235103-1-235103-5.
[12] Z .Feng, X . Zhang, Y . Wang, Z . Y. Li, B . Cheng, and D . Z .Zhang. Negative refraction and imaging using 12 fold Symmetry quasicrystals [J]. Phys. Rev. Lett. 2005,94:247402-1247402-4.
[13] S. G. Johnson and J. D. Joannopoulos. Block-iterative frequency domain methods for Maxwell' s equations in a planewave basis [J], Opt. Express 2001,8(3): 173-190.
[14] C Luo, S G Johnson, J D Joannopoulos, and J B Pendry. All angle negative refraction without negative effective index [J],Phys. Rev. B, 2002, 65: 201104-1-201104-4
[15] P V Parimi, W T Lu, P Vodo et al. Negative Refraction andLeft-Handed Electromagnetism in Microwave Photonic Crystals [J], Phys. Rev. Lett., 2004, 92(12): 127401-1 - 127401-14
[16] S. Enoch, G. Tayeb and B. Gralak, The richness of the dispersion relation of electromagnetic band gap materials [J]. IEEE Trans. Ant. Prop., 2003, 51(10) : 2659-2666.
[17] A. Berrier, M. Mulot, M. Swillo, Negative refraction at infrared wavelengths in a two-dimensional photonic crystal [J]. Phys. Rev. Lett. 2004,93(7): 073902-1-073902-4.
[18] Huang Bi qin, et al. Numerical Study about the Abnormal Refraction in One-dimensional Photonic Crystals[J]. Acta Photonica Sinica, 2004, 33(10): 1222-1225.
[19] Liang Hua qiu, et al. Giant Band Gaps of Rectangle Lattice 2D Photonic Crystal at High Frequency [J]. Acta Photonica Sinica, 2005,34(5): 781-784.
[20] A Berrier, M Mulot, M Swillo, M Qiu et al. Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal, Phys. Rev. Lett., 2004, 93(7): 073902-1-079302-4
[21] Martinez A, Marti J. Analysis of wave focusing inside a negative-index photonic-crystal slab [J]. Opt. Express, 2005, 13(8): 2858-2868
[22] S. Foteinopouloul, and C. M. Soukoulis. Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects[J]. Phys. Rev. B. , 2005, 72: 165112-1 - 165112-20.
[23] CUBUKCU E, AYDIN K, OZBAY E, et al. Negative refraction by photonic crystals [J]. Nature, 2003, 423: 604-604.
[24] Parimi P V, LU W T, VODO P, et al. Imaging by flat lens using negative refraction [J]. Nature, 2003, 426:404-404.
[25] Kong Fan rain, Li Kang, Guo Yi feng et al. FDTD Analysis of Planar Optical Waveguide Structures [J]. Acta Photonica Sinica, 2004, 33(3): 281- 283.
[2]J B Pendry.Negative refraction makes a perfect lens.Phys Lett,2000,85:3966-3969.
[3]J B Pendry.Extremely Low Frequency Plasmons in Metallic Mesosotructures.Phys.Rev.Lett.,1966,76:4773-4776.
[4]J B Pendry,A J Holden,D J Robbins and W J Stewart.Low frequency plasmons in thin-wire structures.J.Phys:Condens.Matter,1998,10:4785-4808.
[5]J B Pendry,A J Holden,Robbins D J.Magnetism from conductors and enhanced nonlinear phenomena.IEEE Trans.Microwave Theory Tech,1999,47(11):2075-2084.
[6]J B Pendry.Negative Refractive Makes a Perfect Lens.Phys.Rev.Lett.,2000,85(18):3966-3969.
[7]Anthony Grbic.Disperison Analysis of a Microstrip-Based Negative Refractive Index Periodic Structure.IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS,2003,13(4):155-157.
[8]X H Hu,Y F Shen,X H Liu,et al.Superlensing effect in liquid surface waves.Phys.Rev.E,2004,69:030201-1-030201-4.
[9]X D Zhang,Z Y Liu.Negative refractive of acoustic waves in two-dimensional phononic crystals.Appl.Phys.Lett.,2004,85(2):341-343.
[10]S X Yang,J H Page and Z Y Liu,et al.Focusing of Sound in a 3D Photonic Crystal.Phys.Rev.Lett.,2004,93(2):034301-1-034301-4.
[11]K Imamura and S Tamura.Negative refraction of phonons and acoustic lensing effect of a crystalline slab.Phys.Rev.B,2004,70:174308-1-174308-7.
[12] J Li and C T Chan. Double-negative acoustic metamaterial. Phys. Rev. E, 2004, 70:055602-1-055602-4.
[13] Yi Jin and Sailing He. Focusing by a slab of chiral medium. Opt. Expr., 2005, 13(13): 4974-4979.
[14] C Monzon and D W Forester. Negative Refraction and Focusing of Circularly Polarizecd Waves in Optically Active Media. Phys. Rev. Lett., 2005, 95: 123904-1-123904-4.
[15] R Ruppin, Electromagnetic energy density in a dispersive and absorptive material, Phys. Lett. A, 299: 309-312.
[16] J Canning, D Moss and M Aslund, et al. Negative index gratings in germanosilicate planar waveguides. Electronics Letters, 1998, 34(4):366-367.
[17] A L Pokrovsky and A L Efros. Sign of refractive index and group velocity in left-handed media. Solid State Communications, 2002, 124: 283-287.
[18] P M Valanju, R M Walser and A P Valanju. Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous. Phys. Rev. Lett., 2002, 88(18):187401-l-187401-4.
[19] J B Pendry and D R Smith. Commnet on "Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogenous". Phys. Rev. Lett., 2003, 90(2):029703.
[20] D R Smith and D Schuring. Negative refraction of modulated electromagnetic waves. Appl. Phys. Lett., 2002, 81(15):2713-2715.
[21] D R Smith and Norman Kroll. Negative Refractive Index in Left-handed Materials. Phys. Rev. Lett., 2000,85(14):2933-2936.
[22] W T Lu, J B Sokoloff and S Sridhar. Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative. Phys. Rev. E, 2004, 69:026604-1-026604-5.
[23] Richard W Ziolkowski. Wave propagation in media having negative permittivity and permeability. Phys. Rev. E, 2001, 64: 056625-1-4356625-15.
[24]F J Rachford,D L Smith and P E Loschialpo.Calcultions and measurements of wire and/or split-ring negative index media.Phys.Rev.E,2002,66:036613-1-036613-5.
[25]A Grbic and G V Eleftheriades.Experimental verification of backward-wave radiation from a negative refractive index metamaterial.J.Appl.Phys.,92(10):5930-5935.
[26]A K Iyer and G V Eleftheriades.Negativd Refractive Index Metamaterials Supporting 2-D Waves.IEEE MTT-S CDROM,2002,1067-1070.
[27]R Ruppin.Surface polaritons of a left-handed material slab.J.Phys:Condens.Matter,2001,13:1811-1819.
[28]J N Gollub,D R Simth,et al.Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability.Phys.Rev.B,2005,71:195402-1-195402-7.
[29]Lei Zhou and C T Chan.Vortex-like surface wave and its role in the transient phenomena of meta-material focusing.Appl.Phys.Lett.,2005,86:101104-1-101104-3.
[30]J Yoon,S H Song,C H Oh and P S Kim.Backpropagating modes of sureface polaritons on a cross-negative interfave.Opt.Expr.,2005,13(2):417-427.
[31]Z M Zhang and C J Fu.Unusual photon tunneling in the presence of a layer with a negative refractive index.Appl.Phys.Lett.,2002,80(6):1097-1099.
[32]Chiyan Luo,S G Johnson and J D Joannopoulos.All-angle negative refraction without negative effective index.Phys.Rev.B,2002,65:201104-1-201104-4.
[33]Kyoung-Youm Kim.Photon tunneling in composite layers of negativeand positive-index media.Phys.Rev.E,2004,70:047603-1-047603-4.
[34]Kyoung-Youm Kim.Properties of photon tunneling through single-negative materials. Opt. Lett, 2005, 30(4): 430-432.
[35] P R Berman. Goos-Hanchen shift in negatively refractive media. Phys. Rev. E, 2002, 66: 067603-1-067603-3.
[36] A D Scher, C T Rodenbeck and K Chang. Compact gap coupled resonator using negative refractive index microstrip line. Electronics Letters, 2004, 40(2).
[37] J Hult, I S Burns and C F Kaminski. Measurements of the indium hyperfine structure in an atmospheric-pressure flame by use of diode-laser-induced fluorescence. Opt. Lett., 2004, 29(8): 827-829.
[38] X L Hu, Y D Huang and Wei Zhang. Opposite Goos-Hanchen shifts for transverse-electric and transverse-magnetic beams at the interface associated with single-negative materials. Opt. Lett., 2005, 30(8): 899-901.
[39] L V Shadrivov, A A Zharov and Y S Kivshar. Giant Goos-Hanchen effect at the reflection from left-handed metamaterials. Appl. Phys. Lett., 2003, 83(13): 2713-2715.
[40] C Fu, Z M Zhang and P N First. Brewster angle with a negative-index material. Appl. Opt., 2005, 44(18): 3716-3724.
[41] T M Grzegorczyk, Z M Thomas and J A Kong. Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials. Appl. Phys. Lett., 2005, 86: 251909-1-251909-3.
[42] D R Simth and D Schuring. Negative refraction of modulated electromagnetic waves. Appl. Phys. Lett., 2002, 81(15): 2713-2715.
[43] I V Shadrivov, A A Sukhorukov and Y S Kivshar. Guided modes in negative-refractive-index waveguides. Phys. Rev. E, 2003, 67: 057602-1-057602-4.
[44] B I Wu, T M Grzegorczyk and et al. Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability. J. Appl. Phys., 2003, 93(11): 9386-9388.
[45] G W Hoofit. Comment on "Negative Refraction Makes a Perfect Lens". Phys. Rev. Lett., 2001, 87(24): 249701-1-249701.
[46] J M Williams, P O Box. Some Problems with Negative Refraction. Phys. Rev.Lett., 2001, 87(24): 249703.
[47] N Garcia and M N Vesperinas. Left-Handed Materials Do Not Make a Perfect Lens. Phys. Rev. Lett., 2002, 88(20): 207403-1-207403-4.
[48] John Pendry. Pendry Replies. Phys. Rev. Lett. 2001, 87(24): 249702.
[49] John Pendry. Pendry Replies. Phys. Rev. Lett. 2001, 87(24): 249704.
[50] J B Pendry. Comment on "Left-Handed Materials Do Not Make a Perfect Lens". Phys. Rev. Lett., 2003, 91(9): 099701.
[51] J T Shen and P M Platzman. Near field imaging with negative dielectric constant lenses. Appl. Phys. Lett., 2002, 80(18): 3286-3288.
[52] Zhen Ye. Optical transmission and reflection of perfect lenses by left handed materials. Phys. Rev. B, 2003, 67: 193106-1-193106-4.
[53] K J Webb, M Yang, D W Ward and K A Nelson. Metrics for negative-refractive-index materials. Phys. Rev. E, 2004, 70: 035602-1-035602-4.
[54] V A Podolskiy and E E Narimanov. Near-sighted superlens. Opt. Lett., 2005, 30(1): 75-77.
[55] Daniel Maystre and Stefan Enoch. Perfect lenses made with left-handed materials Alice's mirror?, J. Opt. Soc. Am. A, 2001, 21(1): 122-131.
[56] S A Ramakrishna. Physics of negative refractive index materials. Rep. Prog. Phys., 2005, 68: 449-521.
[57] D R Smith, D Schurig and et al. Limitations on subdiffraction imaging with a negative refractive index slab. Appl. Phys. Lett., 2003, 82(10): 1506-1508.
[58] S A Cummer and B I Popa. Wave fields measured inside a negative refractive index metamaterial. Appl. Phys. Lett., 2004, 85(20): 4564-4566.
[59]J B Pendry and D R Smith.Reversing Light:Negative Refraction.Physics Today,2003,1-8.
[60]M Maksimovic and Zoran Jaksic.Modification of thermal radiation by periodical structures containing negative refractive index metamaterials.Phys.Lett.A,2005,342:497-503.
[61]L Chen,S He and L Shen.Finite-Size Effects of a Left-Handed Material Slab on the Image Quality.Phys.Rev.Lett.,2004,92(10):107404-1-107404-4.
[62]M W Feise,P J Bevelacqua and J B Schneider.Effects of sureface wave on the behavior of perfect lense.Phys.Rev.B,2002,66:035113-1-035113-5.
[63]P G Kik,S A Maier and H A Atwater.Image resolution of sureface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources.Phys.Rev.B,2004,69:045418-1-045418-5.
[64]Jian Qi Shen.Optical refractive index of massive particles and physical meanings of left-handed media.Phys.Lett.A,2005,344:144-148.
[65]N Fang and X Zhang.Imaging properties of a metamaterial superlens.Appl.Phys.Lett.,2003,82(2):161-163.
[66]Z Liu,N Fang,T J Yen,and Xiang Zhang.A pathway to subwavelength imaging using a metamaterial superlens.Proceedings of SPIE,2003,5221:116-123.
[67]O F Siddiqui,S J Erickson and et al.Time-Domain Measurement of Negative Group Delay in Negative-Refractive-Index Transmission-Line Metamaterials.IEEE Transactions on Microwave Theory and Techniques.2004,52(5):1449-1454.
[68]E Cubukcu,K Aydin and E Ozbay.Subwavelength Resolution in a Two-Dimensional Photonic-Crystal-Based Superlens.Phys.Rev.Lett.,2003,91(20):207401-1-207401-4,
[69]Z W Liu,N Fang and et al.Rapid growth of evanescent wave by a silver superlens. Appl. Phys. Lett., 2003, 83(25): 5184-5186.
[70] O S David, J B Richard and W O Conrad. Submicron imaging with a planar silver lens. Appl. Phys. Lett., 2004, 84(22): 4403-4405.
[71] O S M David and J B Richard. Super-resolution imaging through a planar silver layer. Opt. Expr., 2005, 13(6): 2127-2134.
[72] D F Sievenpiper, M E Sickmiller and E Yablonovitch. 3D Wire Mesh Photonic Crystals. Phys. Rev. Lett., 1996, 76(14): 2480-2483.
[73] D R Smith, W J Padilla and et al. Composite Medium with Simultaneously Negative Permeability and Permittivity. Phys. Rev. Lett., 2000, 84(18): 4184-4187.
[74] R A Shelby, D R Smith and et al. Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial. Appl. Phys. Lett., 2001, 78(4): 489-491.
[75] C Caloz, C C Chang and T Itoh. Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations. J Appl. Phys., 2001, 90(11): 5483-5486.
[76] Koray Aydin and Kaan Guven. Experimental observation of true left-handed transmission peaks in metamaterials. Opt. Lett., 2004, 29(22): 2623-2625.
[77] Koray Aydin and Kaan Guven. Observation of negative refraction and negative phase velocity in left-handed metamaterials. Appl. Phys. Lett., 2005, 86: 124102-1-124102-3.
[78] C G Parazzoli, R B Greegor, and et al. Experimental verification and Simulation of Negative Index of Refraction Using Snell's Law. Phys. Rev. Lett., 2003, 90(10): 107401-1-107401-4.
[79] A A Houck, J B Brock and I L Chuang. Experimental Observations of a Left-Handed Material That Obeys Snell's Law. Phys. Rev. Lett., 2003, 90(13): 137401-1-137401-4.
[80] Jensen Li, Lei Zhou and et al. Photonic Band Gap from a Stack of Positive and Negative Index Materials. Phys. Rev. Lett., 2003, 90(8): 083901-1-083901-4.
[81] L X Ran, J Huangfu and et al. Beam shifting experiment for thecharacterization of left-handed properties. J. Appl. Phys., 2004, 95(5): 2238-2241.
[82] P Markos and C M Soukoulis. Transmission studies of left-handed materials. Phys. Rev. B, 2001, 65: 033401-1-033401-4.
[83] A L Pokrovsky and A L Efros. Sign of refractive index and group velocity in left-handed media. Solid State Communications, 2002, 124:283-287.
[84] X Gao, W D Xu and F X Gan. The tunable negative refractive index in granular composite. Phys. Lett. A, 2005,339: 123-130.
[85] P G Balmza and O J F Martin. Efficient isotropic magnetic resonators. Appl. Phys. Lett. 2002, 81(5): 939-941.
[86] T Weiland and R Schuhmann. Ab initio numerical simulation of eft-handed metamaterials: Comparison of calculations and experiments. J Appl. Phys., 2001, 90(10): 5419-5424.
[87] J Gerardin and A Lakhtakia. Spectral response of Cantor multilayers made of materials with negative refractive index. Phys. Lett. A, 2002. 301: 377-381.
[88] G Burmell, D J Kang and D A Ansell. Directly coupled superconducting quantum interference device magnetometer fabricated in magnesium diboride by focused ion beam. Appl. Phys. Lett., 2002, 81(1): 102-104.
[89] C R Simovski and Sailing He. Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Ω particles. Phys. Lett. A, 311: 254-263.
[90] P M Poman, H L Du and J R Wolfgang. Modeling of Metamaterials With Negative Refractive Index Using 2-D Shunt and 3-D SCN TLM Networks. IEEE Transactions on Microwave Theory and Techniques, 2005, 53(4): 1496-1505.
[91] E Verney, B Sauviac and C R Simovski. Isotropic metamaterial electromagnetic lens. Phys. Lett. A, 2004, 331: 244-247.
[92] H S Chen, L X Ran and et al. Left-handed materials composed of only S-shaped resonators. Phys. Rev. E, 2004, 70: 057605-1-057605-4.
[93] G V Eleftheriades, A K Iyer and P C Kremer. Planar Negative Refractive Index Media Using Periodically L-C Loaded Transmission Lines. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(12): 2702-2712.
[94] O F Siddiqui, G V Eleftheriades. Periodically Loaded Transmission Line With Effective Negative Refractive Index and Negative Group Velocity. IEEE Transactions on Antennas and Propagation, 2003, 51(10): 2619-2625.
[95] Lei Liu, C Caloz and et al. Forward coupling phenomena between artificial left-handed transmission lines. J. Appl. Phys., 2002, 92(9): 5560-5565.
[96] A Gribic and G V Eleftheriades. Negative Refraction, Growing Evanescent Waves, and Sub-Diffraction Imaging in Loaded Transmission-Line Metamaterials. IEEE Transactions on Microwave Theory and Techniques, 2003, 51(12): 2297-2304.
[97] A Grbic and G V Eleftheriades. Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens. Phys. Rev. Lett., 2004, 92(11): 117403-1-117403-4.
[98] L Gao, C J Tang and S M Wang. Photonic band gap from a stack of single-negative materials. J. Magnetism and Magnetic Materials, 2006, 301:371-377.
[99] H Kosaka, T Kawashima and et al. Superprism phenomena in photonic crystals. Phys. Rev. B, 1998, 58(16): 10096-10099.
[100] C Luo, S G Johnson and J D Joannopoulos. All-angel negative refraction without negative effective index. Phys. Rev. B, 2002, 65: 201104-1-201104-4.
[101] W J Padilla, D N Basov and D R Smith. Negative refractive index metamaterials. Materials Today, 2006, 9: 28-35.
[102] Ulf Leonhardt. Notes on Waves With Negative Phase Velocity. IEEE Journal of Selected Topics in Quantum Electronics, 2003, 9(1): 102-105.
[103] S O Brien and J B Pendry. Photonic band-gap effects and magnetic activity in dielectric composites. J. Phys.: Condens. Matter, 2002, 14: 4035-4044.
[104] S O Brien and J B Pendry. Magnetic activity at infrared frequencies in structured metallic photonic crystals. J. Phys.: Condens. Matter, 2002, 14: 6383-6394.
[105] S Foteinopoulou, E N Economou and C M soukoulis. Refraction in Media with a Negative Refractive Index. Phys. Rev. Lett., 2003, 90(10): 107402-1-107402-4.
[106] Z L Lu, S Y Shi and et al. Experimental demonstration of negative refraction imageing in both amplitude and phase. Opt. Expr., 2005, 13(6): 2007-2008.
[107] L V Panina, A N Grigorenko and D P Makhnovskiy. Optomagnetic composite medium with conducting nanoelements. Phys. Rev. B, 2002, 66: 155411-1-155411-17.
[108] S A Ramakrishna. Physics of negative refractive index materials. Rep. Prog. Phys., 2005, 68: 449-521.
[109] P V Parimi, W T Lu and et al. Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals. Phys. Rev. Lett., 2004, 92(12): 127401-1-127401-4.
[110] S T Chui and L B Hu. Theoretical investigation on the possibility of preparing left-handed materials in metallic magnetic granular composites. Phys. Rev. B, 2002, 65: 144407-1-144407-6.
[111] P W Milonni and G J Maclay. Quantized-field description of light in negative-index media. Opt. Comm., 2003, 228: 161-165.
[112] I S Nefedov and S A Tretyakov. Photonic band gap structure containing metamaterial with negative permittivity and permeability. Phys. Rev. E, 2002, 66: 036611-1-036611-4.
[113] H X Zheng and D Y Yu. Transient Propagation in Meida with a Negative Refractive Index Simulated by ADI-FDTD Method. Progress In Electromagnetics Research Symposium, 2005.
[114] H Liu, S N Zhu and et al. Coupling of electromagnetic waves and superlattice vibrations in a piezomagnetic superlattice: Creation of a polariton through the piezomagnetic effect. Phys. Rev. B, 2005, 71: 125106-1-125106-5.
[115] V A Podolskiy and E E Narimanov. Strongly anisotropic waveguide as a nonmagnetic left-handed system. Phys. Rev. B, 2005, 71: 201101-1-201101-4.
[116] D R Smith and D Schuring. Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors, Phys. Rev. Lett., 2003, 90(7): 077405-1-077405-4
[117] L B Hu and Z F Lin. Imaging properties of uniaxially anisotropic negative refractive index materials, Phys. Lett. A, 2003, 313: 316-324
[118] M K Karkkainen. Numerical study of wave propagation in uniaxially anisotropic Lorentzian backward-wave slabs, Phys. Rev. E, 2003, 68: 026602-r026602-6
[119] D R Smith, D Schurig, J J Mock et al. Partial focusing of radiation by a slab of indefinite media, Appl. Phys. Lett., 2004, 84(13): 2244-2246
[120] Zheng Liu, J J Xu, Z F Lin. Omnidirectional reflection from a slab of uniaxially anisotropic negative refractive index materials, Opt. Comm., 2004, 240: 19-27
[121] D R Smith, P Kolinko and D Schurig. Negative refraction in indefinite media, J. Opt. Soc. Am. B, 2004, 21(5): 1032-1043
[122] A L Pokrovsky and A L Efros. Sign of refractive index and group velocity in left-handed media, Solid State Communications, 2002, 124: 283-287
[123] C D Moss, T M Grzegorczyk et al. Numerical Studies of Left Handed Metamaterials, Progress In Electromagnetics Research, 2002, 35: 315-334
[124] P Markos and C M Soukoulis. Numerical studies of left-handed materials and arrays of split ring resonators, Phys. Rev. E, 2002, 65: 036622-1-036622-8
[125] I V Shadrivov A A Sukhorukov and Y S Kivshar. Beam shaping by a periodic structure with negative refraction, Appl. Phys. Lett., 2003, 82(22): 3820-3822
[126] H X Da, C Xu and Z Y Li. Negative refractive index of layered nonmagnetic/magnetic composites, Journal of Magnetism and Magnetic Materials, 2005, 285: 155-163
[127] L F Shen, S L He and S S Xiao. Stability and quality factor of a one-dimensional subwavelength cavity resonator containing a left-handed material, Phys. Rev. B, 2004, 69: 115111-1 - 115111-6
[128] S Guenneau, B Gralak and J B Pendry. Perfect corner reflector, Opt. Lett., 2005, 30(10): 1204-1206
[129] Liu Liu and S L He. Near-field optical storage system using a solid immersion lens with a left-handed materials slab, Opt. Exp., 2004, 12 (20): 4835-4840
[130] Z C Ruan and S L He. Open cavity formed by a photonic crystal with negative effective index of refraction, Opt. Lett., 2005, 30(17): 2308-2310
[131] Jian Qi Shen. Optical refractive index of massive particles and physical meanings of left-handed media, Phys. Lett. A, 2005, 344: 144-148
[132] Q Cheng, T J Cui and W B Lu. A compact structure for energy localization using a thin grounded left-handed medium slab, Opt. Exp., 2005, 13(3): 770-775
[133] Qiang Cheng and T J Cui. Structure for localizing electromagnetic waves with a left-handed-medium slab and a conducting plane, Opt. Lett., 30(10): 1216-1218
[134] Q Cheng, T J Cui and W B Lu. Lossy and retardation effects on the localization of EM waves using a left-handed medium slab, Phys. Lett., A, 2005, 336:235-244
[1]Yee K S.Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media,IEEE Trans.Antennas Propagat.,1966,14(3):302-307
[2]Tallove A,Umashankar K R,Beker B,Harfoush F and Yee K S.Detailed FDTD analysis of EM fields penetrating narrow slots and lapped joints in thick conducting screens,IEEE Trans.Antennas Propagat.,1988,36(2):247-257
[3]Shlager K L and Schneider J B.A selective survey of the finite-difference time-domain literature,IEEE Antennas Propagate.Magazine,1995,37(4):39-7
[4]Davi Correia and Jian-Ming Jin.3D-FDTD-PML Analysis of Left-Handed Metamaterials,Microwave and Opticl Technology Letters,2004,40(3):201-205
[5]R W Ziolkowski and E Heyman,Wave Propagation in meida having negative permittivity and permeability,Phys.Rev.E,2001,64:056625
[6]Richard W.Ziolkowski.Superluminal transmission of information through an electromagnetic metamaterial.Phys.Rev.E 63:046604
[7]S C Winton,P Kosmas and C M Rappaport.FDTD Simulation of TE and TM Plane Waves at Nonzero Incidence in Arbitrary Layered Media,IEEE Trans.Antennas Propagat.,2005,53(5):1721-1728
[8]M K Karkkainen and S I Maslovski.Wave Propagation,Refraction,and Focusing Phenomena in Lorentzian Double-Negative Materials: A Theoretical and Numerical Study, Microwave and Opticl Technology Letters, 2003, 37(1): 4-7
[9] Michael W F, Yuri S K. Sub-wavelength imaging with a left-handed material flat, Phys. Lett. A, 2005, 334: 326-330
[10]Berenger J P. A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 1994, 114(2): 185- 200
[11] Berenger J P. Three-dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 1996, 127(2): 363-379
[12] Berenger J P. Perfectly matched layer for the FDTD solution of wave-structure interaction problem, IEEE Trans. Antennas Propagat., 1996, 44(1): 110-117
[13] Pendry J B. Negative refraction makes a perfect lens[J]. Phys. Lett., 2000, 85: 3966-3969.
[14] Zhang Z M and Fu C J. Unusual photon tunneling in the presence of a layer with a negative refractive index[J] . Appl. Phys. Lett. , 2002, 80: 1097-1099
[1]Yablonovitch E.Inhibited spontaneous emission in solid-state physics and electronics,Phys.Rev.Lett.,1987,58:2059-2062
[2]John S.Strong localization of photons in certain disordered dielectric superlattices,Phys.Rev.Lett.,1987,58:2486-2489
[3]RosenBerg A,Tonucci R J,Lin H Bet al.Near-infrared two-dimmensional photonic band-gap materials,Opt.Lett.,1996,21:830-832
[4]Robertson W et al.Measurement of photonic band structure in a two-dimensional periodic dielectric array,Phys.Rev.Lett.,1992,68:2023-2036
[5]Meade R,Brommer K,Rappe A et al.Nature of the photonic band gap:some insights from a field analysis,J.Opt.Soc.Am,1993,B10:328-332
[6]Cassague D,Jouanin C,Bertho D.Hexagonal photonic-band-gap structure,Phys.Rev.,1996,B53:7134-7142
[7]Fan Shanhui,Villencuve P R,Meade R D et al.Design of three-dimensional photonic crystals at submicron lengthscales,Appl.Phys.Lett.,1994,65:1466-1468
[8]Joannopoulos J D,Villencuve P R,Fan Shanhui.Photonic crystals:putting a new twist on light,Nature,1997,386
[9] A Suryanto. Transmission Characteristics of one-dimensional photonic bandgap structures with some defects, Journal of Nonlinear Optical Physics & Materials, 2006, 15(3): 331-343
[10] Y Zhang, B Y Gu and C P Liu. Investigation of properties of the confined states in photonic quantum-well structures, Int. J. Modern Phys. B, 2005, 19(24): 3705-3712
[11] S Z Han, Jie Tian et al. Y-type photonic crystal waveguide with minimum branches space, Int. J. Nanoscience, 2006, 5(6): 743- 746
[12] C P Liu, C J Wu et al. Flat pass-bands of one-dimensional photonic crystal composed of multiple quantum wells with gaussian-distributed refractive indices, 2006, 20(24): 1497- 1506
[13] Xu B S, Dang S H, Han P D et al. Band gaps of two-dimensional photonic crystal structure using conjugated polymer (3-octythiophenes), Opt. Comm., 2006, 267(2): 362-366
[14] Li Z Y, Lin L L et al. Light coupling with multimode photonic crystal waveguides, Appl. Phys. Lett., 2004, 84(23): 4699-4701
[15] Rung Andreas, Ribbing C G. Polaritonic and photonic gap interactions in a tow-dimensional photonic crystal, Phys. Rev. Lett., 2004, 92(12): 123901-1-123901-4
[16] Chen Chao, Li X C, Xu Kun et al. Photonic crystal waveguide sampled gratings, Opt. Comm., 2007, 276(2): 237-241
[17] Li Z Y, Ho K M. Anomalous Propagation Loss in Photonic Crystal Waveguides, Phys. Rev. Lett., 2004, 92(6): 63904-1-63904-4
[18] Lu X D, Han P D et al. Optical response of high-order band gap in one-dimensional photonic crystal applying in-plane integration, Opt. Comm., 2007, 277(2): 315-321
[17] Jensen Li, Lei Zhou. Photonic Band Gap from a Stack of Positive and Negative refractive index materials, Phys. Rev. Lett., 2003, 90(8): 083901
[18] Jing Li, Degang Zhao and Zhengyou Liu. Zero-n photonic band gap in a quasiperiodic stacking of positive and negative refractive index materials, Phys. Lett. A, 2004, 332: 461-468
[19]National Bureau of Standards Washington(Applied Mathematics Series 9 1952)
[20]Max Born and Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Seventh (Expanded) Edition [M], Publishing House of Electronics Industry, 2005, 46-63
[1]H Kosaka,T Kawashima and et al.Superprism phenomena in photonic crystals.Phys.Rev.B,1998,58(16):10096-10099.
[2]Daniel Maystre and Stefan Enoch.Perfect lenses made with left-handed materials Alice' s mirror?, J. Opt. Soc. Am. A, 2001, 21(1): 122-131.
[3] M Notomi. Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap, Phys. Rev. B, 2000, 62(16): 10696-10705
[4] S Foteinopoulou, E N Economou and C M soukoulis. Refraction in Media with a Negative Refractive Index. Phys. Rev. Lett., 2003, 90(10): 107402-1-107402-4.
[5] B.Gralak, S. Enoch, and G. Tayeb, Anomalous refractive properties of photonic crystals [J]. Opt. Soc. Am. A. 2000,17(6): 1012-1020.
[6] H .T. Chien, H .T .Tang.C .H .Kuo, C .C .Chen, and Z .Ye .Directed difraction without negativer efraction [J]. Phys. Rev. B. 2004. 70: 113101-1-113101-4.
[7] P. V Parimi, W. T. Lu, P. Vodo, J. Sokolof, J. S. Derov, and S. Sridhar Negative refraction and left handed electromagnetism crystals [J]. Phys. Rev. Lett. 2004, 92(12): 127401-1-127401-4.
[8] X . H . Hu and CT, " Chan, Photonic crystals with silver nanowires as a near infrared superlens[J]. Appl Phys. Lett. 2004, 85 (9.): 1520-1522.
[9] C. Luo, S. G . Johnson, J. D . Jo annopoulos, and J . B . Pendry. Negativere fraction without negative index in metallic photonic crystals [J]. Opt. Express. 2003, 11 (7) :746-754.
[10] C .Luo, S. G .Johnson, and J .D . Joannopoulos .All-angle negative refraction in a three dimensionally periodic photonic crystal [J]. Appl. Phys. Lett. 2002, 81(13) :2352-2354.
[11] X. D. Zhang, Tunable non-near-field focus and imaging of an unpolarized electromagnetic wave [J]. Phys. Rev. B, 2005,71: 235103-1-235103-5.
[12] Z .Feng, X . Zhang, Y . Wang, Z . Y. Li, B . Cheng, and D . Z .Zhang. Negative refraction and imaging using 12 fold Symmetry quasicrystals [J]. Phys. Rev. Lett. 2005,94:247402-1247402-4.
[13] S. G. Johnson and J. D. Joannopoulos. Block-iterative frequency domain methods for Maxwell' s equations in a planewave basis [J], Opt. Express 2001,8(3): 173-190.
[14] C Luo, S G Johnson, J D Joannopoulos, and J B Pendry. All angle negative refraction without negative effective index [J],Phys. Rev. B, 2002, 65: 201104-1-201104-4
[15] P V Parimi, W T Lu, P Vodo et al. Negative Refraction andLeft-Handed Electromagnetism in Microwave Photonic Crystals [J], Phys. Rev. Lett., 2004, 92(12): 127401-1 - 127401-14
[16] S. Enoch, G. Tayeb and B. Gralak, The richness of the dispersion relation of electromagnetic band gap materials [J]. IEEE Trans. Ant. Prop., 2003, 51(10) : 2659-2666.
[17] A. Berrier, M. Mulot, M. Swillo, Negative refraction at infrared wavelengths in a two-dimensional photonic crystal [J]. Phys. Rev. Lett. 2004,93(7): 073902-1-073902-4.
[18] Huang Bi qin, et al. Numerical Study about the Abnormal Refraction in One-dimensional Photonic Crystals[J]. Acta Photonica Sinica, 2004, 33(10): 1222-1225.
[19] Liang Hua qiu, et al. Giant Band Gaps of Rectangle Lattice 2D Photonic Crystal at High Frequency [J]. Acta Photonica Sinica, 2005,34(5): 781-784.
[20] A Berrier, M Mulot, M Swillo, M Qiu et al. Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal, Phys. Rev. Lett., 2004, 93(7): 073902-1-079302-4
[21] Martinez A, Marti J. Analysis of wave focusing inside a negative-index photonic-crystal slab [J]. Opt. Express, 2005, 13(8): 2858-2868
[22] S. Foteinopouloul, and C. M. Soukoulis. Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects[J]. Phys. Rev. B. , 2005, 72: 165112-1 - 165112-20.
[23] CUBUKCU E, AYDIN K, OZBAY E, et al. Negative refraction by photonic crystals [J]. Nature, 2003, 423: 604-604.
[24] Parimi P V, LU W T, VODO P, et al. Imaging by flat lens using negative refraction [J]. Nature, 2003, 426:404-404.
[25] Kong Fan rain, Li Kang, Guo Yi feng et al. FDTD Analysis of Planar Optical Waveguide Structures [J]. Acta Photonica Sinica, 2004, 33(3): 281- 283.