左手材料光波导的传输特性
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摘要
左手材料(LHM)是当今电磁研究的热点,当电磁波在其中传输时,它的电场、磁场和波矢构成左手关系,而普通的材料中三者构成右手关系。本文从Maxwell方程组出发,对含左手材料光波导的传输特性进行了研究,内容包括:三层、五层平面波导导模的传输特性;单包层光纤导模和表面波模特性;双包层光纤导模特性以及各类波导之间的耦合,具体如下:
1).含左手材料平面波导的传输特性
光波导中最简单是平面波导。本文对含左手材料非对称三层平面波导的TE模和TM模进行了讨论,得到了导模的色散方程,画出了相应的色散曲线,发现了某些新的特性。比如:左手材料平面波导没有TE_0模和TM_0模;它们的基模色散曲线异常,其它一些导模在截止点附近有双值性;由于Goos-Haenchen位移的反向,它们的等效厚度H可以小于零。
然后对含左手材料五层对称平面波导的导模进行了研究,得到了它们的色散方程,画出了相应的色散曲线。通过对色散曲线的分析,我们发现:最低阶偶TE模,在截止频率附近,芯层中无能量;随着归一化频率V的增加,能量由内、外包层向芯层转移,芯层的归一化功率流的绝对值逐渐变大。然而,最低阶奇TE模,在截止频率附近,芯层和内、外包层的能量相等,随着归一化频率的增加,能量向包层里转移,最后,全部能量都集中在包层中,这些新的特性的发现,可能有利于我们开发新型耦合器件。
2).含左手材料单包层光纤的传输特性
光纤是重要的传输线。本文对含左手材料的单包层阶跃型光纤的导模进行了研究,求得了该光纤矢量解的TE模、TM模、HE模和EH模的特征方程。根据这些特征方程,我们分别在截止点附近和远离截止两种情况下进行了讨论;同时,我们又画出了各导模的色散曲线。通过对这些色散曲线的分析,得到了左手材料光纤的某些新的特性。比如:该种光纤的HE_(11)模不是最低模;它存在TE_0模和TM_0模,而这又不同于左手材料平面波导的传输特性。
我们讨论了含左手材料阶跃型单包层光纤的表面模,分别求得了该种光纤的表面模TE_0(TM_0)、HE_m和EH_m模的特征方程,画出了相应的色散曲线,并与相应的左手材料单包层光纤导模的色散曲线进行比较、分析,得到了左手材料光纤表面模的新的特性。例如:该种光纤的表面模TE_0和对应的导模TE_(01)在截至点连续;表面模HE_1,HE_2,HE_3不是分别和对应的导模HE连续,反而分别和对应的导模EH_(11),EH_(21),EH_(31)在截至点连续,等等。
3).含左手材料双包层光纤的传输特性
本文对含左手材料的双包层光纤进行了详细的研究。我们通过对该光纤导模的传输特性进行了分析,精确地求得了该种光纤的混合模、TE模和TM模的色散方程。根据它们的色散方程,我们画出了该种光纤TE模的色散曲线,同时,分别讨论了内包层折射率和内包层厚度对色散曲线的影响,得到了某些新的特性。比如:该种光纤的内包层折射率增加,截止频率变大;当该光纤内包层厚度的增加时,截止频率减小等等。
由于求解精确解的复杂性,我们又对含左手材料的双包层光纤的导模进行了近似求解。我们分别得到了HE、EH、TE和TM模的色散方程,并将这些色散方程在远离截止的情况下举行了简化,得到了最低阶导模色散方程的简化条件。同时,我们画出了部分导模的色散曲线,得到了许多左手材料光纤导模的新特性。比如:该种光纤的最低阶导模的反常色散,各导模的截止频率都不等于零,等等.
4).含左手材料光波导之间的耦合特性
关于光波导之间的耦合特性的研究,对于它们的实际应用有很重要的意义。本文首先对含左手材料光波导之间的耦合特性进行了研究,经过数学计算,得到了含左手材料光波导的拓展耦合波方程,定义了相应的拓展耦合系数。在含左手材料光波导的耦合系数的方程中,不仅包含了电场分量,而且还包含了磁场分量,因此比普通光波导的耦合系数要复杂的多。我们将该拓展的耦合系数方程应用于三层含左手材料对称平面波导之间的耦合,求出了该平面波导之间的耦合系数,画出了相应的耦合曲线。比较这些耦合曲线,我们发现:对于同一个归一化频率Ⅴ,两波导之间的的距离越近,耦合越强;导模的模阶数越小,耦合越强。
其次,我们利用拓展的耦合系数,对含左手材料五层对称的平面波导之间的耦合进行了研究,求得了偶TE模的耦合系数。显而易见,该耦合系数的表达式比对应的右手材料平面波导的耦合系数要复杂得多。
最后,我们还讨论了纤芯是左手材料,包层是右手材料的相同的左手材料的阶跃型光纤之间的耦合。通过计算,我们得到了含左手材料光纤TE_(01)模的耦合系数,画出了耦合曲线。分析这些耦合曲线,我们发现:该光纤的纤芯折射率的绝对值越大,耦合越强。
Now,the research for the left-handed material(LHM) is one of hot points for the electromagnetic fields.As electromagnetic wave propagates in the material,its electric field,magnetic field and wave vector construct left system.However,for convensional materials,its electric field,magnetic field and wave vector construct right system.The paper investigates the propagation characteristics for the LHM optical waveguides through Maxwell equations.The contents include that:guided modes in the three-layer and five-layer slab waveguide;guided modes and surface modes in a single clad fiber;guided modes in a doubly clad fiber and the coupling between optical waveguides.
1).Guided modes in a slab waveguide including LHM
A slab waveguide is the simplest in all waveguides.The paper discusses the guided modes(TE and TM) in the three-layer slab waveguide including LHM and their dispersive equations are obtained.According the dispersive equations,we plot their dispersive curves.Compared these curves,we can find that:the three-layer slab waveguide with LHM cannot exist TEo mode and TMo mode;the dispersive curves for TE_(11) mode and TM_(11) mode are abnormal;the effective thickness H for the guided modes can be less zero;for the same normalized frequency,some guided modes have two different values near cutoff.
Secondly,the TE modes for the five-layer slab waveguide including LHM are investigated and their dispersive equations are obtained.According to these dispersive equations,we plot some dispersive curves.The curves are studied and found that:for TE_(21) mode,the core has no energy near cutoff,however,as the normalized fi'equency adds,the energy shifts from claddings to the core; for TE_(11) mode,the energy in the core is the same as that in the clad,but,as the normalized frequency adds,energy can shift from the core to the clad,in the end,all energy is all in the clad.That benefits us to build new couplers in the future.
2).The guided modes and surface modes in the single clad fiber with left-handed material
The fiber is the most important for the optical transmission.This paper investigates the single fiber with LHM and obtains some characteristic equations for the oscillating modes(TE modes,TM modes,HE modes and EH modes).These equations are discussed near cutoff and far from cutoff.Besides,their dispersive curves are plotted and some new characteristics are found.Such as:in the LHM fiber, there are TE_0 mode and TMo mode and that is different with that of LHM slab waveguide;HE_(11) is no longer the lowest mode.
Secondly,the surface modes for the TE、TM、HE and EH modes are discussed and their dispersive equations are obtained.By using these equations,we plot their dispersive curves.Then,the curves are compared with that of relative guided modes. They show that the curves for the surface mode TEo and the guided mode TE_(01) are continuous;the curves for the surface modes HE_1,HE_2,HE_3 and the guided modes EH_(11),EH_(21),EH_(31) are continuous,respectively.
3).Guided modes in the doubly clad fiber with LHM
The doubly clad fiber with LHM is studied carefully.First,by an accurate way, we obtain the characteristic equations for hybrid modes,TE modes and TM modes in that fiber.According to the equation of TE mode,we plot some dispersive curves for the different refractive index and different thickness of inner cladding.Compare these curves,we can find that:as the refractive index of the inner cladding adds,the cutoff frequency becomes big;as the thickness of the inner cladding adds,the cutoff frequency becomes small.
Second,by an approximate way,we obtain the characteristic equations for the guided modes in that fiber.These equations are simplified far from cutoff.Their dispersive curves are plotted and the simple conditions are obtained.Besides, compare the curves,we find that:the dispersive characteristics for fundamental modes are abnormal;the cutoff frequencies of all guided modes can exist,etc.
4).The coupling between the LHM waveguides
The research of the coupling between LHM waveguides has more significance for its applications.First,we obtain the extended coupling wave equations and extended coupling coefficient between LHM waveguides.The expression for the extended coupling coefficient includes electric field and magnetic field,so,it is more complicated than that of common waveguides.We use the extended coupling coefficient to deal with the coupling between the three-layer slab waveguides with LHM.The coupling coefficient for TE modes is found and its coupling curves are plotted,too.Compare these curves,we find that:the nearer distance two waveguides, the stronger the coupling;the smaller the mode order,the stronger the coupling.
Second,we investigate the coupling between five-layer slab waveguide including LHM through the extended coupling coefficient.The extended coupling coefficient for the even TE mode is obtained.Clearly,the coefficient expression is more complicated than that of common slab waveguide.
In the end,using the extended coupling coefficient,we study the coupling between optical fibers i.e.the core is lefc-handed and the cladding fight-handed material.The extended coupling coefficient for TE_(01) mode is obtained and some coupling curves are plotted.Researching these coupling curves,we find that:the bigger the absolute of refractive index in the core,the stronger the coupling.
1).含左手材料平面波导的传输特性
光波导中最简单是平面波导。本文对含左手材料非对称三层平面波导的TE模和TM模进行了讨论,得到了导模的色散方程,画出了相应的色散曲线,发现了某些新的特性。比如:左手材料平面波导没有TE_0模和TM_0模;它们的基模色散曲线异常,其它一些导模在截止点附近有双值性;由于Goos-Haenchen位移的反向,它们的等效厚度H可以小于零。
然后对含左手材料五层对称平面波导的导模进行了研究,得到了它们的色散方程,画出了相应的色散曲线。通过对色散曲线的分析,我们发现:最低阶偶TE模,在截止频率附近,芯层中无能量;随着归一化频率V的增加,能量由内、外包层向芯层转移,芯层的归一化功率流的绝对值逐渐变大。然而,最低阶奇TE模,在截止频率附近,芯层和内、外包层的能量相等,随着归一化频率的增加,能量向包层里转移,最后,全部能量都集中在包层中,这些新的特性的发现,可能有利于我们开发新型耦合器件。
2).含左手材料单包层光纤的传输特性
光纤是重要的传输线。本文对含左手材料的单包层阶跃型光纤的导模进行了研究,求得了该光纤矢量解的TE模、TM模、HE模和EH模的特征方程。根据这些特征方程,我们分别在截止点附近和远离截止两种情况下进行了讨论;同时,我们又画出了各导模的色散曲线。通过对这些色散曲线的分析,得到了左手材料光纤的某些新的特性。比如:该种光纤的HE_(11)模不是最低模;它存在TE_0模和TM_0模,而这又不同于左手材料平面波导的传输特性。
我们讨论了含左手材料阶跃型单包层光纤的表面模,分别求得了该种光纤的表面模TE_0(TM_0)、HE_m和EH_m模的特征方程,画出了相应的色散曲线,并与相应的左手材料单包层光纤导模的色散曲线进行比较、分析,得到了左手材料光纤表面模的新的特性。例如:该种光纤的表面模TE_0和对应的导模TE_(01)在截至点连续;表面模HE_1,HE_2,HE_3不是分别和对应的导模HE连续,反而分别和对应的导模EH_(11),EH_(21),EH_(31)在截至点连续,等等。
3).含左手材料双包层光纤的传输特性
本文对含左手材料的双包层光纤进行了详细的研究。我们通过对该光纤导模的传输特性进行了分析,精确地求得了该种光纤的混合模、TE模和TM模的色散方程。根据它们的色散方程,我们画出了该种光纤TE模的色散曲线,同时,分别讨论了内包层折射率和内包层厚度对色散曲线的影响,得到了某些新的特性。比如:该种光纤的内包层折射率增加,截止频率变大;当该光纤内包层厚度的增加时,截止频率减小等等。
由于求解精确解的复杂性,我们又对含左手材料的双包层光纤的导模进行了近似求解。我们分别得到了HE、EH、TE和TM模的色散方程,并将这些色散方程在远离截止的情况下举行了简化,得到了最低阶导模色散方程的简化条件。同时,我们画出了部分导模的色散曲线,得到了许多左手材料光纤导模的新特性。比如:该种光纤的最低阶导模的反常色散,各导模的截止频率都不等于零,等等.
4).含左手材料光波导之间的耦合特性
关于光波导之间的耦合特性的研究,对于它们的实际应用有很重要的意义。本文首先对含左手材料光波导之间的耦合特性进行了研究,经过数学计算,得到了含左手材料光波导的拓展耦合波方程,定义了相应的拓展耦合系数。在含左手材料光波导的耦合系数的方程中,不仅包含了电场分量,而且还包含了磁场分量,因此比普通光波导的耦合系数要复杂的多。我们将该拓展的耦合系数方程应用于三层含左手材料对称平面波导之间的耦合,求出了该平面波导之间的耦合系数,画出了相应的耦合曲线。比较这些耦合曲线,我们发现:对于同一个归一化频率Ⅴ,两波导之间的的距离越近,耦合越强;导模的模阶数越小,耦合越强。
其次,我们利用拓展的耦合系数,对含左手材料五层对称的平面波导之间的耦合进行了研究,求得了偶TE模的耦合系数。显而易见,该耦合系数的表达式比对应的右手材料平面波导的耦合系数要复杂得多。
最后,我们还讨论了纤芯是左手材料,包层是右手材料的相同的左手材料的阶跃型光纤之间的耦合。通过计算,我们得到了含左手材料光纤TE_(01)模的耦合系数,画出了耦合曲线。分析这些耦合曲线,我们发现:该光纤的纤芯折射率的绝对值越大,耦合越强。
Now,the research for the left-handed material(LHM) is one of hot points for the electromagnetic fields.As electromagnetic wave propagates in the material,its electric field,magnetic field and wave vector construct left system.However,for convensional materials,its electric field,magnetic field and wave vector construct right system.The paper investigates the propagation characteristics for the LHM optical waveguides through Maxwell equations.The contents include that:guided modes in the three-layer and five-layer slab waveguide;guided modes and surface modes in a single clad fiber;guided modes in a doubly clad fiber and the coupling between optical waveguides.
1).Guided modes in a slab waveguide including LHM
A slab waveguide is the simplest in all waveguides.The paper discusses the guided modes(TE and TM) in the three-layer slab waveguide including LHM and their dispersive equations are obtained.According the dispersive equations,we plot their dispersive curves.Compared these curves,we can find that:the three-layer slab waveguide with LHM cannot exist TEo mode and TMo mode;the dispersive curves for TE_(11) mode and TM_(11) mode are abnormal;the effective thickness H for the guided modes can be less zero;for the same normalized frequency,some guided modes have two different values near cutoff.
Secondly,the TE modes for the five-layer slab waveguide including LHM are investigated and their dispersive equations are obtained.According to these dispersive equations,we plot some dispersive curves.The curves are studied and found that:for TE_(21) mode,the core has no energy near cutoff,however,as the normalized fi'equency adds,the energy shifts from claddings to the core; for TE_(11) mode,the energy in the core is the same as that in the clad,but,as the normalized frequency adds,energy can shift from the core to the clad,in the end,all energy is all in the clad.That benefits us to build new couplers in the future.
2).The guided modes and surface modes in the single clad fiber with left-handed material
The fiber is the most important for the optical transmission.This paper investigates the single fiber with LHM and obtains some characteristic equations for the oscillating modes(TE modes,TM modes,HE modes and EH modes).These equations are discussed near cutoff and far from cutoff.Besides,their dispersive curves are plotted and some new characteristics are found.Such as:in the LHM fiber, there are TE_0 mode and TMo mode and that is different with that of LHM slab waveguide;HE_(11) is no longer the lowest mode.
Secondly,the surface modes for the TE、TM、HE and EH modes are discussed and their dispersive equations are obtained.By using these equations,we plot their dispersive curves.Then,the curves are compared with that of relative guided modes. They show that the curves for the surface mode TEo and the guided mode TE_(01) are continuous;the curves for the surface modes HE_1,HE_2,HE_3 and the guided modes EH_(11),EH_(21),EH_(31) are continuous,respectively.
3).Guided modes in the doubly clad fiber with LHM
The doubly clad fiber with LHM is studied carefully.First,by an accurate way, we obtain the characteristic equations for hybrid modes,TE modes and TM modes in that fiber.According to the equation of TE mode,we plot some dispersive curves for the different refractive index and different thickness of inner cladding.Compare these curves,we can find that:as the refractive index of the inner cladding adds,the cutoff frequency becomes big;as the thickness of the inner cladding adds,the cutoff frequency becomes small.
Second,by an approximate way,we obtain the characteristic equations for the guided modes in that fiber.These equations are simplified far from cutoff.Their dispersive curves are plotted and the simple conditions are obtained.Besides, compare the curves,we find that:the dispersive characteristics for fundamental modes are abnormal;the cutoff frequencies of all guided modes can exist,etc.
4).The coupling between the LHM waveguides
The research of the coupling between LHM waveguides has more significance for its applications.First,we obtain the extended coupling wave equations and extended coupling coefficient between LHM waveguides.The expression for the extended coupling coefficient includes electric field and magnetic field,so,it is more complicated than that of common waveguides.We use the extended coupling coefficient to deal with the coupling between the three-layer slab waveguides with LHM.The coupling coefficient for TE modes is found and its coupling curves are plotted,too.Compare these curves,we find that:the nearer distance two waveguides, the stronger the coupling;the smaller the mode order,the stronger the coupling.
Second,we investigate the coupling between five-layer slab waveguide including LHM through the extended coupling coefficient.The extended coupling coefficient for the even TE mode is obtained.Clearly,the coefficient expression is more complicated than that of common slab waveguide.
In the end,using the extended coupling coefficient,we study the coupling between optical fibers i.e.the core is lefc-handed and the cladding fight-handed material.The extended coupling coefficient for TE_(01) mode is obtained and some coupling curves are plotted.Researching these coupling curves,we find that:the bigger the absolute of refractive index in the core,the stronger the coupling.
引文
[1]Veselago V.G,Electrodynamics of substances with simultaneously negative electrical and magnetic properties[J].Soy Phyis USPEKHI,Vol.10,No.41968,pp.509-517.
[2]Pendry J.B.,Holden A.J.,Stewart W.J.,Youngs I.,Extremely low frequency plasmons in metallic mesostructure[j].Phys.Rev.Lett.,Vol.76,No.25,1996,pp.4773-4776.
[3]Pendty J.B.,Holden A.J.,Robbins D.J.,Stewart,W.J.Low frequency plasmons in thin-wire structures[J].J.Phys.:Condens.Matter,Vol.10,1998,pp.4785-4808.
[4]Pendry J.B.,Holden A.J.,Robins D.J.,Stewart W.J.,Magnetism from conductors and enhanced nonlinear phenomena[J].IEEE Trans.Micr.Theory Tech.,Vol.47,No.11,1999,pp.2075-2084.
[5]J.B.Pendry,Negative refraction makes a perfect lens[J].Phys.Rev.Lett.,Vol.85,No.18,2000,pp.3966---3969.
[6]N.Garcia,M.Nieto-Vesperinas,Left-handed materials do not make a perfect lens[J].,Phys.Rev.Lett.,Vol.88,No.20,2002,pp.207403:1-4.
[7]Valanju P.M.,Walser R.M.,Valanju A.P.,Wave refraction in negative-index media:Always positive and very inhomogeneous[J].Phys.Rev.Lett.,Vol.88,No.18,2002,pp.187401:1-4.
[8]Ziolkowski R.W.,Heyman E.,Wave propagation in media having negative permittivity and permeability[J].Phys.Rev.E,Vol.64,No.5,2001,pp.056625:1-15.
[9]Ye Z.,Optical transmission and reflection of perfect lenses by left-handed materials[J],Phys.Rev.B,Vol.67,2003,pp.193106:1-4.
[10]Smith D.R.,Kroll N.,Negative refractive index in left-handed materials[J].Phys.Rev.Lett.,Vol.85,No.14,2000,pp.2933-2936.
[11]Kuzmiak V.,Maradudin A.A.,Scattering properties of a cylinder fabricated from a left-handed material[J].Phys.Rev.B,Vol.64,No.4,2002,pp.045116:1-7.
[12] Zhang G. M., Peng J. C., Jian Z. J., Huang X. Y., Transmission Loss due to Modes Conversion Caused by Random Surface Imperfections in Left-Handed-Material Slab Waveguides [J].Chinese Phys. Lett., Vol. 23, No.7, 2006, pp. 1826-1829.
[13] Smith D. R., Padilla Willie J., Vier D. C, Nemat-Nasser S. C, Schultz S., Composite Medium with Simultaneously Negative Permeability and Permittivity [J]. Phys. Rev..Lett., Vol.84, No. 18,2000, pp.4184-4187.
[14] Shelby R. A., Smith D. R., Schultz S., Experimental verification of a negative index of refraction [J]. Science, Vol.292,2001, pp. 77-79.
[15] Pacheco J., Grzegorczyk T. M., Wu B. I., et al Power propagation in homogeneous isotropic frequency-dispersive left-handed media [J]. Phys. Rev. Lett., Vol.89, No.25,2002, pp.257401: 1 -4.
[16] Pendry J. B., Smith D. R., Comment on "Wave refraction in negative index media: always positive and very inhomogeneous" [J]. Phys. Rev. Lett., Vol.90, 2003, pp.029303.
[17] Kong J. A., Wu B., Zhang Y., Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability [J]. Appl. Phys. Lett., Vol.80, No.12, 2002, pp.2084-2086.
[18] Ran L., Huangfu J., Chen H., Zhang X., Chen K., Grzegorezyk T. M., Kong J. A., Beam shifting experiment for the characterization of left-handed properties[J]. J. Appl. Phys., Vol.95, No.5, 2004, pp.2238-2241.
[19] Grbic A., Eleftheriaded G. V., Experimental verification of backward wave radiation from a negative refractive index metamaterial [J]. J. Appl. Phys., Vol.92, No. 10, 2002, pp.5930-5935.
[20] Eleftheriades G. V., Iyer A. K., Kremer P. C., Planar negative refractive index media using periodically L-C loaded transmission lines [J]. IEEE Trans. Microwave Theory Tech., Vol.50, No.12,2002, pp.2702-2712.
[21] Iyer A. K., Kremer P. C., Eleftheriades G. V., Experimental and theoretical verification of focusing in a large,periodically loaded transmission line negative refractive index metamatedal[J]Optics Express,Vol.11,No.7,2003,pp.696-708.
[22]杨立功,顾培夫,黄弼勤等,光波在左右手系材料界面处的传输特性[J].光子学报,Vol.32,No.10,2003,pp.1225-1227
[23]田秀劳,光波在左手材料中中的非涅尔公式和布儒斯特定律[J].光子学报,Vol.35,No.7,2006,pp.1103-1106.
[24]Qing D.,Chen G..,Goose-Haenc.hen shifts at the interfaces between left-and fight-handed media[J].Optics Letters,Vol.29,No.8,2004,pp.872-874
[25]Berman P.R.,Goose-Haenchen shift in negatively refractive media[J].Physical Review E,Vol.66,2002,pp.067603:1-3.
[26].Grzegorczyk T.M.,Chen X.,Pacheco J.,Chen J.,Wu B.-I.,and Kong J.A.,Reflection Coefficients and Goos-Hanchen Shifts in Anisotropic and Bianisotropic Left-Handed Metamaterials[J].Progress In Electromagnetics Research,PIER 51,2005,pp.83-113,
[27]Wang L.G.,Chen H.,Liu N.H.,Zhu S.Y.,Negative and positive lateral shift of a light beam reflected from a grounded slab[J].Optics Letters,Vol.31,No.8,2006,pp.1124-1126.
[28]Wu B.,Grzegorczyk T.M.,Zhang Y.,Kong J.A.,Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability[J].J.Appl.Phys.,2003,93(11):9386-9388.
[29]He Y.,Cao Z.,Shen Q.,Guided optical modes in asymmetric left-handed waveguides[J].Optics Communication,No.245,2005,pp.125-135.
[30]Xiao Z.Y.,Wang Z.H.,Dispersion characteristics of asymmetric double-negative material slab waveguides[J].J.Opt.Soc.Am.B,Vol.23,No.9,2006,pp.1757-1760.
[31]Shadrivov I.V.,Sukhorukov A.A.,Kivshar Y.S.,Guided modes in negative-refractive-index waveguides[J].Phys.Rev.E,Vol.67,2003,pp.057602:1-4.
[32]Peacock A.C.and Broderick N.G.R.,Guided modes in channel waveguides with a negative index of refraction[J].Opt.Exper.,Vol.20,No.11,2003,pp.2502-2510.
[33]He J.,He S.,Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate[J].IEEE Micro.Wireless Components Lett.,Vol.16,No.2,2006,pp.96-98.
[34]沈陆发,王子华,非对称含左手材料平面波导的传输特性[J].光电子.激光,Vol.17,No.6,2006,pp.688-692.
[35]Lufa Shen,Zihua Wang,TM Modes in Asymmetric slab Wave-guides with Left-handed materials[J].J.Shanghai University(English Edition),Vol.11,No.4,2007,pp.391-395.
[36]Cory H.,Barger A.,Surface-wave propagation along a metmaterial slab[J].Microwave Opt.Technol.Lett.,Vol.38,No.5,2003,pp.392-395.
[37]Suwailam M.M.B.,Chen Z.,Surface waves on a grounded double-negative (DNG) slab waveguide[J].Microwave Opt.Technol.Lett.,Vol.44,No.6,2005,pp.494-498.
[38]Cory H,Blum T.Surface-wave propagation along a metamaterial cylinder guide[J].Microwave and Optical Technology Letters,Vol.44,No.1,2005,pp.31-35
[39]Tsakmakidis K.L.,Hermann C.,Klaedtke A.,Jamois C.,Hess O.,Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability[J].Phys.Rev.B,Vol.73,2006,pp.085104:1-11.
[40]邸岳淼,王晓萍,肖丙刚,负折射率材料用于表面波传感的特性分析[J],光子学报,Vol.36,No.2,2007,pp.328-331.
[41]张高明,彭景翠,翦知渐,黄小益,左手材料薄板波导中模式之间的正交关系[J],物理学报,Vol.55,No.4,2006,pp.1846-1850.
[42]Marques R.,Baena J.,Effect of Losses and Dispersion on the Focusing Properties of Left--Handed Media[J].Microwave and Optical Technology Letters,Vol.41,No.4,2004,pp.290-294
[43]Cory H.and Zach C.,Wave propagation in metamaterial multi-layered structures[J].Microwave and Optical Technology Letters,Vol.40,No.6,2004,pp.460-465
[44]宋磊,李康,孔繁敏等,PML-FDTD法在分析负折射率材料中的应用[J],光子学报,Vol.36,No.8,2007,pp.1422-1425.
[45]Markos P.,Soukoulis C.M.,Numerical studies of a left-handed materials and arrays of split ring resonators[J].Phys.Rev.E,Vol.65,No.3,2002,pp.036622:1-8.
[46]Kolinko P.,Smith D.R.,Numerical study of electromagnetic waves interacting with negative index materials[J].Optics Express,Vol.11,No.7,2003,pp.640-648.
[47]Novitsky A.V.,Barkovsky L.M.,Guided modes in negative-refractive-index fibres[J].J.Opt.Pure.Appl.Opt.,No.7,2005,pp.S51-S56.
[48]何金龙,沈林放,何赛灵,软智超,负折射率光纤的导模异常特性分析[J].光子学报,Vol.33,No.11,2004,pp.1327-1329
[49]Lu Fa Shen,Zi Hua Wang.Guided modes characteristics in a fiber with left-handed material[J].Microwave and Optical Technology Letters,Vol.49,No.5,2007,pp.1039-1041
[50]Lu Fa Shen,Zi Hua Wang,Approximate solution in a doubly clad optical fiber including left-handed material[J].J.Opt.Soc.Am.B,2007,Vol.24,No.8,2007,pp.1847-1852
[51]熊天信,杨儒贵,左手介质椭圆光波导基模传播特性[J].光子学报,Vol.35,No.7,2006,pp.1099-1102.
[52]LuFa Shen,ZiHua Wang,Coupling between optical fibers with left-handed materials[J].J.Opt.Soc.Am.B,Vol.24,No.9,2007,pp.2461-2464
[53]沈陆发,王子华,汪敏,左手材料平面波导之间的耦合特性[J].半导体光电,Vol.27,No.3,2006,pp.257-259
[54]Cory H.,Skorka O.,Metamaterial slabs coupling[J].Microwave Opt.Technol.Lett.,Vol.40,No.4,2005,pp.340-343.
[55]Alu A.,Engheta N.,Anomalous mode coupling in guided-wave structures containing metamaterial with negative permittivity and permeability[J].Proceedings of the 2002 2nd IEEE Conference,pp.233-234.
[56]Xiao S.,Shen L.,He S.,A Novel Directional Coupler Utilizing Left-Handed Material[J].IEEE Photon Technol.Lett.,Vol.16,No.1,2004,pp.171-173.
[57]Engheta N.,Ziolkowski R.W.,A positive future for double-negative metamaterial[J].IEEE Trans.Micr.Theory Tech.,Vol.53,No.4,2005,pp.1535-1556
[58]Hooft G.W.t.,Comment on 'negative refraction makes a perfect lens[J].Phys.Rev.Lett.,Vol.87,No.24,2001,pp.249701(1).
[59]Qing D.K.,Chen G.,Enhancement of evanescent waves in waveguides using metamaterials of negative permittivity and permeability[J].Appl.Phys.Lett.,Vol.85,No.5,2004,pp.669-671.
[60]Grbic A.,Eleftheriades G.V.,Growing evanescent waves in negative-refractive-index transmission-line media[J].Appl.Phys.Lett.,Vol.82,No.12,2003,pp.1815-1817.
[61]郭剑兰,冉立新,陈红胜,陈抗胜,孔金瓯,异向媒质恢复倏势波作用的研究[J].浙江大学学报(工学版),Vol.39,No.6,2005,pp.906-909
[62]Ramakrishna S.A.,Pendry J.B.,The asymmetric lossy near-perfect lens[J].J.Modern Opt.,Vol.49,No.10,2002,pp.1747-1762.
[63]Engheta N.,An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability[J].IEEE Antennas and Wireless Propagation Letters,Vol.1,No.1,2002,pp.10-13.
[64]蒋美萍,陈光,陈先锋等,介质厚度对含负折射率介质Bragg微腔的影响[J].光子学报,Vol.36,No.5,2007,pp.912-917.
[65]蒋美萍,陈光,陈先锋等,含负折射率介质非线性Bragg腔的双稳态特性[J].光子学报,Vol.35,No.4,2006,pp.535-539.
[66]J.Gerardin,A.Lakhtakia,"Negative index of refraction and distributed bragg reflectors," Mire.Opt.Tech.Lett.,2002,34(6):409-411.
[67]Zhang Z.M.,Fu C.J.,Unusual photon tunneling in the presence of a layer with a negative refractive index[J].Appl.Phys.Lett.,Vol.80,No.6,2002,pp.1097-1099.
[68]Ziolkowski R.W.,Kipple A.,Application of double negative metamaterials to increase the power radiated by electrically small antennas[J].IEEE Trans.Antennas Ppropag,Vol.51,No.10,2003,pp.2626-2640
[69]Tamir T.集成光学[M].北京,科学出版社,1982:14-62(梁民基、张福初译)
[70]Kogelnik H.,Ramaswamy V.,Scaling Rules for Thin-Film Wave-guides[J].Applied Optics,Vol.13,No.8,1974,pp.1857----1862
[71]Marcuse D.,Light Transmission Optics[M].New York:Van Nostrand Reinhold Company Inc.1982:308-320
[72]叶培大,吴彝尊,光波导技术基本理论[M].人民邮电出版社,1981.pp.199-219
[73]Kawakami S.and Nishida S.,Characteristics of a doubly clad optical fiber with a low-index inner cladding[J],IEEE J.Quantum Electron,No.10,1974,pp.879-887.
[74]Kawakami S,and Nishida,S.Perturbation theory of a doubly clad optical fiber with a low-index inner cladding,IEEE Journal of Quantum Electronics,No.4,1975,pp.130-138.
[75]Vladimir M.Shalaev,Wenshan Cai,Uday K.Chettiar,et al.Negative index of refraction in optical metamaterials[J].Optics Letters,Vol.30,No.24,2005,pp.3356-3358
[76]范崇澄,彭吉虎.导波光学[M].北京:北京理工大学出版社,1987,p.68
[77]Snyder A.W.,Coupled-Mode Theory for Optical Fibers[J].J.Opt.Soc.Am.Vol.62,1972,pp.1267-1277
[78]马库塞D.,介质光波导理论[M],北京:人民邮电出版社,1982(刘弘度译)
[79]方志豪,易小波,朱秋萍,光纤波导HE_(mn)模和EH_(mn)模的划分方法[J],武汉大学学报(自然科学版),Vol.43,No.3,1997,PP:405-411.
[2]Pendry J.B.,Holden A.J.,Stewart W.J.,Youngs I.,Extremely low frequency plasmons in metallic mesostructure[j].Phys.Rev.Lett.,Vol.76,No.25,1996,pp.4773-4776.
[3]Pendty J.B.,Holden A.J.,Robbins D.J.,Stewart,W.J.Low frequency plasmons in thin-wire structures[J].J.Phys.:Condens.Matter,Vol.10,1998,pp.4785-4808.
[4]Pendry J.B.,Holden A.J.,Robins D.J.,Stewart W.J.,Magnetism from conductors and enhanced nonlinear phenomena[J].IEEE Trans.Micr.Theory Tech.,Vol.47,No.11,1999,pp.2075-2084.
[5]J.B.Pendry,Negative refraction makes a perfect lens[J].Phys.Rev.Lett.,Vol.85,No.18,2000,pp.3966---3969.
[6]N.Garcia,M.Nieto-Vesperinas,Left-handed materials do not make a perfect lens[J].,Phys.Rev.Lett.,Vol.88,No.20,2002,pp.207403:1-4.
[7]Valanju P.M.,Walser R.M.,Valanju A.P.,Wave refraction in negative-index media:Always positive and very inhomogeneous[J].Phys.Rev.Lett.,Vol.88,No.18,2002,pp.187401:1-4.
[8]Ziolkowski R.W.,Heyman E.,Wave propagation in media having negative permittivity and permeability[J].Phys.Rev.E,Vol.64,No.5,2001,pp.056625:1-15.
[9]Ye Z.,Optical transmission and reflection of perfect lenses by left-handed materials[J],Phys.Rev.B,Vol.67,2003,pp.193106:1-4.
[10]Smith D.R.,Kroll N.,Negative refractive index in left-handed materials[J].Phys.Rev.Lett.,Vol.85,No.14,2000,pp.2933-2936.
[11]Kuzmiak V.,Maradudin A.A.,Scattering properties of a cylinder fabricated from a left-handed material[J].Phys.Rev.B,Vol.64,No.4,2002,pp.045116:1-7.
[12] Zhang G. M., Peng J. C., Jian Z. J., Huang X. Y., Transmission Loss due to Modes Conversion Caused by Random Surface Imperfections in Left-Handed-Material Slab Waveguides [J].Chinese Phys. Lett., Vol. 23, No.7, 2006, pp. 1826-1829.
[13] Smith D. R., Padilla Willie J., Vier D. C, Nemat-Nasser S. C, Schultz S., Composite Medium with Simultaneously Negative Permeability and Permittivity [J]. Phys. Rev..Lett., Vol.84, No. 18,2000, pp.4184-4187.
[14] Shelby R. A., Smith D. R., Schultz S., Experimental verification of a negative index of refraction [J]. Science, Vol.292,2001, pp. 77-79.
[15] Pacheco J., Grzegorczyk T. M., Wu B. I., et al Power propagation in homogeneous isotropic frequency-dispersive left-handed media [J]. Phys. Rev. Lett., Vol.89, No.25,2002, pp.257401: 1 -4.
[16] Pendry J. B., Smith D. R., Comment on "Wave refraction in negative index media: always positive and very inhomogeneous" [J]. Phys. Rev. Lett., Vol.90, 2003, pp.029303.
[17] Kong J. A., Wu B., Zhang Y., Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability [J]. Appl. Phys. Lett., Vol.80, No.12, 2002, pp.2084-2086.
[18] Ran L., Huangfu J., Chen H., Zhang X., Chen K., Grzegorezyk T. M., Kong J. A., Beam shifting experiment for the characterization of left-handed properties[J]. J. Appl. Phys., Vol.95, No.5, 2004, pp.2238-2241.
[19] Grbic A., Eleftheriaded G. V., Experimental verification of backward wave radiation from a negative refractive index metamaterial [J]. J. Appl. Phys., Vol.92, No. 10, 2002, pp.5930-5935.
[20] Eleftheriades G. V., Iyer A. K., Kremer P. C., Planar negative refractive index media using periodically L-C loaded transmission lines [J]. IEEE Trans. Microwave Theory Tech., Vol.50, No.12,2002, pp.2702-2712.
[21] Iyer A. K., Kremer P. C., Eleftheriades G. V., Experimental and theoretical verification of focusing in a large,periodically loaded transmission line negative refractive index metamatedal[J]Optics Express,Vol.11,No.7,2003,pp.696-708.
[22]杨立功,顾培夫,黄弼勤等,光波在左右手系材料界面处的传输特性[J].光子学报,Vol.32,No.10,2003,pp.1225-1227
[23]田秀劳,光波在左手材料中中的非涅尔公式和布儒斯特定律[J].光子学报,Vol.35,No.7,2006,pp.1103-1106.
[24]Qing D.,Chen G..,Goose-Haenc.hen shifts at the interfaces between left-and fight-handed media[J].Optics Letters,Vol.29,No.8,2004,pp.872-874
[25]Berman P.R.,Goose-Haenchen shift in negatively refractive media[J].Physical Review E,Vol.66,2002,pp.067603:1-3.
[26].Grzegorczyk T.M.,Chen X.,Pacheco J.,Chen J.,Wu B.-I.,and Kong J.A.,Reflection Coefficients and Goos-Hanchen Shifts in Anisotropic and Bianisotropic Left-Handed Metamaterials[J].Progress In Electromagnetics Research,PIER 51,2005,pp.83-113,
[27]Wang L.G.,Chen H.,Liu N.H.,Zhu S.Y.,Negative and positive lateral shift of a light beam reflected from a grounded slab[J].Optics Letters,Vol.31,No.8,2006,pp.1124-1126.
[28]Wu B.,Grzegorczyk T.M.,Zhang Y.,Kong J.A.,Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability[J].J.Appl.Phys.,2003,93(11):9386-9388.
[29]He Y.,Cao Z.,Shen Q.,Guided optical modes in asymmetric left-handed waveguides[J].Optics Communication,No.245,2005,pp.125-135.
[30]Xiao Z.Y.,Wang Z.H.,Dispersion characteristics of asymmetric double-negative material slab waveguides[J].J.Opt.Soc.Am.B,Vol.23,No.9,2006,pp.1757-1760.
[31]Shadrivov I.V.,Sukhorukov A.A.,Kivshar Y.S.,Guided modes in negative-refractive-index waveguides[J].Phys.Rev.E,Vol.67,2003,pp.057602:1-4.
[32]Peacock A.C.and Broderick N.G.R.,Guided modes in channel waveguides with a negative index of refraction[J].Opt.Exper.,Vol.20,No.11,2003,pp.2502-2510.
[33]He J.,He S.,Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate[J].IEEE Micro.Wireless Components Lett.,Vol.16,No.2,2006,pp.96-98.
[34]沈陆发,王子华,非对称含左手材料平面波导的传输特性[J].光电子.激光,Vol.17,No.6,2006,pp.688-692.
[35]Lufa Shen,Zihua Wang,TM Modes in Asymmetric slab Wave-guides with Left-handed materials[J].J.Shanghai University(English Edition),Vol.11,No.4,2007,pp.391-395.
[36]Cory H.,Barger A.,Surface-wave propagation along a metmaterial slab[J].Microwave Opt.Technol.Lett.,Vol.38,No.5,2003,pp.392-395.
[37]Suwailam M.M.B.,Chen Z.,Surface waves on a grounded double-negative (DNG) slab waveguide[J].Microwave Opt.Technol.Lett.,Vol.44,No.6,2005,pp.494-498.
[38]Cory H,Blum T.Surface-wave propagation along a metamaterial cylinder guide[J].Microwave and Optical Technology Letters,Vol.44,No.1,2005,pp.31-35
[39]Tsakmakidis K.L.,Hermann C.,Klaedtke A.,Jamois C.,Hess O.,Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability[J].Phys.Rev.B,Vol.73,2006,pp.085104:1-11.
[40]邸岳淼,王晓萍,肖丙刚,负折射率材料用于表面波传感的特性分析[J],光子学报,Vol.36,No.2,2007,pp.328-331.
[41]张高明,彭景翠,翦知渐,黄小益,左手材料薄板波导中模式之间的正交关系[J],物理学报,Vol.55,No.4,2006,pp.1846-1850.
[42]Marques R.,Baena J.,Effect of Losses and Dispersion on the Focusing Properties of Left--Handed Media[J].Microwave and Optical Technology Letters,Vol.41,No.4,2004,pp.290-294
[43]Cory H.and Zach C.,Wave propagation in metamaterial multi-layered structures[J].Microwave and Optical Technology Letters,Vol.40,No.6,2004,pp.460-465
[44]宋磊,李康,孔繁敏等,PML-FDTD法在分析负折射率材料中的应用[J],光子学报,Vol.36,No.8,2007,pp.1422-1425.
[45]Markos P.,Soukoulis C.M.,Numerical studies of a left-handed materials and arrays of split ring resonators[J].Phys.Rev.E,Vol.65,No.3,2002,pp.036622:1-8.
[46]Kolinko P.,Smith D.R.,Numerical study of electromagnetic waves interacting with negative index materials[J].Optics Express,Vol.11,No.7,2003,pp.640-648.
[47]Novitsky A.V.,Barkovsky L.M.,Guided modes in negative-refractive-index fibres[J].J.Opt.Pure.Appl.Opt.,No.7,2005,pp.S51-S56.
[48]何金龙,沈林放,何赛灵,软智超,负折射率光纤的导模异常特性分析[J].光子学报,Vol.33,No.11,2004,pp.1327-1329
[49]Lu Fa Shen,Zi Hua Wang.Guided modes characteristics in a fiber with left-handed material[J].Microwave and Optical Technology Letters,Vol.49,No.5,2007,pp.1039-1041
[50]Lu Fa Shen,Zi Hua Wang,Approximate solution in a doubly clad optical fiber including left-handed material[J].J.Opt.Soc.Am.B,2007,Vol.24,No.8,2007,pp.1847-1852
[51]熊天信,杨儒贵,左手介质椭圆光波导基模传播特性[J].光子学报,Vol.35,No.7,2006,pp.1099-1102.
[52]LuFa Shen,ZiHua Wang,Coupling between optical fibers with left-handed materials[J].J.Opt.Soc.Am.B,Vol.24,No.9,2007,pp.2461-2464
[53]沈陆发,王子华,汪敏,左手材料平面波导之间的耦合特性[J].半导体光电,Vol.27,No.3,2006,pp.257-259
[54]Cory H.,Skorka O.,Metamaterial slabs coupling[J].Microwave Opt.Technol.Lett.,Vol.40,No.4,2005,pp.340-343.
[55]Alu A.,Engheta N.,Anomalous mode coupling in guided-wave structures containing metamaterial with negative permittivity and permeability[J].Proceedings of the 2002 2nd IEEE Conference,pp.233-234.
[56]Xiao S.,Shen L.,He S.,A Novel Directional Coupler Utilizing Left-Handed Material[J].IEEE Photon Technol.Lett.,Vol.16,No.1,2004,pp.171-173.
[57]Engheta N.,Ziolkowski R.W.,A positive future for double-negative metamaterial[J].IEEE Trans.Micr.Theory Tech.,Vol.53,No.4,2005,pp.1535-1556
[58]Hooft G.W.t.,Comment on 'negative refraction makes a perfect lens[J].Phys.Rev.Lett.,Vol.87,No.24,2001,pp.249701(1).
[59]Qing D.K.,Chen G.,Enhancement of evanescent waves in waveguides using metamaterials of negative permittivity and permeability[J].Appl.Phys.Lett.,Vol.85,No.5,2004,pp.669-671.
[60]Grbic A.,Eleftheriades G.V.,Growing evanescent waves in negative-refractive-index transmission-line media[J].Appl.Phys.Lett.,Vol.82,No.12,2003,pp.1815-1817.
[61]郭剑兰,冉立新,陈红胜,陈抗胜,孔金瓯,异向媒质恢复倏势波作用的研究[J].浙江大学学报(工学版),Vol.39,No.6,2005,pp.906-909
[62]Ramakrishna S.A.,Pendry J.B.,The asymmetric lossy near-perfect lens[J].J.Modern Opt.,Vol.49,No.10,2002,pp.1747-1762.
[63]Engheta N.,An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability[J].IEEE Antennas and Wireless Propagation Letters,Vol.1,No.1,2002,pp.10-13.
[64]蒋美萍,陈光,陈先锋等,介质厚度对含负折射率介质Bragg微腔的影响[J].光子学报,Vol.36,No.5,2007,pp.912-917.
[65]蒋美萍,陈光,陈先锋等,含负折射率介质非线性Bragg腔的双稳态特性[J].光子学报,Vol.35,No.4,2006,pp.535-539.
[66]J.Gerardin,A.Lakhtakia,"Negative index of refraction and distributed bragg reflectors," Mire.Opt.Tech.Lett.,2002,34(6):409-411.
[67]Zhang Z.M.,Fu C.J.,Unusual photon tunneling in the presence of a layer with a negative refractive index[J].Appl.Phys.Lett.,Vol.80,No.6,2002,pp.1097-1099.
[68]Ziolkowski R.W.,Kipple A.,Application of double negative metamaterials to increase the power radiated by electrically small antennas[J].IEEE Trans.Antennas Ppropag,Vol.51,No.10,2003,pp.2626-2640
[69]Tamir T.集成光学[M].北京,科学出版社,1982:14-62(梁民基、张福初译)
[70]Kogelnik H.,Ramaswamy V.,Scaling Rules for Thin-Film Wave-guides[J].Applied Optics,Vol.13,No.8,1974,pp.1857----1862
[71]Marcuse D.,Light Transmission Optics[M].New York:Van Nostrand Reinhold Company Inc.1982:308-320
[72]叶培大,吴彝尊,光波导技术基本理论[M].人民邮电出版社,1981.pp.199-219
[73]Kawakami S.and Nishida S.,Characteristics of a doubly clad optical fiber with a low-index inner cladding[J],IEEE J.Quantum Electron,No.10,1974,pp.879-887.
[74]Kawakami S,and Nishida,S.Perturbation theory of a doubly clad optical fiber with a low-index inner cladding,IEEE Journal of Quantum Electronics,No.4,1975,pp.130-138.
[75]Vladimir M.Shalaev,Wenshan Cai,Uday K.Chettiar,et al.Negative index of refraction in optical metamaterials[J].Optics Letters,Vol.30,No.24,2005,pp.3356-3358
[76]范崇澄,彭吉虎.导波光学[M].北京:北京理工大学出版社,1987,p.68
[77]Snyder A.W.,Coupled-Mode Theory for Optical Fibers[J].J.Opt.Soc.Am.Vol.62,1972,pp.1267-1277
[78]马库塞D.,介质光波导理论[M],北京:人民邮电出版社,1982(刘弘度译)
[79]方志豪,易小波,朱秋萍,光纤波导HE_(mn)模和EH_(mn)模的划分方法[J],武汉大学学报(自然科学版),Vol.43,No.3,1997,PP:405-411.