光频段球形负折射超常材料的特性研究
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摘要
负折射超常材料(Negative-Index Metamaterials,NIMs)是一种折射率为负的新型人工电磁材料。由于这样的超常材料能够实现很多新颖的应用如完美透镜,光纳米电路,隐形斗篷等,近年来关于负折射超常材料的研究取得了巨大的进展。随着负折射超常材料的快速发展,研究三维光频段的负折射超常材料成为科学界新的课题。基于这样的背景,本文对全介电球形颗粒和全介电球壳进行了分析研究,理论上证实了全介电纳米球壳在光频段可以展现负的折射系数。
首先,本文介绍了负折射超常材料的原理与应用,在详细了解国内外负折射超常材料研究背景的情况下,提出了本文的研究目的和内容。
其次,总结了已有的三维光频段负折射超常材料的研究方法。对三维几何构造的负折射超常材料方法中的开口谐振环(Split Ring Resonators,SRRs)和金属线模型进行了全波仿真,从理论和实验的角度证实了其在微波频段的可行性。对比各种方法后,提出本文的研究理论基础为基于米氏散射理论扩展的有效介质理论。
再次,本文提出了新的实现光频段磁响应和电响应的方法。该方法以全介电纳米颗粒为模型,以米氏扩展(Mie-extended)的有效介质理论为基础。对电介质纳米颗粒,负的有效磁导率源于强的磁偶极子响应,而负的有效介电常数源于强的电偶极子响应。通过数值模拟得到了在不同半径,数量密度,颗粒的介电常数以及外部主介质的介电常数条件下的磁响应和电响应,并定性描述了这些参数对磁响应频率和有效磁导率大小的影响趋势。
最后,对全介电纳米球壳的特性进行了研究,理论结果表明以纳米球壳为基本单元的复合材料可以展现等效的负折射系数。根据上面总结的规律,对材料参数与磁、电响应的影响大小做了一定的折中,从而把磁响应和电响应耦合在相同的频段范围。其中,低介电常数的球核产生磁响应,较高介电常数的纳米球壳产生电响应。数值模拟得到了共心的介电球壳在265THz频段折射系数为-1.2,结果证实了用全介电共心纳米球壳可以实现三维光频段负折射超常材料。这为构造三维光频段负折射超常材料提供了一条可行性的途径。
Negative-Index Metamaterials (NIMs) are new man-made electromagnetic materials with a negative index of refraction (NIR).Since these metamaterials enable a variety of novel applications such as superlens,optical nanocircuits and cloaking, marvelous progresses on the NIMs have been made in recent years.Along with the rapid development of NIMs,it has been a new task to research three-dimensional NIMs at optical frequencies.Motivated by this background,we analyse and study all dielectric nanospheres and nanoshells.It has been demonstrated theoretically that all dielectric nanoshells would exhibit negative index of refraction at optical frequencies.
Firstly, fundamentals and applications of negative-index metamaterials have been presented.Based on the detailed understanding on the progress of NIMs at home and abroad, the research target and content are proposed.
Secondly, methods on construction of three-dimensional negative-index metamaterials at optical frequencies studied by other researchers are summarized.For three-dimensional geometric construction method, a structure constructed by split-ring resonators and metal wires has been investigated using full wave simulation to verify its feasibility at microwave frequencies.After comparison of each method, Mie-exptended effective theory is selected for our research theoretical basis.
Thirdly, a new method to achieve the magnetic and electric responses at optical frequencies is proposed.It is modeled by all dielectric nanospheres,on the foundation of the Mie-extended effective medium theory.For dielectric nanospheres,a negative effective permeability originates from the strong magnetic dipole resonance.And an electric dipole resonance leads to the negative effective permittivity.On the condition of different radius,the number density, the permittivity of the nanospheres as well as the permittivity of the host medium,magnetic/electric responses have been obtained through numerical simulations.Meanwhile,the impact trend of these parameters on the resonant frequencies and effective permeability has been described qualitatively.
Finally, characteristics of all dielectric nanoshells have been researched.The theoretical result shows that a material composed of all dielectric nanoshells would exhibit equivalent negative refraction.According to the law summarized in the above, compromise between the material parameters and the magnetic/electric responses has been made in order to couple these two resonances within overlapped frequencies. The dielectric core results in the magnetic response, and the corresponding electric response is induced by the shell with higher dielectric constant. Numerical simulations are used to achieve a negative index of refraction of-1.2 at 265THz, which verify that three-dimensional NIMs can be realized with all dielectric nanospheres. This provides a practicable way for the construction of three-dimensional NIMs at optical frequencies.
首先,本文介绍了负折射超常材料的原理与应用,在详细了解国内外负折射超常材料研究背景的情况下,提出了本文的研究目的和内容。
其次,总结了已有的三维光频段负折射超常材料的研究方法。对三维几何构造的负折射超常材料方法中的开口谐振环(Split Ring Resonators,SRRs)和金属线模型进行了全波仿真,从理论和实验的角度证实了其在微波频段的可行性。对比各种方法后,提出本文的研究理论基础为基于米氏散射理论扩展的有效介质理论。
再次,本文提出了新的实现光频段磁响应和电响应的方法。该方法以全介电纳米颗粒为模型,以米氏扩展(Mie-extended)的有效介质理论为基础。对电介质纳米颗粒,负的有效磁导率源于强的磁偶极子响应,而负的有效介电常数源于强的电偶极子响应。通过数值模拟得到了在不同半径,数量密度,颗粒的介电常数以及外部主介质的介电常数条件下的磁响应和电响应,并定性描述了这些参数对磁响应频率和有效磁导率大小的影响趋势。
最后,对全介电纳米球壳的特性进行了研究,理论结果表明以纳米球壳为基本单元的复合材料可以展现等效的负折射系数。根据上面总结的规律,对材料参数与磁、电响应的影响大小做了一定的折中,从而把磁响应和电响应耦合在相同的频段范围。其中,低介电常数的球核产生磁响应,较高介电常数的纳米球壳产生电响应。数值模拟得到了共心的介电球壳在265THz频段折射系数为-1.2,结果证实了用全介电共心纳米球壳可以实现三维光频段负折射超常材料。这为构造三维光频段负折射超常材料提供了一条可行性的途径。
Negative-Index Metamaterials (NIMs) are new man-made electromagnetic materials with a negative index of refraction (NIR).Since these metamaterials enable a variety of novel applications such as superlens,optical nanocircuits and cloaking, marvelous progresses on the NIMs have been made in recent years.Along with the rapid development of NIMs,it has been a new task to research three-dimensional NIMs at optical frequencies.Motivated by this background,we analyse and study all dielectric nanospheres and nanoshells.It has been demonstrated theoretically that all dielectric nanoshells would exhibit negative index of refraction at optical frequencies.
Firstly, fundamentals and applications of negative-index metamaterials have been presented.Based on the detailed understanding on the progress of NIMs at home and abroad, the research target and content are proposed.
Secondly, methods on construction of three-dimensional negative-index metamaterials at optical frequencies studied by other researchers are summarized.For three-dimensional geometric construction method, a structure constructed by split-ring resonators and metal wires has been investigated using full wave simulation to verify its feasibility at microwave frequencies.After comparison of each method, Mie-exptended effective theory is selected for our research theoretical basis.
Thirdly, a new method to achieve the magnetic and electric responses at optical frequencies is proposed.It is modeled by all dielectric nanospheres,on the foundation of the Mie-extended effective medium theory.For dielectric nanospheres,a negative effective permeability originates from the strong magnetic dipole resonance.And an electric dipole resonance leads to the negative effective permittivity.On the condition of different radius,the number density, the permittivity of the nanospheres as well as the permittivity of the host medium,magnetic/electric responses have been obtained through numerical simulations.Meanwhile,the impact trend of these parameters on the resonant frequencies and effective permeability has been described qualitatively.
Finally, characteristics of all dielectric nanoshells have been researched.The theoretical result shows that a material composed of all dielectric nanoshells would exhibit equivalent negative refraction.According to the law summarized in the above, compromise between the material parameters and the magnetic/electric responses has been made in order to couple these two resonances within overlapped frequencies. The dielectric core results in the magnetic response, and the corresponding electric response is induced by the shell with higher dielectric constant. Numerical simulations are used to achieve a negative index of refraction of-1.2 at 265THz, which verify that three-dimensional NIMs can be realized with all dielectric nanospheres. This provides a practicable way for the construction of three-dimensional NIMs at optical frequencies.
引文
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[3]Pendry J B,Holden A J, Stewart W J,et al.Extremely Low Frequency Plasmons in Metallic Mesostructures. Physical Review Letters,1996,76(25):4773-4776
[4]Pendry J B,Holden A J, Robins D J, et al.Magnetism from conductors and enhanced nonlinear phenomena. IEEE Transactions on Microwave Theory and Techniques,1999,47(11):2075-2084
[5]Shelby R A,Smith D R, Schultz S.Experimental verification of a negative index of refraction.Science,2001,292(5514):77-79
[6]Pendry J B.Negative Refraction Makes a Perfect Lens.Physical Review Letters, 2000,85(18):3966-3969
[7]邹勇卓.新型人工电磁材料器件的设计、制作和应用研究：[浙江大学博士学位论文].浙江：浙江大学光学工程,2007,1-14
[8]付全红,赵小鹏.左手材料设计与制备的研究进展.材料导报,2008,22(6)：95-99
[9]李瑞莲.左手材料的电磁特性.人工晶体学报,2008,37(2)：316-321
[10]张世鸿,陈良,徐彬彬.左手材料研究进展及应用前景.功能材料,2006,37(1)：1-5
[11]Engheta N, Salandrino A, Alu A.Circuit Elements at Optical Frequencies: Nanoinductors, Nanocapacitors and Nanoresistors.Physical Review Letters, 2007,95(9):095504-1-4
[12]Alu A,Engheta N.Plasmonic Materials in Transparency and Cloaking Problems: Mechanism, Robustness,and Physical Insights.Optics Express,2007,15(6): 3318-3332
[13]Fang N, Lee H,Sun C,et al.Sub-Diffraction-Limited Optical Imaging with a Silver Superlens.Science,2005,208(5721):534-537
[14]Shalaev V M, Cai W S,Chettiar U K, et al.Negative index of refraction in optical metamaterials.Optics Letters,2005,30(24):3356-3358
[15]Yen T J, Padilla W J, Fang N,et al.Terahertz magnetic response from artificial materials.Science,2004,303(5663):1494-1496
[16]Linden S,Enkrich C,Wegener M,et al.Magnetic response of metamaterials at 100 terahertz.Science,2004,306(5700):1351-1353
[17]Zhang S,Fan W J, Minhas B K, et al.Midinfrared resonant magnetic nanostructures exhibiting a negative permeability. Physical Review Letters,2005, 94(3):037402-1-4
[18]Enkrich C, Wegener M, Linden S,et al.Magnetic metamaterials at telecommunication and visible frequencies.Physical Review Letters,2005, 95(20):203901-1-4
[19]Yuan H K,Chettiar U K, Cai W S,et al.A negative permeability material at red light.Optics Express,2007,15(3):1076-1083
[20]Podolskiy V A, Sarychev A K,Shalaev V M.Plasmon modes in metal nanowires and left-handed materials.J Nonlin Opt.Phys.Mater.,2002,11(1):65-74
[21]Lagarkov A N, Sarychev A K. Electromagnetic properties of composites containing elongated conducting inclusions.Physical Review B,1996,53(10): 6318-6336
[22]Zhang S,Fan W J, Malloy K J, et al.Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies. Journal of the Optical Society of America B,2006,23(3):434-438
[23]Zhou J,Zhang L,Tuttle G, et al.Negative index materials using simple short wire pairs.Physical Review B,2006,73(4):041101-1-4
[24]Chettiar U K, Kildishev A V, Klar T A, et al.Negative index metamaterial combining magnetic resonators with metal films.Optics Express,2006,14(17): 7872-7877
[25]Valentine J,Zhang S,Zentgraf T, et al.Three-dimensional optical metamaterial with a negative refractive index.Nature,2008,455(1):376-379
[26]Dolling G, Enkrich C,Wegener M,et al.Simultaneous negative phase and group velocity of light in a metamaterial.Science,2006,312(5775):892-894
[27]Holloway C L,Kuester E F, Baker J J,et al.A double negative(DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix. IEEE Transaction on Antennas and Propagation,2003,51(10):2596-2603
[28]Seo B,Ueda T, Itoh T, et al.Isotropic left handed material at optical frequency with dielectric spheres embedded in negative permittivity medium.Applied Physics Letters,2006,88(16):161122-1-3
[29]Jylha L,Kolmakov I,Maslovski S,et al.Modeling of isotropic backward-wave materials composed of resonant spheres.Journal of Applied Physics,2006,99(4): 043102-1-7
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