超材料翻译.doc

Nature materials LETTERSPublished online : 18 APRIL 2010| DOI:10.1038/NMAT2747A single-layer wide-angle negative-index metamaterial at visible frequencies在可见光频率的一种单层广角负折射率超材料Metamaterials are materials with artificial electromagnetic properties defined by their sub-wavelength structure rather than their chemical composition.基于亚波长结构而非化学结构，超材料也叫人工电磁材料。Negative-index materials(NIMs) are a special class of metamaterials characterized by an effective negative index that give rise to such unusual wave behavior as backwards phase propagation and negative refraction.负折射率材料（NIMs）是一类具有有效负折射率的特殊超材料，能够产生逆向传播和负折射的不同寻常的波行为。These extraordinary properties lead to many interesting functions such as sub-diffraction imaging and invisibility cloaking.这些非凡的性能使得有有趣的功能，如子衍射成像和隐蔽伪装So far ,NIMs have been realized through layering of resonant structures,such as spilt-ring resonators ,and have been demonstrated at microwave to infrared frequencies over a narrow range of angles-of-incidence and polarization.到目前，负折射率材料（NIMs）已经通过谐振结构层实现，例如开环谐振器，而且在较窄范围的红外频率内的入射角和偏振也可以证明。However ,resonant-element NIM designs suffer from the limitations of not being scalable to operate at visible frequencies because of intrinsic fabrication limitations,require multiple functional layers to achieve strong scattering and have refractive indices that are highly dependent on angle of incidence and polarization.然而，由于内在的制造受限，谐振元件负折射率超材料设计受到不能扩展至可见光频率的限制，因此NIM设计需要有多个功能层，大都基于入射角和偏振来获得强大的散射和折光率。Here we report a metamaterial composed of a single layer of coupled plasmonic coaxial waveguides that exhibits an effective refractive index of-2 in the blue spectral region with a figure-of -merit larger than 8 .这里我们报告一种超材料，该材料包含一层耦合电浆同轴波导管，展现了在灵敏值大于8的蓝色光谱区有效的折光率，其折光率为2.The resulting NIM refractive index is insensitive to both polarization and angle-of-incidence over a 50angular range,yielding a wide-angle NIM at visible frequencies.结果得到的超材料折射率在50角度范围对偏振和入射角均不敏感，在可见光区产生广角超材料折射率。Negative-index materials were first predicted theoretically by Veselago in 1968,but it was only a decade ago that Pendry defined NIM designs suitable for experimental realization. 1968年 Veselago理论推测了负折射率材料的存在，而仅仅在十年之后 Pendry就将NIM合理设计于实验。In these resonant-element based NIMs,the unusual left handed behaviour of light originates from subwavelength resonant elements that behave like artificial atoms with engineered diamagnetic resonance that are the source of the materials negative-index response.在基于负折射率材料的这些谐振单元中，不同寻常的光的左手现象，光源于亚波谐振单元，表现就像人造原子与工程抗磁共振，该共振引起了材料的负指数反映， As much,NIMs were first demonstrated experimentally with arrays of millimetre-size copper strips and split-ring resonators operating at microwave frequencies. 同样，在很多毫米大小铜带和开环谐振器、微波频率实验条件下NIMs 被第一次证明存在。This discovery sparked a considerate effort to scale down the size of the constituent resonant components to enable operation at higher frequencies.这个发现引发了相当大的努力来缩小所组成谐振元件大小，以便在更高的频率运行。As a result，micrometre-size structures have been successfully fabricated to produce negative refractive indices at terahertz frequencies.如此一来，得以成功制备微米大小的结构，该结构能在太赫兹频率（远红外）产生负折射率。More recently,NIMs have been fabricated to operate in the near-infrared spectral region.最近，NIMs已制备出可在近红外光谱区工作。However ,for operation at optical frequencies the required size of sub wavelength scatterers is very close to practical fabrication limits .然而，在光学频率工作所需的亚波长散射体大小是非常接近实际制造限制的。So far,the highest reported operational frequency of NIMs has been demonstrated at the deep-red side of the visible spectrum (0=780nm) using fishnet structure with features as small as 8nm (ref.14). 到目前为止，通过使用最小为8纳米的“渔网”结构，所报道的NIMs最高操作频率已经在可见光谱波长为780纳米的深红外区证明。 Moreover,to achieve strong scattering ,the materials was built up from a stack of multiple physical layers-thus complicating the fabrication of resonant-element based NIMs for operation at visible frequencies.此外，为了获得强散射，在可见光频率下工作，基于NIMs制备复杂的谐振单元 ，所以以多个物理堆栈层结构制备材料。Recently,using waveguides,a conceptually different approach was taken to achieve a negative refractive index in the optical spectral range.最近，通过使用波导，在光的光谱范围，一种概念性不同的方法被用来获得负折射率。Investigation of the mode structure of two-dimensional metal/insulator/metal(MIM) plasmonic slab waveguides reveals that certain MIM waveguide geometries support negative-index modes at visible frequencies两维金属/绝缘体/金属（MIM）电浆平板波导管的模式结构的研究结果表明，在可见光频率，一定的MIM波导几何结构支持负折射率模式。Arrays of such negative-index MIM slab waveguides can serve as a quasi three-dimensional metamaterial.像这样的负折射率的MIM平板电导阵列可以作为一种准三维超材料。However,the negative-index mode in MIM waveguide can only be excited from free space with the perpendicular polarization and off-normal angles of incidence because of the polarization and symmetry of the mode ,respectively. 然而，因为MIM波导的负折射率模式的偏振和对称性，这种模式只能从正交偏振和非正常入射角的自由空间才得以激发。These practical limitations of planar MIM geometries can be circumvented in a coaxial MIM geometry in which the planar MIM waveguide is wrapped onto itself (Fig.1).平面几何这些实际限制，可以规避到自身（图一）裹在平面MIM波导同轴的MIM几何机构。Similar to the modes supported by planar MIM plasmonic waveguides,the coaxial waveguide geometry is found to also support field symmetric and anti-symmetric modes that correspond to positive and negative-index modes ,respectively. 类似平面MIM电浆波导所支持的模式，被发现支持与正负指数模式分别对应的对称与反对称模式However ,unlike planar MIM waveguides show a negative-index mode that ,owing to the cylindrical symmetry of the structure,is accessible from free space independent of both incidence angle and polarization .然而，与显示负指数模式的平面MIM波导不同的是，由于圆柱形对称，该结构可以以互不干扰的入射角和偏振进入自由空间Here,we demonstrate that a two-dimensional array of vertically oriented MIM coaxial waveguides,arranged in a dense hexagonal configuration,functions as a single-layer wide-angle negative index material down to the blue part of the visible spectrum.这里，我们表明，一个垂直方向的MIM同轴波导的二维数组排列成紧密六方形，其作用为单层广角负折射率下降到可见光谱的蓝色部分的材料。Through parameter retrieval analysis ,we verify the NIM to have a double-negative index band in the 450-500nm spectral range.通过参数检索分析，我们验证的NIM在450-500纳米光谱范围内有双负指数带。Furthermore,we find that the effective refractive index of this geometry is insensitive to both polarization and angle of incidence up to 50.此外，我们发现这种几何结构的有效折射率对于超过50的偏振和入射角均不敏感。Unlike the wire arrays of Liu et al.,which exhibit negative refraction but not a negative index,the coupled coaxial waveguide array exhibits a true negative refractive index characterized by negative refraction and backwards phase propagation.与能展现出负折射而不是负指数的线阵列不同，同轴波导阵列表现出一个真正的负折射率，具有负折射和逆向传播的特点。Figure 1a schematically depicts the NIM,consisting of a hexagonal close-packed array of Ag/GaP/Ag MIM coaxial waveguides composed of 25nm GaP annular channels with a 75nm inner diameter set at a pitch of p=165nm in a Ag layer.图1a示意图描述的NIM，包含一个六方形紧密堆积银/间隙/银MIM同轴波导，该波导在单个银层中165纳米间距有25纳米的间隙环流渠道和75 纳米的内直径。We study the metamaterial response both by analytic waveguide modal analysis for single coaxial structures,and using finite-difference time-domain (FDTD) simulation for the array of coupled coaxial waveguides.我们通过分析波导模态分析单同轴结构，通过使用有限差分时域（FDTD）模拟耦合同轴波导阵列，来研究超材料的反应。To estimate the effective refractive index of the material,we first calculate the mode index dispersion of the constituent coaxial elements by solving Maxwells equations in cylindrical coordinates for a single MIM coaxial waveguide of infinite length.为了估计材料的有效折射率，通过在圆柱体坐标中解答Maxwell方程，我们首先计算所组成同轴元素的模式指数扩散，进而获得单一极长的MIM同轴波导。The waveguide eigenmodes are characterized by a complex propagation constant along the z axis ()= ()+ i(),where and are the real and imaginary parts of the propagation constant ,respectively. 波导本征模可以用沿着Z轴的一组复杂传播常数来表征 ()= ()+ i()，其中 和 分别对应传播常数的实际和理想部分。 Complex optical constants for Ag(ref.25) and GaP (ref.26) are taken from tabulated literature data.Ag和GaP复杂的光常数引用于表格中的文献材料。Figure 2a and b show the calculated dispersion relations ()and ()of a single Ag/GaP/Ag coaxial waveguide.图2a和b表明了单层Ag/GaP/Ag同轴波导 ()和 ()的预计扩散关系。Figure1|Negative-index metamaterial geometry.a,Single-layer NIM slab consisting of a hexagonal array of subwavelength coaxial waveguide structures.The inner radius r1,outer radius r2 and array pitch p are defined in the image.b, Unit cell of the periodic structure.The angle-of-incidence is shown,as well as the in-plane(p-)and out-of-plane(s-)polarization directions associated with the incident wavevector k.图一|负指数超材料几何结构。a图，单层NIM板包含一个亚波长同轴波导结构的六方阵列。内半径r1，外半径r2和列队P在图中已标出。b图，周期结构中的单体。入射角如图所示，入射平面和射出平面偏振方向与入射光波k相关。Figure2|Coaxial waveguide dispersion relations.图2|同轴波导扩散关系The coaxial waveguide consists of an infinitely long 25nm GaP annular channel with a 75nm inner diameter embedded in Ag.同轴波导包含极长的25nm和75nm内直径GaP嵌入银层中的环状隧道，Plotted are the two lowest order linearly polarized modes that most strongly couple to free space radiation.图中有序标出了与自由空间辐射最匹配的两条最低偏振模式的线条。a-c，Energy is plotted versus （a），（b）and mode index nmode(c).a-c图，能量分别对应a图，b图和c图模式指数。d.The figure-of-merit FOM=| /|.d图对应的FOM值特点为/的绝对值。The Ag/GaP planar surface plasmon energy at hwsp=2.3eV(0=540nm)is indicated by the black dashed horizontal line.Ag/GaP 平面的表面等离子体能量在hwsp为2.3eV波长为540nm处用黑色水平虚线在图中表示出。All panels show one mode with positive index (red curve)and one mode with a negative index (blue curve) below an energy of 2.7eV(0=460nm).在波长为460nm处，2.7eV能级以下实验所有的板面都有正指数（红色曲线）模式和负指数（蓝色曲线）模式 The insets in a show the Re(Hy)(out-of-page) field distribution in the waveguide at a wavelength of 0=650nm for the positive-index mode and at 0=483nm for the negative-index mode.图a中的插图展示了在波长为650nm的正指数模式和483nm处的负指数模式的波导中的场分布。The mode index nmode=c/ is plotted in Fig.2c.模式指数nmode=c/已在图2c中标出。Similar to what is reported for planar MIM structures we find one mode with a positive index over the entire spectral range(red curve),and a second mode with a negative index for energies below 2.7ev(blue curve).与报道的平面MIM结构相似，在整个光谱区我们发现一种正指数模式（红色曲线），和在低于2.7eV能级时的负指数模式（蓝色曲线）The index of the second mode ranges from -9nmode1 in the energy range of Fig.2在图2中的能级范围中，第二模式指数范围是 -9nmode1.The insets in Fig.2a show the Re(Hy) field profiles corresponding to the positive-index mode at 0=650nm(nmode=8.5) and the negative-index mode at 0=483nm(nmode=-2.0) .图2a中的插图表明了与650nm波长(nmode=8.5)时的正指数模式和483nm波长（nmode=-2.0）相对应的Re（Hy）场分布A full field map of the negative-index mode can be found in Supplementary Fig.S1.负指数模式的全场分布图见附图S1.Figure 2b shows that for energies below hsp=2.3ev the positive-index mode (red curve) has the lowest attenuation and will therefore be dominant ,whereas for energies above hsp the negative-index mode(blue curve)is dominant.图2b表明在能级低于hsp=2.3ev时的正指数模式（红色曲线）有最小衰减值，因此起决定作用。相反，能级高于hsp时负指数（蓝色曲线）起决定作用。Figure 2d shows the figure-of-merit,FOM= | /|（ref.27）,of the two modes. 图2d为两种模式中的质量因数。The lowest attenuation constant for the negative-index mode is found at 0=483nm ,with a corresponding FOM of 8.3.在波长为483nm处，表征负指数模式的常数 有最小衰减程度，对应FOM为8.3Next ,we analyse the collective response of the coupled coaxial waveguide array using the FDTD method.通过使用FDTD方法，我们分析了与同轴波导阵列匹配的集体反应。Figure 3a shows a time-snapshot of Re(Hy)inside a 165nm pitch coaxial waveguide array illuminated by a 0=483nm p-polarized plane wave incident at 30.图3a展示了在以p偏振平面入射角为30度波长为483nm波谱照射时，在165nm的同轴波导内部的Re（Hy）快照。At this pitch the waveguides are separated by 40nm,corresponding to twice the radical skin depth(20nm)of an isolated coaxial waveguide mode into the Ag cladding.以此角度波导被分为40nm的小段，相应于2倍孤立同轴波导模式下的投射银层辐射表面深度。Phase fronts are observed to clearly refract in the negative direction,that is ,to the same side of the interface normal.我们清楚地观察到Phase fronts 以负方向折射，也就是，折射到法线的同一方向。By following the phase fronts in time(Supplementary Movie S1)we observe backward phase propagation at an angle of -12.5with respect to the interface normal,as indicated in Fig.3a by the blue arrow labeled k通过及时追踪Phase fronts （附短片S1），我们观察到到达法线是以-12.5度角的后相传播进行的，如图3a中蓝色箭头k所示. Using Snells law and the wavevector refraction angle inside the material,we find that the metamaterial has an effective refractive index of neff=-2.3,close to the mode index found for an individual coaxial waveguide at this wavelength(n mode=-2.0).运用Snell 定律和材料内部的波矢折射角度，我们发现该超材料的有效折射率为-2.3，与此波长下单体同轴波导的模式指数相近。Furthermore,the direction of energy flow S inside the NIM layer, depicted by the green arrow in Fig.3a,is found to be anti-parallel to the phase velocity- a signature of a true negative index material.此外，我们发现，NIM层内部的能量流S的流动方向与相速度（真正的负折射率材料的标志）反平行，如图3a中的绿色箭头所示，Thus ,at a separation of 40nm ,the waveguides are coupled just enough to allow both power and phase to refract negatively across the waveguide structures with anti-parallel directions, while only perturbing the metamaterials effective index from that of a single coax byn= -0.3.因此，波导以间距40nm，足够使得功率和相位以反平行方向负折射波导结构。From the wavelength in the metamaterial and the exponential energy decay in the waveguides we find a metamaterial FOM of 8,equal to the FOM calculated for isolated coaxial structures.从超材料中的波长和波导中的能量衰减指数，我们得以发现一种FOM为8的超材料，与所计算得到的孤立同轴结构FOM等同。By repeating this analysis for angles ranging from 10 to 50 ,for both s- and p-polarized light at 0=483nm,we find very similar results for the materials response, with neff varying between -2.1 and -2.4.通过重复分析波长为483纳米以10到50度角偏振的s和p偏振光，我们发现它们的neff 在-2.1和-2.4区间浮动，对于材料的反应有非常相近的结果。The data for p-polarized light are summarized in Supplementary Fig.S2.P偏振光的材料已在图S2中有所概述。 Such a small dependence of the index on polarization and angle-of incidence has not been demonstrated in any other NIM reported so far. 偏振率与入射角度如此小的相关性目前在任何NIM还未有报道过。For example, Valentine etal. Investigated only normal incidence excitation for a NIM operational in the near-infrared spectral region, whereas the negative-index mode in planar MIM structures can only be excited at off-normal incidence angles and at a specific polarization. We note that simulations as in Fig.3a show the semi-infinite NIM slab to reflect35% of the incident light,depending on angle ,indicating that a significant fraction of light coupled into the NIM layer . Notably ,for oblique incidence,in addition to exciting the lowest order linearly polarized coaxial waveguide modes (n=1),we also excite a minor contribution from the radially polarized mode (n=0). However ,this small modal overlap does not significantly change the material index response,as both modes have similar dispersion relations around the operation wavelength of 0=483nm. Further details regarding the modal decomposition can be found in the Supplemental Information. To further investigate the effect of coupling between coaxial waveguides, we also performed calculations for which the pitch is set to p=330nm,corresponding to a waveguide separation of 10 skin depths. As expected,we find that for the same excitation conditions of 0=483nm light incident at 30,the waveguides are effectively decoupled with power flowing straight down the coaxial waveguides. Indeed ,by calc