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1、左手材料负折射率材料左手材料负折射率材料左手材料（LHM）与负折射率 在经典电动力学中，介质的电磁性质可以用介电常数和磁导率两个宏观参数来描述。正弦时变电磁场的波动方程（Helmholtz方程）为： （1） 其中&2000年，Smith等人将金属丝板和SRR板有规律地排列在一起，制作了世界上第一块等效介电常数和等效磁导率同时为负数的介质。Smith D.R. ,Willie J. ,et al. , Phys. Rev. Lett. ,2000,84,4184左手材料的研究与进展&2003年，Parazzoli等人在实验和数值模拟上进一步验证了NIM中的Snell定律，为左手物质是否真实存在的
2、争论暂时划下了一个句点 。Parazzoli C. G. ,Greegor R. B. ,et al , Phys. Rev. Lett. ,2003,90,107401&2001年，Shelby等人首次在实验上证实了当电磁波斜入射到左手材料与右手材料的分界面时，折射波的方向与入射波的方向在分界面法线的同侧。Shelby R. ,Smith D.R. ,et al ,Science ,2001,292,77负折射率的应用发展前景 负折射率材料可以用于平板透镜，光束控制，耦合器等方面。v“完美透镜” (Perfect Lens)的概念与应用L传统透镜的分辨率限制(diffraction limi
3、t)： x2/k= 这也是造成DVD读写密度限制和光刻电路密度限制的主要原因。J左手材料制成的透镜，在合适的条件下，可以成为“完美透镜”，实现亚波长分辨率。v“完美透镜”的局限与解决方法 虽然负折射率材料制成的“完美透镜”可以实现亚波长分辨率，但是实现“完美透镜”的条件是相当苛刻的。目前还只能在微波区段实现负折射率，而且频率范围很窄。它们都是对电磁波有较大的损耗，而且很难将尺寸制作到足够小以至于在光学频率下使用。 光子晶体 (Photonic Crystals)Fig 11. Photonic Crystals: (a), (b) Holes-in-dielectric; (c) rods-i
4、n-air(c)光子晶体(PC)是由两种或两种以上的电介质材料周期性排列而成的人造材料，排列周期为波长量级，具有光电带隙，可以控制电磁波在其中的传播。在一定条件下，它也可以表现出负折射率的现象。Parimi P., Lu W., et al. ,Phy. Rev. Lett. ,2004,92,127401Fig 12 (a) Experimental setup (not to scale). (b) Propagation vectors for positive and negative refraction. (c) (f ) Microwave electric field maps
5、 in the far field region. (c) Negative and (e) positive refraction by the metallic PC prism for the incident beam along K (incident angle 30 ). WF(wave front) with respect to refracting surface. (d) Negative refraction for the incident beam along M (incidence angle 60). (f ) Positive refraction by a
6、 polystyrene prism. In all the field maps, approximate area of each field map is 43 40 cm2. 光子晶体的 “等效负折射率”可以由构成材料的电介质的介电常数和材料周期性来调整，而且在高频率下有着很低的电磁损耗，三维PC比较容易制成，因此PC比左手材料更容易实现红外和光学频率下的应用。展望 光刻蚀技术(photolithography) 近场光学显微仪 (near-field optical microscopy) 可选波长的滤光器 (wavelength-tunable filter) 光学显示器 (opt
7、ical displays) 新材料往往伴随着新现象和新技术的发展。随着负折射率材料的发展，许多原有的技术将得到新的发展。Fig 5. (A) A negative index metamaterial formed by SRRs and wires deposited on opposite sides lithographically on standard circuit board. The height of the structure is 1 cm. (B) The power detected as a function of angle in a Snells law ex
8、periment performed on a Teflon sample (blue curve) and a negative index sample (red curve).Shelby R. ,Smith D.R. ,et al ,Science ,2001,292,77Fig 6. Unit cell of the 901 HWD structure. The direction of propagation of the electromagnetic field is along the x axis, the electric field is oriented along
9、the z axis, and the magnetic field is along the y axis. C=0.025 cm, D=0.030 cm, G=0.046 cm, H= 0.0254 cm, L= 0.33 cm, S= 0.263 cm, T= 17.010-4 cm, W= 0.025 cm, and V= 0.255 cm.Fig 7. Schematic of the setup used in the Snells law experiment showing the conical horn, lens, sample, and waveguide detect
10、or. The measurements were made in the focused and collimated mode at 33 and 66 cm away from the sample.Parazzoli C. G. ,Greegor R. B. ,et al , Phys. Rev. Lett. ,2003,90,107401Fig 8. Surface plot of measured normalized Ez(r,f ). Refracted peaks :by Teflon at 48.2(n=1.4) and is independent of frequenc
11、y; by the NIM , however, at 12.6GHz,-30.6 (n=-1.0454) that are a function of the frequency.Fig 9. (a) Measured angular profile of the normalized Ez(r), at f =12.6 GHz for detector distances of 33 and 66 cm from the wedges. (b) Measured 33 cm data compared to simulated results at 33, 66, and 238 cm (
12、100)from the wedges.Fig 10. Perfect lensing in action: (A) the far field and (B) the near field, translating the object into a perfect image. (C) Microwave experiments* demonstrate that subwavelength focusing is possible, limited only by losses in the system. (D) Measured data compared to the perfect results. Losses limit the resolution to less than perfect but better than the diffraction limit.CD* Grbic A. ,Eleftheriades G. , Phy. Rev. Lett. ,2004,92,117403mo磁共振频率； mp磁等离子化频率eo电子共振频率； ep电等离子化频率只要0 p，e、就可以同时为负数。
