负折射率材料

1、负折射率材料中超短脉冲的研究进展2008.4.18,2003年，美国著名的科学杂志science将负折射率介质评为年度十大科学进展之一。负折射率介质是当今非常热门的研究领域。 英国皇家学院 ，美国的加州大学圣迭戈分校、普渡大学等率先在该方面进行了理论和实验研究。 我国浙江大学、苏州大学、复旦大学、同济大学、上海理工大学、东南大学铁军教授、南京大学等对负折射人工电磁材料及微波器件进行了不同程度的研究。这些研究主要集中于对不同材料、不同波段的各种负折射率介质的研制以及介质的奇异电磁特性研究。,主要内容,什么是负折射率材料 负折射率材料的研究与进展 微波波段的负折射率材料的研究进展 光波波段的负折射

2、率材料的研究进展 负折射率材料中短脉冲的研究进展,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,什么是负折射率材料,自然界中,物质的和一般都与电磁波频率有关，并且在大多数情况下都为正数，此时方程(1)有波动解，电磁波能在其中传播。对于无损耗、各向同性、空间均匀的介质，由maxwell方程组能推出 可见， 、 、 之间满足右手螺旋关系。,通常的介质就被称为“右手材料” (right-handed materials, rhm),如果介质的和都小于零，则 k2 0，方程(1)有波动解，电磁波能在其中传

3、播。但 、 、 之间不再满足右手螺旋关系而是满足左手螺旋关系。这种介质就被称为“左手材料” （left-handed metamaterials, lhm),如果介质的和两者之间一个为正数, 而另一个为负数，则 k2 0，k无实数解；即方程(1)无波动解，电磁波不能在其中传播。,e 0, m 0 e 0, m 0 (right-handed) (left-handed),由于电磁波能流的方向取决于玻印廷矢量s的方向，而 ， 即 、 、 始终构成右手螺旋关系。因此在左手材料中，（它的方向代表电磁波相速的方向）和 的方向相反。 为负数，所以这种介质也被称为“负折射率物质”（negative ind

4、ex materials, nim) 左手材料中，电磁波的相速度和群速度方向相反。,左手材料又称为负折射率物质,相速度和群速度,normal refraction,negative refraction,折射光仍然满足snell定律,(a) 入射光在经过一般介质与左手材料接口时，折射光偏折方向会与入 射光在法线的同一边。 (b) 以左手材料为材质制作的凸透镜或凹透镜，分别会表现出散光或聚 光效果。 (c) 平板状的左手材料，会有类似一般凸透镜的聚光效果。,pendry et al. j phys. cond. matter 15 6345 (2003),反常的doppler效应,若光源发出频率

5、 w0 的光，而侦测器以速度v接近光源时，在一般介质之中侦测器所接收到的电磁波频率将比 w0高，而在左手材料中，则会收到比w0低的频率。,反常的切伦柯夫（cerenkov）效应和光压,在 cerenkov 辐射效应中，当一个粒子在介质中以速度 v 沿一直线运动，其辐射出的场会遵循 的形式，波向量 k (k=kz/cosq) 的方向会主要顺着v的方向，但 kr 方向分量则在一般介质与左手材料中恰好会完全相反。 电磁辐射对反射体造成的光压，在左手材料的环境之中形成对反射体的拉曳力，而不是如在一般介质中的压力。,一般介质与左手材料中的比较：(a) cerenkov效应；(b) 光压,负折射率材料的研

6、究与进展,微波波段负折射率材料,1968年前苏联物理学家veselago对电磁波在介电常数和磁导率同时为负数的介质中的传播特点作过纯理论的研究。,1996-1999年，英国皇家学院pendry等人相继提出了用周期性排列的金属条和开口金属谐振环(split-ring resonator)可以在微波波段产生负等效介电常数和负等效磁导率。,pendry j.b. ,et al. , phys. rev. lett. , 76, 4773 (1996) pendry j.b. ,et al. , ieee trans. microwave theo. and tech. ,47,2075 (1999)

7、,veselago v.g. , sov. phys. usp. 10, 509 (1968),smith d.r. ,willie j. ,et al. , phys. rev. lett. 84 ,4184 (2000),2000年，美国加州大学圣迭戈分校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。,毫米尺寸,first lhm,two concentric split-ring resonators (srrs), which be regarded as an electronic circuit consistin

8、g of inductive and capacitive elements, were predicted to give rise to 0. the rings form the inductances and the two slits as well as the gap between the two rings can be considered as capacitors. a magnetic field oriented perpendicular to the plane of the rings induces an opposing magnetic field in

9、 the loop owing to lenzs law. this leads to a diamagnetic response and hence to a negative real part of the permeability.,the upper curve (solid line) is that of the srr array with lattice parameter a 8.0 mm. by adding wires uniformly between split rings, a passband occurs where and are both negativ

10、e (dashed curve).,the lhm sample consists of square copper split ring resonators and copper wire strips on fiber glass circuit board material. the rings and wires are on opposite sides of the boards.,_ is for the lhm data. is for the regions where the index is expected to be either outside our limit

11、 of detection (|n|3) or could not be reliably determined experimentally. _ is the real component . is the imaginary component of the theoretical expression for the refractive index,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 292,77(2001

12、),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争论暂时划下了一个句点 。,parazzoli c. g. ,greegor r. b. ,et al , phys. rev. lett. 90,107401 (2003),measured angular profile of the normalized electric field amplitude ez, at a constant frequency f= 12.6 ghz for detector distances of 33 and 66 cm from t

13、he teflon and 901 hwd nim wedges.,optical negative-index materials,there are several approaches to obtaining nims, such as photonic crystals, transmission lines and their optical analogues.,index for optical frequencies has only been achieved by the approach of magnetically active media.,for natural

14、ly occurring materials at optical frequencies, the magnetic permeability is close to its free space value(=1). this is because the magnetic-field component of light couples to atoms much more weakly than the electric component.,as a magnetic response is a precursor for negative refraction, it is of

15、critical importance to address the fundamental problem above by engineering optical magnetism.,a double-periodic array of pairs of parallel gold nanorods with n= -0.3 at the optical communication wavelength of 1.5 m.,v. m. shalaev, et al.opt. lett. 30, 3356 (2005).,the metal rods can also be thought

16、 of as inductors, where the gaps at the ends form two capacitors.,the first experimental demonstrations of negative refractive index in the optical range,arrays of ellipsoidal voids in a pair of metal sheets with a negative index at about = 2 m.(f = 0.5 ),zhang,s.et al. prl 95, 137404 (2005).,the na

17、no-fishnet where re(n)=-2, 1.5m , and the largest figure of merit f = 3 was obtained at 1.4 m.,dolling, g. et al. opt.lett. 31, 1800 (2006).,2007, g. dolling,et al miniaturized a silver-based nim design and obtainded a real part of the refractive index of 0.6. at a 780 nm wavelength in the laborator

18、y.,g. dolling, et al, opt. lett. 32, 53 (2007).,the properties of nims were studied in the linear regime of wave propagation, when both and are considered to be independent of the field intensities.,recent progress of short optical pulses in nims,2003, m.lapine studied a possibility to construct a m

19、eta-material which possesses nonlinear response by inserting diode into resonant conductive elements in the microwave frequency range. (no specific structure),m. lapine, et al, phys. rev. e 67, 065601 (2003).,2003, zharov, et al, for the first time, nonlinear properties of lhms composed of a lattice

20、 of the split-ring resonators and wires with a nonlinear dielectric.,a. a. zharov, i. v. shadrivov, and y. kivshar, prl 91, 037401(2003).,they shown that the hysteresis-type dependence of the magnetic permeability on the field intensity allows changing the material properties from left- to right-han

21、ded and back.,schematic of the composite metamaterial structure.,2005, lazarides and tsironis, within the slowly varying envelope approximation, derived a system of coupled nonlinear schrdinger equations for electromagnetic wave propagation in nonlinear left-handed materials.,n. lazarides and g. p.

22、tsironis, phys. rev. e 71, 036614 (2005).,where,main difference in nonmagnetic fiber m=0,manakov model,the kink-shaped compound soliton,2005, scalora et al derived a new generalized nonlinear schrodinger equation describing the propagation of ultrashort pulses in nims.,m. scalora, et al, phys. rev.

23、lett. 95, 013902 (2005).,the linear and nonlinear coefficients can be tailored through the linear properties of the medium to attain any combination of signs unachievable in ordinary matter, with significant potential to realize a wide class of solitary waves.,substituting and retaining linear deriv

24、atives up to second order, and neglecting nonlinear second order temporal derivatives, the above equations can be writed as,under the retarded coordinates,and approximations,then,compared to the case of ordinary nonlinear dynamics, the equations includes a lot of new, richer dynamical characteristic

25、s due to special linear and nonlinear coefficient.,first, the sign of the gvd can be positive or negative, depending on the particular choice of parameters. second, assuming a positive(3) , the sign of the leading nonlinear coefficient is always positive. the quintic correction term is always positi

26、ve, and its effect is to enhance the nonlinearity. for ordinary materials the effect of this term is to quench the nonlinearity. third, usually the coefficient of the shock term is negative , but it can be positive in a frequency range in nims.,in optical fiber,in nims,in optical fibers, the shock t

27、erm causes the pulse to steepen along its trailing edge and the spectrum to split asymmetrically with larger identifiable redshifted peaks. in nims the opposite occurs.,m. marklund, et al, phys. rev. e 73, 037601 (2006).,2006, m. marklund et al investigated the stability of ultrashort pulses in nega

28、tive refractive index media using methods of quantum statistics. they presented a unique short pulse soliton, which is found analytically, can propagate in the medium.,model,0, the case of a normal bulk materials. 0, for metamaterials. the larger growth rate for metamaterials is clearly seen.,there

29、exists an exact bright solitons solution in the form,the features of the soliton solution for two different values of z.,thus, it is reasonable to conclude that soliton formation and filamentation of ultrashort pulses can be much more effective in nims as compared to normal bulk media,2006, s. wen,

30、et al investigated mi in nim with a kerr nonlinear polarization based on a derived nlse for ultrashort pulse propagation by a standard linear stability analysis.,model,conclusion: the difference between the mi in nim andin ordinary material is due to the fact that negative refraction reverses the si

31、gn of the diffraction term, with the signs of dispersion and nonlinearity unchanged. the most notable property of mi in nim is that it can be manipulated by engineering the self-steepening effect by choosing the size of split-ring resonator circuit elements.,s. wen, et al phys. rev. e 73, 036617 (20

32、06).,2006, s. wen, et al studied the role of the anomalous self-steepening effect in mi in nims.,conclusion: the negative ss parameter can have a very large value compared to an ordinary positive-index material. in nims, ss effect can be either positive or negative, with the zero ss point determined by the size of split-ring resonator circuit elements.the controllable zero ss point can be used to manipulate mi, and thus manipulate the generation of solitons.,model,s. wen,et al, opt. express 14, 1568 (2006).,2007, y.j. xiang, s.c. wen,