关 键 词：

金属 介质 复合 结构 色散 特性 研究 说明书 开题

资源描述：

金属—介质复合结构的色散特性研究说明书及开题,金属,介质,复合,结构,色散,特性,研究,说明书,开题

内容简介：

VOLUME85, NUMBER18PHYSICAL REVIEW LETTERS30 OCTOBER2000Negative Refraction Makes a Perfect LensJ.B. PendryCondensed Matter Theory Group, The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom(Received 25 April 2000)With a conventional lens sharpness of the image is always limited by the wavelength of light. Anunconventional alternative to a lens, a slab of negative refractive index material, has the power to focusall Fourier components of a 2D image, even those that do not propagate in a radiative manner. Such“superlenses” can be realized in the microwave band with current technology. Our simulations show thata version of the lens operating at the frequency of visible light can be realized in the form of a thin slabof silver. This optical version resolves objects only a few nanometers across.PACS numbers: 78.20.Ci, 42.30.Wb, 73.20.Mf, 78.66.BzOptical lenses have for centuries been one of scientistsprime tools. Their operation is well understood on the ba-sis of classical optics: curved surfaces focus light by virtueof the refractive index contrast. Equally their limitationsare dictated by wave optics: no lens can focus light ontoan area smaller than a square wavelength. What is therenew to say other than to polish the lens more perfectly andto invent slightly better dielectrics?In this Letter I wantto challenge the traditional limitation on lens performanceand propose a class of “superlenses,” and to suggest a prac-tical scheme for implementing such a lens.Let us look more closely at the reasons for limitationin performance. Consider an infinitesimal dipole of fre-quency v in front of a lens. The electric component of thefield will be given by some 2D Fourier expansion,E?r,t? ?Xs,kx,kyEs?kx,ky?3 exp?ikzz 1 ikxx 1 ikyy 2 ivt?,(1)where we choose the axis of the lens to be the z axis.Maxwells equations tell us thatkz? 1qv2c222 k2x2 k2y,v2c22. k2x1 k2y.(2)The function of the lens is to apply a phase correction toeach of the Fourier components so that at some distancebeyond the lens the fields reassemble to a focus, and animage of the dipole source appears. However, somethingis missing: for larger values of the transverse wave vector,kz? 1iqk2x1 k2y2 v2c22,v2c22, k2x1 k2y.(3)These evanescent waves decay exponentially with z and nophase correction will restore them to their proper ampli-tude. They are effectively removed from the image whichgenerally comprises only the propagating waves. Since thepropagating waves are limited tok2x1 k2y, v2c22,(4)the maximum resolution in the image can never be greaterthanD ?2pkmax?2pcv? l,(5)and this is true however perfect the lens and however largethe aperture.Thereis anunconventionalalternativetoalens. Materialwith negative refractive index will focus light even whenin the form of a parallel-sided slab of material. In Fig. 1,I sketch the focusing action of such a slab, assuming thatthe refractive indexn ? 21.(6)A moments thought will show that the figure obeys Snellslaws of refraction at the surface as light inside the mediummakes a negative angle with the surface normal. The othercharacteristic of the system is the double focusing effect re-vealed by a simple ray diagram. Light transmitted througha slab of thickness d2located a distance d1from the sourcecomes to a second focus whenz ? d22 d1.(7)The underlying secret of this medium is that both the di-electric function, , and the magnetic permeability, m, hap-pen to be negative. In that instance we have chosenFIG. 1.A negative refractive index medium bends light to anegative angle with the surface normal. Light formerly divergingfrom a point source is set in reverse and converges back to apoint. Released from the medium the light reaches a focus fora second time.39660031-9007?00?85(18)?3966(4)$15.00 2000 The American Physical SocietyVOLUME85, NUMBER18PHYSICAL REVIEW LETTERS30 OCTOBER2000 ? 21,m ? 21.(8)At first sight this simply implies that the refractive indexis that of vacuum,n ?pm,(9)but further consideration will reveal that when both andm are negative we must choose the negative square root in(9). However, the other relevant quantity, the impedanceof the medium,Z ?rmm00,(10)retains its positive sign so that, when both ? 21 andm ? 21, the medium is a perfect match to free spaceand the interfaces show no reflection. At the far boundarythere is again an impedance match and the light is perfectlytransmitted into vacuum.Calculations confirm that all of the energy is perfectlytransmittedinto themediumbutina strangemanner: trans-port of energy in the 1z direction requires that, in themedium,k0z? 2qv2c222 k2x2 k2y.(11)Overall the transmission coefficient of the medium isT ? tt0? exp?ik0zd? ? exp?2iqv2c222 k2x2 k2yd?,(12)where d is the slab thickness and the negative phase resultsfrom the choice of wave vector forced upon us by causality.It is this phase reversal that enables the medium to refocuslight by canceling the phase acquired by light as it movesaway from its source.All this was pointed out by Veselago 1 some time ago.The new message in this Letter is that, remarkably, themedium can also cancel the decay of evanescent waves.The challenge here is that such waves decay in amplitude,not in phase, as they propagate away from the object plane.Therefore to focus them we need to amplify them ratherthan to correct their phase. We shall show that evanescentwaves emerge from the far side of the medium enhanced inamplitude by the transmission process. This does not vio-late energy conservation because evanescent waves trans-port no energy, but nevertheless it is a surprising result.The proof is not difficult. Let us assume S-polarizedlight in vacuum. The electric field is given byE0S1? ?0,1,0?exp?ikzz 1 ikxx 2 ivt?,(13)where the wave vector,kz? 1iqk2x1 k2y2 v2c22,v2c22, k2x1 k2y,(14)implies exponential decay.At the interface with themedium some of the light is reflected,E0S2? r?0,1,0?exp?2ikzz 1 ikxx 2 ivt?,(15)and some transmitted into the medium,E1S1? t?0,1,0?exp?ik0zz 1 ikxx 2 ivt?,(16)wherek0z? 1iqk2x1 k2y2 mv2c22,mv2c22, k2x1 k2y.(17)Causality requires that we choose this form of the wave inthe medium: it must decay away exponentially from theinterface. By matching wave fields at the interface, weshow thatt ?2mkzmkz1 k0z,r ?mkz2 k0zmkz1 k0z.(18)Conversely a wave inside the medium incident on the inter-face with vacuum experiences transmission and reflectionas follows:t0?2k0zk0z1 mkz,r0?k0z2 mkzk0z1 mkz.(19)To calculate transmission through both surfaces of the slabwe must sum the multiple scattering events,TS? tt0exp?ik0zd? 1 tt0r02exp?3ik0zd?1 tt0r04exp?5ik0zd? 1 .?tt0exp?ik0zd?1 2 r02exp?2ik0zd?.(20)By substituting from (19) and (20) and taking the limit,limm!21!21TS? limm!21!21tt0exp?ik0zd?1 2 r02exp?2ik0zd? limm!21!212mkzmkz1 k0z2k0zk0z1 mkzexp?ik0zd?1 2 ?k0z2mkzk0z1mkz?2exp?2ik0zd? exp?2ik0zd? ? exp?2ikzd?.(21)3967VOLUME85, NUMBER18PHYSICAL REVIEW LETTERS30 OCTOBER2000The reflection coefficient is given bylimm!21!21RS? limm!21!21r 1tt0r0exp?2ik0zd?1 2 r02exp?2ik0zd? 0.(22)A similar result holds for P-polarized evanescent waves:limm!21!21TP? limm!21!212kzkz1 k0z2k0zk0z1 kz3exp?ik0zd?1 2 ?k0z2kzk0z1kz?2exp?2ik0zd? exp?2ikzd?.(23)Thus, even though we have meticulously carried througha strictly causal calculation, our final result is that themedium does amplify evanescent waves.Hence weconclude that with this new lens both propagating andevanescent waves contribute to the resolution of theimage. Therefore there is no physical obstacle to perfectreconstruction of the image beyond practical limitationsof apertures and perfection of the lens surface. This is theprincipal conclusion of this Letter.No scheme can be of much interest if the means ofrealizing it are not available. Fortunately several recentdevelopments make such a lens a practical possibility, atleast in some regions of the spectrum. Some time ago itwas shown that wire structures with lattice spacings of theorder of a few millimeters behave like a plasma with aresonant frequency, vep, in the GHz region 2. The idealdielectric response of a plasma is given by ? 1 2v2epv2(24)and takes negative values for v , vep. More recentlywe have also shown 3 that a structure containing loopsof conducting wire has properties mimicking a magneticplasma,m ? 1 2v2mpv2,(25)and, although the analogy is less perfect, it has been shownthat 2yem has been attained in these structures 4. Thusby tuning the design parameters it is certainly possible toproduce a structure closely approaching the ideal of ? 21,m ? 21,(26)at least at a single frequency.At optical frequencies several metals behave like anearly perfect plasma with a dielectric function modeledby (24): silver, gold, and copper are perhaps the bestexamples. The magnetic properties of known materials areless obliging. However we can still make some progresseven in this case. Consider the electrostatic limit: a systemin which all dimensions are smaller than the wavelengthof light. In this system we can neglect radiative effectsdecoupling electrostatic and magnetostatic fields:theelectrostatics claim ownership of the P-polarized fields,and the magnetostatics claim the S-polarized fields.In the electrostatic limit,v c0qk2x1 k2y.(27)It follows from (14) thatlimk2x1k2x!kz?limk2x1k2x!iqk2x1 k2y2 v2c220? iqk2x1 k2x(28)and, from (17)limk2x1k2x!k0z?limk2x1k2x!iqk2x1 k2y2 mv2c220? iqk2x1 k2x? kz.(29)Hence in this limit we see that, for the P-polarized fields,dependenceonmis eliminatedandonlythe dielectricfunc-tion is relevant. The transmission coefficient of the slabbecomeslimk2x1k2x!TP?limk2x1k2x!2kzkz1 k0z2k0zk0z1 kz3exp?ik0zd?1 2 ?k0z2kzk0z1kz?2exp?2ik0zd?4exp?ikzd? 1 1?22 ? 2 1?2exp?2ikzd?,(30)and hence, in this limit, we need only assumelim!21limk2x1k2x!TP? lim!214exp?ikzd? 1 1?22 ? 2 1?2exp?2ikzd? exp?2ikzd? ? exp?1qk2x1 k2xd?(31)to obtain focusing of a quasielectrostatic field, withoutplacing any conditions on m. It is interesting to note that ? 21 is exactly the condition needed for a surface plas-mon 5 to exist: there is a link between focusing actionand the existence of well-defined surface plasmons.Let us estimate how well we can focus an image using alayer of silver. We shall assume that the object comprisesan electrostatic potential with two spikes shown in Fig. 2.In the absence of the silver the electrostatic potential isblurred at a distance z ? 2d ? 80 nm away from the ob-ject and we can no longer resolve the two spikes becausethe higher order Fourier components of the potential arereduced in amplitude,V?x,z ? 2d? ?Xkxykxexp?1ikxx 2 2kxd?.(32)This result is shown in Fig. 2.We wish to use a slab of silver, thickness d, as a lensto restore the amplitude of the higher order Fourier com-ponents and to focus the image.We use the followingapproximate dielectric function for silver:3968VOLUME85, NUMBER18PHYSICAL REVIEW LETTERS30 OCTOBER2000objectplaneimageplanesilverslab40nm(a)z-axis80nm0+100-100x-axis (nanometers)objectintensity -2V0+100-100image withsilver slabimage withoutsilver slabx-axis (nanometers)imageintensity -2V(b)(c)FIG. 2.(a) Plan view of the new lens in operation. A quasi-electrostatic potential in the object plane is imaged by the actionof a silver lens. (b) The electrostatic field in the object plane.(c) The electrostatic field in the image plane with and withoutthe silver slab in place. The reconstruction would be perfectwere it not for finite absorption in the silver. ? 5.7 2 92v221 0.4i .(33)Evidently the imaginary part of the dielectric functionwill place some practical limitations on the focusing ef-fect and, by choosing the optimum frequency for focusingof 3.48 eV, the “focused” image becomesVf?x,z ? 2d? ?Xkxykxexp?1ikxx 2 2kxd?0.04 1 exp?22kxd?.(34)This result is also plotted in Fig. 2. Evidently only thefinite imaginary part of the dielectric function preventsideal reconstruction. However, considerable focusing isachieved.Intense focusing of light by exploiting surface plas-mons can also be achieved via a completely different routeas Ebbesen et al. 6 and Porto et al. 7 have recentlydemonstrated.The quasistatic limit also considerably eases design cri-teria at microwave frequencies.For example we couldmake a near field electrostatic lens operating in the GHzband by using a slab of material containing thin gold wiresoriented normal to the surface and spaced in a square lat-tice cell side 5 mm. Perhaps the most interesting possibil-ity for imaging in the GHz band is the magnetostatic limit.A structure comprising a set of metallic rings as describedin an earlier paper would give m ? 21 at an appropri-ate frequency, and would focus sources of magnetic fieldsinto sharp images. Since many materials are transparentto magnetic fields, this would make an interesting imagingdevice for peering inside nonmagnetic objects.We have given a prescription for bringing light to a per-fect focus without the usual constraints impose