William L. Barnes, W. Andrew Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, Physical Review Letters, Vol. 92, article 107401 (2004). "Copyright © 2004 by the American Physical Society."We present results of the transmitted, reflected, and absorbed power associated with the enhanced transmittance of light through a silver film pierced by a periodic array of subwavelength holes. Comparing experimentally acquired dispersion curves under different polarization conditions shows that the transmission features of the array are consistent with p-polarized resonant modes of the structure. By exploring the regime in which no propagating diffracted orders are allowed, we further show that the transmittance maxima are associated with both reflectance minima and absorption maxima. These new results provide strong experimental evidence for transmission based on diffraction, assisted by the enhanced fields associated with surface plasmon polaritons

E. Devaux

J. Dintinger

J. R. Sambles

N. Bonod

P. B. Johnson

T. W. Ebbesen

W. A. Murray

W. L. Barnes

Physical Review Letters

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Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Light through Periodic Arrays of Subwavelength Holes in a Metal Film

Barnes, William L.

Murray, W. Andrew

Dintinger, J.

Devaux, E.

Ebbesen, T. W.

Open Research Exeter

P H Y S I C A L R E V I E W L E T T E R S week ending12 MARCH 2004VOLUME 92, NUMBER 10Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Lightthrough Periodic Arrays of Subwavelength Holes in a Metal FilmW. L. Barnes,1 W. A. Murray,1 J. Dintinger,2 E. Devaux,2 and T.W. Ebbesen21School of Physics, University of Exeter, Stocker Road, Exeter, United Kingdom2ISIS, Universite´ Louis Pasteur, 8 rue Gaspard Monge, Strasbourg 67000, France(Received 17 June 2003; published 9 March 2004)107401-1We present results of the transmitted, reflected, and absorbed power associated with the enhancedtransmittance of light through a silver film pierced by a periodic array of subwavelength holes.Comparing experimentally acquired dispersion curves under different polarization conditions showsthat the transmission features of the array are consistent with p-polarized resonant modes of thestructure. By exploring the regime in which no propagating diffracted orders are allowed, we furthershow that the transmittance maxima are associated with both reflectance minima and absorptionmaxima. These new results provide strong experimental evidence for transmission based on diffraction,assisted by the enhanced fields associated with surface plasmon polaritons.DOI: 10.1103/PhysRevLett.92.107401 PACS numbers: 78.20.Ci, 41.20.Jb, 42.25.Fx, 73.20.MfDiffraction of the incident plane wave by the array pro-duces waves with the required evanescent character; dif-the two periodicities of the array, and i and j are integersindicating the order of the scattering event that couplesThe observation of the enhanced transmission of lightthrough a metallic film perforated by an array of sub-wavelength holes [1] sparked a wealth of research seekingto explain the underlying physics. For light of wavelength, a hole less than=2 in diameter in a thick metal filmdoes not support any propagating modes; energy canpropagate only by an evanescent tunneling process lead-ing to very weak transmittance —in marked contrast tothe experimental observations.Initial explanations considered coupling of the incidentlight via diffraction to surface plasmon polariton (SPP)modes of the metallic structure [1,2]. Many differenttheoretical approaches have since been adopted, all rep-licating the normal incidence transmission spectra [3–7];consequently, more than just the normal incidence trans-mission spectrum needs to be explored if one is to obtaina clearer picture of the underlying physics. Despite aconvergence of views among many theorists that theenhanced transmission involves multiple diffraction en-hanced by SPPs [5–9], there remains some controversysurrounding the transmission mechanism; not all authorsagree that surface plasmons are involved. (Note that ex-planations based on results from 1D arrays of slits cannotbe used, and the physics is very different; sub-=2 slitscan support propagating modes, while sub-=2 holescannot [10].) As noted elsewhere [8], the experimentalevidence obtained thus far is consistent with the involve-ment of SPPs rather than conclusive about their involve-ment. We present new experimental data not just of thetransmittance, but also of the reflectivity and absorbance.We investigate two unexplored far-field signatures ofSPPs in this context, their polarized nature and theirdissipative character; we are thus able to identify therole played by SPPs in the transmission process.Diffraction is central to the transmission process.0031-9007=04=92(10)=107401(4)$22.50 fraction of the transmitted evanescent wave on the farside of the array then produces the propagating trans-mitted light. However, these diffraction processes areindependent of the material from which the array isfabricated, whereas it has already been shown that goodmetals show higher transmittance than poor ones [11].Therefore, although diffraction is central to the trans-mission process, the transmission in metallic structuresis being enhanced in some way.In our view, the key to the enhancement comes whendiffraction is such as to allow coupling between the in-cident light and SPP modes; this may occur in three ways.(i) Incident light couples to an SPP mode supported bythe surface facing the incident light. The enhanced fieldassociated with an SPP mode increases the probability oftransmission through the holes, where it is again scatteredby the periodic array to produce light. (ii) Incident lightcannot couple to an SPP mode on the incident side,instead matching conditions allow light that is weaklytransmitted through the array to couple to an SPP modeon the far side; the enhanced electric field associated withthe SPP mode increases the probability of transmission,and subsequent scattering again results in transmittedlight. (iii) Matching conditions allow processes (i) and(ii) to take place simultaneously.When the frequency, !, and in-plane wave vector, kk,of light that has been scattered by one or more gratingvectors matches that of a mode of the structure both thetransmittance and reflectance are modified. The matchingcondition isk 0 sin iGx  jGy  kmode; (1)where k0 is the wave vector of the light incident at a polarangle , Gx and Gy are the Bragg vectors associated with2004 The American Physical Society 107401-12.02.2 (+1,0) air(+1,0) glassTPP-1 ) 20%25%30%P H Y S I C A L R E V I E W L E T T E R S week ending12 MARCH 2004VOLUME 92, NUMBER 10incident light and a mode of the structure with wavevector kmode. By obtaining optical data as a function ofincident frequency and in-plane wave vector, the disper-sion of any modes involved may be ascertained [12]. Weacquired such data for reflectance and transmittance asdescribed elsewhere [13]. Briefly, samples were illumi-nated by a collimated ( 0:5), spectrally filteredbeam ( 2 nm). Measurements of the transmitted/reflected intensity were then recorded as a function ofthe incident wavelength and angle.Samples were formed in 180 5 nm silver films de-posited on silica glass substrates by thermal evaporation.Focused ion-beam lithography (FEI DB235) was used tomill the arrays. A period of 420 5 nm and a holediameter of 250 5 nm ensured the holes were smallenough to be sub-=2 for the lowest energy transmittancepeak (710 nm), but large enough to exhibit high trans-mittance and thus good contrast in the reflectivity data.Samples of area 1 mm2 were produced by tessellating alarge number of smaller arrays, account being taken of theresulting diffraction.Transmittance data as a function of frequency and in-plane wave vector, for unpolarized incident light, areshown in Fig. 1(b), together with a normal incidencespectrum [Fig. 1(a)]. These data are similar to thoseobtained by Ghaemi et al. [12] and show the dispersionof the transmittance features. To within experimentalerror, we found the transmittance of light incident from0.0 0.1 0.2 0.3 0.48508007507006506005505004500 10 20 308508007507006506005505004500.0 0.2 0.4 0.6 0.8 1.01.21.41.61.82.02.2(±1,±1)glass(0,±1) glass(-1,0) air(-1,0) glass(+1,0)glass(b)Frequency   ω / 2π  (µm-1 )(2  / a)In-plane wave vector k// / 2π (µm-1) π(a) Transmittance (%)Wavelength (nm)FIG. 1. Measured transmittance of the silver hole array forunpolarize light. To the left (a) is the normal incidence trans-mittance spectrum. To the right (b) transmittance is displayedas a function of in-plane wave vector and frequency in the formof a grey-scale dispersion diagram; black is low transmittance,white is high, and the data in (b) are shown on a logarithmicscale [the array period is (a)]. Also shown are the light lines(dotted lines) where diffracted orders become tangent to thesurface; the different diffracted orders are indicated accordingto whether they occur in the substrate (glass) or air. [Theselight lines can be found by replacing kmode in Eq. (1) with thevalue 0.]107401-2the air and substrate (glass) side of the sample to be thesame, as expected from the reciprocity theorem [14].A key feature of SPPs is that the electric field associ-ated with them is polarized [15,16]. Transmittance dis-persion data were acquired for p- and s-polarized light(Fig. 2) and indicate a marked polarization dependenceconsistent with the involvement of SPPs; but what of theirdispersion? To explore this we indicate as solid lines thecalculated dispersion of the SPP modes of planar silver/air and silver/glass interfaces. To calculate the modaldispersion, we used a well-established technique thatincorporated the complex refractive indices of the mate-rials involved together with their dispersion [17,18].For both the p- and s-polarized data the theoreticallyderived mode is offset to higher frequency than theexperimental data.Two observations can be made concerning thes-polarized transmittance data. First, the transmittanceat normal incidence is independent of polarization, asexpected from the symmetry of the array. Second, thes-polarized transmittance peaks exhibit very limited dis-persion, matching that expected for SPP modes that can0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.71.21.41.61.8(-1,0) glass(a)(-1,0) air ω /2π  (µm0%5.0%10%15%0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.71.21.41.61.82.02.2(b)(0,±1) air(0,±1) glassTSS  k// / 2π  (µm-1) ω/2π  (µm-1 )0%5.0%10%15%20%25%30%FIG. 2. Measured transmittance as a function of in-planewave vector and frequency in the form of a grey-scale dis-persion diagram for p-polarized incident light (a) ands-polarized incident light (b). Also shown are the calculatedSPP dispersion curves for planar surfaces. Data are shown on alinear scale and dark regions are the primary indication ofcoupling to modes. The arrows indicate the offset between theexperimentally derived and the theoretically predicted modedispersions.107401-20.0 0.1 0.2 0.3 0.4 0.5 0.6 0.71.21.41.61.82.02.2 (+1,0) air(-1,0) airRP(a) Air side ω /2π  (µm-1 )0%20%40%60%80%100%0.0 0.1 0.2 0.3 0.4 0.5 0.61.21.41.61.82.02.2(+1,0) glass(-1,0) glassRP(b) Glass side  k// / 2π (µm-1)ω /2π  (µm-1 )0%20%40%60%80%100%FIG. 3. Measured reflectance as a function of in-plane wavevector and frequency in the form of a grey-scale dispersiondiagram for p-polarized incident light incident from the airside (a) and the glass side (b). Also shown are the relevantcalculated SPP dispersion curves for planar surfaces. Data areshown on a linear scale. The dark vertical stripes near kk  0are an experimental artifact. Arrows to indicate the offsetbetween the experimentally derived and theoretically predictedmode dispersions have been omitted in this figure.P H Y S I C A L R E V I E W L E T T E R S week ending12 MARCH 2004VOLUME 92, NUMBER 10be coupled with s-polarized light, the 0;1 silver/glassand 0;1 silver/air SPP modes.Most of the essential features of the p-polarized data,Fig. 2(a), can also be associated with incident lightcoupling to SPP modes. Again, dashed lines indicatethe calculated dispersion of the SPP modes. Coupling ofincident light via 1; 0 scattering to the silver/glass SPPmode is quite clear, though offset slightly from the pre-dicted feature. The dispersion of the transmittance fea-ture associated with the silver/air SPP is not so welldefined, possibly due to surface roughness and/or chemi-cal interaction of the silver with the atmosphere.The predicted SPP mode positions are based on planarinterface calculations. For modulated surfaces, the dis-persion of SPP modes will be altered, a stop band mayopen up around kk  0 [8,19]. Further analysis of ourdata (not shown) reveals a modest stop band, of order2% for the silver/glass SPP. We are not aware of anyquantitative calculations for the SPP dispersion appropri-ate for our structure, but this would be interesting toexplore. We also note enhanced transmission !=c2 1:6 m	1, kk=2  0:6 m	1, where the modes associ-ated with the two surfaces are degenerate, in accord withprocess (iii).To probe the system further, we measured the disper-sion of the reflectance for p-polarized light incident fromboth the air and the glass sides. These data (Fig. 3) exhibitmarkedly different behavior from the transmittance data,and from each other. The data for light incident fromthe glass side are dominated by features associated withthe silver/glass SPP mode, while it is only from the airside that features associated with the silver/air SPP modeare seen.Deeper insight can be gained by combining the trans-mittance, T, and reflectance, R to infer the absorbance, A,via A  1	 R	 T. This can only give a good measure ofabsorbance provided no propagating diffracted orders areallowed, i.e., the zero-order regime [below the 	1; 0glass light line, Fig. 1(b)]. We show in Fig. 4(a) trans-mittance, reflectance, and inferred absorbance spectrafor an in-plane wave vector of 0:03 m	1 (closer tonormal incidence the detector obscured the incidentbeam). Data are shown for p-polarized light incidentfrom both glass and air sides. Further measurements(not shown) exhibited identical results for s-polarizedlight.From Fig. 4(a), we see that the long wavelength trans-mittance peak (715 nm) is associated with a reflectivityminimum and an absorbance maximum. Though perhapsinitially surprising, this absorption feature is again con-sistent with the involvement of SPPs [6,7,20]. The fields atthe metal surface are enhanced when incident light cou-ples to a SPP mode, thus aiding transmission. However,the SPP mode is also damped by absorption in the metalso that enhanced absorption is expected for the sameconditions that give enhanced transmission. The form of107401-3the reflectance, transmittance, and absorption spectra[Fig. 4(a)] and the relative position of their extremabear a striking resemblance to recent calculations [6](see Fig. 9 of Ref. [6]). The slight differences in positionsof the different extrema are to be expected as they rep-resent slightly different responses of the system. As acheck, we also acquired data at an in-plane wave vectorof 0:15 m	1 [Fig. 4(b)]. We see that in the zero-orderregion the single transmission peak of Fig. 4(a) hassplit into two, as expected from Fig. 2(a), and that bothfeatures correspond to reflectance minima/absorptionmaxima.We also note that where the transmittance is low,around 700 nm, the reflectance is high and the inferredabsorbance is consequently low. It might be tempting toattribute the low transmittance at this wavelength topower being coupled to SPPs and, hence, lost to absorp-tion rather than transmitted. Such a view might appear tobe supported by a recent report [21] that associated theexcitation of SPPs with transmittance minima. However,that work was based on slits rather than holes and, asnoted above, the physics of the two situations is verydifferent. Instead the observation of low transmittance,107401-3500 600 700 8000.00.20.40.60.81.00.20.40.60.81.0Zero orderAbsReflTrans Reflectance, Transmittance, AbsorbanceWavelength (nm)(b)    k// / 2π = 0.15 µm-1          Air          Glass AbsReflTransZero orderReflectance, Transmittance, Absorbance(a)    k// / 2π = 0.03 µm-1          Air          GlassFIG. 4. Transmittance, reflectance, and inferred absorbancespectra for p-polarized incident light at in-plane wave vectorsof 0:03 m	1 (a) and 0:15 m	1 (b).P H Y S I C A L R E V I E W L E T T E R S week ending12 MARCH 2004VOLUME 92, NUMBER 10high reflectance, and low absorbance is probably a con-sequence of the lack of available modes by which thetransmission may be enhanced.It is tempting to try to infer more from the absorptiondata, especially the feature associated with the silver/airSPP mode. However, caution must be exercised becausean account needs to be taken of how much power goesinto propagating diffracted orders when one is not in thezero-order regime. The importance of such diffractioncan be gauged from the fact that, when conditions weresuch that only diffraction in the glass was allowed, wemeasured the fraction of incident power that goesinto each of the four diffracted orders to be 5%. Onlyin the zero-order regime can absorption data be easilyinterpreted.We can summarize our findings with four observations.First, the dispersion of the transmittance features depends107401-4on the polarization of the incident light, being consistentwith the involvement of p-polarized resonant modes[Fig. 2]. Second, the transmission and reflection spectraof metallic hole arrays are associated with modes on thetwo surfaces, not just for normal incidence, but for allangles [Figs. 1–3]. Third, in the zero-order regime trans-mission maxima are associated with reflectivity minimaand with absorbance maxima [Fig. 4]. Fourth, again inthe zero-order regime, the transmission minima are as-sociated with reflectance maxima and absorbance min-ima [Fig. 4]. All four observations are consistent with theview that SPP modes act to enhance the fields associatedwith the evanescent waves, thus providing a way to in-crease the transmittance. In this picture, enhanced trans-mission naturally occurs when coupling conditions allowsurface plasmon polaritons on one or both metal surfacesto be excited. We note that enhanced transmittance mightperhaps also occur through the involvement of othersurface waves such as surface phonon polaritons [22].[1] T.W. Ebbesen et al., Nature (London) 391, 667 (1998).[2] J. R. Sambles, Nature (London) 391, 641 (1998).[3] L. Martı´n-Moreno et al., Phys. Rev. Lett. 86, 1114 (2001).[4] V. M. Vigoureux, Opt. Commun. 198, 257 (2001).[5] M. M. J. Treacy, Phys. Rev. B 66, 195105 (2002).[6] M. Sarrazin, J. P. Vigneron, and V. M. Vigoureux, Phys.Rev. B 67, 085415 (2003).[7] N. Bonod et al., Opt. Express 11, 482 (2003).[8] S. A. Darmanyan and A.V. Zayats, Phys. Rev. B 67,035424 (2003).[9] S. Enoch et al., J. Opt. A Pure Appl. Opt. 4, S83 (2002).[10] E. Popov et al., Phys. Rev. B 62, 16 100 (2000).[11] D. E. Grupp et al., Appl. Phys. Lett. 77, 1569 (2000).[12] H. F. Ghaemi et al., Phys. Rev. B 58, 6779 (1998).[13] M. G. Salt and W. L. Barnes, Opt. Commun. 166, 151(1999).[14] G. N. Afanasiev, J. Phys. D 34, 539 (2001).[15] J. R. Sambles, G.W. Bradbery, and F. Yang, Contemp.Phys. 32, 173 (1991).[16] S. C. Hohng et al., Appl. Phys. Lett. 81, 3239 (2002).[17] W. L. Barnes, J. Mod. Opt. 45, 661 (1998).[18] In addition to the complex refractive index of the silver[P. B. Johnson and R.W. Christy, Phys. Rev. B 6, 4370(1972)], we included the effect of a sulfide layer at thesilver/air interface typical of samples exposed to a pol-luted atmosphere; see G. J. Kovacs, Surf. Sci. 78, L245(1978).[19] W. L. Barnes et al., Phys. Rev. B 54, 6227 (1996).[20] I. R. Hooper and J. R. Sambles, Phys. Rev. B 67, 235404(2003).[21] Q. Cao and P. Lalanne, Phys. Rev. Lett. 88, 057403(2002).[22] J. J. Greffet et al., Nature (London) 416, 61 (2002).107401-4

Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Light through Periodic Arrays of Subwavelength Holes in a Metal Film

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