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[Physical Review Letters 96 (2006) 97401.pdf](https://mdr.nims.go.jp/filesets/ad078f1c-b12f-4e8f-8b48-9bca6a09c6c4/download)

## Creator

[Hideki T. Miyazaki](https://orcid.org/0000-0003-4152-1171), Yoichi Kurokawa

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[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Squeezing Visible Light waves into a 3-nm-thick and 55-nm-long Plasmon Cavity](https://mdr.nims.go.jp/datasets/ceeba9ab-7a0f-49dd-8966-a951f95a341c)

## Fulltext

untitledPRL 96, 097401 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending10 MARCH 2006Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon CavityHideki T. Miyazaki*Materials Engineering Laboratory, National Institute for Materials Science,1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanYoichi KurokawaInternational Center for Young Scientists, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan(Received 30 August 2005; published 7 March 2006)0031-9007=We demonstrate controlled squeezing of visible light waves into nanometer-sized optical cavities. Thelight is perpendicularly confined in a few-nanometer-thick SiO2 film sandwiched between Au claddings inthe form of surface plasmon polaritons and exhibits Fabry-Perot resonances in a longitudinal direction. Asthe thickness of the dielectric core is reduced, the plasmon wavelength becomes shorter; then a smallercavity is realized. A dispersion relation down to a surface plasmon wavelength of 51 nm for a red light,which is less than 8% of the free-space wavelength, was experimentally observed. Any obvious break-downs of the macroscopic electromagnetics based on continuous dielectric media were not disclosed for3-nm-thick cores.DOI: 10.1103/PhysRevLett.96.097401 PACS numbers: 78.67.�n, 71.36.+c, 71.45.Gm, 73.20.MfλλλFIG. 1 (color). Dispersion relations of MIM waveguides forTM modes propagating in the z direction. The geometry, thecoordinate system, and the field components of the TM mode areillustrated in the inset. The black solid curve shows the disper-sion for a single interface, and colored ones those for low-energymodes for various T values. We used the value of 2.1 and thereported values [27] for the dielectric constants of SiO2 and Au,respectively.Surface plasmons, electromagnetic surface wavescoupled to free electron plasma in metals [1,2], are nowa-days familiar to us in biomolecule detection. Since thediscovery of the single-molecule sensitivity of Ramanscattering at the contact point of silver nanoparticles [3],plasmon resonance at small gaps in metallic subwave-length structures has attracted attention in terms of en-hanced spectroscopy. Various geometries have beenextensively studied both theoretically [4,5] and experimen-tally [6–10]. However, the vital problem of reproduciblefabrication of nanometer-sized gaps has been left unsolved.In this Letter, we propose a clear-cut architecture of plas-mon cavity resonators, in which a nanometer-thick dielec-tric film is employed as the gap. The spatial extent of theenergy can be reduced perpendicularly by metal claddings[11] and longitudinally by large wave vectors of the sup-ported plasmons [12]. We demonstrate the resonant con-finement of visible light waves in a dielectric core as thin as3.3 nm and as short as 55 nm. The minimum wavelength ofthe plasmon polariton observed is 51 nm for a red light,which is less than 8% of the free-space wavelength. A softx-ray wavelength for a visible frequency is almost withinour reach [13].The structure of our resonator is simple; it is a so-calledMIM (metal-insulator-metal) waveguide with a finitelength. Consider a dielectric sheet with a thickness of Tbetween two noble metal slabs. Here we restrict our dis-cussion to Au=SiO2=Au systems. Figure 1 depicts theanalytical dispersion curves [14] of propagating TM (trans-verse magnetic) modes for various T values. When twoinsulator-metal interfaces are brought closer to each other,the dispersion curve of a single interface splits into high-and low-energy modes. Figure 1 shows only the low-energy ones for simplicity. Surface plasmons can be ex-cited from a free space without momentum matching sim-ply by perpendicular incidence to the end face [15].06=96(9)=097401(4)$23.00 09740However, due to the matching of the field symmetry,only the low-energy mode is excited. Here we utilize thismode.When T � 100 nm, the dispersion is not so differentfrom that of a single interface. However, when T is re-duced, the interaction of two interfaces gets stronger andthe dispersion curve of the lower mode becomes flat.Particularly, for T values less than 10 nm, we can obtainplasmons with small wavelengths (�p) on the order of10 nm, i.e., extreme ultraviolet wavelengths, for free-spacewavelengths (�) ranging from visible to near-infrared; they1-1 © 2006 The American Physical Societyhttp://dx.doi.org/10.1103/PhysRevLett.96.097401PRL 96, 097401 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending10 MARCH 2006open a route to nanocavities. Moreover, small T values leadto higher amplitude of excited fields [5]. This can also beunderstood from the viewpoint of the plasmon density ofstates inversely proportional to the slope of the dispersioncurves [16]. While reproducible realization of gaps nar-rower than 10 nm by current lithography-based technolo-gies is difficult [9], deposition of nanometer-thick thin filmis sufficiently feasible with conventional techniques.In the course of the investigation on the extraordinarytransmission through nanohole arrays [17], Fabry-Perotresonance in narrow slits has been unveiled [18–21]. Theplasmon modes supported by the slits are reflected by theend faces, so that the electric field becomes the maximumat the ends, and can form standing waves between twosurfaces. In other words, a MIM waveguide with a finitelength (L) works as a resonator [19]. Our original point isto realize this slit by depositing a dielectric thin film. Sincethe nanometer-thick dielectric sheet functions as a cavityresonator for plasmons, we would like to call such astructure a nanosheet plasmon cavity.FIG. 2 (color). Energy density distribution in a MIM wave-guide with a finite length. The first-order resonance for T �3:3 nm and L � 65 nm. The thickness of the Au slabs in the xdirection is 150 nm. A TM (x)-polarized plane wave of � �970 nm is incident from the left. The dashed lines are the bordersbetween Au, SiO2, and free space. Right: Electric and magneticfields at z � 2 nm and L=2, respectively. These are typicalprofiles of the MIM guided mode. Below: Fields at x � 0. Theelectric field shows the maximum amplitudes near both endfaces, and the magnetic field exhibits a peak at the center; atypical standing wave of m � 1. The fields are the snapshots atthe moment of the maximum amplitude. The energy density andthe fields are normalized by those of the incident wave. Theenergy was calculated taking account of the frequency dispersionof the dielectric constant of Au [16,28]. Each corner of the modelhas a radius of 0.25 nm to avoid unphysically singular values.09740Figure 2 shows the theoretical results of the energydensity distribution in a cavity at a typical first-orderresonance (order number: m � 1). In this Letter, we usedthe two-dimensional (2D) boundary element method [22]for calculation. Perpendicular (x) and longitudinal (z) en-ergy confinement is clearly visualized. Furthermore, thefield distribution suggests that the simple standing wavepicture inside a MIM waveguide is surely applicable. Notethat the electric field is maximized near the entrance andthe exit surfaces (z � 0 and L). Consequently, we canexpose molecules approximately to the maximum fieldby just letting the molecules adsorbed on the end face ofthe SiO2 sheet. This is a novel feature, which was notpresent in conventional optical cavities, and is especiallyimportant for the application to enhanced Ramanspectroscopy.MIM geometries have not attracted attention as trans-mission lines due to their limited propagation lengths [11]:The imaginary part of the dielectric constant of the metalinduces Joule heating losses. Nonetheless, giant Ramanenhancements were demonstrated in dimers of silver nano-particles [3], which can be regarded as MIM configura-tions. From this fact, we expect that the profit from thestrong energy confinement of MIM cavities can outweighthe disadvantage of losses.To fabricate the cavities, Au=SiO2=Au multilayers werefirst deposited on fused silica substrates by magnetronsputtering. The thickness of the Au layers was fixed to150 nm and those of the SiO2 film were T � 56, 14, and3.3 nm. Transmission electron microscopy was employedto measure T and to inspect the morphology of SiO2 layers.The result is exemplified in the inset in Fig. 3. Next theAu=SiO2=Au multilayers were processed with a focusedFIG. 3. Scanning electron micrograph of a fabricated nano-sheet plasmon cavity. T � 14 nm, L � 107 nm, and W �3 �m. Scale bar, 500 nm. Inset: The transmission electronmicrograph of the cross section for T � 3:3 nm. Scale bar,20 nm. Although the SiO2 film is wavy due to the surfaceroughness of the first Au layer, this feature had no influenceon the optical properties in this study. The SiO2 film looksduplicated because the microscope specimen has a finite thick-ness and the vicinities of convex and concave points of the filmlook brighter.1-2PRL 96, 097401 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending10 MARCH 2006ion beam from the normal direction, so that rectangularcavities with widths ofW and lengths of L are left unmilledas shown in Fig. 3. For each T value, about 20–30 cavitieswith different L values (L � 55–483 nm) were arrayedalong one of the edges of the substrate. The structuresare assumed to be infinitely long in the y direction inFigs. 1 and 2. To minimize the discrepancy of the experi-mental samples from the theoretical models, W was set to3 �m, which is sufficiently long compared with �p.Resonance in a nanostructure can be probed with far-field signals in most cases [4–9]. In this study, the en-trance surfaces of the cavities were vertically illuminatedwith a nearly collimated white light, and the backscatteringspectrum only from a selected area around the center ofeach single cavity was measured, as depicted in Fig. 4(b).The measured quantity is hereafter simply called reflec-tance. Representative results are displayed in Fig. 4(a).Dips were observed in the reflection spectra for TM polar-ization, and they systematically shifted as a function of L.Calculated results of the reflectance and the field enhance-ment at the center of the entrance surface are compared inFig. 4(c). It is obvious that the reflection dips are the signsof the resonances. At the peaks of the field enhancementFIG. 4 (color). (a) Measured reflectance for various L values.T � 14 nm and TM polarization. The individual spectra areoffset by 0.04 from one another for visibility. Arrows indicatethe major dips. (b) Schematic drawing illustrating the incident,the collected scattered light, and the measurement area (diame-ter: 2 �m). (c) Calculated reflectance (upper) and intensityenhancement at the center of the entrance surface (lower) forTM polarization for representative T and L values. The field isnormalized by that of the incident light. The thin lines indicatethe experimental reflection spectra for similar parameters (left:L � 106 nm; right: 61 nm). The reflection dips and the fieldpeaks are denoted by arrows. The fields in Fig. 2 correspond tothe m � 1 peak in the right panel. The Q values of the reso-nances are 10–20.09740spectra, standing waves as exemplified in Fig. 2 wereconfirmed by the calculation of the field distributions. Inaddition, Fig. 4(c) manifests the agreement of the dippositions in the experimental reflection spectra with thoseby the calculation. By comparison with the calculation, themajor dips in Fig. 4(a) were assigned to the resonances ofm � 1–4. Similar results were obtained also for T � 56and 3.3 nm. In contrast, remarkable features were notfound in the reflection for TE (transverse electric) po-larization. Thus, the Fabry-Perot resonance of plasmonpolaritons in the fabricated cavities was successfully dem-onstrated. Several minor dips discernible in the spectra forsmall L values in Fig. 4(a) were not reproduced by thecalculation. These could be due to the transverse modes inthe y direction.At the mth resonance in a cavity with a length of L, thecorresponding wave vector of the propagating plasmon, k,is expressed as k � 2�=�p � m�=L. Therefore, the dis-persion relations of the plasmon in the cavities can beexperimentally determined [23]. In Fig. 5, the reflectiondips observed were plotted. The resonances of variousorders for various L values formed single dispersion curvesunique to each T value. Furthermore, the experimentalresults showed fairly good agreement with the analyticaldispersion curves [14] of MIM waveguides. This alsoproves that the macroscopic electromagnetics, in whichthe spatial dispersion effects [24] are neglected, is appli-cable to a 3-nm-thick core so far as far-field responses arediscussed. Nanometric slits can be regarded as media witha large refractive index n [19]. The dashed lines in Fig. 5indicate the dispersions for representative n values. A redlight of � � 651 nm in vacuum is confined in the cavity asλλFIG. 5 (color). Experimentally obtained dispersion relations.Solid curves: Analytical dispersion of MIM waveguides. Dashedlines: Propagation in the media with refractive indices of ndrawn for reference. The non-negligible discrepancy betweenthe analytical model and the experiment for T � 14 nm proba-bly originates from an error in the thickness measurement.1-3PRL 96, 097401 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending10 MARCH 2006a surface plasmon polariton with a wavelength of �p �51 nm. This wavelength is equivalent to that for n ’ 13.Such a large index is unattainable by bulk materials.Larger wave vectors enable us to realize smaller cavities.The minimum modal volume in this study is V �0:000 95 �m3 � 0:0012�3 � 1:6TLW [25]. This valuewas estimated according to the definition of Foresi et al.[26] with a slight modification; we used the maximumenergy density on the z axis for the normalization insteadof the maximum density in the whole space, because themaximum but singular value at the edge of the Au clad-dings gives an unrealistically small V value. Despite thelarge width of W � 3 �m, the estimated modal volume isvery small. For cavities of W ’ �p, further reduction ofmore than one order is possible. Although the Q value issmall, Q=V values comparable to those of the conventionaloptical resonators might be obtained because of the verysmall V.In summary, we proposed the nanosheet plasmon cavityas a new configuration of optical resonators and demon-strated energy confinement in volumes much smaller thanthe free-space wavelengths (’0:001�3). Although the esti-mated intensity enhancements for the fabricated cavitiesresulted in modest values as high as jEj2 ’ 103 [Fig. 4(c)],a further enhancement should be possible for periodicallyarrayed cavities by the interaction with the plasmons alongthe entrance and the exit surfaces [18]. Reduction of thewidth W would also lead to a larger field enhancement bythe energy confinement in a much smaller volume. For athinner core, a breakdown of the macroscopic electromag-netics is expected; it would probably result in enhancedlosses [24] and resultant deterioration in resonances. Wavevector dependence of the dielectric functions should beconsidered.We are grateful to H. Miyazaki, K. Miyano, H. Tamaru,K. Ohtaka, and T. Ochiai for discussion and the MaterialsAnalysis Station of the National Institute for MaterialsScience and N. Ishikawa for technical support. This workwas supported by PRESTO of the Japan Science andTechnology Agency and by Special Coordination Fundsfor Promoting Science and Technology from the Ministryof Education, Culture, Sports, Science and Technology.09740*Electronic address: MIYAZAKI.Hideki@nims.go.jp[1] W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature(London) 424, 824 (2003).[2] J. Pendry, Science 285, 1687 (1999).[3] H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys.Rev. Lett. 83, 4357 (1999).[4] M. Futamata, Y. Maruyama, and M. Ishikawa, J. Phys.Chem. B 107, 7607 (2003).[5] E. Hao and G. C. Schatz, J. Chem. Phys. 120, 357 (2004).[6] H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano,Appl. Phys. Lett. 80, 1826 (2002).[7] W. Rechberger et al., Opt. Commun. 220, 137 (2003).[8] D. P. Fromm et al., Nano Lett. 4, 957 (2004).[9] L. Gunnarsson et al., J. Phys. Chem. B 109, 1079 (2005).[10] P. Mühlschlegel et al., Science 308, 1607 (2005).[11] R. Zia, M. D. Selker, P. B. Catrysse, and M. L.Brongersma, J. Opt. Soc. 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