Magnetic Plasmon Formation and Propagation in Artificial AromaticMoleculesNa Liu,†,¶,* Shaunak Mukherjee,‡,¶ Kui Bao,§,¶ Lisa V. Brown,‡ Jens Dorfmuller,⊥ Peter Nordlander,†,§,∥

and Naomi J. Halas†,‡,§,∥,*†Department of Electrical and Computer Engineering, ‡Department of Chemistry, §Department of Physics and Astronomy, and∥Laboratory for Nanophotonics, Rice University, 6100 Main Street, Houston, Texas 77005, United States⊥4th Physics Institute and Research Center SCoPE, University of Stuttgart, D-70569 Stuttgart, Germany

*S Supporting Information

ABSTRACT: The plasmonic properties of coupled metallic nanostructuresare understood through the analogy between their collective plasmon modesand the electronic orbitals of corresponding molecules. Here we expand thisanalogy to planar arrangements of plasmonic nanostructures whose magneticplasmons directly resemble the delocalized orbitals of aromatic hydrocarbonmolecules. The heptamer structure serves as a benzene-like building block for afamily of plasmonic artificial aromatic analogs with fused ring structures.Antiphase magnetic plasmons are excited in adjacent fused heptamer units,which for a linear multiheptamer structure is a behavior controlled by thenumber of units in the structure. This antiphase coupling gives rise toplasmonic “antiferromagnetic” behavior in multiple repeated heptamerstructures, supporting the propagation of low-loss magnetic plasmons in thisnew waveguide geometry.

KEYWORDS: Magnetic plasmons, oligomers, coupling, Fano resonances, organic chemistry

Metallic oligomers of various symmetries are of intensecurrent interest, as systems of fundamental importance

to our understanding of plasmon coupling as well as for theirpotential as artificial molecules with novel electromagneticproperties. For example, collections of gold nanoparticlesassembled in tetrahedral symmetry using DNA scaffolds canlead to the plasmonic analog of chiral molecules.1 Circularloops of gold nanoparticles with increasing rotational symmetryexhibit enhanced performance in plasmon-enhanced spectros-copy and Raman sensing.2 Heptamers, seven-membered planarclusters with the D6h spatial symmetry of a benzene molecule,give rise to plasmonic Fano resonances resulting from theinterference between their broad continuum-like and narrowlocalized modes.3,4 These specially designed nanoparticleassemblies are the nanophotonic embodiments of a variety ofconcepts that originate in biology and chemistry, opening up anexciting multidisciplinary area of research.In organic chemistry, carbon-based aromatic molecules form

six-membered rings, which can be “fused” into more complexstructures by the sharing of two or more atoms on adjacentrings.5 For example, benzene is a monocyclic ring of six carbonatoms, naphthalene is a bicyclic ring with two shared atoms,and anthracene consists of three rings in a linear arrangementwith two shared atoms between each pair of adjacent hexagonalrings. This ring-joining motif gives rise to a large family ofmolecules of various symmetries. A defining characteristic ofaromatic molecules is their delocalized π-electron cloud, whichoriginates from the hybridization of the p orbitals of the

constituent carbon atoms. When an aromatic molecule interactswith a magnetic field, the delocalized π-electrons can circulatearound the aromatic ring, forming a current loop that gives riseto an induced local magnetic response.An important emergent property of plasmonic systems is

their optical frequency magnetic response,6,7 also known as“artificial magnetism”, a unique characteristic not found innaturally occurring materials. A strong magnetic response canbe achieved in artificial plasmonic molecules in the opticalrange, where naturally occurring molecules exhibit a perme-ability of unity. While initial interest in this property stemmedfrom the goal of creating metamaterials with negativepermeabilities and negative refractive indices,8 recent interesthas begun to focus specifically on magnetic plasmon modes andtheir unique characteristics.9,10 Plasmonic structures such assplit-ring resonator chains have been theoretically proposed tosupport propagation of long-range magnetic plasmons in themid-infrared.11 In contrast to electric plasmon propagation thatsuffers from significant dissipation, the radiation loss ofmagnetic plasmons can be substantially lower. As a result,magnetic plasmons are a highly promising candidate for thepropagation of electromagnetic energy over greater distancesthan first-generation electric plasmon waveguides12−14 and may

Received: October 15, 2011Revised: November 18, 2011Published: November 28, 2011

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provide a practical alternative strategy for subwavelength opticalfrequency transmission lines in on-chip applications.15,16

In this Letter, we demonstrate optical frequency magneticplasmons in a family of plasmonic analogs of aromaticmolecules. The plasmonic heptamer serves as a benzene-analogbuilding block for the construction of cyclic aromatic structuresof increasing complexity. We first show magnetic plasmonformation in a plasmonic naphthalene analog, which can beviewed as the fusion of a pair of benzene-analog rings. In eachheptamer, ring currents are excited circulating around the sixnanoparticles (A2g symmetry). The ring currents flow throughthe shared junction of the plasmonic naphthalene analog,leading to the excitation of two antiparallel magnetic dipolemoments. For optical excitation at normal incidence, suchmagnetic ring modes only occur for even numbers of fusedbenzene-analog heptamer units. We further demonstrateefficient magnetic plasmon propagation along a chain of twelveheptamer units using a dipole excitation source. Magneticplasmons propagate along the chain via excitation of alternatingring currents in adjacent heptamers due to strong near-fieldcoupling. This constitutes “antiferromagnetic” magneticplasmon behavior, in which the induced magnetic momentsare aligned in a fully antiparallel manner with respect to eachother along the entire multiple heptamer chain. This“antiferromagnetic” plasmon mode composed of alternatingring currents is subradiant in nature and radiates very weakly.Our magnetic plasmon waveguide exhibits a field decay lengthof 2.65 μm, seven times larger than that of an electric plasmonwaveguide composed of nanoparticles in a linear chain. Theseresults provide significant new insight into the types of plasmonmodes that can be excited and propagate along plasmonic

structures, and may provide new opportunities for nanoscaleintegrated optical devices or waveguides.17

In Figure 1, the molecular structures of benzene andnaphthalene and their corresponding plasmonic analogs areshown. In the plasmonic naphthalene molecule, the twoheptamers are bonded by two shared gold nanoparticles, justas the two fused rings of a naphthalene molecule share twocarbon atoms. It is well-known that a plasmonic heptamer cansupport a Fano resonance due to the interference of hybridizedsubradiant and superradiant modes.3,4 To investigate the opticalproperties of the plasmonic naphthalene structure, wefabricated samples using electron-beam lithography in apositive resist (PMMA) on a glass substrate. The structureswere deposited by electron-beam evaporation of a 2 nmchromium adhesion layer followed by 80 nm of gold. ThePMMA was then removed by lift-off in N-methyl-2-pyrrolidone. Each sample has a footprint of 100 μm ×100 μm. Electron micrographs of the fabricated samples wereobtained by environmental scanning electron microscopy(ESEM, FEI Quanta 400). Figure 2a shows an overview SEMimage of a plasmonic naphthalene structure. The perio-dicities in both directions are 2200 nm. The diameter andthickness of the gold particles are 260 and 80 nm,respectively. The interparticle gap distance is 30 nm. Theinset of Figure 2a displays a higher resolution view of theplasmonic naphthalene structure, clearly showing thehomogeneity of the interparticle gaps.For excitation of the structure, we used normal incidence,

linearly polarized light parallel to the direction of the twoshared gold nanoparticles (see Figure 2a inset). Figure 2ashows the extinction (1-transmittance) spectrum of the sample,

Figure 1. Upper row: illustrations of the molecular geometries of a benzene molecule and a naphthalene molecule in organic chemistry. Bottom row:artificial molecules of the same symmetries, a gold heptamer and a gold heptamer pair in plasmonics. The formation of plasmonic molecules drawson the compelling analogy to the formation of molecules in organic chemistry.

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Figure 2. (a) Left: SEM image of a plasmonic naphthalene sample fabricated by electron-beam lithography. The periodicities in both directions are2200 nm. The interparticle gap distance is 30 nm and the thickness of the gold particles is 80 nm. The diameter of the gold particles is 260 nm. Inset:enlarged view of the sample. Right: experimental and simulated extinction spectra of the plasmonic naphthalene sample. The light polarization isalong the direction of the two shared gold particles. Bottom: charge density and magnetic field plots at resonances I and II. Resonance I correspondsto a double Fano resonance mode. Resonance II corresponds to a magnetic ring mode, in which antiphase magnetic plasmons are excited. (b) Left:SEM image of a plasmonic naphthalene sample with the removal of one center gold particle. Right: experimental and simulated extinction spectra ofthe sample. Bottom: charge density and magnetic field plots at resonances I and II. Resonance I is mostly associated with the Fano resonance in theright heptamer. The magnetic ring mode at resonance II is still clearly visible, demonstrating the robustness of this resonance.

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which was measured using a Fourier-transform infraredspectrometer (Bruker Vertex 80v) equipped with a microscope(Hyperion 3000). The overall shape of the extinction spectrumis determined by a broad superradiant mode in which thecharges in all of the nanoparticles oscillate in phase. Twosubradiant resonances are observable within the broad superradiantresonance profile: Resonance I, a weaker resonance at 1100 nm;and Resonance II, a more pronounced resonance at 1550 nm. Toidentify the origin of these observed resonances, simulations wereperformed using a commercial implementation of the FiniteElement Method (COMSOL Multiphysics). In these simulations,the permittivity of the glass substrate is taken as 2.1, and thepermittivity of gold is taken from the empirical dielectric functionof bulk gold (Johnson and Christy).18 The simulated spectrumagrees well with the experimental result (Figure 2a). Charge densitycalculations for both resonances clearly show the differencebetween the two plasmonic modes of the structure. Resonance Iis essentially a double Fano resonance mode, where the charges inthe two center particles oscillate antiphase relative to those in thesurrounding particles.19,20 Resonance II is characterized by ringcurrents circulating in opposite directions around the two fusedrings with the two shared gold nanoparticles functioning as amutual current link. The magnetic field plot at Resonance II inFigure 2a explicitly shows the excitation of two antiparallelmagnetic dipole moments in the plasmonic naphthalene structure.Interestingly, even if one center gold particle is removed from theplasmonic naphthalene structure (see Figure 2b), forming a mixed,hexamer−heptamer heterostructure, The magnetic ring mode atResonance II is still well preserved, demonstrating the robustness of

this resonance. For this structure, Resonance I is primarilyassociated with the excitation of the Fano resonance in theheptamer side of the structure. The amplitude of resonance II isslightly smaller than that of the heptamer−heptamer structureshown in Figure 2a. However, the antiphase magnetic plasmons arestill clearly observed, as shown in the charge density and magneticfield plots of Figure 2b.To investigate the dependence of the resonant modes on the

number of heptamer units n, we simulated the optical spectra ofa series of linearly fused heptamer structures of increasing n,with optical excitation at normal incidence. The lightpolarization is perpendicular to the long axis of each structure.For simplicity, the simulations were performed in a vacuumenvironment, resulting in plasmonic modes that are slightlyblue-shifted compared to those on a glass substrate. To moreclearly elucidate the evolution of the resonant behavior, wecalculated the optical absorption spectra instead of theextinction spectra. Therefore, all of the subradiant modesappear as absorption peaks as shown in Figure 3. For the n = 1case, the optical spectrum of the heptamer exhibits a singleabsorption peak, corresponding to a Fano resonance.3,4 Forthe n = 2 case, when a second heptamer is attached to thefirst, the Fano resonance shifts to a shorter wavelength.This blueshift is similar to that observed for a coupledplasmonic nanoparticle pair, or dimer, under similar trans-versely polarized optical excitation, whose collective plasmonresonance shifts to a shorter wavelength relative to theqplasmon resonance of the individual nanoparticles. The longerwavelength resonance at 1370 nm corresponds to the magnetic

Figure 3. Simulated absorption spectra of the cyclic aromatic structures in dependence on heptamer unit number n. For simplicity, the simulationswere performed for the case of air ambient. Spectra are shifted upward for clarity. The red-dashed line highlights the Fano resonances of differentstructures. A clear resonance blue shift is visible with increasing n. The charge density plot of the Fano resonance for n = 6 is presented. Themagnetic ring modes (highlighted using the blue bars) only occur when n is even. The charge density plots of the magnetic ring modes are displayedfor n = 2, 4, and 6. The charge density plot of the complex Fano resonance mode at 1200 nm for n = 3 is also presented.

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ring mode discussed earlier in Figure 2a. As highlighted by thered-dashed line in Figure 3, when additional heptamer units areadded to the structure, the Fano resonance successively shifts tothe blue with increasing n. For brevity, only the charge densityplot of the Fano resonance mode for the case of n = 6 isdisplayed in Figure 3.When n is increased to 3, a new plasmonic resonance appears

at around 1200 nm. As evident from the charge density plot,this new resonance is correlated with a complex admixture ofthe Fano resonance mode and nanoparticle quadrupoles.Importantly, we see that for the n = 3 structure, the magneticring mode cannot be excited. The reason is that for the n = 3structure, or more generally, for odd numbered chains, thereare even numbers of shared junctions with opposite electricdipole moments in the magnetic ring modes. The net electricdipole moment therefore is zero along the incident electricfield. For the n = 4 structure, the magnetic ring mode reappearsat 1370 nm. The charge density plot for this resonance clearlyshows that antiphase ring currents are excited in the conjugatedheptamer rings. The magnetic ring mode disappears again whenn = 5 and reappears at 1370 nm when n = 6. The charge densityplot of the magnetic ring mode for the n = 6 structure is shownin Figure 3. In essence, the magnetic ring mode can only beexcited in the cyclic aromatic structures with even numbers ofheptamer units for normal incidence excitation. The rest ofthe plasmonic modes in the spectra in Figure 3 are correlatedwith complicated admixtures of Fano resonance fielddistributions and nanoparticle quadrupoles and will not beanalyzed here in detail.

Because of their subradiant nature, the magnetic ring modesof the heptamer chains may be of interest in plasmonicwaveguiding applications. Because the physical size of surfaceplasmon-based devices is not restricted by the diffractionlimit,21 this has offered a promising scalable path forsubwavelength light-focusing and light-guiding elements inintegrated optics. For propagation of electric plasmons,however, strong damping has been one of the major obstaclesfor development of nanoparticle chains as plasmonic wave-guides.12 Here we propose magnetic plasmon propagationalong plasmonic multi-heptamer chains. To investigate thefeasibility of this idea, in Figure 4 we show the propagation ofmagnetic plasmons along a chain of twelve heptamers using adipole source excitation at the left end of the chain. Only thefirst heptamer is externally excited, while the subsequentheptamers in the chain are excited due to strong near-fieldcoupling. In particular, the ring currents excited in oneheptamer can couple efficiently to the adjoining heptamer viatheir mutual current link, that is, the two shared goldnanoparticles that bond the adjacent heptamers together.Consequently, ring currents are excited successively in allheptamers, giving rise to the propagation of magnetic plasmonsalong the entire chain. The charge density and magnetic fieldplots of the plasmonic aromatic chain at the resonancewavelength (1370 nm) are displayed in Figure 4a. The inducedmagnetic moments are aligned in a fully antiparallel fashion,directly analogous to the configuration of spins in a one-dimensional antiferromagnetic chain.To quantify the field decay length in this structure, we

calculated the time-averaged energy flow P along the structure

Figure 4. (a) Charge density plot of a plasmonic aromatic chain with twelve heptamer units excited using a dipole excitation source. The dipolesource with amplitude of 1 × 10−9 mA is placed 150 nm in front of the first heptamer. Ring currents are excited successively in all heptamers, givingrise to the propagation of magnetic plasmons along the entire chain. The induced magnetic moments are aligned fully antiparallel and this isanalogous to the configuration of “antiferromagnetism”. (b) Positions of the heptamers along the chain axis versus energy flow values at the centersof these heptamers. The fourth to the tenth heptamers were included in the fitting in order to avoid the influence from the light scattering at the twoends of the chain. The fitted energy flow equation is P = 3.608 × 108 exp(−x/2.65). It corresponds to a field decay length of 2.65 μm.

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(Figure 4b). The energy flow values were obtained at thecenters of the individual heptamer units. To minimize theinterference effects due to light scattering from the ends of thestructure,22 only the fourth through the tenth heptamer unitswere included in our exponential fit. This analysis yields a decaylength of 2.65 μm, which corresponds to 5.2 unit cells or 2 freespace wavelengths. For comparison, electric plasmon prop-agation in a linear chain of closely spaced metallic nanoparticlesat 520 nm manifests a field decay length of 410 nm,corresponding to 5.4 unit cells or 0.8 free space wavelengths.In addition, due to its subradiant nature, the magnetic ringmode is only weakly coupled to light, giving rise to muchstronger field confinement in the direction perpendicular to thechain relative to the dominant electric mode (see SupportingInformation, Figure S1).23 The results from this initialstudy clearly show that magnetic plasmon waveguiding couldprovide an efficient alternative to electric plasmon waveguidingin nanoparticle chains. This finding may be of relevancefor the future development of plasmonic waveguiding devicesin on-chip applications, such as image or informationprocessing.24,25

In summary, we have shown that plasmonic artificial aromaticmolecules support magnetic plasmon resonances. With aheptamer structure as a benzene-like building block, we examinedthe magnetic plasmons of fused ring structures consisting of mul-tiple connected heptamer units. In a two-unit heptamer structure,the plasmonic analog of a naphthalene molecule, we find that themagnetic mode consists of two opposite current loops, resultingin an antiphase behavior of the magnetic plasmons supported bythis structure. The magnetic modes of multiple heptamerstructures in a linear configuration depend on this antiphasebehavior and are observed only in extended structures with aneven number of heptamer units. For extended multiunit heptamerlinear structures, we have examined the propagation of elec-tromagnetic energy via magnetic plasmons and have found thatthese structures are capable of supporting low-loss propagation ofplasmon modes. The long field decay length as well as thesignificant subdiffraction character may enable magnetic plasmonwaveguides to be developed as primary components of nanoscalephotonic devices with potential applications in energy transport,16

data storage, near-field microscopy, and so forth.12 This study alsoshows that intuition drawn from molecular orbital theory mayallow us to create new plasmonic structures26 based on theirchemical analogs. As a further extension of the current study, weenvision interesting resonant behavior for even more complexplasmonic aromatic molecules derived from organic moleculessuch as coronene, pyrene, phenanthrene, triphenylene, ovalene,etc.5 This opens up an interesting area of research in which neweffects based on the plasmonic properties of the analogs ofcomplex molecules may be discovered.

■ ASSOCIATED CONTENT

*S Supporting InformationAdditional figure (Figure S1) and information. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: (N.L.) nl7@rice.edu; (N.J.H.) halas@rice.edu.

Author Contributions¶These authors contributed equally to this work.

■ ACKNOWLEDGMENTSWe acknowledge S. Hein for his material visualizations. N.L.thanks the support of K. Bala Texas Instruments VisitingProfessorship in Electrical and Computer Engineering at RiceUniversity. S.M., L.V.B., K.B., P.N., and N.J.H. were supportedby the Robert A. Welch Foundation (C-1220 and C-1222), theAir Force Office of Scientific Research (FA9550-10-1-0469),the Office of Naval Research (N00014-10-1-0989), theNational Science Foundation (IGERT) (DGE-0504425), theDoD NSSEFF (N00244-09-1-0067), and the Defense ThreatReduction Agency (DTRA) (HDTRA1-11-1-0040). J.D. wassupported by DFG, BMBF, and BW Stiftung (KompetenznetzFunktionelle Nanostrukturen).

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