Chemical Physics Letters 458 (2008) 262–266

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Chemical Physics Letters

journal homepage: www.elsevier .com/locate /cplet t

Shedding light on dark plasmons in gold nanorings

Feng Hao a,b, Elin M. Larsson c, Tamer A. Ali b,d, Duncan S. Sutherland e, Peter Nordlander a,b,d,*

a Department of Physics and Astronomy, M.S. 61, Rice University, Houston, TX 77005-1892, USAb Laboratory for Nanophotonics, Rice University, Houston, TX 77005-1892, USAc Department of Applied Physics, Chalmers University of Technology, S-41296 Gothenburg, Swedend Department of Electrical and Computer Engineering, M.S. 366, Rice University, Houston, TX 77005-1892, USAe iNANO Center, University of Aarhus, Aarhus 8000, Denmark

a r t i c l e i n f o a b s t r a c t

Article history:Received 4 April 2008In final form 29 April 2008Available online 9 May 2008

0009-2614/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.cplett.2008.04.126

* Corresponding author.Address: Department of PhRice University, Houston, TX 77005-1892, USA.

E-mail address: nordland@rice.edu (P. Nordlander

We present an experimental and theoretical analysis of the optical properties of gold nanorings of differ-ent sizes and cross-sections. We show that for light polarized parallel to the ring, the optical spectrumcan depend sensitively on the angle of incidence. For normal incidence, the spectrum is characterizedby two dipolar ring resonances. As the angle of incidence becomes more oblique, several previously darkmultipolar ring resonances appear in the spectra. We show that the appearance of the multipolar reso-nances is a consequence of retardation and can be understood in simple general terms.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

The topic of nanoparticle plasmons have recently gained wide-spread interest because of their fundamental importance in manyfields of science [1,2], and because of many promising applicationsin areas such as chemical and biological sensing [3,4], negative in-dex materials [5–7], waveguiding [8,9], and photothermal tumorcell ablation [10,11]. Various nanostructures have been fabricatedand studied in recent years using nanolithographic and chemicalprocesses [12–17]. The plasmon resonance frequency and the in-duced field enhancements are highly dependent on the size andthe shape of the nanostructure and its surrounding dielectric envi-ronment [18–22]. Large electric field enhancements useful for sur-face enhanced spectroscopy and sensing applications can beachieved using either very sharp features as in nanorods and nano-stars [23–25], multi-surface structures such as nanoshells [26], ornarrow junctions between adjacent nanoparticles [27].

Ring-shaped nanostructures are particularly attractive for sens-ing applications due to their ability to contain high volumes ofmolecules and provide uniform electric fields inside the cavity[28,29]. The plasmon frequencies of nanorings are highly tunableand depend both on the diameter and the wall thickness of the ring[30,31]. This tunability of nanorings has recently been exploited inthe design of plasmonic waveguides in the optical telecommunica-tion band [32].

The plasmons of a finite nanostructure can be considered to bediscrete eigenmodes characterized by the spatial symmetry oftheir associated surface charge distribution [33]. For small nano-

ll rights reserved.

ysics and Astronomy, M.S. 61,

).

particles where the quasi-static approximation is valid, only plas-mon modes containing electric dipole moments can couple withthe incident electromagnetic fields. Several recent studies haveshown that by breaking the symmetry of a nanostructure, non-dipolar plasmon modes can be excited [34–36]. One physicalmechanism that can make this happen is that symmetry breakingcan enable hybridization of plasmons of different multipolar sym-metry, i.e. dipolar plasmon modes can mix into normally dark mul-tipolar modes [34]. Such an admixture of a dipole plasmon makesthe hybridized mode dipole active and can strongly enhance itsintensity in the optical spectrum.

Another mechanism for exciting non-dipole active multipolarplasmons is retardation effects [37]. For nanoparticles of a sizecomparable to a quarter of the wavelength of the incident light,the electric field can no longer be assumed uniform across thenanoparticle. For such a system the higher multipolar componentsof the incident wave can directly couple to the corresponding mul-tipolar plasmon modes [18]. As a nanoparticle is made larger, anincreasing number of higher multipolar plasmon resonances canappear in its spectrum [38].

In this Letter, we present an experimental and theoretical inves-tigation of the optical properties of symmetric gold nanorings forlight polarized in the plane of the ring. We show that by varyingthe angle of incidence of the light it is possible to excite multipolarplasmon resonances in a controlled manner. For light incident per-pendicular to the ring, only the dipolar resonances appear and themultipolar ring resonances remain dark. As the angle of incidenceis reduced, several multipolar ring plasmon resonances appear inthe spectra with intensities that increase monotonously as the an-gle of incidence becomes parallel to the plane of the ring. The cal-culated spectra show excellent agreement with the experimentalresults. We show that this effect does not depend sensitively on

F. Hao et al. / Chemical Physics Letters 458 (2008) 262–266 263

the cross-section of the ring but is a general consequence of phaseretardation.

2. Experimental and theoretical approach

In Fig. 1 we schematically illustrate the geometry of the exper-iment and the structural parameters used to model the rings. Thegold nanorings are fabricated on soda lime glass substrates usingcolloidal lithography [30,28]. The samples are illuminated bymonochromatic light with the polarization parallel to the sub-strate. The incidence angle h is defined in Fig. 1b. The extinctionspectra of the ring is calculated using the finite-difference time-do-main method (FDTD) using a four term Lorentzian expansion fittedto experimentally measured dielectric data for gold [39,40]. Thestructural parameters of the rings are determined by AFM andSEM. The wall thicknesses were found to vary slightly with verticalposition with their thickest part having dimensions in the range20–40 nm. For computational simplicity, we do not include thesubstrate when modeling the ring. The inclusion of a dielectric sub-strate would result in small redshifts of the individual plasmon res-onances due to the screening charges induced at the substrate/metal interface but no significant change of the intensities of thespectral features [31].

3. Results

In Fig. 2, we compare the experimental and theoretical spectrafor different values of the incidence angle h and different sizes ofthe rings. The black solid lines in the spectra are the extinctionspectra for normal incidence ðh ¼ 0�Þ. For this incidence, the spec-tra are characterized by a single resonance which is a symmetric

Fig. 1. (a) Geometry of the rings used in the simulations: diameter ðDÞ, wall thickness ðdirection~k and the polarization direction E are denoted on the left. The incident angle h imicrographs showing Au nanorings with D=530 nm on a soda lime glass substrate from

dipolar (SD) ring mode [30]. Another weak antisymmetric dipolar(AD) ring resonance (not shown) with an antisymmetric alignmentof the surface charges on the inner and outer surfaces of the ringappear at a wavelength around 430 nm but is very broad due tothe damping caused by the interband transitions of gold. As thediameter D increases, the energy of the SD resonance red shiftsfrom 1400 nm to about 2100 nm. This tunability is consistent withprevious studies showing that the wavelength of the lowest energydipolar plasmon mode increases with decreasing aspect ratio T=D[30].

When the incidence angle is changed from normal to oblique,several higher energy plasmon resonances begin to appear. As willbe demonstrated below, these are higher order multipolar ring res-onances. For the D ¼ 315 nm ring (panels (a) and (b)), a quadrupo-lar resonance around 900 nm appears with an intensity whichincreases monotonously with h. For the D ¼ 350 nm ring (panels(c) and (d)), a clearly developing quadrupolar resonance appearsaround 970 nm and a weak octupolar feature around 750 nm isemerging for the largest h. For the largest ring with D ¼ 530 nm(panels (e) and (f)), two clearly developed quadrupolar and octupo-lar resonances appear at 1200 nm and 900 nm and a weak hexa-decapolar feature at 750 nm. The figure clearly shows that boththe number of multipolar modes and their intensities increase withthe diameter of the ring D.

The theoretical calculations qualitatively reproduce the experi-mental spectra, except for the slight blueshift of the plasmon res-onance caused by the neglect of the substrate in the modeling.The calculated spectra clearly show a reduction of the intensityof the SD resonance as the higher order resonances appear. This de-crease can simply be understood from the spectral sum rule whichensures that the integral of the spectra is determined by the num-ber of electrons in the system. We believe that the reason why the

TÞ, height ðHÞ. (b) A schematic illustration of the experimental setup. The incidents defined as the angle between the axis of the ring and~k. Panels (c) and (d) are SEMa top (c) and 60� (d) view.

Fig. 2. Experimental absorbance (a,c,e) and theoretical extinction (b,d, f) spectra for three different gold nanorings for fixed polarization but varying angle of incidence h: 0�(solid black), 30� (dashed red), 50� (dash-dotted green), 70� (dash-triple-dotted blue). The geometric parameters used in the FDTD modeling of the nanorings are:D ¼ 316 nm, T ¼ 26 nm, H ¼ 120 nm (a,b), D ¼ 352 nm, T ¼ 26 nm, H ¼ 140 nm (c,d), and D ¼ 528 nm, T ¼ 24 nm, H ¼ 168 nm (e, f). The dielectric function used in the FDTDcalculations is a 4-term Lorentzian model [40]. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)

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experimental spectra do not display this decrease is that a largerarea of the substrate and therefore more rings are excited forincreasing h.

In Fig. 3 we show the calculated charge distributions of the fourlowest resonance frequencies for the D ¼ 528 nm ring shown inFig. 2f. The contour plane is on the top surface of the ring andthe angle of incidence is h ¼ 90�, i.e. light incident from the side.For k ¼ 1934 nm, the charge distribution is dipolar as expectedfrom the excitation of the SD resonance. For k ¼ 1066 nm, twomore nodes show up in the charge distribution which is character-istic of a quadrupole. For the k ¼ 788 nm and k ¼ 667 nm reso-nances, the charge distribution exhibit 6 and 8 nodes,respectively, as expected for octupolar and hexadecapolar plasmonresonances. In panels (e) and (f) we show the charge distributionfor the only two modes that can be excited with normal incidence,h ¼ 0�, i.e. the SD and AD modes. The SD mode exhibits the charac-teristic symmetric alignment of the surface charges as was also

seen in panel (a). The AD mode exhibits an antisymmetric align-ment of the surface charges on the inner and outer surfaces ofthe ring wall [30,31].

4. Discussion

As demonstrated above, only the dipolar resonances of a thinring ðT;H� kÞ are excited for normal incidence. The excitation ofring plasmon modes when light is incident from the side is quitedifferent. In Fig. 4 we illustrate the physical mechanism for excita-tion of the multipolar plasmon modes for light incident from theside. Due to the finite speed of light, the incident wavefrontreaches the left side of the ring first, resulting in polarizationcharges that are localized to the left part of the ring as shown inFig. 4a. The plasmonic modes of a ring can be classified accordingto their multipolar symmetry l. Any instantaneous polarization of

Fig. 3. Calculated surface charge distribution on the top surface of a gold nanoringof D ¼ 528 nm, T ¼ 24 nm, and H ¼ 168 nm. Panels (a–d) show the amplitudes forthe four peaks shown in Fig. 2f for h ¼ 90� . Panels (e, f) show the charge amplitudesfor the SD and AD mode for h ¼ 0� . The incidence angle and the wavelength areshown on top of each panel. The color legend for positive and negative charges isshown on the right.

Fig. 4. Schematic illustrating how phase retardation can enable the excitation ofmultipolar ring plasmons when light is incident from the side: (a) the polarizationas the incident wavefront has reached the left part of the ring, (b) how a localizationof the surface charges toward the left part of the ring can be achieved by superp-osing a dipolar and a quadrupolar mode, and (c) how the surface charges can befurther localized to the left side of the ring by adding the octupole resonance. Thered ‘+’ and blue ‘�’ signs denote the surface charges associated with the plasmonmodes. (For interpretation of the references in color in this figure legend, the readeris referred to the web version of this article.)

F. Hao et al. / Chemical Physics Letters 458 (2008) 262–266 265

the surface charges in the ring can be expressed as a superpositionof the fundamental plasmon modes of the ring. The individual mul-tipolar plasmon resonances of the ring have surface charge distri-butions distributed over the whole ring and do not exhibit alocalization to the left. In Fig. 4b we show schematically how thesurface charges can be localized to the left part of the ring bysuperposing a dipolar and quadrupolar ring plasmon. Except for asmall dipole on the right side of the ring, the charge distributionis localized to the left part of the ring. In Fig. 4c we show schemat-ically how a further charge localization to the left can be accom-plished by adding the octupole ring plasmon. As in any Fourierexpansion, adding higher multipolar components can further local-ize the charge distribution. Thus the instantaneous polarization ofthe left side of the ring can be viewed as a coherent excitation ofseveral of the plasmonic eigenmodes of the ring. As a result, thevariation of the E-field of a plane wave along its direction of prop-agation can lead to excitation of several multipolar ring plasmonresonances. The number of multipoles that can be excited dependson the ratio of the ring diameter to the optical wavelength. Withincreasing ring diameter, more higher order multipolar plasmonmodes can be excited for light incident from the side of the ringstructure.

A similar argument has been used to explain the excitation ofthe dark transverse bonding plasmon mode for a nanoshell dimerwhen light is incident parallel to the dimer axis [27]. The bondingtransverse mode has no dipole moment since it can be described astwo nanoshell dipole modes oscillating out of phase. When theincident wavefront polarizes the first nanoshell, the instantaneouspolarization corresponds to the simultaneous excitation of boththe dark bonding and bright antibonding transverse dimerplasmons.

We have also investigated how the cross-section of the ringinfluences the extinction spectra. In Fig. 5 we compare the extinc-tion spectra of gold nanorings of square, circular and rectangularcross-sections for light incident from the side h ¼ 90�. Panel (a)shows the spectra for square and circular cross-sections of a ringwith relatively small aspect ratio T=D. The spectra are quite similarwith the wavelengths of the SD resonances differing by less than60 nm. The relative intensities of the multipolar resonances arealso very similar. In panel (b) we compare the circular and squarering spectra for a larger aspect ratio T=D. Also for this larger struc-ture, the spectra look similar with the SD resonances differing byless than 20 nm for the two different ring profiles. The plasmonresonances for the rings with larger aspect ratio are blueshiftedcompared to panel (a). This blueshift enhances the retardation ef-fects and consequently the intensity of the multipolar resonances.It is notable that the ring with square cross-section always has ashorter resonance wavelength compared to the ring with circularcross-section. This can be understood physically, from the cross-section area of the ring. For a square cross-section ðT ¼ HÞ the areais T2 while for the circular cross-section, the area is pT2=4. Thus aring with a circular cross-section will have a smaller effective as-pect ratio and a more redshifted SD resonance. To further investi-gate how the cross-section area influence the spectra, in panel (c)we compare the spectra for two rings with approximately the samecross-section area and diameter D but very different T and H. Ascan be seen, the spectra are very similar suggesting that thecross-sectional area is an important factor influencing the plasmonenergies of a ring. A detailed investigation of how the cross-sectionarea influence the tunability of the ring plasmons is in progress.

5. Conclusions

In conclusion, we have presented an experimental and theoret-ical investigation of the optical and plasmonic properties of thin

Fig. 5. FDTD extinction spectra for rings of square (blue), circular (dotted red), andrectangular (black dotted) cross-sections: (a) D ¼ 174 nm, T ¼ 24 nm H ¼ 24 nm;(b) D ¼ 200 nm, T ¼ 50 nm, H ¼ 50 nm; (c) D ¼ 450 nm, T ¼ 45 nm, H ¼ 45 nm andD ¼ 420 nm, T ¼ 12 nm, H ¼ 168 nm. The incidence angle is h ¼ 90� . (For interpre-tation of the references in color in this figure legend, the reader is referred to theweb version of this article.)

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gold nanorings of various sizes. We have shown that for a fixedpolarization parallel to the plane of the ring, the optical spectracan depend strongly on the incidence angle of the light. For lightincident normal to the ring, only the dipolar modes can be excitedand the multipolar ring modes are dark. As the incidence is variedfrom normal to parallel to the ring, multipolar resonances appearin the spectra with intensities that increase monotonously. Usinga simple universal physical model, we have shown that the excita-tion of the multipolar resonances is a consequence of the finite

speed of light, i.e. phase retardation. We also show that thecross-sectional profile of a ring has little influence on its spectrum.These studies have furthered our insights into the role of retarda-tion effects for the excitation of ring plasmons, and the resultsare also likely to be applicable to more complex metallicnanostructures.

Acknowledgements

P.N., T.A.A. and F.H. acknowledge support from the US Army Re-search Laboratory and the US Army Research Office under Con-tract/Grant No. W911NF-04-1-0203, the Robert A. WelchFoundation under Grant C-1222, and by NSF under Grants EEC-0304097 and ECS-0421108 and CNS-0421109. D.S.S. and E.L.acknowledge support by the FNU and SSF (Program PHOTO/NANOGrant No. 2001:0321/53).

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