Fanoshells: Nanoparticles with Built-in Fano Resonances

Fanoshells: Nanoparticles with Built-in FanoResonancesShaunak Mukherjee,†,‡ Heidar Sobhani,‡,| J. Britt Lassiter,‡,§ Rizia Bardhan,†,‡

Peter Nordlander*,‡,§,| and Naomi J. Halas*,†,‡,§,|

†Department of Chemistry, ‡Laboratory for Nanophotonics, §Department of Physics and Astronomy, and|Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005

ABSTRACT A nanoparticle consisting of a dielectric (SiO2) and metallic (Au) shell layer surrounding a solid Au nanoparticle core canbe designed with its superradiant and subradiant plasmon modes overlapping in energy, resulting in a Fano resonance in its opticalresponse. Synthesis of this nanoparticle around an asymmetric core yields a structure that possesses additional Fano resonances asrevealed by single particle dark field microspectroscopy. A mass-and-spring coupled oscillator model provides an excellent descriptionof the plasmon interactions and resultant optical response of this nanoparticle.

KEYWORDS Plasmon, Fano resonance, nanoshell, dark field, harmonic oscillator, coherent phenomena

Noble metal nanoparticles possess a range of inter-esting optical properties due to localized electro-magnetic resonances, known as surface plasmons.

The dependence of nanoparticle plasmon resonances ongeometry and local dielectric environment1,2 has led to avariety of strategies for the systematic design of opticalproperties into nanoparticles and nanostructures. Applica-tions of plasmonic nanoparticles and nanostructures rangefrom therapeutics and biomedical imaging,3–5 surface-enhanced spectroscopies,6–8 and ultrasensitive chemicaland biological sensing9,10 to developing optical frequencymetamaterials.11–13

Many of the optical properties of plasmonic nanoparticlesresult from the interaction between multiple plasmon modesof the same nanostructure. In the core-shell geometry of ananoshell, for example, plasmon resonance frequencies aredetermined by the interaction between the two primitiveplasmons supported by the structure, namely, the sphereand cavity plasmon modes. Symmetry breaking can en-hance the interaction between plasmon modes.14,15 Inhighly symmetric nanostructures such as nanoshells, offset-ting the dielectric core with respect to the metal shell causesmixing of the bright dipole mode with higher order darkmultipolar modes, so named because they do not coupledirectly to the far field and therefore cannot be opticallyexcited.14,16 Since localized plasmons behave remarkablylike simple classical damped oscillators, these systemsprovide a unique opportunity to study, and ultimately de-sign, coherent, coupled-oscillator phenomena using plas-monic nanoparticles and complexes. While coherent effectssuch as subradiance and superradiance,17 Fano reso-nances,18 and electromagnetically induced transparency

(EIT)19 have long been of interest in atomic physics, plas-monic nanoparticles and nanostructures provide a verypractical testbed where coherent effects can be designed,examined, and optimized. The ability to design nanoscalestructures and complexes that support specific coherentplasmonic effects has become a topic of intense currentinterest.

Recently, a variety of reduced-symmetry plasmonic nano-structure complexes such as nanoparticle heterodimers,20,21

septamers,22 and ring/disk nanocavities23–25 with Fanoresonances present in their optical response, have beenreported. Each of these systems supports both broad super-radiant plasmon modes and substantially narrower subra-diant modes. The coexistence of a broad bright mode and anarrow dark mode resonant over the same range of energiescan result in a coupling between these two coherent modes,producing a Fano resonance. In strongly coupled systems,the modulation depth of the asymmetric Fano line shapemay give rise to plasmon-induced transparency.26–29 Thisparticular phenomenon is similar to EIT, observed in atomicsystems.30,31 In plasmonics, plasmon-induced transparencyover a short-range of frequencies has great potential for thedesign of low-loss metamaterials and subwavelength wave-guides with low radiative losses.12,32

A simple multilayered plasmonic nanoparticle consistingof an Au nanocrystalline core, a silica spacer layer, and ametallic shell, has recently been fabricated and analyzedwithin the plasmon hybridization picture.33 The hybridizedplasmonic response of this nanoparticle, originating from thecoupling between the primitive dipolar Au sphere and shellplasmons, gives rise to three hybridized plasmon modes: inincreasing energy, an antisymmetric bonding mode, a sym-metric antibonding mode, and a nonbonding mode. Thelowest energy antisymmetric bonding mode is a subradiant,dark mode, where the individual dipole moments of the Au

* Corresponding authors, (N.J.H.) [email protected] and (P.N.) [email protected] for review: 05/8/2010Published on Web: 05/28/2010

pubs.acs.org/NanoLett

© 2010 American Chemical Society 2694 DOI: 10.1021/nl1016392 | Nano Lett. 2010, 10, 2694–2701

core and the Au shell are out of phase. The higher-energysymmetric antibonding mode is a superradiant mode, wherethe dipole modes of the Au core and the Au shell oscillate inphase. In a recent paper,34 it was shown that for a noncon-centric alignment of the metallic core relative to the shell,higher multipolar modes may become visible in the opticalspectrum due to additional interactions caused by symmetrybreaking. Here we report the controlled synthesis andobservation of the optical properties of such nanoparticlesat the individual particle level using dark field microspec-troscopy. The geometry of the particle is chosen so that thesub- and superradiant modes overlap in energy. The inher-ent asymmetry of this nanoparticle enhances the coherentcoupling between the plasmon modes of different multipolarsymmetry, resulting in multiple, tunable, nearly isotropicFano resonances in the optical response. A Fano resonancecaused by the interaction of the sub- and superradiantmodes is present also for the symmetric (concentric) par-ticle. The higher multipolar Fano resonances are due tosymmetry breaking. We show that optical properties of sucha symmetry broken core-shell metallodielectric nanopar-ticle (Fanoshell) can be qualitatively accounted for using acoupled-oscillator model.

Au/SiO2/Au nanoshells were synthesized as previouslydescribed.33 Au/SiO2/Au nanoshells in a dilute solution wereimmobilized and dispersed on cleaned glass substrates,which were functionalized with a thin layer of poly(4-vinylpyridine).35 In order to identify the exact location ofindividual nanoparticles, glass substrates were numericallyindexed with Au grids deposited using e-beam evaporationthrough TEM grids (Ted Pella). Using environmental scan-ning electron microscopy (FEI Quanta 400), the immobilizedAu/SiO2/Au nanoshells were characterized and identifiedwith respect to the grid indices, to identify their exactposition. A dark field microscope was used to obtain singleparticle scattering spectra from individual nanoparticles.Briefly, single Au/SiO2/Au nanoparticles were identified onthe gridded substrate in an inverted optical microscope(Zeiss Axiovert 200 MAT). White light was obliquely incidenton the nanoparticle at an angle of 75° while the backscat-tered spectra from the nanoparticles were collected in a conehaving a solid angle of 64° as defined by the numericalaperture of the reflection dark field objective (Zeiss, 100×,NA 0.9) used.36 The image of a single nanoparticle wasfocused onto the entrance slit of a spectrograph (ActonMicrospec 2150i) in order to disperse the particle’s light intoits scattering spectrum and then imaged using a CCD (Pixis400, Princeton Instruments). A background spectrum takenfrom a region of the sample containing no nanoparticle wassubtracted from the spectrum, then the resulting data werecorrected for the spectral efficiency of the instrument usingthe spectrum of a white calibration standard (EdmundOptics). To obtain polarized spectra of individual nanopar-ticles, a rotating linear polarizer (LPVIS 100, Thorlabs) wasplaced in the optical path just after the halogen lamp to

polarize the incident beam. The incident beam was alsopartially blocked with a wedge-shaped cutout of metallic foilbetween the polarizer and the halogen light source.37 Thiseliminated the possibility of polarization mixing at the planeof the substrate. Both s-polarized and p-polarized light couldbe obtained at the sample plane by simply rotating thepolarizer with respect to the wedge cutout. In this geometry,s-polarized light excitation corresponds to the electric fieldof the incident illumination being parallel to the substrate,while for p-polarized excitation, the electric field vector ofthe incident light contains a mixture of parallel and perpen-dicular components with respect to the substrate.

Scanning electron microscopy (SEM) images of threesynthesized nanoparticles studied are shown in Figure 1A.It is quite evident that each of these individual Fanoshells(i-iii) has a distinct, asymmetric morphology obtained bythe growth of SiO2 and Au layers on a faceted Au nanopar-ticle core. Irregularities in SiO2 and Au layer thicknesses, andan overall nonspherical geometry, are characteristic of thisnanoparticle. These morphologies deviate from the idealizedsymmetric geometry comprised of perfectly concentricmetal and dielectric layers (Figure 1B). In reality, the experi-mentally fabricated individual structures closely resemblethe more realistic schematic depicted in Figure 1C, wherethe faceted, nanocrystalline Au core38 affects the morphol-ogy of the subsequent SiO2 and Au layer growth. Further-

FIGURE 1. Fanoshells: Au/SiO2/Au nanoparticles. (A) SEM imagesof three individual representative Au/SiO2/Au nanoparticles (i-iii)with overall diameters of ∼150 ( 25 nm on glass substrate. Scalebar ) 100 nm. (B) Schematic of ideal concentric Au/SiO2/Aunanoparticle geometry, where r1 is the core radius, r2 is the radiusof the silica coated core, and r3 is the radius of the nanoparticle.(C) A more realistic nanoparticle schematic representing theirregular morphologies shown in (A). (D) Theoretical model ofFanoshell, where a displaced spherical nanoparticle core (by ∆nm) within a spherical core-shell nanoparticle represents thenanoparticle irregularities.

© 2010 American Chemical Society 2695 DOI: 10.1021/nl1016392 | Nano Lett. 2010, 10, 2694-–2701

more, thin SiO2 layers (e20 nm) on nanoparticle surfacesare typically nonuniform in thickness. The intermediate SiO2

layer of the Fanoshells is on the order of 15-20 nm andtherefore likely to be somewhat nonuniform, introducingadditional asymmetry into the nanoparticle. The plasmonicproperties of this complex can be modeled quite accurately,however, by a much simpler structure with uniform, sym-metric core and shell layers and an offset Au core (Figure1D).

The dark field scattering spectra of the three nanoparticles(i-iii) in Figure 1A were obtained for unpolarized illumina-tion (black), and s (green) and p (red) polarized illumination(Figure 2A-C. A very similar optical response was observedin both the s- and p-polarized cases. The optical spectrum isclearly strongly modulated, with two prominent Fano reso-nances occurring at nominally 650 and 800 nm, respec-

tively. The individual nanoparticle-to-nanoparticle variationsin the shape and location of these features are pronouncedand clearly evident in these spectra. This sensitivity appearsto be related to the size and shape inhomogeneities char-acteristic of this nanostructure. The Fano resonances clearlyobserved in the spectra of individual nanoparticles cannotbe observed in the ensemble nanoparticle spectrum33 dueto the inherent averaging of the spectra from many slightlydifferent nanoparticles. Because these irregularities arisemostly from the faceted shape of the inner Au core, it isunlikely that there is a suitable size regime for the presentAu/SiO2/Au Fanoshells where this inhomogeneous broaden-ing could be sufficiently suppressed. Single crystalline Aunanoparticles are faceted for all sizes and tend to becomeless spherical for larger diameters. However, the relatedgeometry of SiO2/Au/SiO2/Au nanomatryushkas39,40 is typi-cally more homogeneous and symmetric because the nano-particles are fabricated around a spherical SiO2 nanoparticlecore, and the intermediate SiO2 layer is typically thicker andtherefore more uniform. It is likely that such structures alsosupport Fano resonances, which may be observable inensemble, solution-based measurements.

Scattering spectra of individual Fanoshells were modeledusing the finite-difference time-domain (FDTD) method. Anempirical dielectric function (JC) for was used for Au.41 Aninfinite dielectric substrate (ε ) 2.25) was incorporated tosimulate the experimental conditions as accurately as pos-sible.42 To obtain good agreement with the experimentalgeometry, the Fanoshells were modeled as slightly oblatespheroids with a major axis of 150 nm and a minor axis of130 nm. A shell thickness of 25 nm and a core radius of 35nm with different offsets (∆) were used. The SiO2 dielectricspacer layer was calculated using a dielectric of ε ) 2.25.

The two Fano resonances can be understood as interac-tions between the subradiant and superradiant plasmonmodes of the nanoparticle. The dipolar plasmon modes ofthe inner Au core and the outer Au shell hybridize, forminga lower energy narrow subradiant bonding and a higherenergy broad superradiant antibonding plasmon mode thatspectrally overlaps the subradiant mode. The superradiantand the subradiant mode interfere and induce a Fanoresonance, which we denote as the dipole-dipole Fanoresonance (900 nm) due to the dipolar nature of the twointerfering modes. The dipole-dipole Fano resonance canexist in a perfectly symmetric Fanoshell because of the nearfield coupling between the two modes.14,43,44 Underreduced symmetry, the system can also support a seconddipole-quadrupole Fano resonance (650 nm) becausecoupling between the dipolar superradiant mode and thequadrupole mode becomes allowed. We note that theFano resonances in Figure 2 are almost isotropic and thatthe optical response for s and p polarization is very similareven though deposited on a dielectric substrate.

To examine the origin of the two types of Fano reso-nances observed, a more detailed theoretical analysis was

FIGURE 2. Experimental and theoretical spectra of Fanoshells. (A-C)Dark field scattering spectra obtained from the nanoparticles shownin Figure 1A (i-iii), respectively. (D-F) theoretical simulations ofthe Fanoshell spectra shown in (A-C), respectively, obtained usingthe FDTD method and JC dielectric data. Unpolarized (black),s-polarized (green), and p-polarized (red) spectra are shown.


performed by analyzing this structure in the plasmon hy-bridization picture (Figure 3).34,45 Theoretical simulations forthe simplified geometry depicted in Figure 1D were per-formed using the finite element method (COMSOL Mult-iphysics 3.5a) for a Fanoshell of dimensions [r1, r2, r3] ) [35,50, 75] nm with the Au core having an offset of ∆ ) 10 nm.In these calculations, in order to better resolve the higherenergy modes, we use a Drude model permittivity (DM) forAu which neglects the damping caused by interband transi-tions. The plasmonic response can be understood as an

interaction between primitive sphere plasmon and nanoshellplasmon modes. For a nonconcentric alignment, primitivecore and shell modes of different multipolar symmetries caninteract. The dipole bonding mode |ω-⟩(1) of the shell andthe primitive dipole plasmon mode (l ) 1) of the sphericalcore hybridize, giving rise to a subradiant dipole bondingmode |ω-

-⟩(1) at 1.53 eV and a superradiant dipole anti-bonding mode |ω-

+⟩(1) at 2.39 eV. This superradiant modeis significantly broader than the much narrower subradiantmode. The near field coupling between the two modes givesrise to the dipole-dipole Fano resonance observed at ∼1.6eV.

The interaction between the primitive quadrupolar (l )2) bonding modes of the nanoshell |ω- ⟩(2) and the Au coregives rise to a hybridized quadrupole bonding mode |ω-

-⟩(2)

in the Fanoshell. Under reduced symmetry, this narrowquadrupolar dark mode |ω-

-⟩(2) interacts with the broadsuperradiant bright mode |ω-

+⟩(1) and induces the dipole-quadrupole Fano resonance at nominally 2 eV. The excita-tion of the quadrupole is due to its coupling to the dipolarmode and NOT because of phase retardation. A very weakoctupole Fano resonance appears for the same reasonaround 2.25 eV.

Surface charge distributions for the Fanoshell at specificfrequencies characteristic of the coupled modes of thenanoparticle are shown in Figure 3D. The charge profiles for(i) the subradiant mode at 1.53 eV, (ii) 1.79 eV, sufficientlydetuned from both the Fano resonances to clearly show thesuperradiant mode, and (iii) the dipole-quadrupole Fanominimum at 2.0 eV are shown. At 2.0 eV, corresponding tothe minimum in the spectrum associated with the dipole-quadrupole Fano resonance |ω-

-⟩(2), the surface charge onthe shell exhibits a dipolar pattern with a distinct separationof positive (red) and negative (blue) charge, while the coreexhibits a quadrupolar pattern. This charge distributionclearly shows the mixed dipolar-quadrupolar character ofthe dipole-quadrupole Fano resonance. A related planarstructure consisting of a disk inside a ring has been inves-tigated in recent publications.26,27 The hybridization diagramfor these structures is similar to Figure 3 with a bondingsubradiant and an antibonding superradiant hybridizedmode. However, for these planar systems, the interactionsare stronger and the subradiant mode is shifted sufficientlywell below the superradiant continuum that the modeappears as a peak rather than as a Fano resonance. For anonconcentric alignment of the disk and ring, a quadrupolarFano resonance can appear for parallel polarization ofincident light. In contrast, the Fanoshell exhibits an almostisotropic response with a Fano resonance which is observ-able for all incident polarizations.

To investigate the effect of symmetry breaking on theFano resonances, FDTD simulations were performed usinga DM dielectric function initially starting with a concentricFanoshell geometry of [r1, r2, r3] ) [35, 50, 75] nm. Asym-metry was introduced by progressively offsetting the core

FIGURE 3. Energy level diagram of plasmon hybridization ofFanoshells. (A) Extinction spectrum of Au nanoshell [r1, r2] ) [50,75] nm in vacuum with SiO2 as dielectric core. (B) Fanoshell invacuum with dimensions [r1, r2, r3] ) [35, 50, 75] nm with a ∆ ) 10nm offset. (C) Au nanosphere of radius 35 nm embedded in dielectricmedium (ε ) 2.25). All calculations were performed using the finiteelement method with s-polarized light excitation, a DM permittivityfor Au, and a constant permittivity ε ) 2.25 for SiO2. (D) The surfacecharge distribution of the Fanoshell, corresponding to the (i) sub-radiant mode, (ii) superradiant mode, and (iii) quadrupole Fanoresonances at the indicated energies.


with respect to the shell. The variation in the strength of theFano resonances as a function of core offset (∆) is shown inFigure 4A. The scattering spectrum of the concentricFanoshell (∆ ) 0) exhibits a single strong Fano resonancewith a minimum around 750 nm. This is the dipole-dipoleFano resonance, due to the coupling between the subradiantmode |ω-

-⟩(1) at 750 nm and the superradiant mode |ω-+⟩(1)

near 580 nm. With increasing core offset, the quadrupolarmode starts to appear in the spectrum (∆ ) 6). This darkquadrupolar resonance couples to the superradiant dipolar

mode and induces the Fano resonance at ∼650 nm. Thecoupling between the quadrupolar mode and higher ordermodes (e.g., octupole at 640 nm in the ∆ ) 12 nm spec-trum), red shifts the quadrupolar Fano resonance withincreasing offset. The lower energy Fano resonance also redshifts and decreases in intensity with increasing core offset.In Figure 4A for ∆ ) 10 nm, we compare the scatteringspectra for two different polarizations. The curves are verysimilar showing the near isotropic response of individualFanoshells.

FIGURE 4. Dependence of Fano resonances on core offset. (A) Theoretical scattering spectra calculated by FDTD as a function of offset parameter∆. The bottom spectrum (black) corresponds to the concentric nanoparticle geometry [r1, r2, r3] ) [35, 50, 75] nm. Solid curves are forpolarization parallel to the symmetry axis. The blue dashed spectrum for ∆ ) 10 nm is for perpendicular polarization. (B) Near field distributionsat the dipole-dipole and dipole-quadrupole Fano resonance wavelengths. The numbers in white indicate the maximum electromagneticnear field enhancements. (C) Scattering spectra of concentric Fanoshells (∆ ) 0) scaled to different sizes (Mie theory). The bottom spectrumcorresponds to a concentric Fanoshell in the quasi-static limit, of dimensions 20% of the concentric experimental nanoparticle, i.e., [r1, r2,r3] ) [7, 10, 15] nm. The Au metal was modeled using the DM.


The electromagnetic hotspots for the subradiant modebecome more localized and intense with increasing offset∆ (Figure 4B). This is consistent with an increasingcoupling between the subradiant mode and the higherorder modes. The nonradiative nature of the subradiantmode, along with a highly confined electromagnetic nearfield inside the dielectric, may be important in spaser ornanolaser applications.46,47

To investigate retardation effects and the influence ofparticle size on the dipole-dipole Fano resonance, Mietheory calculations were performed starting with a quasi-static-sized concentric Fanoshell and then rescaling it to theexperimental geometry of [r1, r2, r3] ) [35, 50, 75] nm(Figure 4C). In the quasi-static limit, the superradiant peakis narrow. In this size regime it couples only very weaklywith the subradiant mode, and the subradiant mode appearsas a minor but distinct peak. With increasing nanoparticlesize, the superradiant mode broadens due to the increasedradadiative damping and eventually provides a sufficientspectral overlap with the subradiant mode that a character-istic asymmetric Fano resonance is induced.

The optical response of a Fanoshell can be reproducedquite accurately with a mechanical model consisting of threecoupled oscillators. This model is an extension of the clas-sical two-oscillator system used to model electromagneticinduced transparency.48 The hybridized plasmon modes ofthe Fanoshell are modeled as three interacting oscillators offrequencies ω1, ω2, and ω3 where ωi

2 ) ki/mi (Figure 5A).For simplicity we consider the case m1 ) m2 ) m3 ) 1. Thethree oscillators interact with three springs, k12, k23, and k13.The physical analogy between our model and a Fanoshell isas follows. The Fanoshell bright dipole plasmon mode ismodeled with resonance frequency ω1 ) 2.2 eV, the darksubradiant mode with resonance frequency ω2 ) 1.64 eV,and the quadrupolar mode with resonance energy ω3 ) 1.98eV. Oscillator |1⟩ is driven by a periodic harmonic force F(t)) Fe-i(ωt+). This is analogous to optical excitation of thebright, superradiant mode. The subradiant mode repre-sented by oscillator |2⟩, which is connected to oscillator |1⟩via k12, is only excited due to its coupling with oscillator |1⟩.This coupling is due to the near field interaction between thetwo modes. The quadrupole mode, represented by oscillator|3⟩, is connected to both oscillators |1⟩ and |2⟩ via k13 andk23. These couplings are due to the symmetry breaking andresponsible for the red shifting of the subradiant mode withincreasing core offset observed in (Figure 4A). The equationsof motion of oscillators |1⟩, |2⟩, and |3⟩ are solved in termsof the displacements x1, x2, and x3 from their respectiveequilibrium position in a one-dimensional system

where Ωij2 ) kij is the frequency associated with the coherent

coupling between the interconnected oscillators. The frictioncoefficient used to account for energy dissipation of thebroad superradiant mode is given by γ1 ) 0.65. Much lowerfrictional constants were used for the narrower dark modes;γ2 ) 0.08 and γ3 ) 0.12 for the subradiant and the quad-rupole modes, respectively. To calculate absorption we

FIGURE 5. The coupled harmonic oscillator description of theFanoshell optical response. (A) Three-body classical oscillator modelwith masses m1, m2, and m3 coupled with springs. Oscillator |1⟩ isdriven by the periodic harmonic force F(t). (B) The absorbed powerfor various interparticle coupling constants yields the spectra ofsymmetric (i) and asymmetric Fanoshells (ii, iii). (C) Comparisonbetween the FDTD simulation of a Fanoshell [r1, r2, r3] ) [35, 55,75] nm, with an offset parameter ∆ ) 10 nm (red) and the four-body oscillator model (black curve and inset).

x1(t) + γ1x1(t) + ω12x1(t) - Ω12

2x2(t) -

Ω132x3(t) ) Fe-iωt (1)

x2(t) + γ2x2(t) + ω22x2(t) - Ω12

2x1(t) - Ω232x3(t) ) 0

(2)

x3(t) + γ3x3(t) + ω32x3(t) - Ω13

2x1(t) - Ω232x2(t) ) 0

(3)


compute the mechanical power P(t) absorbed by particle 1from the external force, P(t) ) Fe-iωtx1(t). By turning off thecoupling between the quadrupole mode and the othermodes, (Ω13

2 ) Ω232 ) 0) and by assigning a reasonable

coupling between the superradiant mode and the subradiantmode (Ω12

2 ) 0.5), the absorbed power of the oscillatorsystem reproduces the plasmonic response of the Fanoshell(Figure 5B, black curve). For this case, the three-oscillatormodel is reduced to a two-oscillator model48 and, as such,yields a single Fano resonance in its spectrum. To simulatethe effect of symmetry breaking, a coupling (Ω13

2 ) 0.6) isintroduced between the quadrupole and the superradiantoscillators. This results in the immediate appearance of ahigher energy dipole-quadrupole Fano resonance, whichincreases in strength with an increase in the couplingconstant (Ω13

2 ) 0.9) (Figure 5B). By turning on the interac-tion between the subradiant and quadrupolar oscillators(Ω23

2) 0.4) a red shifting of the subradiant mode is observedwith a simultaneous reduction in the strength of thedipole-dipole Fano resonance, in excellent agreement withour FDTD simulation results (Figure 4A).

However, the Ω23 interaction blue shifts the dipole-quadrupole Fano resonance which is opposite to the red shiftobserved in the FDTD result. The FDTD red shift is due tocoupling with higher order multipolar modes which areabsent in the three-oscillator model. By introducing anadditional coupled oscillator |4⟩ (Figure 5C, inset) one canqualitatively account for the interaction with the higher ordermodes and reproduce the FDTD spectrum (Figure 5C). Theparameters used in both the three-body and the four-bodyoscillator model are given in Table 1.

In conclusion, we have shown that plasmonic nanopar-ticles can be designed and synthesized with highly tunablebuilt-in, multiple, nearly isotropic Fano resonances. Usingsingle nanoparticle dark field microspectroscopy, we ob-served that Fano resonances were a prominent characteristicof the optical response of these nanoparticles. The observedFano resonances arise from two distinct origins: (1) thecoupling of a subradiant and superradiant dipolar plasmon,which excites a Fano resonance even in a symmetric nano-particle, and (2) the coupling between the superradiantdipolar and subradiant higher multipolar modes, introducedby symmetry breaking. A three-oscillator model provides a

direct mechanical analogy to the coupling observed in theplasmonic nanoparticle. This analogy may provide addi-tional opportunities to design plasmonic effects and torealize them in nanoscale particles, complexes, and morecomplex systems.

Acknowledgment. This work was supported by RobertA. Welch Foundation under Grants C-1220 (N.J.H.) andC-1222 (P.N.) and Department of Defense National SecurityScience and Engineering Faculty Fellowship (N.J.H.) viagrants N00244-09-0067. Computations are supported in partby the Shared University Grid at Rice funded by NSF underGrant EIA-0216467, and a partnership between Rice Uni-versity, Sun Microsystems, and Sigma Solutions, Inc. We alsothank Dr. Nikolay A. Mirin for helpful discussions andproofreading of the manuscript.

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TABLE 1. Parameters Used for Simulation of Three- andFour-Body Oscillator Model

i ii iii iv

ω1, γ1 2.2, 0.65 2.2, 0.65 2.2, 0.65 2.2, 0.65ω2, γ2 1.64, 0.08 1.64, 0.08 1.64, 0.08 1.64, 0.08ω3, γ3 1.98, 0.12 1.98, 0.12 1.98, 0.12 1.98, 0.12ω4, γ4 2.60, 0.6Ω12

2 0.5 0.4 0.2 0.1Ω13

2 0.0 0.6 0.9 0.3Ω14

2 1.2Ω23

2 0.0 0.4 0.5 0.5Ω24

2 0.9Ω34

2 0.8


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