High Tunability Multipolar Fano Resonancesin Dual-Ring/Disk Cavities

Jing Li & Yi Zhang & Tianqing Jia & Zhenrong Sun

Received: 18 March 2014 /Accepted: 20 May 2014# Springer Science+Business Media New York 2014

Abstract Metallic nanostructures that support multipolarFano resonances have drawn much attention in recent years.Such structures are applicable especially to enhanced nonlin-ear optics, where two resonance wavelengths need to bemodulated simultaneously. However, how to tune multipolarFano resonances independently remains a challenge. In thepaper, the plasmonic nanostructure consisting of two ring/diskcavities (RDCs) is investigated using the finite element meth-od. The dark multipolar modes of each RDC are excited, andsharp multipolar Fano resonances are induced. The multipolarmodes supported by different RDCs can be tuned indepen-dently by changing the sizes. The line-widths of such Fanoresonances nearly keep below 0.05 eV, and the contrast ratio(CR) of the two quadrupolar Fano dips mostly maintain above50 %. In addition, the exciting bonding modes of differentRDCs make the selective storage of resonance energy avail-able. Such plasmonic nanostructures may find applications inenhanced nonlinear optics or nano-optical elements.

Keywords Surface plasmon polariton . Fano resonance .

Optical properties

Introduction

The collective oscillations of conduction electrons in metallicnanostructures result in localized surface plasmon resonances

[1]. Such plasmon modes can be either superradiant (brightmode) or subradiant (dark mode), depending on the couplingstrength between the incident light and the plasmon mode.The destructive interference of the bright and dark plasmonmodes gives rise to a Fano resonance [2, 3]. Many plasmonicnanostructures have been found supporting Fano resonances,such as “dolmen” structures, nanoparticle oligomer structures,and metal-isolator-metal waveguides [4–8]. The resonancespectra of such structures exhibit sharp line shape, and showstrong sensitivity to the geometrical parameters, which haveattracted intensive interest for their potential applications inthe field of sensing, switching, photodetectors, nanorulers,spasers, and nonlinear optics [9–12]. The optical propertiessuch as line-width, contrast ratio (CR), and tunability of thesestructures have been identified as the most important factors,which determine the overall performance of Fano resonance-based devices [6, 13].

Recently, metallic nanostructures with multipolar Fanoresonances, where several Fano resonances are excited simul-taneously, have drawn much attention [14–16]. These plas-monic nanostructures have potential applications in enhancednonlinear light-matter interactions, such as surface-enhancedRaman scattering (SERS) spectroscopy, surface-enhanced in-frared absorption spectroscopy, and higher-order harmonicgeneration [17–20]. For example, the signal intensity ofSERS can be greatly enhanced when both the excitation andthe Stokes shift wavelengths overlap at the Fano resonance[17]. The SERS intensity will be further boosted by tuningtwo separate Fano resonances to match the excitation and theStokes shift wavelengths, respectively [20]. Multilayer oligo-mer structures [14, 15], hetero-oligomer structures [13], splitnanoring clusters [16], etc. have been suggested to formmultipolar Fano resonances, but more efforts are needed toimprove their optical properties.

The metallic ring/disk cavity (RDC) is a highly tunablenanostructure that supports sharp plasmon resonance [21].

J. Li :Y. Zhang (*) : T. Jia : Z. SunState Key Laboratory of Precision Spectroscopy, Department ofPhysics, East China Normal University, Shanghai 200062,People’s Republic of Chinae-mail: yizhang@tjpu.edu.cn

Y. ZhangDepartment of Physics, Tianjin Polytechnic University,Tianjin 300387, People’s Republic of China

PlasmonicsDOI 10.1007/s11468-014-9738-8

Hao et al. reported that symmetry breaking in this structurecan result in the interaction of the bright dipolar mode and thedark quadrupolar mode and form Fano resonance [22]. Fuet al. found that higher-order Fano resonances were generatedwhen the disk size was reduced to a particular range anddesigned the dual-disk ring nanostructure to manipulate theline-shape of the Fano resonance [23, 24]. Verellen et al.proposed a disk-ring nanostructure and showed that multipleFano resonances can arise with structure size large enough[25]. Zhang et al. investigated the coupling mechanism whichindicated that such structure can induce stronger multipolarFano interference than other similar structures [26]. However,the challenge to tune these multipolar modes independentlyremains, which will limit their applications in nonlinearoptics.

In this article, we study the Fano resonances of a dual-ring/disk cavity (DRDC) nanostructure consisting of two RDCs.The multipolar dark modes supported by different RDCs areexcited, which can be tuned independently. Furthermore, se-lective storage of the resonance energy can be realized in suchstructures. The formation mechanism and the influence ofgeometrical parameters are also discussed.

Methodology

The DRDC, as shown in Fig. 1, consists of two RDCs definedas RDC1 and RDC2, whose geometry is characterized by theouter radii of the two nanorings R1 and R3 and the radii of thetwo nanodisks R2 and R4. The gap widths between the nano-rings and the concentric nanodisks d1 and d2 are equal in ourcalculation. The height of the DRDC, the wall width of thenanoring, and the gap width between the RDCs are kept at 60,20, and 10 nm, respectively. In the article, the optical proper-ties of the DRDC are mainly studied by adjusting the relativesize of two RDCs and the ring-gap widths, as the formerdetermined the tunability of the multipolar Fano resonances,while the latter is closely related with the line-width of Fanoresonances. The nanostructure places in free space if withoutspecial description. The electric field is parallel to the linkedline of the centers of the two nanodisks, as shown in Fig. 1.For this polarization, Fig. 2 shows that the Fano resonancesare very strong. If the polarization rotates by 90°, they will notbe excited.

A finite element method (COMSOL) adopting adaptivemesh is used to solve the time-harmonic three-dimensionalMaxwell’s equations. The computation domain included aDRDC, a region of free space surrounding it, and a perfectlymatched layer eliminating the reflections at the domainboundaries. The computation domain is larger enough that itdoes not change the calculation spectra. The permeability ofsilver is μ=1, with the complex permittivity sourced from[27]. In these calculations, all the gap sizes are larger than

2R1

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Fig. 1 Sketch of the DRDC and the incident light

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Fig. 2 Scattering (red solid curve) and absorption (black dashed curve)spectra of DRDCs with R3 of 120 (a), 130 (b), 140 (c), 150 (d), and160 nm (e). The lettersDN andDB represent the narrow and broad dipolarhybridized resonances, respectively, and the letters Q, H, and O stand forquadrupolar, hexapolar, and octupolar Fano resonances, respectively. Thegreen and gray dashed lines indicate the splits of the quadrupolar andhexapolar Fano resonances, respectively

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10 nm which are achievable using top-down nanofabricationtechniques [22]. A normal incident linearly polarized lightsource is used. The absorption and scattering efficiency ofthe metallic nanostructure are calculated through surface inte-gral and volume integral methods, respectively, and the cor-responding equations are from [28]. The scattering spectra arenormalized by their maximum, and the corresponding absorp-tion spectra of the same structure are magnified or minified inequal proportion. In addition, near-field information at theresonance wavelengths can be directly obtained from thesesimulations. Surface charge plots are computed by Gauss’slaw, and the gradient operation is realized by implementingthe up and down operators to the metal-dielectric interfaces inCOMSOL.

Results and Discussion

Figure 2 shows the normalized scattering and absorptionspectra of the DRDC with the increasing size of RDC2. Theradii R1 and R2 are kept at 120 and 90 nm. The radius R3 isincreased from 120 to 160 nm, and the radius R4 is changedcorrespondingly to keep d2 unchanged. The geometrical pa-rameters of the two RDCs used in Fig. 2a are identical. Thequadrupolar, hexapolar, and octupolar Fano dips are observedat 1.35, 1.87, and 2.27 eV, respectively, as shown in Fig. 2a.Each of these Fano dips splits into two individual dips, andthree new multipolar Fano dips are formed at 1.26, 1.76, and2.16 eV with R3 increasing to 130 nm. It is noted that theoriginal Fano dips nearly keep unmoved, while the newformed Fano dips red-shift with increasing size of RDC2.For example, the wavelength of the new formed quadrupolarFano dips moves from 1.35 to 1.03 eV with R3 varying from120 to 160 nm. Besides, the original quadrupolar Fano dipscan be tuned by changing the size of RDC1; thus, two Fanoresonances can be tuned independently. The hexapolar Fanodips and the narrow dipolar peaks at low energy also showsimilar trends. The tunability of the octupolar Fano resonancescan be demonstrated clearly by increasing their intensity [24].

The spectrum of the DRDC shows both high CR andnarrow line-width. The CR is defined as the ratio of thedifference between the peak and the dip values to the peakone, and the line-width is defined as the full width at halfdepth. The outside coupling of bright dipolar and dark multi-polar modes can induce strong Fano interference and result insuper-high CR [26]. Figure 2a–e shows that the CR of originalquadrupolar Fano dips nearly keep above 90 %. Though theCR of the newly formed quadrupolar Fano dip decreasesslightly with increasing size of RDC2, it mostly keeps above50 % as shown in Fig. 2a–d. The decreasing CR of the newlyformed hexapolar Fano dip with the increasing size of RDC2

is mainly caused by the influence of the nearby quadrupolarFano modes, which will be discussed below. The line-width of

these multipolar Fano resonances nearly keeps below 0.05 eV.The high energy stored in the two narrow concentric ring-gap,which is caused by the lightning rod effect, is the main reasonresulting in the narrow Fano line-width [29]. Such charactersmake the application of multipolar Fano resonances possible.For example, two sharp Fano dips can be tuned respectively tothe pump and probe light for SERS.

Figure 3 shows the hybridization diagram of the DRDCdiscussed in Fig. 2c. The Fano resonances are formed by theprimitive plasmon coupling of the two RDCs. The interactionsbetween the primitive plasmons are determined by the sepa-ration between the surfaces of the metals and the relativeenergies of the primitive plasmons [22]. The formation ofthe hybridized DRDC plasmons resulting from the dominantinteractions is depicted by the red dashed lines. Figure 3a, cshows the scattering and absorption spectra of the RDC con-stituents, and Fig. 3b shows the scattering spectrum of theinteracting DRDC system. The hybridized dipolar bondingand antibonding resonances of RDC are excited by perpen-dicular incident light as shown by the black line [21], and theirinteractions result in several hybridized plasmon modes. Thenarrow peaks at 0.64 and 0.53 eV are bonding resonancesconsisting of aligned dipolar antibonding and bonding modesof the two RDCs. The relative large energy difference makesthe interaction weak. The broader hybridized resonance at1.14 eV is a bonding combination of their dipolar antibondingmodes. The antibonding resonance at 2.43 eV is indistinguish-

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E=1.38 eV

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Fig. 3 Hybridization diagram for the DRDC in Fig. 2c. Scatteringspectra of the RDCs (a, c) and the DRDC (b) excited by perpendicularincident light are indicated by a black solid curve. Absorption spectra ofthe RDCs (a, c) induced by parallel incident light are shown by a graydashed curve in panels (a) and (c). The red dotted lines indicate thedipolar interactions. The blue dotted lines indicate the interactions be-tween multipolar dark modes and the broader hybridized mode, whichresult in Fano resonances. The insets show the charge distributions on thetop surfaces at the Fano resonance energies

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able for the other higher-order modes and the strong dampingat high energies [22].

The dashed curves in Fig. 3a, c show the absorption spectraof the RDCs with parallel incidence. For the finite speed oflight, the incident wave front reaches the left side of the RDCsfirst, which makes the multipolar bonding modes activable[22]. The quadrupolar and hexapolar bonding modes of RDC1

are observed at 1.39 and 1.91 eV, respectively, and those ofRDC2 are found at 1.19 and 1.67 eV, respectively. Thesemultipolar bonding modes are all dark for perpendicular inci-dent light, and their interactions with the broader hybridizedmode of DRDC result in Fano resonances and form Fano dipsin the extinction spectra, as shown in Fig. 3b. In addition, theCRs of these multipolar Fano dips are closely associated withthe relative position of the dark and the bright hybridizedmode. The two quadrupolar Fano dips show higher CRs asthey are closer to the bright hybridized mode than othermultipolar Fano dips. Figures 2 and 3 show a series of resultswith fixed R1 and R2 (R1=120 nm and R2=90 nm), but it isalso suitable for other situations. We can change the radii R1

and R2 and then tune the bright mode to the position of thequadrupolar dark mode easily by adjusting other parameters.

Figure 4 shows the enhancements of electric field ampli-tude at dipolar and multipolar bonding resonances in Fig. 3b.Most of the electric field energy is stored in the gaps betweenthe nanorings and the nanodisks. The dipolar, quadrupolar,and hexapolar bonding modes of RDC1 are excited strongly at0.64, 1.38, and 1.89 eV, respectively, and those of RDC2 areinduced at 0.53, 1.18, and 1.65 eV, respectively. This suggeststhat the resonance energy can be stored selectively in one ofthe RDCs by changing the resonance wavelength, which may

find applications in nano-optical elements where the manipu-lation of local energy is required [30].

In the DRDC, the corresponding dipolar and multipolarbonding modes supported by the two RDCs will also interactwith each other. They oscillate in phase at the bonding reso-nances of RDC1, and out of phase at the bonding resonancesof RDC2, which can be distinguished by the electric fieldintensity in the central gap between the RDCs. For example,when they oscillate in phase, the charge polarities at the twosides of the central gap are different from each other.Therefore, strong electric field is induced in the gap as shownin Fig. 4b, d, f. This is similar to the phenomenon described in[31]. Such different interactions of the nearby Fano modessuppress each other and this effect becomes more evident withthe decrease of their wavelength difference, which is the mainreason for CR decreasing of the newly formed hexapolar Fanodip as discussed in Fig. 2.

Figure 5 shows the influence of the ring-gap widths on thequadrupolar Fano resonances that show both high CR andnarrow line-width. The gap width affects the resonance line-width of RDC and so does the Fano line-width [21]. The ring-gap widths of the two RDCs and the overall size of the DRDCare increased simultaneously to keep the quadrupolar darkmode superposed well with the broader hybridized mode.The ring-gap width d is 10, 15, and 20 nm, respectively. Thecorresponding radius R1 is 120, 160, and 200 nm, and theradiusR3 is kept at 20 nm larger thanR1 in the calculation. Theresults show that the two quadrupolar Fano dips red-shift withthe size increasing due to retardation effects [21], andhexapolar Fano dips begin to appear in the figure. However,their line-widths display no distinctive changes. The increas-ing width of the ring-gap reduces the local electric field, whilethe accompanying increase of the overall size enhances it forthe lightning rod effect [29], which makes the energy stored in(a)Max 54 (b)Max 50

(c) Max 54 (d) Max 59

(e) Max 33 (f) Max 36

0 50

Fig. 4 The enhancements of electric field amplitude of the dipolar,quadrupolar, and hexapolar bonding modes in the middle section of theDRDC. The corresponding energies are 0.64 (a), 0.53 (b), 1.38 (c), 1.18(d), 1.89 (e), and 1.65 eV (f)

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Fig. 5 The scattering spectra of the DRDC with ring-gap widths of 10,15, and 20 nm

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the structure still keep at a high level. Therefore, sharp Fanoresonances can still be excited. In addition, the decrease oftheir CR caused by the suppression interactions of the nearbyFano modes (see the blue line in Fig. 5) can be overcome byincreasing the wavelength difference between dark modes.These results provide an easy way for experimental realizationof the DRDC nanostructures.

In Fig. 6, we study the influences of different substrates onthe quadrupolar Fano resonances. In the simulations, thesubstrate occupies the whole space below the nanostructure[24], and a two-step procedure is developed to calculate theextinction spectra [32]. The normal spectrum technique isemployed to eliminate the changes of the total extinctionsection with substrate refractive indexes. The geometricalparameters R1, R3, and d are kept at 120, 140, and 10 nm,respectively. Results show that the CR of the two Fano dipsdecreases by 43 and 44 % with the substrate refractive indexincreasing from 1 to 2. Experimentally, the glass substratewith the refractive index of 1.5 is usually used. In our calcu-lation, the CRs of the two Fano dips are 69 and 68 % with thesubstrate refractive index of 1.5 as shown by the red dashedline. The positions of Fano dips red-shift strongly owing to theinteraction between the DRDC and substrate. In this case, wecan slightly decrease the size of the DRDC nanostructure toobtain the Fano dip we need.

Conclusion

In summary, we study the optical properties of DRDCconsisting of two RDCs. The multipolar dark modes of eachRDC are excited easily, and sharp multipolar Fano resonancesare induced. The multipolar modes supported by differentRDCs can be tuned independently. These multipolar Fanoresonances show both narrow line-width and high CR. The

line-width nearly keeps below 0.05 eV, and their CR mostlymaintain above 50%. In addition, the resonance energy can bestored selectively in one of the RDCs by adjusting the wave-length of the incident light. Such characters make them suit-able for applications in enhanced nonlinear optics or nano-optical elements.

Acknowledgments This work is supported by the National NaturalScience Foundation of China (11304224, 11274116, 61271011).

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