tailoring the negative-refractive-index metamaterials ... · in designing negative-refractive-index...

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Tailoring the negative-refractive-index metamaterialscomposed of semiconductor–metal–semiconductorgold ring/disk cavity heptamers to support strong

Fano resonances in the visible spectrum

Arash Ahmadivand* and Nezih Pala

Department of Electrical and Computer Engineering, Florida International University,10555W Flagler St., Miami, Florida 33174, USA

*Corresponding author: [email protected]

Received July 18, 2014; revised October 9, 2014; accepted November 28, 2014;posted December 1, 2014 (Doc. ID 217303); published January 8, 2015

In this study, we investigated numerically the plasmon response of a planar negative-index metamaterial com-posed of symmetric molecular orientations of Au ring/disk nanocavities in a heptamer cluster. Using the plasmonhybridization theory and considering the optical response of an individual nanocluster, we determined the ac-curate geometrical sizes for a ring/disk nanocavity heptamer. It is shown that the proposed well-organized nano-cluster can be tailored to support strong and sharp Fano resonances in the visible spectrum. Surrounding andfilling the heptamer clusters by various metasurfaces with different chemical characteristics, and illuminatingthe structure with an incident light source, we proved that this configuration reflects low losses and isotropicfeatures, including a pronounced Fano dip in the visible spectrum. Technically, employing numerical methodsand tuning the geometrical sizes of the structure, we tuned and induced the Fano dip in the visible range, while thedark and bright plasmon resonance extremes are blueshifted to shorter wavelengths dramatically. Considering thecalculated transmission window, we quantified the effective refractive index for the structure, while the substanceof the substrate material was varied. Using Si, GaP, and InP semiconductors as substrate materials, we calculatedand compared the corresponding figure of merit (FOM) for different regimes. The highest possible FOM was ob-tained for the GaP–Au–GaP negative-refractive-index metamaterial composed of ring/disk nanocavity heptamersas 62.4 at λ ∼ 690 nm (arounnd the position of the Fano dip). Despite the outstanding symmetric natureof the suggested heptamer array, we provided sharp Fano dips by the appropriate tuning of the geometricaland chemical parameters. This study yields a method to employ ring/disk nanocavity heptamers as a negative-refractive-index metamaterial in designing highly accurate localization of surface plasmon resonance sensingdevices and biochemical sensors. © 2015 Optical Society of America

OCIS codes: (160.3918) Metamaterials; (250.5403) Plasmonics; (280.4788) Optical sensing and sensors;(290.5850) Scattering, particles.http://dx.doi.org/10.1364/JOSAA.32.000204

1. INTRODUCTIONIn recent years, numerous works have shown that the manipu-lation of light-matter interactions in nanoscale dimensionsyields new theoretical aspects of optical physics [1–4]. Oneof the most important branches in the field of optical sciencesis the “plasmonics” that has a wide range of utilization in de-signing subwavelength optical devices such as photovoltaicdevices [5,6], plasmonic waveguides [7–9], bio/chemical sen-sors [10,11], surface-enhanced Raman spectroscopy (SERS)devices [12,13], and enhanced optoelectronic nanostructures[14]. Considering the plasmonic configurations, noble metallicnanoparticles in various shapes play fundamental roles in de-signing numerous optoelectronics devices, and the opticalproperties of these particles strongly depend on the material,shape, and the surrounding medium [15,16]. Recently, artifi-cial plasmonic molecules (oligomers) have extensively beenemployed in manipulating the electromagnetic (EM) plasmonresonance propagation, localization, and coupling in sub-wavelength dimensions [17–24]. It is shown that thesesubwavelength clusters can be exploited efficiently in

designing precise bio/chemical sensors, efficient demulti-plexers, and fast routers [24–28]. Conventionally, two- andthree-dimensional clusters composed of Au and Ag sphere,disk, and shell nanoparticles have broadly been employedin the formation of plasmonic molecular subwavelength struc-tures. Beside the ab initio electronic structure methods andMie scattering theory for nanoparticles in the dipole limit, theplasmon hybridization theory is suggested and applied tocharacterize the plasmon response and optical propertiesof the interacted plasmon resonance modes inside the simpleand complex aggregates [29,30]. Furthermore, particulartypes of particle formations such as core/shell and nanoma-tryushka units have broadly been considered in designing ef-ficient plasmonic devices [31,32]. It is shown that most of thementioned nanoparticles can be tailored to support strongplasmon resonances during excitation by an incident EM field,and as a result, this strong excitation of surface plasmon res-onances leads to the robust localization of surface plasmonresonances (LSPRs) [33]. Moreover, it is well accepted thatmore complex molecular plasmonic clusters in symmetricand antisymmetric regimes (e.g., octamer, decamer, tetramer)

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http://dx.doi.org/10.1364/JOSAA.32.000204

are able to support strong Fano resonances due to the con-structive interference of subradiant dark and superradiantbright plasmon modes [34,35]. By adjusting the identical nano-particles in a close proximity to each other and tuning the geo-metrical dimensions of the particle clusters, a pronouncedFano resonance dip can appear in the cross-sectional profile.For instance, for metallic core/shell spherical nanoparticles ina dielectric host, the magnetic dipole resonance mode arisingfrom the dielectric material and the electric dipole resonancemode (LSPRmode) is supported by the metallic core and shellsections of the configuration [33–35]. On the other hand, it hasbeen proven that dielectric nanoparticles in molecular orien-tations (oligomers) are able to efficiently support strong dipo-lar and multipolar magnetic resonances in visible to the nearinfrared region (NIR) [36]. For instance, Chong et al. [37]showed that completely silicon-based nanosphere clustersin heptamer and hexamer orientations can be tailored to sup-port strong dark magnetic resonant modes, where an interfer-ence between opposite modes gives rise to the observation ofFano resonances in the scattering profile. Also, it is wellunderstood that two concentric spherical metallic nanopar-ticles as a “nanomatryushka” unit with the presence andcoating of given dielectric substances in subwavelength di-mensions provides an extra degree of tunability in the geomet-rical parameters, and this feature can be employed inmagnifying the intensity of a localized field by improvingthe scattering and absorption performances in a certain clus-ter-type structure [36,37]. This geometrical flexibility allowsus to shift the peak of hybridized resonances to the desiredspectrum, while the intensity of the excited modes remainsfixed. Calculating the electric and magnetic polarizabilities,both of the mentioned modes are negative and this featurecan help us to employ the nanosize ring/disk nanocavitiesin designing negative-refractive-index metamaterial compo-nents, which will be discussed in the future sections.

On the other hand, there has been remarkable progresstoward realizing isotropic and negative-refractive-index meta-materials for various purposes [38,39]. Considering this field ofoptical sciences, owning to negative refraction in the visiblerange of the spectrum, numerous configurations such asplanar waveguides [40], metal–insulator–metal coaxial wave-guides [41], and fishnet structures [42] have been designedand fabricated successfully. Studies verified that due to theemergence of dramatic active losses by negative-refractive-index metamaterials, providing an acceptable optical domainis highly problematic [43]. Also, it is shown that plasmonicnegative-refractive-index metamaterials with minor influencesof lossy components can be designed based on structurallydependent Mie excitation theory in subwavelength structures,such as nanomatryushka configurations, core/shell sphericalparticles, and ring/disk nanocavities [44,45]. Numerous workshave shown that ring/disk nanostructures can be tailored tosupport double dipole resonance modes which can be appliedin a negative-refractive-index metamaterial structure with afully negative permittivity and permeability [46–48]. Utilizingthe opportunity of performing pronounced Fano dips in theplasmon response of metamaterial structures, designingprecise LSPR sensors and surface-enhanced Raman spectros-copy (SERS) devices would be possible practically. Techni-cally, due to the formation of magnetic dipole resonancesin a dielectric section of the ring/disk nanocavity, a strong

coupling between arisen LSPRmodes andmagnetic dipole res-onance modes can be performed which suppressed possibledissipation and lossy components by negative-refractive-indexmetamaterial [47,48]. Considering the strength of plasmonresonance interference, highly robust resonance couplingcan be performed in molecular clusters, which leads to thestronger plasmon resonance energy (E eV). Due to the inher-ent anisotropy between the employed metamaterial and Auring/disk nanocavities in the proposed heptamer cluster,strong interference between arisen modes directly leads toobtaining a remarkable quantity for FOM by considering cal-culated imaginary and real parts of the refractive index.

In this study, we first examine the spectral response of aheptamer cluster composed of Au ring/disk nanocavities thatare suited in close proximity to each other and deposited on asemiconductor metasurface as a negative-index metamaterial.Investigating the plasmon response of the symmetric ring/disknanocavity cluster, we evaluate the quality of Fano resonanceappearing and formation in the presence of three differentsemiconductor substances. Using plasmon hybridizationtheory, we characterize the behavior of the appeared Fanodip and its movement from visible to NIR spectra and viceversa. Moreover, we demonstrate that Au ring/disk meta-atoms as a symmetric heptamer cluster yield deep and narrowFano minimums at the visible spectrum in spite of the out-standing inherent symmetry. Also, we verify that the positionand quality of the Fano resonance (including red and blue-shifts) can be dramatically affected by minor perturbationsin the structural and substrate modifications. Assembling fourheptamer clusters in a periodic fashion and determining theeffective refractive index, we show that he proposed configu-ration is able to support strong plasmon and Fano resonanceswithout the expense of symmetry breaking or using morecomplex asymmetric molecular clusters with the highestpossible FOM that have been calculated numerically for anegative-refractive-index metamaterial. Simulation resultsproved that the proposed metamaterial configuration is ableto exploit designing precise LSPR and bio/chemical sensorswith ultrasensitivity.

2. OPTICAL PROPERTIES OF AU RING/DISKNANOCAVITY CLUSTERSConsidering the plasmon hybridization theory, we examinedthe spectral response and optical properties of a simple sym-metric heptamer composed of Au ring/disk nanocavitiesthat are filled and surrounded by a silica (SiO2) host with apermittivity of ε � 2.05. It is shown that a simple heptamercomposed of Au nanodisks that are located in a close prox-imity (a few nanometers) to each other shows strong plasmonresonances, and Fano and Fano-like resonances due to theconstructive interference of sub- and superradiant plasmonmodes in a weak regime [29]. Also, it should be noted thatfor symmetric and regular nanoclusters, the Fano-like dipcan appear by symmetry breaking. This decomposition ofmolecular plasmonic clusters opens a way to discover newdark modes, and the resultant of the destructive interferenceof the opposite modes is the formation of a weak Fano mini-mum. In addition, the Fano mode can be described and con-trolled by the corresponding linewidth [49,50]. Lassiter et al.[35] proved that two fundamental modes are involved in theformation of Fano resonant modes: the superradiant bright

A. Ahmadivand and N. Pala Vol. 32, No. 2 / February 2015 / J. Opt. Soc. Am. A 205

mode and the subradiant dark mode. Accordingly, in thebright mode regime, the dipolar plasmon modes resonate inthe same direction in all of the nanoparticles of a given cluster(in-phase regime). In contrast, in the dark mode regime, thedipolar plasmon modes of the central (middle) particles res-onate in the opposite direction of the peripheral (surrounding)particles (out-of-phase regime). From the technical viewpoint,in the retarded limit, a weak interference between subradiantand superradiant plasmon modes causes inducing of aFano-like dip in the bright mode continuum of the energy levelof the superradiant mode.

Major modifications in the polarization of the incident lightdo not affect the strength of interference between dark andbright modes dramatically in a symmetric heptamer. This sta-bility originates from the inherent symmetry of the heptamercluster, which causes observation of a weak Fano-like dip inthe calculations of the scattering cross-sectional profile. Itis shown that more complex clusters such as decamers,octamers, and tetramers can be tailored to support strongand pronounced plasmon and Fano resonances with high per-formances due to antisymmetric features in the geometricalcomponents. However, this antisymmetric property causesthe appearance of various undesirable dark modes sinceobtaining deep Fano resonances in symmetric configurationsare highly preferred. On the other hand, the spectral responseof symmetric heptamer clusters composed of sphere, rod,shell, nanomatryushka particles, and nanocavities havebroadly been investigated numerically and experimentallyby different research groups [36–46]. However, the spectralresponse of a heptamer composed of Au ring/disk nanocav-ities surrounded by a SiO2 host have rarely been studiedand described. Figure 1(a) illustrates a schematic diagramof the proposed ring/disk nanocavity heptamer that is sur-rounded by the host substance in a three-dimensional (3D)view. Figure 1(b) exhibits a top view of the proposed hep-tamer and includes an introduction of the geometricalparameters. Accordingly, Rd is the radius of the core (disk),Rr is the radius of the outer ring of the cavity unit, tr is thethickness of the ring part, tsi is the thickness of the region be-tween the ring and disk that is filled with the dielectric sub-stance, and D7h is the gap distance between proximal cavityunits. The height of the cavities is identical and is set toh � 80 nm (a carefully examined quantity), while the thick-ness of the substrate is ht � 1.2 μm. Figure 1(c) demonstratesthe scattering cross-sectional diagram for a heptamer com-posed of Au ring/disk nanocavities with the calculated geo-metrical dimensions that are listed in Table 1. The gapdistance between neighboring cavities is identical and is setto D7h � 12 nm to provide strong coupling between adjacentnanocavities. In the numerically calculated diagram, aFano-like dip appears at λ ∼ 1595 nm (NIR spectrum) betweenthe plasmon resonance extremes of subradiant dark(λ ∼ 1900 nm) and superradiant bright (λ ∼ 1090 nm) modes.Evaluating the depicted diagrams for the proposed heptamerwith the other analogous symmetric heptamers of Au nano-disks, and nanoshells, we detected a dramatic enhancementin the Fano-like dip performance for the studied structure[see Fig. 1(d)]. Due to the unique shape of the ring/disk cavity,the hybridized plasmon resonance modes became strongerby tuning the size of the ring and disk cavities accurately.Therefore, we expected a great localization of EM fields in

Fig. 1. (a) A schematic diagram of the examined ring/disk nano-cavity heptamer surrounded and filled by a silica (SiO2) substratein a three-dimensional view. (b) A top view of the proposedheptamer with an introduction of the geometrical parameters.(c) The scattering cross-sectional diagram for the symmetric hep-tamer composed of Au ring/disk nanocavities. (d) A comparisonbetween scattering spectra for the studied Au ring/disk nanocavitiesheptamer, nanodisk, and nanoshell particle heptamers. (e) Two-dimensional snapshot of plasmon hybridization and plasmonresonance coupling between proximal nanocavities in a heptamersystem.


the configuration and this localization and enhancement ofplasmon resonance modes leads to the robust and construc-tive interference of sub- and superradiant plasmon modes.The result of this interaction is a pronounced and narrowFano dip along the scattering spectra. Moreover, a minor red-shift in the position of the Fano dip to the longer spectra forthe proposed heptamer is reported. Figure 1(e) shows thehybridization of plasmon resonance modes and strong near-field coupling in the investigated heptamer under excitationby a transverse electric polarization mode. These results havebeen found based on the structural modifications in the size ofthe nanocavity components and gap distances by comparingthe results of numerous simulation steps using the finite-difference time-domain (FDTD) simulation method. Thespecial shape and structural properties of the examined clus-ter of ring/disk nanocavities provide an interesting opportu-nity to shift and tune the plasmon resonance modes andFano resonance dip in a wide range of the spectrum (fromthe visible to NIR). The important point here is that thesemovements of plasmon and Fano resonances include altera-tions in the scattering efficiency of the structure over thewavelength variations. Table 2 includes the simulation param-eters and settings that are employed in extracting the opticalproperties of the structure. To this end, we employed thethree-dimensional FDTD simulation method (LumericalFDTD Solutions 8.9 package) with perfectly matched layers(PMLs) as boundary conditions with absorbing layers (16layers). Utilizing spatial cell sizes with the size of 0.1 pm,we examined the behavior of the structure with high accu-racy. In addition, a plane wave source with the transversepolarization direction (φ � 0°) is utilized to excite and hybrid-ize the plasmon resonances inside the nanoclusters array.Employing a time-domain field and power monitor as a

near-field monitor in the 2D Z-direction mode (perpendicularto the incident light direction) around the surface of themetamaterial structure allows us to obtain the cross-sectionaldiagrams and two-dimensional snapshots.

Continuing, we studied the spectral response of a symmet-ric heptamer cluster composed of Au ring/disk nanocavitiesthat are surrounded by a semiconductor material as a hostsubstance [silicon (Si)]. Illuminating the cluster system by atransverse electric polarization mode, a strong hybridizationof plasmon resonance modes can be realized with twofoldscattering intensity due to the formation of two different sys-tems in the ring/disk cluster by Si-ring and Si-disk interfaces,which yield different bonding and antibonding resonancefrequencies. Using previous and confirmed geometrical sizesfor the proposed heptamer (see Table 1), we observed anefficient excitation and coupling of plasmon resonances be-tween nanocavities. Figure 2(a) shows a numerically calcu-lated scattering efficiency profile for the studied cluster,where the subradiant and the superradiant peaks are ap-peared at λ ∼ 1200 and 675 nm. In this regime, a dramatic blue-shift in the position of plasmon resonance modes are obviousin comparison to the prior investigation. The result of thisconstructive interference of the dark and bright modes is apronounced Fano dip at λ ∼ 975 nm, which is in accordancewith the plasmon hybridization theory. Technically, consider-ing plasmon hybridization theory in a symmetric cluster, thedark mode appears at the higher energy continuum, while thebright mode is detected at a lower energy level, as expected.Figures 2(b)–2(i) exhibit the plasmon resonance coupling be-tween proximal nanocavities in the symmetric nanoclusterunder transverse electric polarization mode excitation.Figures 2(b)–2(i) demonstrate the charge density distributiondirection through the nanocluster of nanocavities, andaccording to the hybridization theory, the direction of thedipole momentum of central particle units are the same, while

Table 1. Initial Geometrical Dimensions

for the Symmetric Heptamer Composed of

Au Ring/Disk Nanocavities in a SiO2 Host

Parameter Descriptions Settings

Rd 50 nmRr 110 nmT 20 nmtr 40 nmD7h 12 nmh 80 nmSubstrate permittivity (SiO2) ε � 2.05

Table 2. FDTD Parameter Descriptions and

Settings to Study the Plasmon Resonance

Coupling of the Proposed Cluster Structure


Spatial cell sizes 0.1 pmNumber of cells 20,000Number of time steps 10,000Simulation time 800 fsNumber of snapshots 18,874Boundary conditions �x; y; z� axis PML with 16 layersBackground refractive index n � 1Plane wave source amplitude 1.5854e-20Pulse length 2.6533 fs

Fig. 2. (a) The scattering efficiency profile for the Au ring/disk nano-cavity heptamer surrounded by a Si host. (b) [i,ii] Two-dimensionalsnapshots that demonstrate the charge density distribution and plas-mon resonance coupling through the cluster of nanocavities.


peripheral particle units show different directions (indicatedby arrows).

To provide a comprehensive numerical study for the hep-tamer structure composed of ring/disk cavities, we examinedthe effect of geometrical modifications on the quality and po-sition of the Fano dip. As we discussed previously, reductionsin the size of the disk part of the nanocavity structure affectthe quality of the sub- and superradiant plasmon resonancemodes dramatically. This condition directly degrades thequality of the Fano dip significantly, and consequently, theFano minimums become broader and shallower. It is worthyto note that a disk with a small radius cannot support strongplasmon and Fano resonances efficiently and this statement isvalid for the ring/disk heptamer entirely. Figure 3(a) exhibitsthe scattering spectra for the examined cluster, where theradius of the disk section in the cluster is a variant parameter,also, the radii and thicknesses of Si and ring parts are un-changed, respectively. As expected, increasing the radius ofthe disk from 35 to 70 nm gives rise to supporting strong plas-mon resonances, and as a result, a constructive interferencebetween sub- and superradiant plasmon modes can be per-formed at the superradiant continuum. A deep Fano reso-nance minimum in the visible bandwidth is a result of thisrobust and constructive interference of opposite modes.The other noticeable point here is the quality of the Fano mini-mums, and decreasing the radius of the disk section directlyreduces the strength of the Fano dip. As a result of this action,the Fano minimums are redshifted to the longer wavelengths,while becoming broader and shallower. Figure 3(b) depicts

the calculated spectral response of a heptamer cluster, wherethe thickness of the Si part between the ring and disk partsdecrease from 55 to 45 nm. This decrement leads to the blue-shift of the Fano minimums to the shorter spectra, while thequality of Fano resonance remains unchanged. Due to the gen-eration of enough dielectric space between the disk and ringinterfaces t ≫ 12 nm, we observed a strong localization of theEM field in the semiconductor region, and this conditioncauses the formation of a strong interference between thebonding and antibonding plasmon modes. Figure 3(c) showsthe spectral response for the proposed ring/disk cavity hep-tamer, where the thickness of the ring section increases from25 to 35 nm. Noticeable in this profile is that increasing thethickness of the ring reflects analogous results with the diskpart. In this regime, increasing the size of the ring thicknessyields a high-quality Fano dip with a narrow and deep mini-mum, however, the Fano position is redshifted to the longerspectra. Hence, an accurate tuning of the size of the ring thick-ness is highly important due to the appearance of destructivelossy components in the visible spectrum. The reason for thiseffect is directly related to the size of the ring. For the thinnerthicknesses, the strength of the excited resonance modes isdramatically low at the bandwidths of 400–1000 nm, whichleads to a weak Fano dip (Fano-like resonance). In contrast,a thicker ring thickness gives rise to a strong Fano resonancedip with a remarkable redshift to the longer spectra (NIR).Therefore, finding an appropriate and good deal betweengeometrical dimensions of the ring/disk nanocavity helps tosupply a strong and constructive interference of plasmon

Fig. 3. (a) The scattering spectra for the Au ring/disk cluster while the radii of the core section of particles in the cluster is variant. (b) Thecalculated spectral response of a heptamer cluster, while the thickness of the Si part between disk and ring Au metals is decreasing. (c) Thespectral response for the proposed core/shell heptamer, while the thickness of the shell section is increasing.


resonances to perform a high-quality Fano dip in a symmetriccluster. Until now, we have shown that a symmetric clustercomposed of Au ring/disk nanocavities surrounded by a Sihost under illumination with an incident light source is ableto support a strong plasmon resonance coupling inside eachone of the ring/disk nanocavities, and despite an inherent andoutstanding symmetry of the cluster, a robust Fano minimumat the visible spectra is the outcome of the light-matter inter-action and structural adjustment. Furthermore, each one ofthe employed nanocavities can be considered as an individualmeta-atom, while a cluster of these cavities resembles a sin-gular meta-atom similar to each of the cavity components.

3. AU RING/DISK NANOCAVITYHEPTAMER ARRAYS ON METASURFACESNext, we studied the behavior of the proposed symmetricnanocavity clusters in a periodic array, where the structureentirely acts as an isotropic and low-loss negative-refractive-index metamaterial. To this end, we designed a structure com-posed of four nanocavity heptamer units that are suited in acertain distance from each other on a semiconductor hostsubstance. Using prior studies regarding the geometrical di-mensions for a ring/disk nanocavity heptamer (see Table 3),we located these clusters at a 500 nm distance away from eachother to prevent near-field coupling between neighboringclusters. All of the considered sizes are adjusted to providea pronounced Fano dip in a finite configuration with theoverall size of approximately 2.5 μm × 2.5 μm × 1.2 μm.Figure 4(a) illustrates a schematic diagram for the proposedmetamaterial candidate structure composed of fourheptamer arrays with a geometrical introduction inside it.Illuminating the structure by an incident transverse electricpolarization mode, the optical properties of the structure suchas complex transmission, scattering cross-sections, reflection(absorption) coefficients, and S-parameters can be measurednumerically by using the FDTDmethod. Figure 4(b) shows thetwo-dimensional snapshot of the EM field coupling and plas-mon resonance mode excitation through the nanoclusterunits in the proposed metamaterial. To design a metamaterialstructure, the necessary parameters must be determined, andin this regard, the electric and magnetic polarizabilities arethe most important factors in these configurations. Utilizingproposed theoretical method for the studied based on theverified methods by Bohren [51] and Campione et al. [52],we computed the electric and magnetic polarizabilities forthe structure as illustrated in Figs. 4(c) and 4(d), respectively.The negative electric and magnetic polarizabilities have been

obtained in the position of dipole moments at aroundλ ∼ 1075 nm. This condition provides an opportunity to con-sider each one of the clusters as meta-atoms with robustplasmon resonances in the visible domain, and consequently,

Fig. 4. (a) A three-dimensional schematic diagram of a metamaterialstructure composed of four heptamer clusters based on Au ring/disknanocavity particle units. (b) The two-dimensional snapshot of lightpropagation and coupling through the metamaterial structure com-posed of ring/disk heptamers under the transverse electric polariza-tion mode. (c) and (d) Electric and magnetic polarizabilities overthe wavelength variations for the nanocavity cluster surrounded bya Si host substance.

Table 3. Final Geometrical Dimensions

for the Symmetric Heptamer Composed of

Au Ring/Disk Nanocavities in a

Semiconductor Host


Rd 70 nmRr 155 nmt 55 nmtr 30 nmD7h 12 nmh 80 nmSubstrate permittivity (SiO2) ε � 2.05


this ability can be employed in designing low-loss and iso-tropic metamaterial structures with negative-refractive indi-ces that are able to be used in numerous applications. It is wellaccepted that the real part of the refractive index can becharacterized by measuring the wave-vector and on theother hand, the imaginary part of the refractive index canbe determined by using S-parameters [52–54]. Therefore,for the examined configuration, we extracted and calculatedthe refracted wave-vector and transmission through the struc-ture based on determined structural quantities [see Fig. 5(a)].Noticing the depicted profile, a pronounced Fano dip ap-peared at λ ∼ 830 nm, also the superradiant and subradiantextremes performed at λ ∼ 635 and 1040 nm, respectively.The big gap between two opposite modes can be consideredas a transmission window for the proposed cluster, which cor-responds to the negative-refractive-index metamaterial work-ing bandwidths [see Fig. 5(b)], where the Fano dip appearedin this wavelength region. Next, we quantified the correspond-ing FOM for the metamaterial structure based on the achievedresults that are shown in Figs. 5(a) and 5(b). ConsideringFig. 5(c), we plotted a FOM curve for the periodic clusterswhile surrounded by a Si host, and for a Fano dip atλ ∼ 830 nm the effective refractive index is exactlyneff � −1.569� 0.049i. As a result, the corresponding FOMcan be determined as 32.1 [see Fig. 4(c)] by considering fol-lowing equation: FOM � jRe�neff�∕Im�neff�j. Measured FOMis the highest possible quantity for a symmetric-finite-nano-cavity-based passive negative-refractive-index metamaterialin the visible spectrum. Due to the outstanding symmetryof the proposed configuration, the angle of the incident lightdoes not affect the plasmon response and transmission qualityof the negative-refractive-index metamaterial dramatically. Inthis regime, we detected a minor enhancement of the trans-mission at the subradiant and superradiant plasmon reso-nance mode wavelengths (transmission window), while forthe Fano resonance zone and its environmental wavelengths,the transmission window has dropped and its coefficient hasreduced noticeably. Plotting the transmission amplitude overthe wavelength variations, the above claim can be confirmedcorrectly [see Fig. 5(d)], and all of the mentioned regions areindicated by a specific color in the calculated spectra.

Trying to improve the quality of the negative-refractive-in-dex metamaterial by enhancing the FOM parameter, we modi-fied the substance of the metasurface to obtain the highestpossible FOM. To this end, we changed the material of theprior (Si) substrate with the other analogous semiconductorsubstances to study the optical response of the new structurenumerically. Using InP and GaP as two alternative substancesfor the substrate material, we evaluated the plasmon resonan-ces of the structures with each other to obtain the highestpossible performance. Albella et al. [55] and Farrel et al. [56]proved that InP (GaP) with a refractive index of n �3.551�n � 3.45� for the visible spectrum, has a strong potentialas a substrate material in designing various optoelectronicdevices such as laser diodes (light-emitting diodes; LEDs).These substrate substances provide an extremely minor ratioof destructive losses and dissipative components duringoperation, and replacing the Si host by InP (GaP) with thesame geometrical sizes [55–57], and using this feature, wecalculated and plotted the scattering cross-sectional profilefor both of the employed semiconductor substances in a

Fig. 5. (a) Calculated scattering spectral profile for the negative-in-dex metamaterial composed of ring/disk cavity heptamer clusters.(b) The real and imaginary parts of the effective refractive indexfor the cluster composed of Au ring/disk nanocavity units underthe transverse electric polarization mode. (c) The correspondingFOM for the structure over the wavelength variations. (d) Transmis-sion through the negative-index metamaterial cluster for the trans-verse excitation mode. The transmission windows and Fano zoneare indicated by colors.


comparative diagram to evaluate their performance.Figure 6(a) demonstrates the scattering spectra for bothof the semiconductor substrates and as we expected, theFano minimums are blueshifted to the visible spectrum,(shorter wavelengths) λ ∼ 635 and 690 nm for InP and GaPhost, respectively. Due to the strength and position of the plas-mon resonance peaks for dark and bright modes, this blueshiftfor InP is more remarkable than GaP. On the other hand, bothof the employed low-loss semiconductor materials yield re-markable FOM during utilization in designing the negative-re-fractive-index metamaterial structure in comparison with theSi-based metamaterial. Numerical computations indicate thatthe effective refractive index (neff ) for InP (GaP) at λ ∼635 nm (λ ∼ 690 nm) is −1.432� i0.025 (−1.452� i0.232),and as a result, the FOM is quantified as 57.3 (62.4).Figure 5(b) shows the calculated FOM for the proposedmetamaterial based on InP and GaP substrates over thewavelength variations and accordingly, corresponding FOMfor each one of the negative-refractive-index metamaterialcan be defined by the position of the pronounced Fano dip.

4. CONCLUSIONSIn this study, we examined the optical properties and spectralresponse of a negative-index metamaterial composed of sym-metric heptamer clusters with the presence of ring/disk Aunanocavities in periodic arrays. The proposed structure yieldsan enhanced tunability of the plasmon resonance modesfrom the visible to the NIR spectrum under excitation by atransverse electric polarization mode. We verified that the

employed nanocavity heptamer clusters exhibit robust nega-tive electric and magnetic dipole moments, and therefore,they can be considered as meta-atoms. We proved that thisconfiguration can be tailored to support strong Fano resonan-ces in the visible range with low-losses, and isotropic proper-ties. Plotting the calculated scattering cross-sectional profilefor the structure in the presence of a Si host, the negative-re-fractive-index has been measured numerically between λ ∼550 and 1050 nm with a FOM of 32.1 at λ ∼ 830 nm (Fanodip). Replacing the Si substance with GaP and InP, we calcu-lated the spectral response of the metamaterial configuration,and consequently, the negative-refractive indices between λ ∼430 and 840 nm are calculated for both the semiconductorsubstances with the FOM of 57.3 and 62.4 for InP and GaPsubstrates, respectively. This understanding paves the path to-ward the use of the proposed metamaterial configuration indesigning precise plasmonic bioagents and biochemical sen-sors with high sensitivity to environmental perturbations.

ACKNOWLEDGMENTSThis work is supported by the NSF CAREER Programwith theAward No. 0955013.

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Fig. 6. (a) The scattering spectra for the presence of both of the InPand GaP substances as a host material. (b) The corresponding FOMfor the structure over the wavelength variations for the presence ofboth of the GaP and InP materials.


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