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10555W Flagler St., Miami, Florida 33174, USA. *Corresponding ... cluster can be tailored to support strong and sharp Fano resonances in the visible spectrum.

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A. Ahmadivand and N. Pala

Tailoring the negative-refractive-index metamaterials composed of semiconductor–metal–semiconductor gold 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 composed of symmetric molecular orientations of Au ring/disk nanocavities in a heptamer cluster. Using the plasmon hybridization theory and considering the optical response of an individual nanocluster, we determined the accurate geometrical sizes for a ring/disk nanocavity heptamer. It is shown that the proposed well-organized nanocluster can be tailored to support strong and sharp Fano resonances in the visible spectrum. Surrounding and filling the heptamer clusters by various metasurfaces with different chemical characteristics, and illuminating the structure with an incident light source, we proved that this configuration reflects low losses and isotropic features, including a pronounced Fano dip in the visible spectrum. Technically, employing numerical methods and tuning the geometrical sizes of the structure, we tuned and induced the Fano dip in the visible range, while the dark and bright plasmon resonance extremes are blueshifted to shorter wavelengths dramatically. Considering the calculated transmission window, we quantified the effective refractive index for the structure, while the substance of the substrate material was varied. Using Si, GaP, and InP semiconductors as substrate materials, we calculated and compared the corresponding figure of merit (FOM) for different regimes. The highest possible FOM was obtained for the GaP–Au–GaP negative-refractive-index metamaterial composed of ring/disk nanocavity heptamers as 62.4 at λ ∼ 690 nm (arounnd the position of the Fano dip). Despite the outstanding symmetric nature of the suggested heptamer array, we provided sharp Fano dips by the appropriate tuning of the geometrical and chemical parameters. This study yields a method to employ ring/disk nanocavity heptamers as a negativerefractive-index metamaterial in designing highly accurate localization of surface plasmon resonance sensing devices 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. INTRODUCTION In recent years, numerous works have shown that the manipulation of light-matter interactions in nanoscale dimensions yields new theoretical aspects of optical physics [1–4]. One of the most important branches in the field of optical sciences is the “plasmonics” that has a wide range of utilization in designing subwavelength optical devices such as photovoltaic devices [5,6], plasmonic waveguides [7–9], bio/chemical sensors [10,11], surface-enhanced Raman spectroscopy (SERS) devices [12,13], and enhanced optoelectronic nanostructures [14]. Considering the plasmonic configurations, noble metallic nanoparticles in various shapes play fundamental roles in designing numerous optoelectronics devices, and the optical properties of these particles strongly depend on the material, shape, and the surrounding medium [15,16]. Recently, artificial plasmonic molecules (oligomers) have extensively been employed in manipulating the electromagnetic (EM) plasmon resonance propagation, localization, and coupling in subwavelength dimensions [17–24]. It is shown that these subwavelength clusters can be exploited efficiently in 1084-7529/15/020204-09$15.00/0

designing precise bio/chemical sensors, efficient demultiplexers, and fast routers [24–28]. Conventionally, two- and three-dimensional clusters composed of Au and Ag sphere, disk, and shell nanoparticles have broadly been employed in the formation of plasmonic molecular subwavelength structures. Beside the ab initio electronic structure methods and Mie scattering theory for nanoparticles in the dipole limit, the plasmon hybridization theory is suggested and applied to characterize the plasmon response and optical properties of the interacted plasmon resonance modes inside the simple and complex aggregates [29,30]. Furthermore, particular types of particle formations such as core/shell and nanomatryushka units have broadly been considered in designing efficient plasmonic devices [31,32]. It is shown that most of the mentioned nanoparticles can be tailored to support strong plasmon resonances during excitation by an incident EM field, and as a result, this strong excitation of surface plasmon resonances leads to the robust localization of surface plasmon resonances (LSPRs) [33]. Moreover, it is well accepted that more complex molecular plasmonic clusters in symmetric and antisymmetric regimes (e.g., octamer, decamer, tetramer) © 2015 Optical Society of America

A. Ahmadivand and N. Pala

are able to support strong Fano resonances due to the constructive interference of subradiant dark and superradiant bright plasmon modes [34,35]. By adjusting the identical nanoparticles in a close proximity to each other and tuning the geometrical dimensions of the particle clusters, a pronounced Fano resonance dip can appear in the cross-sectional profile. For instance, for metallic core/shell spherical nanoparticles in a dielectric host, the magnetic dipole resonance mode arising from the dielectric material and the electric dipole resonance mode (LSPR mode) is supported by the metallic core and shell sections of the configuration [33–35]. On the other hand, it has been proven that dielectric nanoparticles in molecular orientations (oligomers) are able to efficiently support strong dipolar and multipolar magnetic resonances in visible to the near infrared region (NIR) [36]. For instance, Chong et al. [37] showed that completely silicon-based nanosphere clusters in heptamer and hexamer orientations can be tailored to support strong dark magnetic resonant modes, where an interference between opposite modes gives rise to the observation of Fano resonances in the scattering profile. Also, it is well understood that two concentric spherical metallic nanoparticles as a “nanomatryushka” unit with the presence and coating of given dielectric substances in subwavelength dimensions provides an extra degree of tunability in the geometrical parameters, and this feature can be employed in magnifying the intensity of a localized field by improving the scattering and absorption performances in a certain cluster-type structure [36,37]. This geometrical flexibility allows us to shift the peak of hybridized resonances to the desired spectrum, while the intensity of the excited modes remains fixed. Calculating the electric and magnetic polarizabilities, both of the mentioned modes are negative and this feature can help us to employ the nanosize ring/disk nanocavities in designing negative-refractive-index metamaterial components, which will be discussed in the future sections. On the other hand, there has been remarkable progress toward realizing isotropic and negative-refractive-index metamaterials for various purposes [38,39]. Considering this field of optical sciences, owning to negative refraction in the visible range of the spectrum, numerous configurations such as planar waveguides [40], metal–insulator–metal coaxial waveguides [41], and fishnet structures [42] have been designed and fabricated successfully. Studies verified that due to the emergence of dramatic active losses by negative-refractiveindex metamaterials, providing an acceptable optical domain is highly problematic [43]. Also, it is shown that plasmonic negative-refractive-index metamaterials with minor influences of lossy components can be designed based on structurally dependent Mie excitation theory in subwavelength structures, such as nanomatryushka configurations, core/shell spherical particles, and ring/disk nanocavities [44,45]. Numerous works have shown that ring/disk nanostructures can be tailored to support double dipole resonance modes which can be applied in a negative-refractive-index metamaterial structure with a fully negative permittivity and permeability [46–48]. Utilizing the opportunity of performing pronounced Fano dips in the plasmon response of metamaterial structures, designing precise LSPR sensors and surface-enhanced Raman spectroscopy (SERS) devices would be possible practically. Technically, due to the formation of magnetic dipole resonances in a dielectric section of the ring/disk nanocavity, a strong

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coupling between arisen LSPR modes and magnetic dipole resonance modes can be performed which suppressed possible dissipation and lossy components by negative-refractive-index metamaterial [47,48]. Considering the strength of plasmon resonance interference, highly robust resonance coupling can be performed in molecular clusters, which leads to the stronger plasmon resonance energy (E eV). Due to the inherent anisotropy between the employed metamaterial and Au ring/disk nanocavities in the proposed heptamer cluster, strong interference between arisen modes directly leads to obtaining a remarkable quantity for FOM by considering calculated imaginary and real parts of the refractive index. In this study, we first examine the spectral response of a heptamer cluster composed of Au ring/disk nanocavities that are suited in close proximity to each other and deposited on a semiconductor metasurface as a negative-index metamaterial. Investigating the plasmon response of the symmetric ring/disk nanocavity cluster, we evaluate the quality of Fano resonance appearing and formation in the presence of three different semiconductor substances. Using plasmon hybridization theory, we characterize the behavior of the appeared Fano dip and its movement from visible to NIR spectra and vice versa. Moreover, we demonstrate that Au ring/disk metaatoms as a symmetric heptamer cluster yield deep and narrow Fano minimums at the visible spectrum in spite of the outstanding inherent symmetry. Also, we verify that the position and quality of the Fano resonance (including red and blueshifts) can be dramatically affected by minor perturbations in the structural and substrate modifications. Assembling four heptamer clusters in a periodic fashion and determining the effective refractive index, we show that he proposed configuration is able to support strong plasmon and Fano resonances without the expense of symmetry breaking or using more complex asymmetric molecular clusters with the highest possible FOM that have been calculated numerically for a negative-refractive-index metamaterial. Simulation results proved that the proposed metamaterial configuration is able to exploit designing precise LSPR and bio/chemical sensors with ultrasensitivity.

2. OPTICAL PROPERTIES OF AU RING/DISK NANOCAVITY CLUSTERS Considering the plasmon hybridization theory, we examined the spectral response and optical properties of a simple symmetric heptamer composed of Au ring/disk nanocavities that are filled and surrounded by a silica (SiO2 ) host with a permittivity of ε  2.05. It is shown that a simple heptamer composed of Au nanodisks that are located in a close proximity (a few nanometers) to each other shows strong plasmon resonances, and Fano and Fano-like resonances due to the constructive interference of sub- and superradiant plasmon modes in a weak regime [29]. Also, it should be noted that for symmetric and regular nanoclusters, the Fano-like dip can appear by symmetry breaking. This decomposition of molecular plasmonic clusters opens a way to discover new dark modes, and the resultant of the destructive interference of the opposite modes is the formation of a weak Fano minimum. In addition, the Fano mode can be described and controlled by the corresponding linewidth [49,50]. Lassiter et al. [35] proved that two fundamental modes are involved in the formation of Fano resonant modes: the superradiant bright

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mode and the subradiant dark mode. Accordingly, in the bright mode regime, the dipolar plasmon modes resonate in the same direction in all of the nanoparticles of a given cluster (in-phase regime). In contrast, in the dark mode regime, the dipolar plasmon modes of the central (middle) particles resonate 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 subradiant and superradiant plasmon modes causes inducing of a Fano-like dip in the bright mode continuum of the energy level of the superradiant mode. Major modifications in the polarization of the incident light do not affect the strength of interference between dark and bright modes dramatically in a symmetric heptamer. This stability originates from the inherent symmetry of the heptamer cluster, which causes observation of a weak Fano-like dip in the calculations of the scattering cross-sectional profile. It is shown that more complex clusters such as decamers, octamers, and tetramers can be tailored to support strong and pronounced plasmon and Fano resonances with high performances due to antisymmetric features in the geometrical components. However, this antisymmetric property causes the appearance of various undesirable dark modes since obtaining deep Fano resonances in symmetric configurations are highly preferred. On the other hand, the spectral response of symmetric heptamer clusters composed of sphere, rod, shell, nanomatryushka particles, and nanocavities have broadly been investigated numerically and experimentally by different research groups [36–46]. However, the spectral response of a heptamer composed of Au ring/disk nanocavities surrounded by a SiO2 host have rarely been studied and described. Figure 1(a) illustrates a schematic diagram of the proposed ring/disk nanocavity heptamer that is surrounded by the host substance in a three-dimensional (3D) view. Figure 1(b) exhibits a top view of the proposed heptamer and includes an introduction of the geometrical parameters. Accordingly, Rd is the radius of the core (disk), Rr is the radius of the outer ring of the cavity unit, tr is the thickness of the ring part, tsi is the thickness of the region between the ring and disk that is filled with the dielectric substance, and D7h is the gap distance between proximal cavity units. The height of the cavities is identical and is set to h  80 nm (a carefully examined quantity), while the thickness of the substrate is ht  1.2 μm. Figure 1(c) demonstrates the scattering cross-sectional diagram for a heptamer composed of Au ring/disk nanocavities with the calculated geometrical dimensions that are listed in Table 1. The gap distance between neighboring cavities is identical and is set to D7h  12 nm to provide strong coupling between adjacent nanocavities. In the numerically calculated diagram, a Fano-like dip appears at λ ∼ 1595 nm (NIR spectrum) between the plasmon resonance extremes of subradiant dark (λ ∼ 1900 nm) and superradiant bright (λ ∼ 1090 nm) modes. Evaluating the depicted diagrams for the proposed heptamer with the other analogous symmetric heptamers of Au nanodisks, and nanoshells, we detected a dramatic enhancement in 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 stronger by tuning the size of the ring and disk cavities accurately. Therefore, we expected a great localization of EM fields in

A. Ahmadivand and N. Pala

Fig. 1. (a) A schematic diagram of the examined ring/disk nanocavity heptamer surrounded and filled by a silica (SiO2 ) substrate in a three-dimensional view. (b) A top view of the proposed heptamer with an introduction of the geometrical parameters. (c) The scattering cross-sectional diagram for the symmetric heptamer composed of Au ring/disk nanocavities. (d) A comparison between scattering spectra for the studied Au ring/disk nanocavities heptamer, nanodisk, and nanoshell particle heptamers. (e) Twodimensional snapshot of plasmon hybridization and plasmon resonance coupling between proximal nanocavities in a heptamer system.

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Table 1. Initial Geometrical Dimensions for the Symmetric Heptamer Composed of Au Ring/Disk Nanocavities in a SiO2 Host Parameter Descriptions

Settings

Rd Rr T tr D7h h Substrate permittivity (SiO2 )

50 nm 110 nm 20 nm 40 nm 12 nm 80 nm ε  2.05

the configuration and this localization and enhancement of plasmon resonance modes leads to the robust and constructive interference of sub- and superradiant plasmon modes. The result of this interaction is a pronounced and narrow Fano dip along the scattering spectra. Moreover, a minor redshift in the position of the Fano dip to the longer spectra for the proposed heptamer is reported. Figure 1(e) shows the hybridization of plasmon resonance modes and strong nearfield coupling in the investigated heptamer under excitation by a transverse electric polarization mode. These results have been found based on the structural modifications in the size of the nanocavity components and gap distances by comparing the results of numerous simulation steps using the finitedifference time-domain (FDTD) simulation method. The special shape and structural properties of the examined cluster of ring/disk nanocavities provide an interesting opportunity to shift and tune the plasmon resonance modes and Fano resonance dip in a wide range of the spectrum (from the visible to NIR). The important point here is that these movements of plasmon and Fano resonances include alterations in the scattering efficiency of the structure over the wavelength variations. Table 2 includes the simulation parameters and settings that are employed in extracting the optical properties of the structure. To this end, we employed the three-dimensional FDTD simulation method (Lumerical FDTD Solutions 8.9 package) with perfectly matched layers (PMLs) as boundary conditions with absorbing layers (16 layers). Utilizing spatial cell sizes with the size of 0.1 pm, we examined the behavior of the structure with high accuracy. In addition, a plane wave source with the transverse polarization direction (φ  0°) is utilized to excite and hybridize the plasmon resonances inside the nanoclusters array. Employing a time-domain field and power monitor as a

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near-field monitor in the 2D Z-direction mode (perpendicular to the incident light direction) around the surface of the metamaterial structure allows us to obtain the cross-sectional diagrams and two-dimensional snapshots. Continuing, we studied the spectral response of a symmetric heptamer cluster composed of Au ring/disk nanocavities that are surrounded by a semiconductor material as a host substance [silicon (Si)]. Illuminating the cluster system by a transverse electric polarization mode, a strong hybridization of plasmon resonance modes can be realized with twofold scattering intensity due to the formation of two different systems in the ring/disk cluster by Si-ring and Si-disk interfaces, which yield different bonding and antibonding resonance frequencies. Using previous and confirmed geometrical sizes for the proposed heptamer (see Table 1), we observed an efficient excitation and coupling of plasmon resonances between nanocavities. Figure 2(a) shows a numerically calculated scattering efficiency profile for the studied cluster, where the subradiant and the superradiant peaks are appeared at λ ∼ 1200 and 675 nm. In this regime, a dramatic blueshift in the position of plasmon resonance modes are obvious in comparison to the prior investigation. The result of this constructive interference of the dark and bright modes is a pronounced Fano dip at λ ∼ 975 nm, which is in accordance with the plasmon hybridization theory. Technically, considering plasmon hybridization theory in a symmetric cluster, the dark mode appears at the higher energy continuum, while the bright mode is detected at a lower energy level, as expected. Figures 2(b)–2(i) exhibit the plasmon resonance coupling between proximal nanocavities in the symmetric nanocluster under transverse electric polarization mode excitation. Figures 2(b)–2(i) demonstrate the charge density distribution direction through the nanocluster of nanocavities, and according to the hybridization theory, the direction of the dipole momentum of central particle units are the same, while

Table 2. FDTD Parameter Descriptions and Settings to Study the Plasmon Resonance Coupling of the Proposed Cluster Structure Parameter Descriptions Spatial cell sizes Number of cells Number of time steps Simulation time Number of snapshots Boundary conditions x; y; z axis Background refractive index Plane wave source amplitude Pulse length

Settings 0.1 pm 20,000 10,000 800 fs 18,874 PML with 16 layers n1 1.5854e-20 2.6533 fs

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

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peripheral particle units show different directions (indicated by arrows). To provide a comprehensive numerical study for the heptamer structure composed of ring/disk cavities, we examined the effect of geometrical modifications on the quality and position of the Fano dip. As we discussed previously, reductions in the size of the disk part of the nanocavity structure affect the quality of the sub- and superradiant plasmon resonance modes dramatically. This condition directly degrades the quality of the Fano dip significantly, and consequently, the Fano minimums become broader and shallower. It is worthy to note that a disk with a small radius cannot support strong plasmon and Fano resonances efficiently and this statement is valid for the ring/disk heptamer entirely. Figure 3(a) exhibits the scattering spectra for the examined cluster, where the radius of the disk section in the cluster is a variant parameter, also, the radii and thicknesses of Si and ring parts are unchanged, respectively. As expected, increasing the radius of the disk from 35 to 70 nm gives rise to supporting strong plasmon resonances, and as a result, a constructive interference between sub- and superradiant plasmon modes can be performed at the superradiant continuum. A deep Fano resonance minimum in the visible bandwidth is a result of this robust and constructive interference of opposite modes. The other noticeable point here is the quality of the Fano minimums, and decreasing the radius of the disk section directly reduces 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

A. Ahmadivand and N. Pala

the calculated spectral response of a heptamer cluster, where the thickness of the Si part between the ring and disk parts decrease from 55 to 45 nm. This decrement leads to the blueshift of the Fano minimums to the shorter spectra, while the quality of Fano resonance remains unchanged. Due to the generation of enough dielectric space between the disk and ring interfaces t ≫ 12 nm, we observed a strong localization of the EM field in the semiconductor region, and this condition causes the formation of a strong interference between the bonding and antibonding plasmon modes. Figure 3(c) shows the spectral response for the proposed ring/disk cavity heptamer, where the thickness of the ring section increases from 25 to 35 nm. Noticeable in this profile is that increasing the thickness of the ring reflects analogous results with the disk part. In this regime, increasing the size of the ring thickness yields a high-quality Fano dip with a narrow and deep minimum, however, the Fano position is redshifted to the longer spectra. Hence, an accurate tuning of the size of the ring thickness is highly important due to the appearance of destructive lossy components in the visible spectrum. The reason for this effect is directly related to the size of the ring. For the thinner thicknesses, the strength of the excited resonance modes is dramatically low at the bandwidths of 400–1000 nm, which leads to a weak Fano dip (Fano-like resonance). In contrast, a thicker ring thickness gives rise to a strong Fano resonance dip with a remarkable redshift to the longer spectra (NIR). Therefore, finding an appropriate and good deal between geometrical dimensions of the ring/disk nanocavity helps to supply 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) The calculated spectral response of a heptamer cluster, while the thickness of the Si part between disk and ring Au metals is decreasing. (c) The spectral response for the proposed core/shell heptamer, while the thickness of the shell section is increasing.

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resonances to perform a high-quality Fano dip in a symmetric cluster. Until now, we have shown that a symmetric cluster composed of Au ring/disk nanocavities surrounded by a Si host under illumination with an incident light source is able to support a strong plasmon resonance coupling inside each one of the ring/disk nanocavities, and despite an inherent and outstanding symmetry of the cluster, a robust Fano minimum at the visible spectra is the outcome of the light-matter interaction and structural adjustment. Furthermore, each one of the employed nanocavities can be considered as an individual meta-atom, while a cluster of these cavities resembles a singular meta-atom similar to each of the cavity components.

3. AU RING/DISK NANOCAVITY HEPTAMER ARRAYS ON METASURFACES Next, we studied the behavior of the proposed symmetric nanocavity clusters in a periodic array, where the structure entirely acts as an isotropic and low-loss negative-refractiveindex metamaterial. To this end, we designed a structure composed of four nanocavity heptamer units that are suited in a certain distance from each other on a semiconductor host substance. Using prior studies regarding the geometrical dimensions for a ring/disk nanocavity heptamer (see Table 3), we located these clusters at a 500 nm distance away from each other to prevent near-field coupling between neighboring clusters. All of the considered sizes are adjusted to provide a pronounced Fano dip in a finite configuration with the overall size of approximately 2.5 μm × 2.5 μm × 1.2 μm. Figure 4(a) illustrates a schematic diagram for the proposed metamaterial candidate structure composed of four heptamer arrays with a geometrical introduction inside it. Illuminating the structure by an incident transverse electric polarization mode, the optical properties of the structure such as complex transmission, scattering cross-sections, reflection (absorption) coefficients, and S-parameters can be measured numerically by using the FDTD method. Figure 4(b) shows the two-dimensional snapshot of the EM field coupling and plasmon resonance mode excitation through the nanocluster units in the proposed metamaterial. To design a metamaterial structure, the necessary parameters must be determined, and in this regard, the electric and magnetic polarizabilities are the most important factors in these configurations. Utilizing proposed theoretical method for the studied based on the verified methods by Bohren [51] and Campione et al. [52], we computed the electric and magnetic polarizabilities for the structure as illustrated in Figs. 4(c) and 4(d), respectively. The negative electric and magnetic polarizabilities have been Table 3. Final Geometrical Dimensions for the Symmetric Heptamer Composed of Au Ring/Disk Nanocavities in a Semiconductor Host Parameter Descriptions

Settings

Rd Rr t tr D7h h Substrate permittivity (SiO2 )

70 nm 155 nm 55 nm 30 nm 12 nm 80 nm ε  2.05

Fig. 4. (a) A three-dimensional schematic diagram of a metamaterial structure composed of four heptamer clusters based on Au ring/disk nanocavity particle units. (b) The two-dimensional snapshot of light propagation and coupling through the metamaterial structure composed of ring/disk heptamers under the transverse electric polarization mode. (c) and (d) Electric and magnetic polarizabilities over the wavelength variations for the nanocavity cluster surrounded by a Si host substance.

obtained in the position of dipole moments at around λ ∼ 1075 nm. This condition provides an opportunity to consider each one of the clusters as meta-atoms with robust plasmon resonances in the visible domain, and consequently,

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Fig. 5. (a) Calculated scattering spectral profile for the negative-index metamaterial composed of ring/disk cavity heptamer clusters. (b) The real and imaginary parts of the effective refractive index for the cluster composed of Au ring/disk nanocavity units under the transverse electric polarization mode. (c) The corresponding FOM for the structure over the wavelength variations. (d) Transmission through the negative-index metamaterial cluster for the transverse excitation mode. The transmission windows and Fano zone are indicated by colors.

A. Ahmadivand and N. Pala

this ability can be employed in designing low-loss and isotropic metamaterial structures with negative-refractive indices that are able to be used in numerous applications. It is well accepted that the real part of the refractive index can be characterized by measuring the wave-vector and on the other hand, the imaginary part of the refractive index can be determined by using S-parameters [52–54]. Therefore, for the examined configuration, we extracted and calculated the refracted wave-vector and transmission through the structure based on determined structural quantities [see Fig. 5(a)]. Noticing the depicted profile, a pronounced Fano dip appeared at λ ∼ 830 nm, also the superradiant and subradiant extremes performed at λ ∼ 635 and 1040 nm, respectively. The big gap between two opposite modes can be considered as a transmission window for the proposed cluster, which corresponds to the negative-refractive-index metamaterial working bandwidths [see Fig. 5(b)], where the Fano dip appeared in this wavelength region. Next, we quantified the corresponding FOM for the metamaterial structure based on the achieved results that are shown in Figs. 5(a) and 5(b). Considering Fig. 5(c), we plotted a FOM curve for the periodic clusters while surrounded by a Si host, and for a Fano dip at λ ∼ 830 nm the effective refractive index is exactly neff  −1.569  0.049i. As a result, the corresponding FOM can be determined as 32.1 [see Fig. 4(c)] by considering following equation: FOM  jReneff ∕Imneff j. Measured FOM is the highest possible quantity for a symmetric-finite-nanocavity-based passive negative-refractive-index metamaterial in the visible spectrum. Due to the outstanding symmetry of the proposed configuration, the angle of the incident light does not affect the plasmon response and transmission quality of the negative-refractive-index metamaterial dramatically. In this regime, we detected a minor enhancement of the transmission at the subradiant and superradiant plasmon resonance mode wavelengths (transmission window), while for the Fano resonance zone and its environmental wavelengths, the transmission window has dropped and its coefficient has reduced noticeably. Plotting the transmission amplitude over the wavelength variations, the above claim can be confirmed correctly [see Fig. 5(d)], and all of the mentioned regions are indicated by a specific color in the calculated spectra. Trying to improve the quality of the negative-refractive-index metamaterial by enhancing the FOM parameter, we modified the substance of the metasurface to obtain the highest possible FOM. To this end, we changed the material of the prior (Si) substrate with the other analogous semiconductor substances to study the optical response of the new structure numerically. Using InP and GaP as two alternative substances for the substrate material, we evaluated the plasmon resonances of the structures with each other to obtain the highest possible performance. Albella et al. [55] and Farrel et al. [56] proved that InP (GaP) with a refractive index of n  3.551n  3.45 for the visible spectrum, has a strong potential as a substrate material in designing various optoelectronic devices such as laser diodes (light-emitting diodes; LEDs). These substrate substances provide an extremely minor ratio of destructive losses and dissipative components during operation, and replacing the Si host by InP (GaP) with the same geometrical sizes [55–57], and using this feature, we calculated and plotted the scattering cross-sectional profile for both of the employed semiconductor substances in a

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employed nanocavity heptamer clusters exhibit robust negative electric and magnetic dipole moments, and therefore, they can be considered as meta-atoms. We proved that this configuration can be tailored to support strong Fano resonances in the visible range with low-losses, and isotropic properties. Plotting the calculated scattering cross-sectional profile for the structure in the presence of a Si host, the negative-refractive-index has been measured numerically between λ ∼ 550 and 1050 nm with a FOM of 32.1 at λ ∼ 830 nm (Fano dip). Replacing the Si substance with GaP and InP, we calculated the spectral response of the metamaterial configuration, and consequently, the negative-refractive indices between λ ∼ 430 and 840 nm are calculated for both the semiconductor substances with the FOM of 57.3 and 62.4 for InP and GaP substrates, respectively. This understanding paves the path toward the use of the proposed metamaterial configuration in designing precise plasmonic bioagents and biochemical sensors with high sensitivity to environmental perturbations.

ACKNOWLEDGMENTS This work is supported by the NSF CAREER Program with the Award No. 0955013.

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

comparative diagram to evaluate their performance. Figure 6(a) demonstrates the scattering spectra for both of the semiconductor substrates and as we expected, the Fano minimums are blueshifted to the visible spectrum, (shorter wavelengths) λ ∼ 635 and 690 nm for InP and GaP host, respectively. Due to the strength and position of the plasmon resonance peaks for dark and bright modes, this blueshift for InP is more remarkable than GaP. On the other hand, both of the employed low-loss semiconductor materials yield remarkable FOM during utilization in designing the negative-refractive-index metamaterial structure in comparison with the Si-based metamaterial. Numerical computations indicate that the 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 proposed metamaterial based on InP and GaP substrates over the wavelength variations and accordingly, corresponding FOM for each one of the negative-refractive-index metamaterial can be defined by the position of the pronounced Fano dip.

4. CONCLUSIONS In this study, we examined the optical properties and spectral response of a negative-index metamaterial composed of symmetric heptamer clusters with the presence of ring/disk Au nanocavities in periodic arrays. The proposed structure yields an enhanced tunability of the plasmon resonance modes from the visible to the NIR spectrum under excitation by a transverse electric polarization mode. We verified that the

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