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Double Fano resonant characteristics are investigated in planar plasmonic structure by embedding a metallic nanorod in symmetric U-shaped split ring resonators, which are caused by a strong interplay between a broad bright mode and narrow dark modes. The bright mode is resulted from the nanorod electric dipole resonance while the dark modes originate from the magnetic dipole induced by LC resonances. The overlapped dual Fano resonances can be decomposed to two separate ones by adjusting the coupling length between the nanorod and U-shaped split ring resonators. Fano resonances in the designed structure exhibit high refractive-index sensing sensitivity and figure of merit, which have potential applications in single or double-wavelength sensing in the near-infrared region.
©2013 Optical Society of America
1. Introduction
Fano resonance property in metallic plasmonic nanostructures has drawn many researchers’ attentions in recent years due to its wide and significant applications in the areas such as surface enhanced Raman scattering (SERS) [1], biological and chemical sensors [2, 3], active plasmonic switch [4], waveguide modulator [5] and slow-light devices [6]. Fano resonance, exhibiting an asymmetric line shape and generating a large electromagnetic field congregation, results from plasmonic hybridization between a narrow discrete resonance (dark mode) and a broad spectral line or continuum (bright mode) [7,8]. The dark mode cannot be directly excited by incident light waves. However, the near-field coupling between two neighboring resonators can significantly change its optical behavior and result in localized electromagnetic field distribution in the sub-radiant resonator [9].
Zhang et al. [10] predicted Fano resonance in an individual plasmonic structure. They designed a dolmen-type slab structures consisting of a radiative element and a sub-radiant element to excite Fano resonance and achieved plasmon-induced transparency effect. Subsequently, the Fano resonance in non-concentric ring/disk cavity [11] was demonstrated experimentally, which originated from a quadrupolar ring resonance interacting with a dipolar disk resonance. Fano-like resonances in plasmonic nanoparticle clusters [12], core-shell structure [13], plasmon rulers [14], composite cut-wire structures [15], and other arrangements [16–19] have been investigated theoretically or experimentally since then.
Split ring resonator (SRR) designed by Pendry in 1999 [20] is one of the most important elements to construct plasmonic metamaterials. Recently, structure symmetry breaking was employed to realize single Fano resonance in SRRs [21–25]. Singh & Zhang’s group used a tiny asymmetry U-shaped SRRs to realize electromagnetically induced transparency (EIT) [26] and demonstrated a planar terahertz Fano metamaterial with an ultrahigh quality (Q) factor of 227 [27]. Subsequently, they combined a pair of SRRs with a cut wire to excite and tune the EIT effect, in which the cut wire acted as a bright resonator and the SRRs as a dark element [28, 29].
While most researchers concentrated their interests on the generation of single Fano resonance in various plasmonic metamaterials, several groups reported the formation of multiple Fano resonances in different metallic nanostructures very recently. Fedotov et al. [30] showed that a planar metamaterial composed of asymmetrically split rings not only supports the high-Q (~20) resonance but also can give rise to double-Fano resonances due to the excitation of double bright modes. Although compact plamonic oligomer clusters [31–33] have been demonstrated to exhibit double or multiple Fano resonances, they are difficult to fabricate and manipulate accurately in experiments. Moreover, Wu et al. [6] proposed a concept of a low-symmetry three-dimensional metamaterial that exhibits a double continuum Fano optical resonance to achieve broadband slow light effect in THz frequency range. In this paper, we introduce a metallic nanorod in the middle of two symmetric SRRs to excite LC resonances and analyze the underlying physics of single and double Fano resonances in planar metamaterials, which helps us to specifically understand the coupling process of the bright and the dark modes occurring in the nanoscale volume. Compared with previous works as described above, we propose an active control of Fano resonances in planar metamaterial, single or double Fano resonances are possible to be actively manipulated by adjusting the coupling length between the nanorod and the SRRs. In addition, the single and double Fano resonances in our designed plasmonic structure exhibit high sensing sensitivity and figure of merit (FOM), which can be used to fabricate single or double-wavelength high-sensitive sensors in the near-infrared region. This planar metamaterials is very simple and easy to be fabricated by electron-beam lithography when compared with above mentioned structures.
2. Structures description
The configuration of the planner plasmonic structure is illustrated in Fig. 1(a), which consists of double symmetrical U-shaped split-ring resonators (SRRs) and a nanorod between the two SRRs. For the sake of simplicity, this composite structure is termed as SRRs/Rod in the following. The corresponding geometric parameters in Fig. 1(a) are given as follows: a = b = 300 nm, d1 = d2 = 30 nm, c = e = f = 60 nm. All metallic elements have the same thickness of h = 60 nm. A plane wave is incident along the z-direction with the Ex polarization. The simulation is performed by using the time domain solver of commercial software (CST Micro Studio), where the computational domain is truncated by perfectly matched layers (PMLs) in all directions. The scattering cross section of the designed structure is obtained by the time domain near-to-far zone field transformation. The material of metallic elements are chosen to be silver, whose material properties are given in the literature [34].
Fig. 1 (a) Configuration of the designed planar plasmonic structure SRRs/Rod composed of two metallic SRRs and a nanorod. (b) Simulated scattering spectra of SRRs (green), nanorod (blue) and SRRs/Rod (red) structure. The dotted black curve is a fitting of the scattering spectrum (red) using the two oscillators interference model.
3. Results and discussions
Figure 1(b) presents the simulated far-field back scattering cross sections for the structure of SRRs alone (green line), nanorod alone (blue line), and SRRs/Rod (red line) at normal incidence with electric field E parallel to the x axis. The single nanorod or SRR pair exhibit a typical optical antenna oscillating with same resonance frequencies centered at about 260 THz (blue and green curves in Fig. 1(b)). By induction of a nanorod between the two U-shaped SSRs, a typical Fano-like resonance spectral response with its peak at 206 THz and dip at 211 THz (denoted as D mode) appears in addition to a broad plasmon resonance at 293 THz (denoted as B mode) as indicated in Fig. 1(b). Fano resonance is generally observed in structural symmetry-breaking systems. Here we observed Fano resonance in a non-symmetry breaking system since the introduction of a nanorod between the two U-shaped SRRs does not break the structural symmetry. It can be inferred that the Fano resonance must be caused by destructive interference of a radiative (bright mode) resonance and a non-radiative resonance in the system. From the above results, in our designed planar structure, the nanorod acts as a highly radiative bright plasmon resonator and is directly excited by the incident light wave. At the same time, it acts as a key component of non-radiative dark plasmon resonators for the fundamental LC resonance which is indirectly excited through coupling with the bright resonator. In order to quantify the line-width, characterize the resonance position of the asymmetric Fano resonance, and get insight into the underlying physics, the spectrum is fitted through an analytical model. In the spectral domain, the interference between these two plasmon modes can be expressed with an analytical Fano interference model [35–39],
where is constant background amplitude. and characterize the amplitudes and phases of each plasmon mode, andrepresent their resonance frequencies and line-widths, is nonradiative damping in the metal. A nearly match with a two oscillators (j = 1, 2) model fit (black dotted curve) is obtained for simulated spectrum of SRRs/Rod structure in Fig. 1(b). The line widths of the B and D mode are 165.7 THz and 7.8 THz, and the resonance frequencies of the B and D mode center at 318 THz and 206 THz, respectively.In order to better understand the physical origin of this sharp plasmon resonance, we investigate the current distribution on the SRRs/Rod structure in the x-y plane, as shown in Fig. 2. Figures 2(a) and 2(b) plot the current distribution patterns in the x-y plane at 293THz and 206 THz, respectively. Obviously, both the SRRs and the nanorod support in-phase conduction currents at 293THz (B mode). Similar to an electric dipole oscillation, it corresponds to a broad bright mode due to the radiative damping. For the plasmon resonance at 206 THz (D mode), anti-parallel oscillation currents between the SRRs and the nanorod are observed, where the magnetic dipole moments can be excited by LC resonances. Corresponding magnetic field component Hz in the x-y plane is presented in Fig. 2(c). It is observed that there are two strong magnetic field distributions located in the region between the rod and the SRRs and the two strong magnetic dipoles are out-of-phase. The asymmetric Fano resonance in the scattering spectrum is therefore attributed to the interaction of the electric dipole resonance (the bright mode) with the magnetic dipole resonance (the dark mode), which is governed by the presence of the central nanorod in the plasmonic structures. Obviously, the nanorod plays dual roles in exciting the Fano resonances in our designed structure: as an actor of superradiant bright mode and as a key component of the LC resonators that induce the subradiant dark modes. In addition, the electric filed distribution at 206 THz (Fig. 2(d)) demonstrates strong electric concentrations between the tips of the SRRs and the nanorod. Our result suggests that structural symmetry-breaking may not be necessary for generating Fano resonance, but a bright mode and a dark mode occurring in the same spectral region (or overlapping) is the key for Fano resonance.
Fig. 2 Current and field distributions on the SRRs/Rod structure in the x-y plane. (a) The current distribution of SRRs/Rod structure at 293THz. (b), (c), and (d) show the current, magnetic field component in the z-direction (i.e. Hz), and electric field component in the y-direction (i.e. Ey) distribution of SRRs/Rod structure at 206 THz.
It is the interplay between the electric dipole resonance (bright mode) and magnetic dipoles resonance (dark mode) that leads to the Fano resonance. It is evident from Fig. 2 and the discussions above that the two LC resonances and magnetic dipoles with out-of-phase oscillation can be excited in the structure of SRRs/Rod. They occur at the same frequency due to the symmetric nature of the structure. If the structure symmetry were broken, the two magnetic dipoles would occur at different frequencies. Double Fano resonances are expected by the interaction of the electric dipole resonance with the magnetic dipoles at different frequencies. In order to validate this supposition, we change the resonance frequency of one of two magnetic dipoles by breaking the structure symmetry.
Figure 3(a) shows the scattering spectrum of the asymmetrical SRRs/Rod structure with the parameters d1 = 50 nm and d2 = 30 nm. Apart from the broad plasmon resonance located around 299THz, two plasmon resonance peaks appear at 206 THz (denoted as D1 mode) and 218 THz (denoted as D2 mode), respectively. The dark mode of the symmetrical SRRs/Rod structure (D mode) is decomposed into two independently detuned ones (D1 and D2 mode) for the asymmetrical structure because the difference of coupling distance between the rod and the two SRRs leads to the two magnetic dipoles oscillating at different resonance frequencies. The dotted black line corresponds to the fitting curve of the simulated scattering spectrum (red) by using a three oscillators Fano interference model according to the Eq. (1). The fitted resonance frequencies (line width) of the D1 and D2 mode are 209 THz and 219 THz (22.6 THz and 37.5 THz), respectively. Figures 4(a)-4(f) show the current, magnetic and electric field distributions in the x-y plane at 206 THz (D1 mode) and 218 THz (D2 mode), respectively. It is obvious that the D1 and D2 modes correspond to different magnetic dipole resonances, which result from the coupling between the nanorod and the SRRs with the spacing of d1 = 50 nm and d2 = 30 nm, respectively.
Fig. 3 (a) Simulated scattering spectrum of the asymmetric SRRs/Rod for d1 = 50 nm and d2 = 30 nm. The dotted black curve is a fitting of the scattering spectrum (red) using three oscillators interference model. (b) The evolution of the double Fano resonances against the separation d = d1-d2 (here d2 = 30 nm).
Fig. 4 The current, magnetic field, and electric field distribution of the asymmetric SRRs/Rod structure in the x-y plane in resonance with D1 (a-b) and D2 (d-f) mode, respectively.
Figure 3(b) presents the evolution of the double Fano resonances with the parameter of d, where d = d1-d2, d1 varies and d2 = 30 nm keeps unchanged. With the increase of d, the distance between the top SRR and nanorod becomes large, which leads to the D2 mode shifts to the higher frequency together with an increasing of plasmon resonance intensity, while the D1 mode corresponding to the LC resonance between the bottom SRR and the nanorod is almost unchanged (located at 206 THz) due to the distance between them keeps constant.
The metamaterials with the sharp plasmon resonances have broad practical applications by controlling the line shape of the resonances such as active plasmonic switching, slow-light optical devices, SERS, and sensing. The SRRs/Rod structure can be employed as a tunable refractive-index based sensor because its spectral position substantially depends on the dielectric constants of the surrounding media. To investigate the sensing performance of the SRRs/Rod structure, we calculate the scattering spectra with different dielectric environments, as shown in Fig. 5(a). With the increase of the refractive index of the dielectric environment, the plasmon resonances associated with the bright and dark modes exhibit an obvious red-shift. This can be understood by the fact that the resonance wavelength is proportional to the square root of capacitance between the metallic nanorod and the U-shaped SRRs (i.e. λ∝(C)1/2) according to LC circuit resonance model, which is in turn proportional to the dielectric constants (i.e. λ∝(ε)1/2 = n) [21]. Figure 5(b) shows the plasmon resonance shift vs. refractive index. The refractive index sensitivities of the D1, D2, D and B mode are calculated to be 1380 nm/RIU, 1330 nm/RIU, 1360 nm/RIU and 920 nm/RIU, respectively. Therefore, the dark modes (D1, D2 and D modes) excited in the symmetrical or asymmetrical SRRs/Rod structure present the same magnitude of sensitivity of refractive index which is higher than the bright one (B mode).
Fig. 5 (a) The scattering spectra of asymmetric SRRs/Rod structure with d1 = 50 nm and d2 = 30 nm and (b) the plasmon resonance shift of D1, D2, D, and B modes with different refractive indices of surrounding dielectric environment.
For sensing applications, a high FOM are desired. FOM is usually applied to further evaluate the sensing performance as the following,
whereis the resonance line width as the full width at half maximum (FWHW) centered at the resonance wavelength, is the refractive index sensitivity (i.e. spectral shifts per refractive index). The corresponding FWHW and FOM for different plasmon modes are presented in Table 1.
Table 1. Evaluation of Sensing Performance by Refractive Index Sensitivity (S) and Figure of Merit (FOM)
From the Table 1, the dark modes (D1, D2 and D modes) excited in the symmetrical or asymmetrical DSRRs/Rod structure present the same magnitude of sensitivity of refractive index (S) that are higher than that of the bright one (B mode). Particularly, the FOM of D mode is the highest one among these plasmon modes. Upon the structure symmetry breaking, the single Fano resonance (D mode) separates into two plasmon modes (D1 and D2 mode). The FOM values of double Fano resonances reduce obviously due to the broadening of plasmon resonance peaks. Our results show that the SRRs/Rod structure can be used for the single or double-wavelength high sensitive sensing in near-infrared region.
4. Conclusions
We have demonstrated that the double Fano resonance effect can be achieved in the SRRs/Rod structure due to the strong interplay between the broad bright mode and the narrow dark modes. The bright mode corresponds to the electric dipole plasmon resonance, while the dark modes originate from the magnetic dipole resonance induced by circular currents. Contrast to the symmetrical SRRs/Rod structure that displays a single Fano resonance, the asymmetrical structure obtained by adjusting coupling distance between the nanorod and one of the SRRs generates two detuned dark modes, leading to double Fano resonances. Fano resonances in the SRRs/Rod structure exhibit high refractive-index sensing sensitivity and FOM, which have potential applications in single or double-wavelength sensing in the near-infrared region. Following this design idea, multiple Fano resonances may be realized for the multiple-wavelength active plasmonic switching, sensor, SERS, and slow-light optical devices.
Acknowledgments
We would like to thank Prof. Xinzheng Zhang and Prof. Peter Hertel for careful reading and correcting the manuscript. This work was supported by the Postdoctoral research sponsorship in Henan province (Grant No. 2011002), the National Science Foundation of China (No.10974183 and 11104252), the Ministry of Education of China (No. 20114101110003), the Aeronautical Science Foundation of China (2011ZF55015), the Basic and Frontier Technology Research Program of Henan Province (No. 112300410264), the Foundation for University young Key Teacher by Henan province (No.2012GGJS-146), the fund for Science & Technology innovation team of Zhengzhou (2011-03), and the cooperation fund with Fudan University (No. KL2011_01).
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