A novel planar plasmonic metamaterial for electromagnetically induced transparency and slow light characteristic is presented in this paper, which consists of nanoring and nanorod compound structures. Two bright modes in the metamaterial are induced by the electric dipole resonance inside nanoring and nanorod, respectively. The coupling between two bright modes introduces transparency window and large group index. By adjusting the geometric parameters of metamaterial structure, the transmittance of EIT window at 385 THz is about 60%, and the corresponding group index and Q factor can reach up to 1.2 × 103 and 97, respectively, which has an important application in slow-light device, active plasmonic switch, SERS and optical sensing.
© 2013 Optical Society of America
Electromagnetically induced transparency (EIT) is a quantum interference phenomenon in atomic system, which can dramatically change optical properties of medium . Boller et al.  observed first EIT in Sr vapor and applied a temporally smooth coupling laser between bound state of atom and upper state of transition. Unfortunately, the EIT performance is strictly limited by the experimental conditions such as cryogenic temperatures, coherent pumping and high intensities. Recently, the analogy of EIT-like behavior in metal plasmonic metamaterial in normal environment is relatively attractive due to its outstanding applications by controlling its group velocity in slow-light devices [3–5], active plasmonic switch [6,7], and biological and chemical sensing [8–10]. Unlike EIT in atomic system, plasmonic EIT property in metamaterial can be tuned simply by adjusting its geometry and integrating into nanoplasmonic circuits without external pumping.
Zhang et al.  first achieved Fano resonance and plasmonic EIT in an individual plasmonic structure. They designed a dolmen-type slab structure including a bright and dark element to realize plasmon-induced transparency. Subsequently, Liu et al.  experimentally demonstrated plasmonic EIT at Drude damping limit using stacked metamaterial. Up to date, plasmonic EIT can be realized in a variety of systems such as resonators [13–18], optical electric dipole antennas [19,20], metallic nanoparticles array  and plasmonic-waveguide systems [22–24].
There are two efficient ways  to induce EIT in plasmonic metal nanostructures, namely, the bright-dark mode coupling and the bright-bright mode coupling. In this work, we design a novel planar plasmonic metamaterial to achieve the plamonic EIT-like effect at optical frequencies, which consists of a nanoring and a nanorod. The asymmetry of compound structure leads to the interplay between two plasmon resonance bright modes. The EIT-like effect is produced by hybridization between two bright modes. By adjusting the geometric parameter of metamaterial, the group index and Q factor can reach up to 1.2 × 103 and 97 in the transparency window, respectively, which is a significant improvement compared to existing results [16,25–28] and can be used for slow-light device, active plasmonic switching, SERS and sensing at optical frequencies.
2. Structure description
A unit cell of compound planar plasmonic metamaterial including a nanoring and a nanorod is illustrated in Fig. 1(a). For the sake of simplicity, the terminology Ring/Rod stands for the composite structure without special mention in the rest of paper. The inner and outer radii of the ring are r1 = 70 nm and r2 = 105 nm, respectively. The length and width of the rod are set to be a = 220 nm and b = 30 nm, respectively, and the center-to-center space between the ring and rod is d = 90 nn. All planar metallic elements have the same thickness of h = 50 nm. The unit cells in free space are periodically arranged along the x- and y-directions with the same period p = 390 nm. A plane wave is incident along the z-direction with the Ex polarization. The simulation is carried out by the time domain solver of 3-D electromagnetic package (www.CST.com), where the computational domain is truncated by Perfectly Matched Layers (PMLs) in the z-direction and the periodic boundary conditions are used to truncate the unit cell in the x-y plane. The permittivity of the silver elements is extracted from experimental data in the literature . A simulator “CST Microwave Studio” based on finite integration has been used to investigate S parameters. During simulating, the good convergence for calculated result can be obtained by utilizing adaptive meshing technique to handle the structure boundaries and geometries that need large aspect ratios of meshes. The mesh type was set to hexahedral grids with mesh size of 3 nm in the time domain solver dialog. The adaptive local hexahedral mesh refinement was activated and the S-parameter convergence criterion has been satisfied after calculating 45 frequency samples as for Fig. 1(b) (red solid curve).
3. Results and discussions
The simulated transmission coefficients of different configurations are shown in Fig. 1(b), and the standalone nanoring and nanorod demonstrate a strong plasmon resonance at 390 THz and 340 THz, respectively. Under the irradiation of external light field with the x-polarization, both the floating nanorod and nanoring perform as an optical electric dipole antenna with different resonant frequencies, implying the electric dipole oscillation, namely, bright mode. The plasmon resonances are spectrally broadened due to radiative damping. However, as two elements are combined into a composite structure as shown in Fig. 1(a), a reasonably sharp transparency window with over 85% transmission at 377 THz is observed. The width of transparency window is about 14 THz, and the corresponding Q factor (ω/∆ω) reaches to 27.
In order to insight the physical mechanism behind the EIT-like effect in the proposed planar metamaterial, we plot the electric field (a-c) and current distribution (d-f) on the Ring/Rod structure in the x-y plane at different resonance frequencies in Fig. 2. Different field and current distributions are observed for the plasmon resonances I (363 THz), II (377 THz), and III (391 THz). It is observed from Fig. 2(a) that two intense electric hot spots are located at the ends of nanorod at resonance I, while the charges distribute at the two ends of nanorod and the in-phase current distributions oscillate along the nanorod and nanoring, as shown in Fig. 2(d). As for plasmon resonance III, the optical response of the Ring/Rod primarily concentrates on the nanoring that represents the behavior of the optical antenna and oscillates with the external electric field, as shown in Fig. 2(c) and 2(f). Both the resonances of I and III server as bright mode with electric dipole oscillation. Figures 2(b) and 2(e) show the electric field and current patterns at resonance II. A quadrupole oscillating appears on Ring/Rod and the out-of-phase currents are induced at two parts of Ring/Rod, as shown in Fig. 2(b) and 2(e). Because the four electric field hot spots arise from the quadrupole oscillating, the reosonance II possesses the stronger local fields and serves as the dark mode, which cannot be excited directly by incident light wave. The hybridization coupling of two bright modes (I and III) is the motivation to induce the dark mode and EIT-like effect.
The sharp profile in the EIT window is very powerful to achieve strong dispersion and highly-confined slow light device with a high group index. The controllable slow-light metamaterial can trap photons for a long time inside the structure, which is useful to enhance light-matter interactions. The dispersion of transmission phase with different nanorod length a are represented in Fig. 3(a), and the corresponding group index ng of Ring/Rod will be then estimated in the following formula,
Figures 3(a) and 3(b) show the transmission intensity and phase spectrum with a nanorod length a. It is clear that the resonance I shifts towards the lower frequency as the length of nanorod a increases because the plasmon resonance frequency of single nanorod is inversely proportional to its length. On the other hand, the resonance III keeps unchanged, and the coupling resonance II also moves towards lower frequency. The intensity and width of the resonance II decrease as a decreases, moreover, the transparency window disappears as a≤120 nm and transmission spectrum remains a broad plasmon resonance due to electric dipole oscillation of nanoring. Meanwhile, the transmission phase spectrum has two frequency segments: one for the anomalous phase dispersion and another one for the normal phase dispersion around the transparency window. The strong dispersion of the transmission phase results in a large group index in the transmission band by analogy with EIT in atom system. The large group index implicates longer traversing time of light through the entire structure. Figure 3(c) shows variation of the group index spectra with different lengths of nanorod, and Fig. 3(d) illustrates that the group index and Q factor in the EIT window vary with different a. The maximum group index and Q factor can reach up to 1.4 × 103 and 965, respectively, for a = 140 nm, however, the corresponding transmission intensity is only 17% at EIT frequency. As for a = 160 nm, the group index and Q factor are 1.2 × 103 and 97, respectively, in addition, the transmission intensity can reach as high as 60% at transparency window.
In addition to the effect of nanorod length, the off-set displacement d is also expected to influence the EIT window. Figure 4 show variation of the transmission spectra and corresponding group index with the off-set displacement d. It is obvious that the spacing d has a significant influence on the strength of the EIT effect. The modes I and II disappear gradually as d decreases, which is caused by the weakened asymmetry of the Ring/Rod composite structure. The Ring/Rod structure is symmetrical for d = 0 nm with respect to the incident electric and magnetic fields. The whole structure represents the electric dipole resonance with a wider resonance peak. The corresponding group indexes with different d are plotted in Fig. 4(b).
The radii of nanoring also play an important role on the transmission of the structure. Figure 5 shows the effect of varying the ring radii on the transmission spectrum and group index of the structure. As for fixed r1 = 75 nm, the EIT window will move to high-frequency region and become sharper with lower transmitted intensity while the outer radius r2 be larger, as shown in Fig. 5(a), and the EIT window vanishes in transmission spectrum as r2≥135 nm due to the composite structure reveal only the plasmon resonance of nanoring with larger r2. The corresponding group index spectra are plotted in Fig. 5(b), the maximum group is about 1 × 103 with r2 = 125 nm. For fixed r2 = 105 nm, the EIT frequency and corresponding group index remain almost unchanged as r1 decreases as shown in Fig. 5(c), which is due to the fact that the variation of inner radius r1 has a small impact on quadrupole oscillating on Ring/Rod shown in Fig. 2(b). However, an additional peak appears at higher frequency region, which is a result of emerged cavity plasmon mode of nanoring.
The plasmonic metamaterials with the sharp plasmon resonances have been proposed in this paper and they have broad practical applications by controlling the line-shape of resonances such as active plasmonic switching, slow-light optical devices, SERS, and sensing. In this work, we have successfully demonstrated that the plasmonic EIT effect can be realized in the Ring/Rod composite planar structure through bright-bright mode coupling. The geometric parameters a and d have a significant influence on the EIT effect and group index. The transmittance of EIT window at 385 THZ is about 60% for given a = 160 nm and d = 90 nm, and the corresponding group index and Q factor can reach up to 1.2 × 103 and 97. The controllable slow-light metamaterial can trap photons for a longer time in these structures and enhance light-matter interactions. Furthermore, the high Q factor plasmon resonance can be used for active plasmonic switching, SERS and sensing.
This work was supported by the National Science Foundation of China (No. 11104252 and 61307019), 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 and 132102210396), the Foundation for University young Key Teacher by Henan province (No. 2012GGJS-146), the fund for Science & Technology innovation team of Zhengzhou (2011-03), Henan Educational Committee Natural Science Foundation (Grant No. 12A140002 and 13A140693).
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