In this paper we report the study of the electromagnetically induced transparency (EIT)-like transmission in the bright-dark-bright plasmon resonators. It is demonstrated that the interferences between the dark plasmons excited by two bright plasmon resonators can be controlled by the incident light polarization. The constructive interference strengthens the coupling between the bright and dark resonators, leading to a more prominent EIT-like transparency window of the metamaterial. In contrary, destructive interference suppresses the coupling between the bright and dark resonators, destroying the interference pathway that forms the EIT-like transmission. Based on this observation, the plasmonic EIT switching can be realized by changing the polarization of incident light. This phenomenon may find applications in optical switching and plasmon-based information processing.
©2011 Optical Society of America
The surface plasmons (SPs) excited within metallic nanostructures have attracted great attention due to their intriguing physics and important applications ranging from sensing [1,2], surface-enhanced Raman scattering (SERS) [3,4] to optical modulation and switching [5–8]. For many applications, it is of great importance to tailor the spectral response and strengthen the local field enhancement. Recently, the interference and hybridization of plasmons in metallic nanostructures give rise to many very interesting phenomena such as Fano resonance [9,10] and plasmonic analogue of electromagnetically induced transparency (EIT) [11–13]. EIT is usually realized in a three-level atomic system. It is the result of a quantum destructive interference between two pathways induced by another field that can make an absorptive medium transparent to the probe field.
The EIT analogue in metallic nanostructure is considered as the plasmon coupling between a radiative mode (e.g., electric dipole resonance) in one resonator and a subradiative mode (e.g., quadrupolar resonance) in an adjacent resonator through a manner of destructive interference . The plasmonic EIT in metallic nanostructure leads to sharp resonance and suppresses the radiative loss of the device. These characteristics are very important for applications such as optical sensing and optical communications [14,15]. In contrary to the EIT phenomenon in a three-level atomic system where the transparency window is controlled by an external beam, the plasmonic induced transparency arises from the coupling effects in the near field interaction that inevitably leads to the loss of its tunability. However, active plasmonic devices with externally controllable responses are critical for the realization of functional plasmonic circuits. Thus it is very important to search for strategies to tune the plasmonic transparency window.
In this paper, we propose to use the bright-dark-bright plasmon resonators configuration to control the energy coupling between the bright resonators and the dark resonator. The bright resonators consist of two metal bars that can be strongly excited by the incident wave, while a split-ring resonator (SRR) acts as the dark resonator whose magnetic dipole resonance with circulating surface current can only be excited through the plasmon coupling with the metal bars. The metal bars are spatially arranged such that the direction of the induced surface current has a dependence on the incident light polarization. It is demonstrated that, depending on the incident light polarization, the plasmonic transparency window can be enhanced or suppressed due to the interference effect between the dark plasmon modes excited by the two metal bars. This phenomenon serves the base for an optical switching of the plasmonic EIT transparency window.
2. Plasmonic metamaterial structure and numerical model
Figure 1 shows a schematic illustration of the plasmonic metamaterial unit cell that consists of the bright-dark-bright plasmon resonators. The unit cell of the metamaterial is composed of two metal bars and a SRR. The two metal bars are arranged into L shape. The SRR is formed by a square metal ring with a gap at the center of each side. The light incident perpendicularly onto the plane of structure with polarization angle θ measured from the x-axis. A finite-difference time-domain (FDTD) algorithm with periodic boundary conditions (PBC) is employed in our simulation . The periods in both the x and y direction are 700 nm. Along the propagation direction of light, perfectly match layers (PML) absorbing boundary conditions are utilized. Without losing generality, the structure is immersed in a dielectric with refractive index of 1.5. Gold is used in the numerical model as the metallic material. The permittivity of gold is modeled with Drude formula, where , the electric plasmon frequency and the scattering frequency γ are 1.375 × 1016rad/s and 1.177 × 1014 rad/s, respectively.
3. Numerical simulation results and discussions
Both the electric dipole resonance for metal bar only structure, and the magnetic dipole resonance for SRR only structure have been designed to coincide with each other at the same spectral region around wavelength of 1560 nm. Then the EIT-like transmission is analyzed for the bright-dark plasmon resonators at first. Figure 2(a) shows the transmission spectra for the metal bar (labeled A) only structure, SRR (labeled R1) only structure and the combined SRR and metal bar structure (shown in the inset of Fig. 2(a)) under the illumination with 90 degree incident polarization. For the metal bar only structure, the electric dipole resonance of metal bar can be strongly excited by the incident light. It exhibits a broad dip in the transmission spectra with high electric field localized at its end facets as shown in Fig. 2(c).
For the SRR only structure, the symmetric and anti-symmetric modes can be formed due to the resonance hybridization . But only the symmetric mode located at wavelength 1250 nm can be directly excited by incident light due to the symmetry of the SRR. The corresponding electric field distribution is shown in Fig. 2(b). It is noted that symmetric surface current distribution is excited by the incident light, which creates fields that interfere constructively and results in larger radiation loss. For the anti-symmetric mode located at wavelength 1560 nm, a circulating surface current is formed along the entire SRR circumference. In this case, the magnetic-dipole moment is normal to the SRR plane. According to the induction law, the circulating surface current can be induced by the magnetic field with component normal to the SRR plane. Therefore, when the light is incident normally on the surface of structure, all magnetic field components are parallel to the SRR plane. Then this mode cannot be excited, i.e., a dark mode. However, when the metal bar A is introduced, the dark mode in the SRR can be excited through plasmon near field coupling. A narrow transparent window near 1560 nm is formed within the broad dipole resonance dip background due to the destructive interference between the direct excitation pathway of electric dipole resonance and the indirect excitation pathway of magnetic dipole resonance. The electric field distribution corresponding to the transparency peak is shown in Fig. 2(d). Comparison to the field distribution shown in Fig. 2(c), it can be seen that the interference between the bright and dark resonators gives rise to the field suppression at the ends of metal bar.
Then the second metal bar B, with the same geometry parameters as the metal bar A except for its orientation, is also introduced into the unit cell of the metamaterial shown in Fig. 1. Due to the different spatial orientations of metal bars A and B, their excitation depends on the polarization direction of the incident light. For example, for incident polarization angle at 90 degree, metal bar B cannot be excited by the incident light and the dark mode is only excited through coupling between SRR and metal bar A. Due to the near field coupling, the energy stored in dark mode is also coupled back into the two metal bars. The presence of metal bar B disturbs the interference pathway forming the plasmon-induced transparency and distorts the transparency window. But when the incident polarization angle is changed to 135 degree, both metal bars A and B are excitable by the incident light. The electromagnetic energy transfer from the dipole resonance of metal bars into dark mode of SRR is strengthened due to the presence of two bright resonators, leading to more prominent transparency window. More interestingly, for polarization angle at 45 degree, both metal bars A and B still have the same excitation efficiency as that of 135 degree polarization angle. However, the transparency window disappears and the transmission spectrum has a broad transmission dip. In order to get insights into the physical process, the electric field distribution and the circulating surface current direction in the SRR induced by individual metal bar at wavelength 1560 nm are calculated and shown in Fig. 4 .
For the 135 degree polarization angle shown in Fig. 4(a), it can be seen that the current directions in the SRR induced by metal bars A and B are the same (both clockwise or counter clockwise). The cooperative coupling effect induces the electromagnetic energy to be coupled back and forth between the metal bars and SRR, leading to an EIT-like destructive interference and a suppressed state in metal bars with much weaker electric field at their ends. We denote this situation as the in-phase mode. For the 45 degree polarization angle case shown in Fig. 4(b), the current directions induced by metal bars A and B are opposite to each other. The destructive interference suppresses the electromagnetic energy coupling between the metal bars and the SRR. The dark mode in the SRR cannot be excited. The interference pathways leading to the EIT-like transmission cannot be formed and the electric field energy is mostly localized at the ends of bars. We call this situation as the out-of-phase mode. For other incident polarization angles, the transmission spectra for the plasmonic metamaterial are shown in Fig. 5 . It is found that the transparency peaks around wavelength 1560 nm is strengthened under the in-phase mode excitation, and reach the maximum at 135 degree polarization shown in Fig. 5(a). Under the out-of-phase mode excitation shown in Fig. 5(b), the transmission dips around wavelength 1560 nm become deeper with increasing polarization angles, and reach the minimum at 45 degree polarization. This further confirms the polarization dependent interference effects. Under 135 degree and 45 degree incidence polarization angles, the interference in the dark plasmon resonators reaches its extremes due to the equal excitation efficiency for both bright plasmon resonators.
To further understand the effect of near-field coupling on the transmission under the in or out of phase modes, the transmission spectra with respect to different spatial separation wL are calculated and shown in Fig. 6 . With the increase of coupling efficiency (decreasing spatial separation wL), the transparency window widens and becomes more prominent under the in-phase mode excitation (shown in Fig. 6(a)), which is similar to the quantum EIT in an atomic system. However, under the out-of-phase mode excitation, the broad transmission dips remain almost unchanged with decreasing spatial separation wL (shown in Fig. 6(b)). This indicates that the energy coupling between the metal bars and the SRR is completely suppressed regardless of the separation wL. The transmission dip is attributed to the electric dipole resonance of the metal bars.
We can use a classical coupled resonator model  to provide a qualitative explanation of the characteristics described above. The metal bars A and B are represented by resonators 1 and 3, which can strongly couple with the incident light . The SRR R1 is represented by resonator 2, which can be excited only through coupling with resonators 1 and 3. The mode amplitudes of these three resonators ,and satisfy the coupled differential equations:Eq. (1), the mode amplitude of resonators 1 and 3 can be found as:Fig. 7 ). Under 45 and 135 degree polarization angles, the absorption of the model reaches its maximum and minimum at the zero detuning frequency, respectively, which correspond to the transmission dip and peak around wavelength 1560 nm shown in Fig. 3 .
In summary, we numerically investigated the plasmonic EIT-like transmission in bright-dark-bright plasmon resonators. The dark mode in the SRR can be excited by the bright resonators consisted of two metal bars. Due to the spatial orientations of these metal bars, the direction of induced surface circulating current in SRR is polarization dependent. Surface currents flowing in the same direction in the SRR induced by the two metal bars lead to constructive interferences, which enhances the coupling between the bright and dark resonators and contributes to prominent plasmonic transparency window. Contrarily, surface currents flowing in opposite direction result in destructive interferences that suppress the coupling between the bright and dark resonators and destroy the interference pathway forming the EIT-like transmission. Based on this observation, a plasmonic EIT switching function can be realized by adjusting the polarization of incident light. This phenomenon may find potential applications in optical switching and plasmon-based information processing.
This work is supported by the National Key Basic Research Program of China (No. 2011CB301802), the Key Program of National Natural Science Foundation of China (No. 61036005, 60736037), and the National Natural Science Foundation of China (No. 60977019, 11074240, 11074241). The authors gratefully acknowledge Prof. Z. Zhang (G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology) for stimulating discussion.
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