Broadband plasmon-induced transparency in terahertz metamaterials via constructive interference of electric and magnetic couplings

Mingli Wan; Yueli Song; Liufang Zhang; Fengqun Zhou

doi:10.1364/OE.23.027361

1. Introduction

Electromagnetically induced transparency (EIT) is a quantum phenomenon, arising from destructive interference of different excitation pathways through short- and long-lived resonances in a three-level atomic system, and gives rise to a spectrally narrow optical transmission accompanied with extreme dispersion within a broad absorption spectrum [1]. Due to this drastic modification of the dispersive properties of the medium at transparency frequencies, EIT effect has been utilized extensively to slow light and nonlinear optics. However, limited material choice and cumbersome experimental requirements to preserve the coherence of excitation pathways in atomic systems have tremendously constrained further investigations and practical applications of EIT effect. With the development of nanoscience and nanotechnology in recent years, many new synthesis methods developed to simply fabricate metallic nanoparticles with well-defined geometry ensure us to precisely tailor surface plasmon resonances for specific applications [2–5]. Thus, to mimic the atomic EIT effect in plasmonic metamaterials, named as plasmon-induced transparency (PIT), has drawn significant interest and has been demonstrated theoretically and experimentally [6–10]. Based on the mechanism of the coherent interference of EIT effect, the PIT phenomenon can be realized in metamaterials via destructive interference of multiple plasmonic resonators with different Q-factors [11, 12]. A typical scheme is to control the near-field (electric [13–17] or magnetic [18–20] field) coupling between a bright mode and a dark mode, where the bright mode with low Q-factor can be strongly coupled to incident electromagnetic field; the dark mode with high Q-factor is not directly excited by light but could couple with the bright mode via near-field interaction.

So far most studies have been focused on the optimization of PIT effect to achieve a narrow transparency window for potential applications such as ultra-sensitive sensor [21–23], molecular ruler [4] and so on. However, for other practical applications like broadband band pass filtering, it is more desirable to design PIT metamaterials with high transmission over broad spectral band [24–27]. Wu et al. first proposed the concept of broadband PIT and structured a low-symmetry three-dimensional metamaterial supporting a double-continuum Fano resonance to achieve this optical characteristics [24]. Subsequently, Zhu et al. introduced the scheme of multiple dark modes coupled to the single bright mode to effectively broaden the transparency band of the PIT resonance [25]. Han et al. recently achieved an ultra-broadband transparency window in a self-asymmetric magnetic metamaterial by simply adjusting the depth of the structure [26].

Using a planar metamaterial composed of a U-shaped ring (USR) as the bright resonator and a cut wire pair (CWP) as the bright resonator, Zhang et al. demonstrated a PIT effect at near-infrared frequency, where the authors only focused on the magnetic dipolar modes of both plasmonic elements and ignored the corresponding electric dipole and quadrupole modes, respectively [18]. In this paper, we theoretically demonstrate a broadband PIT effect in the similar metamaterial structure at terahertz region. A tunable bandwidth and an on-off-on switching of transmission spectra of the PIT resonance is clearly observed by gradually moving the USR vertically along the CWP. The quasistatic interaction model reveals that the broadband PIT is a result of the constructive interference of electric and magnetic coupling between bright and dark resonators.

2. Structure and simulation method

Figure 1 displays a schematic illustration of the proposed two-dimensional metamaterial unit cell, which consists of a metallic USR resonator symmetrically placed on the center of a metallic CWP resonator. The geometrical parameters of the USR and CWP structures have been optimized structurally and defined as shown in the caption of Fig. 1. The vertical displacement of the USR with respect to the horizontal symmetry axis of the CWP is defined as s. An incident plane wave with the polarization along the gap of the USR (x-axis) illuminates normally to the nanostructure.

Fig. 1 Top view of the proposed PIT metamaterial unit cell with definitions of the geometrical parameters: l₁ = 46 μm, l₂ = 32 μm, l₃ = 10 μm, W₁ = 5 μm, W₂ = 2 μm and g = 2.5 μm, respectively. The thickness of the metallic film is 5 μm. In all simulations, the periodicities are set to be 90 μm in both x and y directions.

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To study optical responses of the metamaterial, numerical calculations are carried out by solving Maxwell equations based on the finite element method (FEM). In order to improve the computational efficiency, the computational domain only contains one unit cell of the array. Bloch-periodic boundary conditions (BPBC) are employed at lateral boundaries of elementary cell (in the x and y directions) for simulating the periodic array, and perfectly matched layers (PML) are applied to the propagation direction (the z direction) to eliminate nonphysical reflections. The frequency-dependent permittivity of metal, which is selected to be gold here, is described as the Drude model with the plasma frequency ω_p = 1.366 × 10¹⁶ rad/s and the damping factor γ_D = 1.225 × 1014 s⁻¹. Because of the surface scattering and grain boundary effects in thin films, we use damping constant which is three times as large as that in bulk gold in all calculations [8]. To simplify the simulated model, the ambient medium is assumed to be air, which does not affect the PIT feature except for a spectral blue-shift [28].

3. Results and discussions

Figure 2(a) shows the simulated transmission spectra of the sole USR array,the sole CWP array and their combination, respectively, where the vertical displacement s is fixed as −4 μm for the latter. The spectral characteristic of the USR metamaterial indicates that there exists a symmetric Lorenz-type resonance at around 2.4 THz, which arises from the excitation of the radiative inductive-capacitive mode inside the USR resonator [29]. However, the CWP metamaterial exhibits no optical response to the applied electromagnetic field owning to its polarization perpendicular to the horizontal symmetry axis of the CWP and the magnetic field parallel to the CWP plane, although it supports symmetric and anti-symmetric plasmon modes [30, 31]. When the two resonators are arrayed in close proximity to each other within one unit cell, an EIT-like transparency window appears in the transmission spectrum instead of the transmission dip of the USR antenna.

Fig. 2 (a) Transmittance spectra of the sole-USR, the sole-CWP and the PIT metamaterial, where the vertical displacement s = −4 μm for the latter. (b) Distribution of the local electric field at the transparency peak (denoted by a blue arrow in Fig. 2(a)).

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To reveal the physical origin of the PIT resonance in the USR/CWP metamaterial, we plot the electric field distributions at the transparent peak (denoted by a blue arrow in Fig. 2(a)), as shown in Fig. 2(b). From the induced electric-field pattern in the USR and CWP, it can be inferred that the PIT comes from the destructive interference between the radiative inductive-capacitive mode of the USR resonator and the high-Q-factor anti-symmetric mode of the CWP one. The USR is directly excited by external electric field, acting as the bright antenna; then with the help of near-field interaction, the anti-symmetric plasmon mode of the CWP is driven indirectly (dark mode) and then brings a back action on the radiative antenna, which results in suppressing the polarization of the bright resonator simultaneously accompanied by a transparency peak in the broad absorption background. However, in comparison with the spectral bandwidths of previously reported PIT-based metamaterials [10, 14], our investigated nanostructure exhibits a much broader transparency band in the transmittance spectrum where the full width at half maximum (FWHM) of the transparency region reaches up to be 0.49 THz, even broader than that of the USR metamaterial.

To elucidate the underlying physical mechanism of the broadband PIT phenomenon, we theoretically and systematically analyze the near-field interaction behaviour between the bright and dark elements of our interested metamaterial. For the USR resonator, when the polarization of the normally incident field is parallel to the gap of the structure, an electric dipole plasmon oscillating along the gap can be excited electrically, thus giving rise to an electric-type magnetic dipole moment perpendicular to the USR plane. Moreover, the electric and magnetic dipole plasmons interact with each other and finally form the radiative inductive-capacitive resonance with a low Q-factor. Therefore, the USR resonator possesses both electric and magnetic dipole modes. For the CWP structure, the two dipole plasmons of the pair of nano-wire strongly interplay and result in two new resonance modes as a consequence of plasmon hybridization [32]: one with a symmetric alignment (known as symmetric mode), which can be directly and strongly coupled to free space; the other one with an anti-symmetric alignment (called as anti-symmetric mode) that is a high-Q-factor dipole-forbidden plasmon mode. For the latter, the currents oscillating out of phase within the two wires at resonance indicate that this mode can be regarded as a planar electric quadrupole resonance. Meanwhile, the anti-symmetric currents in the wires together with the displacement currents between both wires can lead to a resonance excitation of the magnetic dipole moment, penetrating the CWP plane. Thus, the CWP resonator supports both electric quadrupole and magnetic dipole modes.

Although the CWP resonator cannot be directly coupled to the incident field in the planar configuration, its anti-symmetric mode resonance may be indirectly excited by the USR inductive-capacitive mode via near-field coupling and hybridizes in turn with it, thus giving rise to a low-energy bonding resonance and a high-energy anti-bonding resonance (corresponding to the two transmittance dips in Fig. 2(a)). The spectrum width between both resonances mainly depends on their near-field coupling strength, similar to the so-called Autler-Townes doublet in atomic systems [33]. In order to intuitively express their coupling strength, we calculate the interactive energy in the quasi-static approximation. As shown in Fig. 3(a), the interactive electric energy between the dipole moment of the USR resonator the planar quadrupole moment of the CWP one can be expressed as below [31, 34]:

\begin{array}{l} V_{e} = \frac{1}{4 π ε_{0}} (\frac{{\vec{P}}_{1} \cdot {\vec{P}}_{3}}{r_{13}^{3}} - \frac{3 ({\vec{P}}_{1} \cdot {\vec{r}}_{13}) ({\vec{P}}_{3} \cdot {\vec{r}}_{13})}{r_{13}^{5}} + \frac{{\vec{P}}_{2} \cdot {\vec{P}}_{3}}{r_{23}^{3}} - \frac{3 ({\vec{P}}_{2} \cdot {\vec{r}}_{23}) ({\vec{P}}_{3} \cdot {\vec{r}}_{23})}{r_{23}^{5}}) \\ = \frac{- 3}{4 π ε_{0}} (\frac{({\vec{P}}_{1} \cdot {\vec{r}}_{13}) ({\vec{P}}_{3} \cdot {\vec{r}}_{13})}{r_{13}^{5}} + \frac{({\vec{P}}_{2} \cdot {\vec{r}}_{23}) ({\vec{P}}_{3} \cdot {\vec{r}}_{23})}{r_{23}^{5}}) \end{array}

Because of structural symmetry with respect to the polarization of the incident electric field, the following relations are obtained

\begin{array}{l} {\vec{P}}_{1} \cdot {\vec{r}}_{13} = P_{1} r_{13} \cos (π / 2 - θ) = P_{1} r_{13} \sin (θ) \\ {\vec{P}}_{2} \cdot {\vec{r}}_{23} = P_{2} r_{23} \cos (π / 2 + θ) = - P_{2} r_{23} \sin (θ) \end{array}

Therefore, the electric interactive energy is simplified to be as following:

V_{e} = \frac{- 3}{4 π ε_{0}} \frac{P_{1} P_{3} r_{12}}{r_{13}^{4}} {\begin{cases} \cos (π / 2 - θ) < 0 for θ > 0 \\ 0 for θ = 0 \\ \cos (π / 2 - θ) > 0 for θ < 0 \end{cases}

Similarly, for quasistatic coupling between the magnetic dipole moments of the USR and CWP resonators, as shown in Fig. 3(b) the interactive magnetic energy can be written:

V_{m} = \frac{μ_{0}}{4 π} \frac{M_{1} M_{2}}{r^{3}}

The total interactive energy of the two resonators of the PIT metamaterial can be written as a sum of the electric and magnetic energies,

Fig. 3 (a) Interaction between in-plane electric dipole and planar electric quadrupole moments, where anti-parallel dipoles ${\vec{P}}_{1}$ and ${\vec{P}}_{2}$ represent the planar electric quadrupole moment and ${\vec{P}}_{3}$ denotes the electric dipole moment. (b) Interaction between magnetic dipole moments ${\vec{M}}_{1}$ and ${\vec{M}}_{1}$ .

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\begin{array}{l} V = V_{e} + V_{m} \\ = \frac{- 3}{4 π ε_{0}} \frac{P_{3} r_{12} P_{1} \cos (π / 2 - θ)}{r_{13}^{4}} + \frac{μ_{0}}{4 π} \frac{M_{1} M_{2}}{r^{3}} \end{array}

From above equation, we can deduce that, when the gap of the USR is placed under the horizontal symmetry axis of the CWP, the constructive interference between the electric and magnetic interactions leads to an enhanced coupling strength between the bright and dark modes, thus broadening spectral bandwidth of the transparency window; as the gap spatially coincides with the symmetry axis, the electric excitation is completely cancelled due to the structural symmetry and only the magnetic coupling happens; when the gap is located above on the symmetry axis, the magnetic excitation behavior remain constant but its electric coupling displays adverse change. Thus, the two excitation pathways interact destructively to weaken each other and suppress the excitation of the CWP dark mode. According to the above discussion and the configuration of the PIT metamaterial, we firmly believe that the ultra-broadband property arises from the constructive interference between the electric and magnetic interactions.

Equation (4) indicates that displacing the USR vertically along the CWP plays a remarkable influence on the spectral response of the PIT metamaterial. In order to approve the deduction and obtain a spectrally broader transparency band, Fig. 4(a) displays the transmittance spectra in dependence on the vertical displacement s while other dimensional parameters are fixed. It can be seen that, a much broader transparency frequencies with the FWHM = 0.61 THz is achieved when the USR element is located to be −11 μm. In this case, the gap of the USR is considerable close to the bottom edge of the CWP in the y axis direction, so the planar electric quadrupole mode of the dark resonator is effectively excited by the electric field of the bright resonator. The constructive interaction between the electric and magnetic excitations gives rise to a broad transmission band (see Fig. 4(b)). As moving the USR forward, the electric excitation efficiency gradually becomes weaker and disappears when s = 0 μm. For the CWP anti-symmetric mode, because the USR structure is completely embedded into the CWP in all cases, the magnetic excitation is not sensitive to the vertical displacement s. Although the structural symmetry suppresses the electric coupling between the two resonators [8, 13], the magnetic coupling still ensures the existence of the broad transparency band (see Fig. 4(c)). As the CWP further moves forward, the electric excitation again works due to symmetry breaking but displays opposite behavior, and as a result their destructive interaction reduces the PIT broadband. When s = 11.2 μm, the electrically induced surface current increases to be equal to the magnetically excited surface current and the destructive coupling results that the PIT feature completely disappears, leaving behind a broad single resonance dip in the transparency window (see Fig. 4(d)). When s is greater than 11.2 μm, the electric field coupling plays a dominant role in the excitation of the CWP dark resonance and the transparency window appears again (see Fig. 4(e)).

Fig. 4 (a) Transmittance spectra of the PIT metamaterials as a function of the vertical displacement. (b-e) Surface current distributions of the two excitations of the dark mode at s = −11, 0, 11.2 and 23 μm, respectively. The black solid and red dot lines within the CWP represent electrically and magnetically induced surface currents, respectively. Arrows indicate instantaneous directions of the current flow, while their width corresponds to the current intensity. (f-i) The corresponding distributions of the local electric field at the transparency peak.

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To more solidly defend our explanations above, the corresponding near-field patterns at transparency peak are plotted for each case of s, which are shown in Figs. 4(f-i), respectively. It is evident that the resonant near-field displays a perfect agreement with the schematic surface current shown in Figs. 4(b-e). The oscillating direction of the electric fields in the CWP arising from the electric and magnetic excitations at the cases of s = 0 and 11 μm is opposite to that of s = 23 μm due to a directional inverse of the electric coupling (denoted by black arrows). Obviously, this is impossible if there exists only the magnetic coupling between the USR and CWP. As for the case of s = 11.2 μm, the surface currents from the electric and magnetic coupling cancel each other, which suppresses the excitation of the dark resonator and no induced fields are seen clearly in the CWP.

4. Conclusions

In this paper, based on constructive interference between dual excitation pathways of the dark modes, we demonstrate theoretically a broadband PIT effect in a planar terahertz metamaterial, which is composed of a USR inserted into a CWP. The dark resonance modes of the CWP can be excited simultaneously via the near-field coupling by both the electric and magnetic dipole modes of the USR. A developed quasistatic interaction model reveals that the constructive or the destructive interference between the electric and the magnetic excitation pathways of the CWP dark plays a significant influence on the spectral response of the PIT metamaterial. By vertically displacing the USR along the CWP one, a broad transparency window across a frequency range greater than 0.61 THz is observed in the transmittance spectrum, meanwhile the evolution of the spectral lineshape has an excellent agreement with prediction of the interaction model. Because the electric coupling is high sensitive to the relative position of the resonators, the bandwidth can be further increased by decreasing their spacing. Such EIT metamaterials are promising candidates for designing slow light devices and broadband filters operating over a broad frequency range.

Acknowledgments

This work is supported by the Research Project for Basic & Forefront Technology of Henan Province, China (No.132300410301), the Key Research Project for Science and Technology of the Education Department of Henan Province, China (Nos.13B430181 and 15B140007), and the National Natural Science Foundation of China (No. 11575090).

References and links

1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]

2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

3. N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011). [CrossRef] [PubMed]

4. N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science 332(6036), 1407–1410 (2011). [CrossRef] [PubMed]

5. J. F. Li, Y. F. Huang, Y. Ding, Z. L. Yang, S. B. Li, X. S. Zhou, F. R. Fan, W. Zhang, Z. Y. Zhou, Y. Wu, B. Ren, Z. L. Wang, and Z. Q. Tian, “Shell-isolated nanoparticle-enhanced Raman spectroscopy,” Nature 464(7287), 392–395 (2010). [CrossRef] [PubMed]

6. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008). [CrossRef] [PubMed]

7. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef] [PubMed]

8. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009). [CrossRef] [PubMed]

9. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef] [PubMed]

10. J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012). [CrossRef] [PubMed]

11. L. Zhu, F. Y. Meng, J. H. Fu, Q. Wu, and J. Hua, “Multi-band slow light metamaterial,” Opt. Express 20(4), 4494–4502 (2012). [CrossRef] [PubMed]

12. J. Chen, C. Wang, R. Zhang, and J. Xiao, “Multiple plasmon-induced transparencies in coupled-resonator systems,” Opt. Lett. 37(24), 5133–5135 (2012). [CrossRef] [PubMed]

13. X. R. Jin, Y. Lu, H. Zheng, Y. Lee, J. Y. Rhee, K. W. Kim, and W. H. Jang, “Plasmonic electromagnetically-induced transparency in metamaterial based on second-order plasmonic resonance,” Opt. Commun. 284(19), 4766–4768 (2011). [CrossRef]

14. Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express 19(9), 8912–8919 (2011). [CrossRef] [PubMed]

15. J. Shao, J. Q. Li, J. Li, Y. K. Wang, Z. G. Dong, P. Chen, R. X. Wu, and Y. Zhai, “Analogue of electromagnetically induced transparency by doubly degenerate modes in a U-shaped metamaterial,” Appl. Phys. Lett. 102(3), 034106 (2013). [CrossRef]

16. Z. G. Dong, H. Liu, M. X. Xu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Plasmonically induced transparent magnetic resonance in a metallic metamaterial composed of asymmetric double bars,” Opt. Express 18(17), 18229–18234 (2010). [CrossRef] [PubMed]

17. Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H. T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys. 107(9), 093104 (2010). [CrossRef]

18. J. Zhang, S. Xiao, C. Jeppesen, A. Kristensen, and N. A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express 18(16), 17187–17192 (2010). [CrossRef] [PubMed]

19. P. C. Wu, W. T. Chen, K. Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012). [CrossRef]

20. L. Qin, K. Zhang, R. W. Peng, X. Xiong, W. Zhang, X. R. Huang, and M. Wang, “Optical-magnetism-induced transparency in a metamaterial,” Phys. Rev. B 87(12), 125136 (2013). [CrossRef]

21. R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett. 12(3), 1367–1371 (2012). [CrossRef] [PubMed]

22. Z. G. Dong, H. Liu, J. X. Cao, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett. 97(11), 114101 (2010). [CrossRef]

23. X. J. He, L. Wang, J. M. Wang, X. H. Tian, J. X. Jiang, and Z. X. Geng, “Electromagnetically induced transparency in planar complementary metamaterial for refractive index sensing applications,” J. Phys. D Appl. Phys. 46(36), 365302 (2013). [CrossRef]

24. C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011). [CrossRef] [PubMed]

25. Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24(21), 214003 (2013). [CrossRef] [PubMed]

26. S. Han, H. L. Yang, and L. Y. Guo, “Ultra-broadband electromagnetically induced transparency using tunable self-asymmetric planar metamaterials,” J. Appl. Phys. 114(16), 163507 (2013). [CrossRef]

27. C. Li, D. Qi, Y. Wang, and X. Zhang, “Wideband slow light based on plasmon-induced transparency at telecom frequency,” Opt. Commun. 351(15), 26–29 (2015). [CrossRef]

28. X. X. Xia, Y. M. Sun, H. F. Yang, H. Feng, L. Wang, and C. Z. Gu, “The influences of substrate and metal properties on the magnetic response of metamaterials at terahertz region,” J. Appl. Phys. 104(3), 033505 (2008). [CrossRef]

29. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]

30. P. W. Kolb, T. D. Corrigan, H. D. Drew, A. B. Sushkov, R. J. Phaneuf, A. Khanikaev, S. H. Mousavi, and G. Shvets, “Bianisotropy and spatial dispersion in highly anisotropic near-infrared resonator arrays,” Opt. Express 18(23), 24025–24036 (2010). [CrossRef] [PubMed]

31. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010). [CrossRef] [PubMed]

32. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

33. S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955). [CrossRef]

34. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1975).

Broadband plasmon-induced transparency in terahertz metamaterials via constructive interference of electric and magnetic couplings

Abstract

1. Introduction

2. Structure and simulation method

3. Results and discussions

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (4)

Equations (5)

Optics Express