Independently tunable dual-band plasmonically induced transparency based on hybrid metal-graphene metamaterials at mid-infrared frequencies

Chen Sun; Zhewei Dong; Jiangnan Si; Xiaoxu Deng

doi:10.1364/OE.25.001242

1. Introduction

Metamaterials have attracted tremendous interest in recent years for their unique properties not existing in natural materials. With the unit cells much smaller than the operating wavelengths, the values of permittivity and permeability can be artificially modulated, which is highly desirable for manipulating light to realize new electromagnetic phenomena, such as invisibility cloaks and perfect optical concentrators, etc. [1, 2] Plasmonically induced transparency (PIT) in metamaterials [3–7] is a kind of analogues of electromagnetically induced transparency (EIT) [8, 9] allowing for a very narrow transparency window within a broad transmission spectrum, which can remarkably slow down photons and enhance nonlinear properties, underlying many practical applications, such as photonic components, integrated chip scale buffers and highly sensitive sensors [10–12]. So far, plasmonic structures in metallic metamaterial systems, including cut wires [3, 13], split-ring resonators (SRR) [4, 14–18], and coupled waveguide resonators [19], have been proposed to realize the PIT effect, of which PIT peaks can be modulated only by carefully changing geometric parameters of structures [5,20].

Graphene is a promising platform to design active tunable plasmonic devices and systems from near-infrared to terahertz region [21–24] due to its unique properties such as electrical tunability [25], strong light confinement [26], and relatively low plasmonic losses [27, 28]. Recently, the PIT effect in graphene-based metamaterials have been proposed from terahertz to mid-infrared frequencies, and most of them focus on single PIT peak [29–35] which is tuned through changing the Fermi energy. In our previous work [36], multiple PIT peaks at terahertz frequencies have been obtained, which cannot be tuned separately. The PIT effect in hybrid metal-graphene systems [37, 38] works in the mid-infrared region, however is rarely seen in current research.

In this paper, the hybrid metal-graphene nanostructures are proposed to realize multiple PIT peaks at mid-infrared frequencies, which consist of two kinds of dolmen-like structures with different sizes placed on the graphene interdigitated finger sets, respectively. According to the coupled Lorentz oscillator model, the PIT peaks at multiple frequency domains are analyzed. The simulation results based on the finite-difference time-domain (FDTD) solutions indicate that multiple PIT peaks are tuned separately by changing the Fermi energy of corresponding graphene finger sets, which agrees well with theoretical analysis. By combining the metallic nanostructures with the graphene layer, the working wavelength of hybrid metal-graphene dual-band PIT device is in the mid-infrared region. The multiple PIT responses in the hybrid metal-graphene dual-band PIT device are independently tuned by changing bias voltages applied on corresponding graphene fingers other than changing the geometrical parameters in metallic PIT devices, which can be widely applied in fields as tunable sensors, switches, and filters.

2. Structural design and research method

The schematic of hybrid metal-graphene dual-band PIT device, which is composed of the dolmen-like gold nanostructures separated with the dielectric substrate SiN_x by a monolayer of graphene, is illustrated in Fig. 1(a). The unit cell of the device consists of two kinds of dolmen-like structures with different sizes, and each dolmen-like structure is formed by a horizontal cut wire (the dipole antenna) and a vertical cut wire pair (the quadrupole antenna), which is shown in the black dashed box of Fig. 1(b). The periods of unit cell are 5μm on x direction and 10μm on y direction. In the small size dolmen-like structure, the vertical cut wire has L_b1 = 1560nm length and w_b1 = 600nm width, and the horizontal cut wire pair has L_d1 = 1500nm length and w_d1 = 400nm width, respectively; the separation between the horizontal cut wire pair is p₁ = 300nm; the separation between the horizontal cut wire and vertical cut wire pair is denoted as parameter s₁. In the big size dolmen-like structure, the vertical cut wire has L_b2 = 2600nm length and w_b2 = 600nm width, and the horizontal cut wire pair has L_d2 = 2400nm length and w_d2 = 500nm width, respectively; the separation between the horizontal cut wire pair is p₂ = 200nm; the separation between the horizontal cut wire and vertical cut wire pair is denoted as parameter s₂. The thickness of gold cut wires is t_m = 0.08μm. The thickness and index of the SiN_x substrate are t_d = 0.25μm and 2.05, respectively. The graphene layer is structured into interdigitated fingers with width w_g = 4.8μm and spacing s_g = 0.2μm. The small and big dolmen-like structures are on interdigitated finger sets G₁ and G₂, respectively. The graphene finger set G₁ are connected to the metallic strip at the left far ends as the top contact; the graphene finger set G₂ are connected to the metallic strip at the right far ends as the top contact; the square gold ring at the back of substrate SiN_x is used as the bottom contact. Therefore, all big dolmen-like structures are electrically separated from small dolmen-like structures. Two gate voltages V₁ and V₂ are applied on the graphene interdigitated finger set G₁ and G₂, respectively, as shown in Fig. 1(a), which makes the Fermi energies E_F1 and E_F2 of graphene finger sets G₁ and G₂ tuned independently.

Fig. 1 (a) Schematic of the hybrid metal-graphene dual-band PIT device and the incident light polarization. (b) Top view of the unit cell. The black dashed box represents a unit cell, containing two kinds of dolmen-like structures with different sizes. (c)Geometrical parameters of the unit cell.

Download Full Size | PDF

The FDTD solutions (Lumerical Solutions, Inc.) are employed to numerically study the properties of hybrid metal-graphene dual-band PIT device. The transmissions of the vertical cut wire only structure, the horizontal cut wire pair only structure and the dolmen-like structures are simulaeted by the FDTD simulation, which are shown in Fig. 2. The Fermi energies E_F1 and E_F2 of graphene finger sets are both 0.5eV. In Fig. 2(a), the vertical cut wire only structure, the horizontal cut wire pair only structure and the small dolmen-like structure are on the graphene finger set G₁, while there is no gold cut wires on graphene finger set G₂. A typical localized surface plasmon (LSP) resonance in the transmission spectrum of vertical cut wire only structure is excited with the incident electric field E along the y axis, shown by the black curve in Fig. 2(a), which acts as the bright mode. A resonance is excited with the incident electric field E along the x axis instead of y axis in the transmission spectrum of horizontal cut wire pair only structure, shown by the red curve in Fig. 2(a), which is considered as the dark mode. The transparency peak in the resonance notch, namely, the PIT effect, emerges in the transmission of the small dolmen-like structure with the incident electric field E along the y axis, shown by the blue curve in Fig. 2(a). In Fig. 2(b), the vertical cut wire only structure, the horizontal cut wire pair only structure and the big dolmen-like structure are on the graphene finger set G₂, while there is no gold cut wires on graphene finger set G₁. The simulated transmission results of big dolmen-like structure are similar with those of small dolmen-like structure. The bright and dark modes in the dolmen-like structures are expressed as |D_1,2〉 and |Q_1,2〉, respectively. The subscripts 1 and 2 represent the small and big dolmen-like structures, respectively. As the separation between the vertical cut wire and horizontal cut wire pair (s₁ and s₂) decreases, the near-field coupling between the horizontal cut wire pair and vertical cut wire gradually increases, causing the indirect excitation of dark mode with the incident electric field E along the y axis. The dolmen-like structures can be described as a three-level system with two possible pathways of |0〉 − |D_1,2〉 and |0〉 − |D_1,2〉 − |Q_1,2〉 − |D_1,2〉 (ground state |0〉) interfering with each other destructively, which leads to the emerging of transparency peak in the resonance notch.

Fig. 2 (a) The simulated transmission spectra of the vertical cut wire only structure, the horizontal cut wire pair only structure and the dolmen-like structure (s₁ = 500nm) of small size when Fermi energy E_F = 0.5eV. The corresponding geometric structures with the direction of incident electrical field are shown below, respectively. (b) The simulated transmission spectra of the vertical cut wire only structure, the horizontal cut wire pair only structure and the dolmen-like structure (s₂ = 300nm) of big size when Fermi energy E_F = 0.5eV. The corresponding geometric structures with the direction of incident electrical field are shown below, respectively.

Download Full Size | PDF

The coupled Lorentz oscillator model is employed to explain the transmission characteristics of the hybrid metal-graphene dual-band PIT device with the dolmen-like structures. The external driving field is denoted as E₀e^iωt. The bright and dark modes in the small and big dolmen-like structures are expressed as |D_1/2〉 = D̃_1/2e^iωt and |Q_1/2〉 = Q̃_1/2e^iωt, respectively. The field amplitude of (|D_1,2〉, |Q_1,2〉) is obtained [20]

[\begin{matrix} ω - ω_{D, 1} + i γ_{D, 1} & κ_{1} & 0 & 0 \\ κ_{1} & ω - ω_{Q, 1} + i γ_{D, 1} & 0 & 0 \\ 0 & 0 & ω - ω_{D, 2} + i γ_{D, 2} & κ_{2} \\ 0 & 0 & κ_{2} & ω - ω_{Q, 2} + i γ_{D, 2} \end{matrix}] [\begin{matrix} {\tilde{D}}_{1} \\ {\tilde{Q}}_{1} \\ {\tilde{D}}_{2} \\ {\tilde{Q}}_{2} \end{matrix}] = [\begin{matrix} g_{1} {\tilde{E}}_{0} \\ 0 \\ g_{2} {\tilde{E}}_{0} \\ 0 \end{matrix}]

where ω_D,1/2, ω_Q,1/2, κ_1/2, g_1/2, γ_D,1/2, and γ_Q,1/2 are the resonance frequencies of bright modes, the resonance frequencies of dark modes, the coupling parameters, the geometrical parameters, the damping rates of bright modes, and the damping rates of bright modes in the small and big dolmen-like structures, respectively. The amplitudes of bright modes in the small and big dolmen-like structures are [20,36]

{\tilde{D}}_{1 / 2} = \frac{- g_{1 / 2} {\tilde{E}}_{0} (ω - ω_{Q, 1 / 2} + i γ_{Q, 1 / 2})}{(ω - ω_{D, 1 / 2} + i γ_{D, 1 / 2}) (ω - ω_{Q, 1 / 2} + i γ_{Q, 1 / 2}) - {(κ_{1 / 2})}^{2}}

The transmission of hybrid metal-graphene dual-band PIT device is [29,36,39]

T (ω) = 1 - {| \frac{{\tilde{D}}_{1}}{{\tilde{E}}_{0}} |}^{2} - {| \frac{{\tilde{D}}_{2}}{{\tilde{E}}_{0}} |}^{2} .

The coupling parameters κ_1/2 indicating the coupling between the bright and dark modes increases with the decrease of the separation s₁ and s₂ [3]. The bright modes are directly excited with the incident light at the resonance frequencies ω_D,1/2, which brings out the corresponding resonance notch. As the separation (s₁/s₂) decreases, the indirect excitation of dark mode in the corresponding dolmen-like structure results in the emerging of transparency peak (ω_Q,1/ω_Q,2) in the corresponding resonance notch.

3. Results and discussion

The transmission spectra of hybrid metal-graphene dual-band PIT device is simulated by the FDTD solutions (Lumerical Solutions, Inc.). In the three-dimensional simulations, a y-polarized beam normally incidents on the unit cell in z direction with periodic boundary conditions in both x–z plane and y–z plane. The graphene layer is characterized using a surface conductivity rather than a volumetric permittivity. The surface conductivity of graphene σ is computed from the Kubo formula [40]

σ (ω) = \frac{i e^{2} (ω - 2 i Γ)}{π ℏ^{2}} [\frac{1}{{(ω - 2 i Γ)}^{2}} \int_{0}^{\infty} ∊ (\frac{\partial f_{d} (∊)}{\partial ∊} - \frac{\partial f_{d} (- ∊)}{\partial ∊}) d ∊ - \int_{0}^{\infty} \frac{f_{d} (- ∊) - f_{d} (∊)}{{(ω - 2 i Γ)}^{2} - 4 {(∊ / ℏ)}^{2}} d ∊]

where, f_d (∊) = (e^{(∊−E_F)/(k_BT)} + 1)⁻¹, E_F is the Fermi energy of graphene, ω is the angular frequency, ħΓ = 0.01eV is the scattering rate [41], and T = 300K is temperature. The complex permittivity of the gold is modeled using the Palik mode. The geometrical parameters of hybrid metal-graphene dual-band PIT device used in the simulation are the same as those provided in Section Structural design and research method.

The transmission spectra of hybrid metal-graphene dual-band PIT device with different Fermi energies but E_F1 = E_F2 by employing FDTD solutions are demonstrated in Fig. 3. The separations s₁ and s₂ are both large enough (s₁/s₂ = 1100/900nm) that the bright-dark mode coupling can be ignored. When E_F1 = E_F2 = 0.2eV, the resonance notches of small and big dolmen-like structures are achieved at wavelengths of 47.68THz and 36.98THz, respectively. As the Fermi energy E_F1 and E_F2 increases from 0.2eV to 0.8eV via modulating the voltage bias applied on graphene, the resonance notches generated by small and big dolmen-like structures are both enhanced and blue shifted. The shift of resonance notch generated by the small dolmen-like structures is Δf₁ = 1.61THz (3.38% shift), and that by the big dolmen-like structures is Δf₂ = 2.04THz (5.52% shift). The difference of resonance shift between small and big dolmen-like structures is caused by the wavelength dependent change of the imaginary conductivity which is larger at shorter frequencies [42].

Fig. 3 Simulated transmission spectra of the hybrid metal-graphene dual-band PIT device with different Fermi energies for graphene interdigitated finger sets (s₁/s₂ = 1100/900nm).

Download Full Size | PDF

The simulated transmission spectra of hybrid metal-graphene dual-band PIT device is demonstrated in Fig. 4 when the Fermi energy of only one graphene finger set is various. The separations s₁ and s₂ are set at 1100nm and 900nm, respectively. As the Fermi energy E_F1 increases from 0.2eV to 0.8eV while E₂ is fixed at 0.5eV, the resonance notch of the small dolmen-like structures is enhanced and blue shifted from 47.63THz to 49.29THz, while that of the big dolmen-like structures remains nearly 38.05THz, as shown in Fig. 4(a). As the Fermi energy E_F2 increases from 0.2eV to 0.8eV while maintaining the Fermi energy E_F2 at 0.5eV, the resonance notch of the big dolmen-like structures are enhanced and blue shifted from 36.98THz to 39.06THz, while keeping that of small dolmen-like structures fixed at 48.54THz, as shown in Fig. 4(b). The resonance frequencies of dolmen-like structures are modulated independently by tuning the Fermi energy of corresponding graphene finger set.

Fig. 4 (a) Simulated transmission spectra of the hybrid metal-graphene dual-band PIT device with different E_F1 while maintaining E_F2 at 0.5eV (s₁/s₂ = 1100/900nm). (b) Simulated transmission spectra of the hybrid metal-graphene dual-band PIT device with different E_F2 while maintaining E_F1 at 0.5eV (s₁/s₂ = 1100/900nm).

Download Full Size | PDF

The simulated transmission spectra of hybrid metal-graphene dual-band PIT device are demonstrated in Fig. 5 when the separation of only one dolmen-like structure is various. The Fermi energies of graphene finger sets are both fixed at 0.5eV. As the separation s₁ of the small dolmen-like structure decreases from 1100nm to 500nm while maintaining the separation s₂ of the big dolmen-like structures at 900nm, the transparency peak emerges in the resonance notch at 48.97THz, while the resonance notch of the big dolmen-like structure is fixed, as shown in Fig. 5(a). In the other case, when the separation s₂ of the big dolmen-like structure decreases from 900nm to 300nm while maintaining the separation s₁ of the small dolmen-like structures at 1100nm, the transparency peak emerges in the resonance notch at 36.59THz, while the resonance notch of small dolmen-like structure unchanged, as shown in Fig. 5(b). The top view electrical field distributions E_z at the transparency peaks of dolmen-like structures are shown in Fig. 5(c) and (d), respectively, where the dark modes are strongly excited in both dolmen-like structures. The emergence of transparency peak in different resonance notch is modulated independently by changing the separations (s₁ and s₂) of corresponding dolmen-like structures.

Fig. 5 (a) Simulated transmission spectra of the hybrid metal-graphene dual-band PIT device with different separations s₁ for E_F1/E_F2 = 0.5/0.5eV and s₂ = 900nm. (b) Simulated transmission spectra of the hybrid metal-graphene dual-band PIT device with different separations s₂ for E_F1/E_F2 = 0.5/0.5eV and s₁ = 1100nm. (c) The top view electrical field distributions at the PIT peaks 48.97THz when s₁/s₂ = 500/900nm. (d) The top view electrical field distributions E_z at the PIT peaks 36.59THz when s₁/s₂ = 1100/300nm.

Download Full Size | PDF

The simulated multiple PIT peaks of the hybrid metal-graphene nanostructures are tuned separately in different directions through the Fermi energy of corresponding graphene finger set, which is shown in Fig. 6. The separations s₁ and s₂ of the small and big dolmen-like structures are set at 500nm and 300nm, respectively. When E_F1 = E_F2 = 0.5eV, the transparency peaks emerge in the PIT windows. With E_F1 increasing to 0.8eV and E_F2 decreasing to 0.2eV, the PIT peaks of the small dolmen-like structure is blue shifted and that of big dolmen-like structure is red shifted. Thus, multiple PIT peaks of the device are modulated arbitrarily in different directions through tuning the Fermi energy of corresponding graphene finger set. The black and red circles are the theoretical fittings based on Eq. 3, which traces the numerical simulation results very well. The fitting parameters of the black circle when E_F1 = 0.5eV and E_F2 = 0.5eV are ω_D,1/ω_D,2 = 47.83/38.01THz, ω_Q,1/ω_Q,2 = 47.65/37.91THz, g₁/g₂ = 1.75/2.22, γ_D,1/γ_D,2 = 2.48/2.00THz, γ_Q,1/γ_Q,2 = 1.81/1.50THz and κ₁/κ₂ = 1.54/2.03THz, and those of the red circle when E_F1 = 0.2eV and E_F2 = 0.8eV are ω_D,1/ω_D,2 = 48.64/36.75THz, ω_Q,1/ω_Q,2 = 48.60/36.55THz, g₁/g₂ = 1.80/2.22, γ_D,1/γ_D,2 = 2.52/2.00THz, γ_Q,1/γ_Q,2 = 1.77/1.58THz and κ₁/κ₂ = 1.60/2.06THz.

Fig. 6 The simulated multiple PIT peaks of the hybrid metal-graphene nanostructures are modulated arbitrarily in different directions through tuning the Fermi energy of corresponding graphene finger set.

Download Full Size | PDF

By combining the metallic nanostructures with graphene layer, the working wavelength of the designed hybrid metal-graphene nanostructures is in the mid-infrared region. Due to employing two kinds of gold dolmen-like structures with different sizes, the PIT peaks are obtained at two frequency domains. More importantly, by integrating the gold nanostructures with the graphene finger sets, the multiple transparency peaks are independently modulated by changing the Fermi energy of corresponding graphene finger set. The number of independently tunable PIT windows can be further increased by adding more kinds of dolmen-like structures with different sizes.

4. Conclusions

In summary, a dynamically tunable hybrid metal-graphene dual-band PIT device is proposed at mid-infrared frequencies by integrating the dolmen-like structures with different sizes into separate graphene interdigitated finger sets. By introducing the coupled Lorentz oscillator model, the physical mechanism of multiple PIT effects are demonstrated. Numerical simulations based on FDTD solutions shows that the spectral location of multiple transparency peaks are independently and dynamically modulated through the Fermi energy by tuning the bias voltages applied on corresponding graphene finger sets, which enables the proposed device to provide potential applications in tunable sensors, switches and filters.

Funding

National Natural Science Foundation of China (61378067, 61675131).

References and links

1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef] [PubMed]

2. D. R. Smith, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004). [CrossRef] [PubMed]

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

4. 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]

5. C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107, 043901 (2011). [CrossRef] [PubMed]

6. V. Yannopapas, E. Paspalakis, and N. V. Vitanov, “Electromagnetically induced transparency and slow light in an array of metallic nanoparticles,” Phys. Rev. B 80, 035104 (2009). [CrossRef]

7. X. Duan, S. Chen, H. Cheng, Z. Li, and J. Tian, “Dynamically tunable plasmonically induced transparency by planar hybrid metamaterial,” Opt. Lett. 38, 483–485 (2013). [CrossRef] [PubMed]

8. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36 (1997). [CrossRef]

9. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001). [CrossRef] [PubMed]

10. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011). [CrossRef] [PubMed]

11. C.-Y. Chen, I.-W. Un, N.-H. Tai, and T.-J. Yen, “Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance,” Opt. Express 17, 15372–15380 (2009). [CrossRef] [PubMed]

12. 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, 114101 (2010). [CrossRef]

13. X. Duan, S. Chen, H. Yang, H. Cheng, J. Li, W. Liu, C. Gu, and J. Tian, “Polarization-insensitive and wide-angle plasmonically induced transparency by planar metamaterials,” Appl. Phys. Lett. 101, 143105 (2012). [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, 8912–8919 (2011). [CrossRef] [PubMed]

15. Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, and X. Luo, “Electromagnetically induced transparency (eit)-like transmission in side-coupled complementary split-ring resonators,” Opt. Express 20, 24348–24355 (2012). [CrossRef] [PubMed]

16. X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100, 131101 (2012). [CrossRef]

17. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Planar designs for electromagnetically induced transparency in metamaterials,” Opt. Express 17, 5595 (2009). [CrossRef] [PubMed]

18. 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, 053901 (2009). [CrossRef] [PubMed]

19. L. Zhou, T. Ye, and J. Chen, “Coherent interference induced transparency in self-coupled optical waveguide-based resonators,” Opt. Lett. 36, 13 (2010). [CrossRef]

20. A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett. 11, 1685–1689 (2011). [CrossRef] [PubMed]

21. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, et al., “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011). [CrossRef] [PubMed]

22. S. A. Maier, “Graphene plasmonics: All eyes on flatland,” Nat. Phys. 8, 581–582 (2012). [CrossRef]

23. T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014). [CrossRef] [PubMed]

24. M. Amin, M. Farhat, and H. Bagci, “A dynamically reconfigurable fano metamaterial through graphene tuning for switching and sensing applications,” Sci. Rep. 3, 2105 (2013). [CrossRef] [PubMed]

25. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008). [CrossRef] [PubMed]

26. W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6, 7806–7813 (2012). [CrossRef] [PubMed]

27. A. Vakil and N. Engheta, “Transformation Opt. using graphene,” Science 332, 1291–1294 (2011). [CrossRef] [PubMed]

28. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013). [CrossRef]

29. H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103, 203112 (2013). [CrossRef]

30. H. Cheng, S. Chen, P. Yu, J. Li, B. Xie, Z. Li, and J. Tian, “Dynamically tunable broadband mid-infrared cross polarization converter based on graphene metamaterial,” Appl. Phys. Lett. 103, 223102 (2013). [CrossRef]

31. H. Cheng, S. Chen, P. Yu, J. Li, L. Deng, and J. Tian, “Mid-infrared tunable optical polarization converter composed of asymmetric graphene nanocrosses,” Opt. Lett. 38, 1567 (2013). [CrossRef] [PubMed]

32. X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, and J. Zi, “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Express 21, 28438–28443 (2013). [CrossRef]

33. H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015). [CrossRef]

34. X. Zhao, C. Yuan, W. Lv, S. Xu, and J. Yao, “Plasmon-induced transparency in metamaterial based on graphene and split-ring resonators,” IEEE Photon. Tech. Lett. 27, 1321–1324 (2015). [CrossRef]

35. X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8, 15273–15280 (2016). [CrossRef] [PubMed]

36. C. Sun, J. Si, Z. Dong, and X. Deng, “Tunable multispectral plasmon induced transparency based on graphene metamaterials,” Opt. Express 24, 11466–11474 (2016). [CrossRef] [PubMed]

37. A. M. Gilbertson, Y. Francescato, T. Roschuk, V. Shautsova, Y. Chen, T. P. H. Sidiropoulos, M. Hong, V. Giannini, S. A. Maier, L. F. Cohen, and R. F. Oulton, “Plasmon-induced optical anisotropy in hybrid graphene–metal nanoparticle systems,” Nano Lett. 15, 3458–3464 (2015). [CrossRef] [PubMed]

38. M. M. Jadidi, A. B. Sushkov, R. L. Myers-Ward, A. K. Boyd, K. M. Daniels, D. K. Gaskill, M. S. Fuhrer, H. D. Drew, and T. E. Murphy, “Tunable terahertz hybrid metal–graphene plasmons,” Nano Lett. 15, 7099–7104 (2015). [CrossRef] [PubMed]

39. J. Chen, P. Wang, C. Chen, Y. Lu, H. Ming, and Q. Zhan, “Plasmonic eit-like switching in bright-dark-bright plasmon resonators,” Opt. Express 19, 5970 (2011). [CrossRef] [PubMed]

40. G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008). [CrossRef]

41. P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for terahertz applications,” Science 341, 620–621 (2013). [CrossRef] [PubMed]

42. B. Vasić and R. Gajić, “Graphene induced spectral tuning of metamaterial absorbers at mid-infrared frequencies,” Appl. Phys. Lett. 103, 261111 (2013). [CrossRef]

Independently tunable dual-band plasmonically induced transparency based on hybrid metal-graphene metamaterials at mid-infrared frequencies

Abstract

1. Introduction

2. Structural design and research method

3. Results and discussion

4. Conclusions

Funding

References and links

Cited By

Figures (6)

Equations (4)

Optics Express