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Abstract
We explore the use of tunable inter-resonator coupling to reshape the spectral absorptivity of a graphene-based metamaterial. The metamaterial comprises of a periodic array of coupled metal-insulator-metal resonators, with two resonators per unit cell. One resonator supports a bright mode, and the other a dark mode. We use coupled-mode theory to show that, by tuning the resonant wavelength of the bright mode through the dark mode, the spectrum can be reconfigured from a single-peak shape to a split-peak shape. We then propose specific, realistic device geometries to allow realization of this concept.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials have attracted considerable attention due to their ability to manipulate light-matter interactions at the subwavelength scale [1,2]. They have been used to design absorptive and emissive features in the electromagnetic spectrum [3–10], an important capability for applications including thermal management [11–14], energy harvesting [15,16] and sensing [17–19].
More recent work has focused on designing tunable metamaterials that can be used to reshape the spectral response on demand. Graphene has emerged as a promising material for this purpose [20–23], due to its electrically-tunable optical properties [24–29]. Previous work has studied metamaterials incorporating graphene to achieve tunable absorption in the infrared [30–46]. One promising approach is to incorporate graphene within a metal-insulator-metal (MIM) absorber [47,48]. Previous work has shown that a resonant mode of the MIM can be tuned by applying a voltage to the graphene [49–57]. However, this work focused on either single or multiple, uncoupled resonances.
Meanwhile, recent work has explored the use of coupled resonator modes to produce a complex, adaptive spectral response [58,59]. In one previous paper [58], we showed that tuning the coupling between two MIM resonators can change the spectral response from a single peak to a double peak. However, the proposed tuning scheme required the fabrication of multiple devices with varying structural parameters to achieve different spectra. It is of great interest to find a method for achieving in situ tuning within a single device, for which the spectral response can be tuned with an applied voltage.
Here, we propose a design for in situ tuning of the infrared absorption spectrum from single- to double-peaked response, using coupled graphene MIM resonators. We first describe the effects of inter-resonator coupling abstractly, using temporal coupled-mode theory. We consider a system of two resonators. One resonator supports a bright mode, a mode that can be excited by normally-incident light [60]. The other resonator supports a dark mode, which cannot be excited by normally-incident light due to symmetry considerations. For sufficiently large detuning between the resonators, only the bright mode appears in the absorption spectrum, producing a single-peaked spectral response. We show that as the resonance wavelength of the bright mode is tuned toward the dark mode, the resonances couple and split, producing a double-peaked response. We then propose specific implementations of bright-dark tuning within graphene MIM devices. The predicted spectra clearly show the evolution from single- to double-peaked response as a function of applied voltage.
Our results provide a key physical insight for spectral tuning. Uncoupled dark resonances are typically “invisible,” as they produce no response within the absorption spectrum. However, when a bright resonance is tuned within the vicinity of a dark resonance, a new spectral feature emerges, revealing the signature of a previously hidden mode. Such an effect suggests intriguing possibilities within multi-resonator systems, which might potentially incorporate multiple bright and dark modes. We thus expect that the results shown here will provide a pathway for flexible reshaping of the infrared spectral response in tunable, coupled-resonator systems.
2. Tunable bright-dark mode coupling
We first use temporal coupled-mode theory (CMT) to consider how a dark-bright mode coupling scheme can be used to generate and tune the absorption spectrum. A bright mode is one that can be excited by a plane wave source at normal incidence, producing an absorption peak. On the other hand, a dark mode is symmetry-forbidden and does not couple to a normally-incident plane wave. We consider a system consisting of a bright resonator coupled to a dark resonator. We assume that the resonant frequency of the bright resonator can be tuned, for example by locally perturbing the refractive index in or near the bright resonator (e.g. via an electrooptic shift), while leaving the dark resonator unperturbed.
The spectral absorptivity of this system when excited by a plane wave can be written in terms of the resonant wavelengths of the two resonators, their respective decay times and the inter-resonator coupling. The frequency-dependent absorption spectrum is given by the following equation [58]:
The resonant frequency of the bright mode is indicated by ω0 = 2πc/λ0, while the dark mode frequency is indicated by ω1 = 2πc/λ1. λ0 and λ1 are the bright and dark mode resonance wavelengths, respectively.
Figure 1 shows example spectra of this system as the resonance wavelength of the bright resonator is tuned with respect to the dark resonator. The top schematic shows the position of the dark resonance (D) and five possible positions of the bright resonance (B1 through B5). For the sake of illustration, the intrinsic and extrinsic decay constants were set to τ0b = 8.88 × 10−13 s, τeb = 5.2 × 10−13 s, and τ0d = 1.48 × 10−13 s, and the coupling constant β = 1013 rad/s.
Fig. 1. Schematic showing the absorption spectra for a tunable bright resonator coupled to a dark resonator at spectral position D. As the bright resonator is tuned from B1 (top panel) through B5 (bottom panel), its coupling to the dark resonator is affected resulting in a change in the absorption spectrum.
At position B1, the bright resonance has a large, blue detuning from the dark resonance position, D. For this large detuning, the coupling between the resonances is low. The absorption spectrum shows a strong absorption peak close to B1 and a very weak peak close to D. As the bright resonator is tuned towards D (position B2), the coupling increases, resulting in an increase in the amplitude of the higher wavelength absorption peak. The resonators are maximally coupled when the bright resonator is at position B3, coinciding with the position D of the dark resonator, and the spectrum exhibits split peaks of equal amplitude. As the bright resonator is tuned away from this position (B4 through B5), the coupling reduces, resulting in a decrease in the amplitude of the lower wavelength peak.
Conceptually, Fig. 1 illustrates that tuning the position of the bright mode in a bright-dark coupled system allows the spectrum to be tuned from a single-peak response to a split-peak response. This response is fundamentally different than for a single-resonator system, which will exhibit a single peak that shifts with tuning. The response of Fig. 1 is also fundamentally different than for two uncoupled bright resonators, for which the amplitude of the two peaks is independent of their relative position.
Such a mechanism allows for on-demand spectral absorption tailoring. By dynamically tuning the coupling between a bright and a dark resonator, one can modulate the shape of the absorption spectrum. In the next section, we provide details of our proposed absorber structure and the tuning mechanism. Subsequently, we present the absorption spectra for our structure as the bright resonator is tuned either towards or away from the dark resonator.
3. Metamaterial design and simulation
We first identify the bright and dark modes of a single resonator, shown in Fig. 2(a). A 50 nm thick gold cross with arm length L sits on top of a monolayer graphene film. This is followed by a 190 nm Al2O3 spacer layer and a 500 nm thick gold back reflector. The length of the periodic unit cell is 2 µm along the x and y directions. The presence of graphene allows us to electrically modulate the refractive index of the MIM cavity. This change in refractive index tunes the resonance frequency of the resonator. Previous work has used similar structures to experimentally demonstrate tunable absorption in the mid-infrared [56]. The procedure used for the fabrication of the metamaterial absorber in [56] can potentially be adapted to our design.
Fig. 2. (a) Unit cell of a metamaterial with a single resonator. (b) Absorption spectra of the bright and dark modes (magenta and green curves respectively) of the structure with L = 1.6 µm. The corresponding electric field profiles (Ex) are shown in the inset.
We simulate the structure using Lumerical FDTD. The optical constants of gold and Al2O3 are taken from the inbuilt material library while those of graphene are based on Lumerical’s surface conductivity model. We calculate the scattering rate of graphene as evf2/µEf [31]. Here µ = 23600 cm2/Vs is the electron mobility [61], vf = c/300 is the drift velocity, e is the electronic charge, c is the speed of light and Ef is the Fermi energy. The absorption spectrum for L = 1.6 µm is displayed in Fig. 2(b), taking the Fermi energy to be 0.026eV (the unbiased value at room temperature). To obtain the absorption spectrum of the bright mode (solid magenta line), we illuminate the structure with a normally-incident plane wave polarized along the x direction and record the reflection. As there is no transmission through the structure, absorptivity is given as 1 minus reflectivity. For obtaining the dark mode spectrum (solid green line), we excite the structure with a cloud of randomly oriented dipoles and record the field intensity using a cluster of time monitors. The absorption spectrum of the dark mode is the sum of Fourier transforms of time signals from all time monitors. In both these cases, we use periodic boundary conditions along the x and y directions.
The resonator of Fig. 2(a) supports both a bright mode and a dark mode, at different wavelengths. The bright mode lies close to 5.5 µm, while the dark mode lies close to 4.5 µm. The field profiles (Ex) on the x-y plane passing through the middle of the spacer layer for the bright and dark modes are shown in the inset of Fig. 2(b). It can be observed that for the bright mode, the Ex component is even with respect to the y-axis (as explained in Ref. [60], this corresponds to “odd vector symmetry” with respect to the y-axis). For an x-polarized plane wave, Ex is also even with respect to the y-axis. As a result, the bright mode couples to the x-polarized plane wave. On the other hand, the dark mode has an odd Ex (even vector symmetry). Since the symmetry is opposite to that of an x-polarized plane wave, coupling is inhibited.
4. Results and discussion
Next, we consider unit cell consisting of two resonators, which we design to include both a tunable, bright resonator and a static, dark resonator. Figure 3(a) shows the unit cell. We wish to couple a dark mode of resonator 2 to a bright mode of resonator 1. To this end, L1 and L2 are chosen to have different values. For resonator 2, we choose the same parameters as Fig. 1 above, setting L2 to 1.6 µm and the Fermi energy of the graphene sheet lying under resonator 2, Ef2, to 0.026eV. The dark mode for the isolated resonator is shown in the top panel of Fig. 3(b). We now choose L1 so that tuning the Fermi energy of the graphene sheet lying under the bright resonator (Ef1) will shift the bright mode of resonator 1 toward the dark mode of resonator 2. The bottom panel of Fig. 3(b) shows the shift. Setting L1 = 0.97um, tuning Ef1 from the unbiased value of 0.026eV up to 1.5eV moves the bright mode of resonator 1 toward the dark mode of resonator 2. We note that for the purposes of identifying the position of the isolated mode, the calculations in Fig. 3(b) are performed using only a single resonator in the full unit cell, removing the top metal cross in the other resonator.
Fig. 3. (a) Unit cell of a metamaterial absorber consisting of a bright resonator of length L1 = 0.97 µm and a dark resonator of length L2 = 1.6 µm. (b) (top panel) Absorption spectrum of the isolated dark resonator for Ef1 = 1.5 eV and Ef2 = 0.026 eV. (bottom panel) Absorption spectra of isolated bright resonator with Ef2 = 0.026 eV and Ef1 varying as shown. (c) Absorption spectrum of combined two-resonator metamaterial absorber with Ef2 = 0.026 eV for and Ef1 varying from 0.026 eV to 1.5 eV.
4.1 Tuning λbright towards λdark
We now study the effect of coupling between the modes, as the wavelength of the bright resonator is tuned toward the dark resonator. Figure 3(c) shows the absorption spectrum calculated for the full unit cell, containing both resonators. We assume the two resonators can be tuned independently and fix Ef2 = 0.026eV while tuning Ef1. For Ef1 = 0.026eV, the bright mode lies below the dark mode. The spectrum in Fig. 3(c) shows a tall peak at lower wavelength, and a shorter peak at higher wavelength. As Ef1 is increased to 1.5eV, the peaks move closer together, and the higher wavelength peak increases in magnitude.
As mentioned previously, an isolated dark mode cannot couple to an incoming plane wave by itself. In our proposed absorber, it does so through the bright resonator. As λbright is tuned towards λdark, the coupling between the two resonators increases. Tuning the two resonators closer together enhances the coupling of the dark resonator to an incoming plane wave resulting in the amplitude of the higher wavelength peak to increase from 0.2 to 0.85. We note that the increase in absorptivity of the two-resonator system above 5.2 µm is due to a higher-order, bright mode of the resonator of length L2.
These trends observed in Fig. 3(c) correspond to the qualitative spectral reshaping observed for positions B1 through B3 of Fig. 1. Thus, by tuning the initially blue-detuned bright resonator toward the dark resonator, we can shift the relative heights and position of the spectral peaks. While further increase of Ef1 is expected to tune the bright mode wavelength above the dark mode, obtaining values above 1.5eV may prove challenging in experiment. We thus consider a second design below, to illustrate red detuning of the bright mode relative to the dark mode.
4.2 Tuning λbright away from λdark
To illustrate the effect of red detuning the bright resonance away from the dark resonance, we choose L1 = 1.17 µm, keeping the value of L2 the same as in previous simulations. Figure 4(a) shows the absorption spectra for isolated dark and bright resonators. As seen from the figure, this choice of L1 ensures that λbright coincides with λdark at Ef1 = 0.026eV and is red-shifted relative to λdark at Ef1 = 1.5eV.
Fig. 4. (a) (top panel) Absorption spectrum of isolated dark resonator with arm length 1.6 µm for Ef1 = Ef2 = 0.026 eV. (bottom panel) Absorption spectra of isolated bright resonator with L1 = 1.17 µm, Ef2 = 0.026 eV and Ef1 varying from 0.026 eV to 1.5 eV. (b) Absorption spectrum of combined two resonator metamaterial absorber with L1 = 1.17 µm, L2 = 1.6 µm, for Ef2 = 0.026 eV and Ef1 varying from 0.026 eV to 1.5 eV.
Figure 4(b) shows the absorption spectrum of the full, two-resonator system for different values of Ef1. As Ef1 increases, the resonant wavelength of the bright resonator moves above the dark resonator. Two peaks can be observed at each value of Ef1, while the relative amplitude and position change. As Ef1 increases, the coupling between the resonators decreases, reducing the amplitude of the lower-wavelength peak (0.95 at Ef1 = 0.026eV and 0.46 at Ef1 = 1.5eV). The higher-wavelength peak meanwhile shifts to the right, increasing in amplitude. These trends agree qualitatively with the behavior for B3 through B5 of Fig. 1.
5. Conclusion
In this work, we explore the use of tunable inter-resonator coupling to tailor the infrared absorption spectrum of a graphene-based metamaterial. The metamaterial absorber is modeled as an array of coupled graphene-based MIM resonators. Each unit cell of the absorber consists of a tunable bright resonator kept in the vicinity of a static dark resonator. Using this structure, we implemented a dynamically tunable, dark-bright mode coupling scheme in the context of CMT. Tuning the bright resonator towards the dark resonator causes the inter-resonator coupling to increase, resulting in an increase of the amplitude of the higher-wavelength peak in the spectrum. On the contrary, tuning the bright resonator away from the dark resonator reduces the coupling, causing the amplitude of the lower-wavelength peak to decrease. We theoretically investigated both these cases by modulating the Fermi energy of the bright resonator, Ef1 from 0.026eV to 1.5eV. For the first case, we noticed an absorption peak increase from 0.2 to 0.85 while in the second case, a decrease from 0.95 to 0.46.
While the numerical study presented here focuses on tuning the bright mode relative to the dark mode, one could similarly consider the tuning of the dark mode relative to the bright mode. Such behavior can easily be studied qualitatively using the same coupled-mode theory given in Eq. (1).
Overall, the results illustrate the utility of including dark-mode resonances in tunable, coupled-resonator systems. Qualitatively, for sufficiently large detuning of a dark resonance from any bright resonances in the system, the absorption spectrum will only exhibit peaks corresponding to the bright modes. As the dark modes are tuned toward the bright modes, additional peaks will appear. Our results thus suggest the possibility of achieving tunable multi-band absorption using metamaterials composed of multiple coupled resonators. In an experimental implementation, we expect that interleaved comb contacts [62] can be used to tune the set of graphene ribbons in contact with the bright resonators separately from those in contact with the dark resonators. Overall, we expect that the proposed mechanism for using inter-resonator coupling to dynamically modulate spectral absorptivity can potentially benefit several applications such as infrared imaging and thermal management.
Funding
Defense Advanced Research Projects Agency (HR0011820046).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002). [CrossRef]
2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef]
3. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect Metamaterial Absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef]
4. H. Tao, C. M. Bingham, A. C. Strikwerda, D. Pilon, D. Shrekenhamer, N. I. Landy, K. Fan, X. Zhang, W. J. Padilla, and R. D. Averitt, “Highly flexible wide angle of incidence terahertz metamaterial absorber: Design, fabrication, and characterization,” Phys. Rev. B 78(24), 241103 (2008). [CrossRef]
5. X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared Spatial and Frequency Selective Metamaterial with Near-Unity Absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010). [CrossRef]
6. K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2(1), 517 (2011). [CrossRef]
7. R. Audhkhasi and M. L. Povinelli, “Spectral emissivity design using aluminum-based hybrid gratings,” Opt. Express 28(6), 8076–8084 (2020). [CrossRef]
8. R. Audhkhasi and M. L. Povinelli, “Gold-black phosphorus nanostructured absorbers for efficient light trapping in the mid-infrared,” Opt. Express 28(13), 19562–19570 (2020). [CrossRef]
9. X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the Blackbody with Infrared Metamaterials as Selective Thermal Emitters,” Phys. Rev. Lett. 107(4), 045901 (2011). [CrossRef]
10. M. Makhsiyan, P. Bouchon, J. Jaeck, J.-L. Pelouard, and R. Haidar, “Shaping the spatial and spectral emissivity at the diffraction limit,” Appl. Phys. Lett. 107(25), 251103 (2015). [CrossRef]
11. A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014). [CrossRef]
12. P. C. Hsu, C. Liu, A. Y. Song, Z. Zhang, Y. Peng, J. Xie, K. Liu, C.-L. Wu, P. B. Catrysse, L. Cai, S. Zhai, A. Majumdar, S. Fan, and Y. Cui, “A dual-mode textile for human body radiative heating and cooling,” Sci. Adv. 3(11), e1700895 (2017). [CrossRef]
13. Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017). [CrossRef]
14. J. Mandal, Y. Fu, A. C. Overvig, M. Jia, K. Sun, N. N. Shi, H. Zhou, X. Xiao, N. Yu, and Y. Yang, “Hierarchially porous polymer coatings for highly efficient passive daytime radiative cooling,” Science 362(6412), 315–319 (2018). [CrossRef]
15. A. Kohiyama, M. Shimizu, H. Kobayashi, F. Iguchi, and H. Yugami, “Spectrally Controlled Thermal Radiation Based on Surface Microstructures for High Efficiency Solar Thermophotovoltaic system,” Energy Procedia 57, 517–523 (2014). [CrossRef]
16. A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanovic, M. Soljacic, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9(2), 126–130 (2014). [CrossRef]
17. J. Feng, V. S. Siu, A. Roelke, V. Mehta, S. Y. Rhieu, G. T. R. Palmore, and D. Pacifici, “Nanoscale Plasmonic Interferometers for Multispectral, High-Throughput Biochemical Sensing,” Nano Lett. 12(2), 602–609 (2012). [CrossRef]
18. H. T. Miyazaki, T. Kasaya, M. Iwanega, B. Choi, Y. Sugimoto, and K. Sakoda, “Dual-band infrared metasurface thermal emitter for CO2 sensing,” Appl. Phys. Lett. 105(12), 121107 (2014). [CrossRef]
19. D. Etezadi, J. B. Warner, F. S. Ruggeri, G. Dietler, H. A. Lashuel, and H. Altug, “Nanoplasmonic mid-infrared biosensor for in vitro protein secondary structure detection,” Light: Sci. Appl. 6(8), e17029 (2017). [CrossRef]
20. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef]
21. N. L. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012). [CrossRef]
22. T. V. Huynh, B. S. Tung, B. X. Khuyen, N. T. Tung, and V. D. Lam, “Electrically tunable graphene-based metamaterials: A brief review,” Mod. Phys. Lett. B 33(33), 1950404 (2019). [CrossRef]
23. R. Wang, X.-G. Ren, Z. Yan, L.-J. Jiang, W. E. I. Sha, and G.-C. Shan, “Graphene based functional devices: A short review,” Front. Phys. 14(1), 13603 (2019). [CrossRef]
24. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009). [CrossRef]
25. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011). [CrossRef]
26. S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive Tuning of Fano-Resonant Metasurfaces Using Plasmonic Response of Graphene in the Mid-Infrared,” Nano Lett. 13(3), 1111–1117 (2013). [CrossRef]
27. A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013). [CrossRef]
28. B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012). [CrossRef]
29. W. Zhu, I. D. Rukhlenko, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102(24), 241914 (2013). [CrossRef]
30. Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014). [CrossRef]
31. H. Meng, L. Wang, G. Liu, X. Xue, Q. Lin, and X. Zhai, “Tunable graphene-based plasmonic multispectral and narrowband perfect metamaterial absorbers at the mid-infrared region,” Appl. Opt. 56(21), 6022–6027 (2017). [CrossRef]
32. A. Safaei, S. Chandra, A. Vazquez-Guardado, J. Calderon, D. Franklin, L. Tetard, L. Zhai, M. N. Leuenberger, and D. Chanda, “Dynamically tunable extraordinary light absorption in monolayer graphene,” Phys. Rev. B 96(16), 165431 (2017). [CrossRef]
33. S. Kim, M. S. Jang, V. M. Brar, K. W. Masser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018). [CrossRef]
34. A. Safaei, S. Chandra, M. N. Leuenberger, and D. Chanda, “Wide Angle Dynamically Tunable Enhanced Infrared Absorption on Large-Area Nanopatterned Graphene,” ACS Nano 13(1), 421–428 (2019). [CrossRef]
35. L. Wang, D. Xia, Q. Fu, X. Ding, and Y. Wang, “An electrically switchable wideband metamaterial absorber based on graphene at P band,” Open Phys. 19(1), 460–466 (2021). [CrossRef]
36. Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752 (2014). [CrossRef]
37. M. Huang, Y. Cheng, Z. Cheng, H. Chen, X. Mao, and R. Gong, “Based on graphene tunable dual-band terahertz metamaterial absorber with wide-angle,” Opt. Commun. 415, 194–201 (2018). [CrossRef]
38. M. L. Huang, Y. Z. Cheng, Z. Z. Cheng, H. R. Chen, X. S. Mao, and R. Z. Gong, “Design of a Broadband Tunable Terahertz Metamaterial Absorber Based on Complementary Structural Graphene,” Materials 11(4), 540 (2018). [CrossRef]
39. F. Wang, S. Huang, L. Li, W. Chen, and Z. Xie, “Dual-band tunable perfect metamaterial absorber based on graphene,” Appl. Opt. 57(24), 6916–6922 (2018). [CrossRef]
40. C. Cen, Y. Zhang, C. Liang, X. Chen, Z. Yi, T. Duan, Y. Tang, X. Ye, Y. Yi, and S. Xiao, “Numerical investigation of a tunable metamaterial perfect absorber consisting of two-intersecting graphene nanoring arrays,” Phys. Lett. A 383(24), 3030–3035 (2019). [CrossRef]
41. J. Wu, “Tunable multi-band terahertz absorber based on graphene nano-ribbon metamaterial,” Phys. Lett. A 383(14), 1589–1600 (2019). [CrossRef]
42. Z. Yi, J. Chen, C. Cen, X. Cen, Z. Zhou, Y. Tang, X. Ye, S. Xiao, W. Luo, and P. Wu, “Tunable Graphene-based Plasmonic Perfect Metamaterial Absorber in the THz Region,” Micromachines 10(3), 194 (2019). [CrossRef]
43. Y. Qi, Y. Zhang, C. Liu, T. Zhang, B. Zhang, L. Wang, X. Deng, Y. Bai, and X. Wang, “A tunable terahertz metamaterial absorber composed of elliptical ring graphene arrays with refractive index sensing application,” Results Phys. 16, 103012 (2020). [CrossRef]
44. M.-T. Passia and T. V. Yioultsis, “Coupled-Mode Theory for Graphene-Based Metasurfaces,” IEEE Trans. Magn. 57(6), 1–4 (2021). [CrossRef]
45. Z. Madadi, “A Tunable Plasmonic Refractive Index Sensor Based on Metal-Insulator-Graphene-Metal Structure,” (2021).
46. Q. He, S. Sun, and L. Zhou, “Tunable/Reconfigurable Metasurfaces: Physics and Applications,” Research 2019, 1–16 (2019). [CrossRef]
47. Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong Light - Matter Coupling in Subwavelength Metal-Dielectric Microcavities at Terahertz Frequencies,” Phys. Rev. Lett. 102(18), 186402 (2009). [CrossRef]
48. Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the THz frequency range,” Opt. Express 18(13), 13886–13907 (2010). [CrossRef]
49. Y. Zhang, Y. Shi, and C.-H. Liang, “Broadband tunable graphene-based metamaterial absorber,” Opt. Mater. Express 6(9), 3036–3044 (2016). [CrossRef]
50. S. Ogawa, M. Shimatani, S. Fukushima, S. Okuda, and K. Matsumoto, “Graphene on metal-insulator-metal-based plasmonic metamaterials at infrared wavelengths,” Opt. Express 26(5), 5665–5674 (2018). [CrossRef]
51. H. Xiong, Y.-B. Wu, J. Dong, M.-C. Tang, Y.-N. JIang, and X.-P. Zeng, “Ultrathin and broadband tunable metamaterial graphene absorber,” Opt. Express 26(2), 1681–1688 (2018). [CrossRef]
52. Y. Jia, H. Yin, H. Yao, J. Wang, and C. Fan, “Realization of multi-band perfect absorber in graphene based metal-insulator-metal metamaterials,” Results Phys. 25, 104301 (2021). [CrossRef]
53. Y. Yao, M. A. Kats, R. Shankar, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Wide Wavelength Tuning of Optical Antennas on Graphene with Nanosecond Response Time,” Nano Lett. 14(1), 214–219 (2014). [CrossRef]
54. B. Liu, C. Tang, J. Chen, N. Xia, L. Zhang, and S. Wang, “Tri-band absorption enhancement in monolayer graphene in visible spectrum due to multiple plasmon resonances in metal-insulator-metal nanostructure,” Appl. Phys. Express 11(7), 072201 (2018). [CrossRef]
55. S. Cao, T. Wang, Q. Sun, Y. Tang, B. Hu, U. Levy, and W. Yu, “Graphene-Silver Hybrid Metamaterial for Tunable and High Absorption at Mid-Infrared Waveband,” IEEE Photonics Technol. Lett. 30(5), 475–478 (2018). [CrossRef]
56. Y. Zou, J. Cao, X. Gong, R. Qian, and Z. An, “Ultrathin and Electrically Tunable Metamaterial with Nearly Perfect Absorption in Mid-Infrared,” Appl. Sci. 9(16), 3358 (2019). [CrossRef]
57. B. Vasić and R. Gajić, “Graphene induced spectral tuning of metamaterial absorbers at mid-infrared frequencies,” Appl. Phys. Lett. 103(26), 261111 (2013). [CrossRef]
58. A. M. Morsy and M. L. Povinelli, “Coupled metamaterial optical resonators for infrared emissivity spectrum modulation,” Opt. Express 29(4), 5840–5847 (2021). [CrossRef]
59. C. Yeung, J.-M. Tsai, B. King, B. Pham, D. Ho, J. Liang, M. W. Knight, and A. P. Raman, “Multiplexed supercell metasurface design and optimization with tandem residual networks,” Nanophotonics 10(3), 1133–1143 (2021). [CrossRef]
60. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, “Symmetries and Solid-State Electromagnetism,” in Photonic Crystals: Molding the Flow of Light, I. Gnerlich, ed. (Princeton University Press, 2008), pp. 25–43.
61. L. Liao, J. Bai, Y. Qu, Y.-C. Lin, Y. Li, Y. Huang, and X. Duan, “High-κ oxide nanoribbons as gate dielectrics for high mobility top-gated graphene transistors,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6711–6715 (2010). [CrossRef]
62. H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically Driven Nonreciprocity Induced by Interband Photonic Transition on a Silicon Chip,” Phys. Rev. Lett. 109(3), 033901 (2012). [CrossRef]
