Open Access
Add to BibSonomy
Abstract
Metamaterials have shown great potential for modulation on the amplitude, phase and polarization of the terahertz wave. Here vacancies were introduced into the metamaterial arrays to tune the mutual interaction between the constituent resonators, which could heavily affect the electromagnetic response of the whole metamaterial arrays. We show that the introduced vacancies in the metamaterial arrays can effectively affect the resonance mode of the metamaterial arrays. Based upon the vacancy mediated coupling, a silicon-metal hybrid metamaterial arrays were designed to achieve active modulation of propagating terahertz waves.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Recently, terahertz (THz) science has aroused significant interests among researchers due to their unique properties that bridge the optical and microwave electromagnetic spectra [1], which enable their use in many promising technologies such as imaging [2], nondestructive examination [3], and high speed wireless communication [4]. To implement these technologies, THz electronic components should be developed to emit [5], detect [6], modulate [7] and absorb [8] the THz waves. However, due to the weak interaction between THz wave and naturally occurring substance, special materials and structures were often necessary to overcome these adverse conditions. Artificially structured material (metamaterials) is one of the effective methods to achieve strong THz wave-matter interactions [9]. The most common THz metamaterials is consisted of subwavelength metallic split-ring resonators (SRRs), which is often placed on dielectric substrates [10]. When THz wave passes through these SRRs, the oscillating electrical field of THz wave would drive the free electrons in the metallic SRRs to induce an oscillating current [11]. The SRRs act as a LC circuit for the oscillating current with equivalent capacitance from the split [11,12]. When the frequency of THz wave coincide with the resonance frequency of the SRRs, strong absorption of THz wave could be observed [12].
Based upon metamaterial arrays, active and passive components have been designed to manipulate the propagating THz waves [13–16]. Usually, active modulation by THz metamaterials was often achieved by tuning the resonator’s dielectric environment [13,17] or to dynamically reconfigure their structures [18] by external stimuli. Alternatively, the electromagnetic response of the THz metamaterial arrays is also very sensitive to the interaction among the constituent resonators in the array [19]. For example, by coupling two types of metamaterials with bright and dark resonance mode respectively, THz metamaterial analogue of electromagnetically induced transparency could be observed [19]. Recently, active THz modulation devices have been demonstrated by dynamically tuning the coupling between the metamaterial resonators in arrays with external excitations such as electrical [20], optical [21], and mechanical [22] stimuli to manipulate their amplitude, phase and even chirality [23,24] of THz wave.
From naturally occurring atomic crystals, we have learnt that atomic vacancies in crystal lattice could cause different optical response of the materials. For example, diamond, a usual transparent allotrope of the carbon element, can appear green by introducing carbon vacancies under gamma ray irradiation [25]. As a result, it could be that the electromagnetic response be altered by introducing vacancies in a THz metamaterial arrays. In this work, using only one type of THz resonators, we show that the metamaterial coupling could be strongly affected by simply introducing vacancies in the THz metamaterial arrays, which can strongly affect their response to the THz wave. This vacancy mediated electromagnetic properties of THz metamaterials arrays could be very useful for passive and active THz modulation components.
2. Methods
Design of metamaterial arrays. CST Microwave StudioTM was used to simulate the spectral response of the metamaterials. Structural parameters were adjusted to locate the resonance frequency of the arrays between 0.3 and 1 THz for later characterizations. In the simulation, sapphire was used and regarded as a lossless dielectric substrate with ɛSap = 9.4 [26], silicon was used and regarded as a lossless dielectric substrate with ɛsi= 11.7, and copper as a lossy metal with conductivity of σ = 5.96×107 S/m. The constituent metamaterial resonator is designed and shown in Fig. 1(a). The metamaterial resonators were put in arrays with unit cell as such in Fig. 1(d) and 1(e) for arrays with and without vacancies respectively. Figure 1(a) shows the unit cell of a hybrid metamaterial arrays consisting of three metallic SRRs and a silicon SRRs (grey color), which have the same geometrical parameters. The silicon SRRs can be optically excited to switch from insulting to conductive. The unit cell boundary conditions virtually repeat all the modeled structure periodically in two directions up to infinity.
Fig. 1. a) Top and (b) lateral view of the hybrid metamaterial array; c) three-dimensional scheme of the optical modulation of THz wave by the hybrid metamaterial; and the unit cell of the metallic metamaterial arrays (d) with and (e) without resonator vacancies.
Fabrication of the metamaterial arrays. To fabricate the hybrid metamaterial arrays in Fig. 1(a), silicon SRRs were firstly fabricated by photolithography and dry etching using a silicon-on-sapphire (SOS) wafer with silicon layer thickness of 600 nm. After that, photolithography was used to make under-cut pattern with negative photoresist AZ5214. Electron beam evaporation were then used to deposit 30 nm Ti as the adhesion layer. After that, 600 nm copper layer was deposited by magnetron sputtering. Finally, the photoresist was then washed away by acetone to make the final product. The pure metallic metamaterial arrays in Fig. 1(d) and (e) were also fabricated on sapphire substrate by above standard photolithography, film deposition and lift-off process.
THz time domain spectroscopy (THz-TDS) characterization. A fiber-coupled THz-TDS FiCO system was used to characterize the THz spectral response of these metamaterial arrays. A laser (1550 nm with 20 fs FWHM) were divided by optical fibers into two lasers. One of the laser beams is used to excited THz pulse from a photoconductive antenna. Another was delayed to control the detection of the THz wave at different delay time. Dry air was used as the reference signal. By performing the Fourier transform of the time-domain pulse, the corresponding frequency domain signal can be obtained, and then the ratio to the reference sample is calculated to obtain transmission spectra of the samples.
Optical pump terahertz probe characterization. An optical-pump terahertz-probe system (OPTP) was used to characterize the dynamic response of the hybrid metamaterial arrays with silicon SRRs. An 800 nm femtosecond laser (Spectra-physics, FWHM∼37fs, repetition frequency∼1 kHz) was divided into three beams, two of which were used to generate and detect terahertz waves as above THz-TDS system. The third beam acts as a pump light for the silicon SRRs on the sapphire. The diameter of the pump beam is ∼10 mm, which is much larger than the focused terahertz spot (∼3 mm) at the sample to provide uniform excitation of the metamaterial array. By changing the optical path of the pump beam, the relative time delay between the pump laser and the THz pulse can be varied. At each delay time, the THz-TDS spectroscopy were recorded. By performing fast Fourier transform on the time domain signal, the transmission spectra can be obtained at each delay time by using dry air as the reference.
3. Results and discussion
To enhance the coupling among the resonators in the THz metamaterial array, widely opened radiating C-type THz resonators were used instead of the traditional SRRs with small gap opening. The optimized C-type resonators, as showed in Fig. 1(a), have the geometrical parameters as such a = 39 µm, b = 4.5 µm, c = 36 µm, d = 21.5 µm, w = 9.5 µm, w0 = 4.5 µm, Px = 150 µm, Py = 90 µm. With these structural parameters, three samples were fabricated, namely, hybrid, vacancy and perfect metamaterial arrays. The incident electrical field of THz wave is perpendicular to the arms of the resonators as shown in Fig. 1(a).
To study the effect of vacancies on the coupling of resonators in the arrays, the THz transmission spectra was simulated using S21 parameters in CST Microwave Studio software for pure metallic metamaterial arrays with and without vacancies, as showed in Fig. 2(a). It can be seen that the metamaterial arrays with vacancies has two strong resonance dips in the transmission spectra at ∼0.51 THz and ∼0.64 THz respectively. Between the two resonance dips, there is a transparent window with maximum transmittance at ∼0.554 THz, which as discussed later is a result of near-field coupling of two bright modes in the symmetry breaking metamaterial arrays. As a result, the vacancies in the metamaterial arrays could also cause metamaterial analogue of EIT effect, which is different from the EIT effect through tuning the coupling between the ‘dark’ and ‘bright’ mode of THz resonators [19]. In the contrast, the perfect metamaterial arrays only have one resonance dip in the spectra at ∼0.558 THz, as shown in Fig. 2(a). The metamaterial array with and without vacancies were then fabricated and characterized by the THz-TDS system. The experimental THz transmission spectra was obtained by taking the ratio of the sample to the dry air of their Fourier transformed intensity of THz wave in the frequency domain, which is shown in Fig. 2(b). The simulated results are consistent with the experimental results as compared between Fig. 2(a) and (b). The slight shift of the resonance dips could be due to the inaccurate fabrication of these resonators.
Fig. 2. The THz transmission spectra obtained from the (a) CST simulation and (b) experimental testing of the metamaterial arrays with and without vacancies.
To understand the coupling among the resonators in the metamaterial arrays, electromagnetic simulation at the resonance dips and transparency peak were carried out using the CST software, which is shown in Fig. 3. At the resonance dip f = 0.51 THz of the vacancy array, the two resonators on the left side of the unit cell are strongly coupled by electric dipole interactions as shown in Fig. 3(a). The resonator on the right side has opposite and weaker polarization with respect to the left side ones. And the magnetic dipole interaction and surface current of all three resonators are trivial as shown in Fig. 3(e) and 2(i) respectively. Here the resonance at f = 0.51 THz is mainly attributed to the coupled dipole mode resonance of the left side resonators, which will be discussed latter. At the resonance dip f = 0.64 THz, the three resonators in the unit cell has the same electrical dipole polarization direction due to the coupling. However, the single resonator on the right side has much stronger electrical and magnetic dipole polarization as well as surface current than the two resonators on the left as shown in Fig. 3(c), (g) and (k), which indicates the main contribution of the LC mode resonance of the single resonator on the right side. It should be noting that the strong magnetic dipole of the right-side resonator also induced an enhanced surface current and magnetic dipole on the top left resonator in the unit cell.
Fig. 3. Spatial distribution of (a)-(c) electric field and (e)-(g) magnetic field and (i)-(k) surface current in the x-0-y plane of the metamaterial arrays with vacancies at the resonance dips of 0.51THz and 0.64THz and the transparency peak at 0.554THz respectively. (d), (h) and (l) show the corresponding simulation for the perfect metamaterial arrays at the transmission dip f = 0.558.
At the transparency peak of f = 0.554 THz, the three resonators in the unit cell are coupled by both electrical and magnetic dipole interactions as shown in Fig. 3(b) and(f) respectively. The resonator on the right side has opposite electric polarization to the left side ones. The right-side resonator also has strong magnetic dipole interaction with the top left one with the same magnetic dipole polarization direction. The two resonators on the left side are also strongly coupled by magnetic dipole interaction, however with opposite polarization direction. The three resonators all have strong surface current along the C-type structures, as shown in Fig. 3(g), which indicates that coupled LC mode resonance of the three resonators were excited. Under this condition, the metamaterial analogue of the EIT effect were also observed, resulting in a high transparency window at f = 0.554 THz as shown in Fig. 2. Figure 3(d), (h) and (l) show the electrical field, magnetic field and surface current of the perfect metamaterial array. At the absorption peak of f =0.558THz, the resonator arrays show coupled electrical dipole mode resonance with trivial magnetic dipole interaction and surface current. And only one resonance mode was observed for the perfect metamaterial arrays in the observing band as shown in Fig. 2.
From above discussion, the two resonance dips at 0.51 THz and 0.64 THz in the vacancy metamaterial arrays in Fig. 2 is mainly attributed to the resonance of the two resonators on the left side and the single resonator on the right side respectively. To clarify, the vacancy metamaterial array was divided into two sub unit cells. One has the two resonators on the left side as shown in Fig. 4(c), and one has the single resonator on the right side as shown in Fig. 4(d). Figure 4(e) compares the transmission spectra of the vacancy metamaterial array with its two sub-resonator arrays. The two sub-resonator arrays both have only one resonance dip in the observing window, which coincides with the resonance of the vacancy metamaterial arrays at 0.51 THz and 0.64 THz respectively. The minor shift could be due to the mutual coupling between the two sub-resonator arrays. At the resonance, the electrical dipole polarization of the two sub-resonator arrays is consistent with that when they are in the whole vacancy metamaterial array as compared between Fig. 4(a) and (c) and between Fig. 4(b) and (d) respectively. When the two oscillation modes are strongly coupled at f= 0.554THz in the vacancy metamaterial array, its EIT analogue is observed with large transparency in the transmittance spectra. This EIT analogue is due to the bright-bright mode coupling of the two sub-resonator arrays. The bright-bright mode coupling induced EIT analogue were also observed in graphene metamaterial arrays [27,28].
Fig. 4. The electric field distribution of the vacancy metamaterial arrays at (a) 0.51 THz and (b) 0.64 THz. (c) and (d) are the electric field distribution of the two sub-resonator arrays at 0.51 and 0.64 THz respectively. (e) show the spectral transmission of the vacancy metamaterial arrays and their sub-resonator arrays.
Since resonators have different interaction and resonance mode between the vacancy and perfect metamaterial arrays, here we introduced a C-type silicon metamaterial at the vacancy position in the metamaterials arrays to actively tune the coupling among the metamaterial arrays. The unit cell of the silicon resonator implanted hybrid metamaterial array is shown in Fig. 5(a). Femtosecond pump laser was used to excite charge carriers to tune the transient conductivity of silicon, which could tune the interaction in the terahertz metamaterial arrays and thereby achieve active modulation of THz wave. The hybrid metamaterial arrays could behave like the vacancy metamaterial arrays when not illuminated. When the hybrid metamaterials were illuminated by strong transient femtosecond laser, the photo-excited charge carriers can oscillate in the silicon metamaterials [29]. When the silicon become conductive enough, it could convert the metamaterial arrays from vacancy type to perfect type. As a result, the coupling among resonators in the array can be actively tuned to realize the manipulation of the traveling THz wave. The sample picture and its optical microscopic image of the silicon hybrid metamaterial array are shown in Fig. 5(b) and (c) respectively. The silicon resonators appear aqua color, and the metallic resonator appear gold in the optical image as shown in Fig. 5(c).
Fig. 5. (a) Three-dimensional schematic diagram, (b) sample picture, and (c) microscopic image of the silicon hybrid metamaterial arrays.
OPTP system was used to study the active modulation of THz wave by the hybrid metamaterials arrays. Figure 6(a) shows the measured transmission spectra at delay time Δt = 10 ps after the femtosecond laser pumping. At the Δt = 10 ps, the optically excited charge carrier concentration reaches its maximum, resulting in minimum transmission as shown in the inset of Fig. 6(b). At this delay time, the pump laser power was varied from 0 to 800 mW in an area of 1 cm2 to study the effect of charge carrier concentration. When no pump laser is shined on the sample, the transmittance at 0.585 THz is 48%. When the pump laser power is gradually increased to 300 mW, 600 mW and 800mW, the transmittance at 0.585 THz is gradually reduced to 0.415, 0.395 and 0.363 respectively. No further transmittance reduction and complete transformation from vacancy-type to perfect-type arrays were observed due to the limited conductivity increase of the silicon ring under the experimental conditions. Figure 6(c) show the simulation of the transmission spectra of the metamaterial arrays when the silicon conductivity is varied from 0 to 3000 S/m, which has the similar trend with experimental results. The experimental resonance peak intensity is weaker than the simulation results, which might be due to the inaccurate production of the arrays during the experiment. The transformation from vacancy-type to perfect-type metamaterial array pattern starts when the silicon conductivity reaches 104 S/m as simulated in Fig. 6(d). And the transformation is completed when the silicon conductivity is 105 S/m, where the dual transmittance dips becomes a single transmittance peak at 0.554. However, at the conductivity of 104 S/m, large modulation of THz wave at 0.585 THz have already been achieved. Upon pump laser illumination, the concentration of generated electron-hole pair by each laser pulse is given as follow: $G = \eta \alpha I/h\nu $, where G, η, α, I, h and ν are generated charge carrier concentration, quantum efficiency, light absorption coefficient, energy density of each laser pulse, Plank constant and frequency of light respectively [30]. The light absorption coefficient of silicon is 850 /cm at 800 nm, namely, α=850 /cm [31]. In our experiment, the maximum energy density of each laser pulse is ∼ 0.8 mJ/cm2. As a result, the maximum estimated transient charge carrier concentration is ∼1.4×1018/cm3 upon femtosecond laser excitation by assuming 50% quantum efficiency, which gives maximum achieved conductivity $\mathrm{\sigma } = \textrm{nq}{\mu _n} \cong 200\; S/cm = 2 \times {10^4}\; S/m$ in our experiment. As a result, more significant change of the transmission spectra should be observed. However, the maximum achieved silicon conductivity could be limited by pump laser reflection, rapid surface recombination [32,33] and reduced charge carrier mobility due to increased phonon and Coulomb scattering in thin silicon layer [34]. In our case, the achieved silicon conductivity is reduced by almost one order of magnitude in comparison with ideal case. To study the modulation speed, the THz transmittance at 0.585 THz of the hybrid metamaterials is recorded at different delay time. As shown in Fig. 6(b), it takes about 10 ps for the transmittance to decrease from original 0.48 to its lowest point of 0.363 for 0.8 mJ laser pulse. When the delay time Δt >10 ps, the transmittance slowly increases due to the recombination of the photoexcited charge carriers, as shown in Fig. 6(b). The restore time is ∼1 ns according to the exponential function fitting by Origin software.
Fig. 6. (a) The measured transmission spectra of the silicon hybrid metamaterial array at delay time of 10 ps, (b) the measured transmission at 0.554 THz of the silicon hybrid metamaterial arrays at different delay time. (c) and (d) show the simulated transmission spectra of the silicon hybrid metamaterials at different conductivity of the silicon.
Such vacancy tuned electromagnetic response of THz metamaterial arrays have potential application for both passive and active THz components. By designing the vacancy distribution in the pure metallic arrays, broadband passive THz filters could be realized. Alternatively, inclusion of conductivity tunable materials at the vacancy positions could result in high performance active THz modulators. However, the limited conductivity increases in these materials currently prevent us from obtaining the expected modulation depth. By re-designing the basic resonators in the arrays and/or re-constructing the unit at the vacancy positions, significant modulation depth could be achieved. Further, the modulation rate could be improved by introducing atomic defects in the silicon [32]. These works are in progress.
4. Conclusion
Introduction of vacancies is an effective means to tune the coupling among THz metamaterial arrays. In our designed C-type metamaterials arrays, perfect metamaterial arrays have only one transmittance dip due to a coupled resonance mode. In the contrast, the vacancy introduction results in two resonance dips due to two distinctive resonance modes. When the two bright modes were coupled, metamaterial analogue of electromagnetically induced transparency was observed with a high transparency window between the two resonance in the transmittance spectra. The vacancy positions were then filled with silicon resonators to make a hybrid metamaterial arrays for active optical modulation. The active modulation speed is ∼ 1 GHz using femtosecond laser as the stimuli. The vacancy mediated coupling among metamaterials could provide a new avenue for terahertz wave modulation.
Funding
National Key Research and Development Program of China (2018YFE0115500); National Natural Science Foundation of China (51772045, 61734002); National Key Scientific Instrument and Equipment Development Projects of China (51827802); Sichuan Province Science and Technology Support Program (2019YJ0186, 2021JDTD0026).
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. B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat Mater 1(1), 26–33 (2002). [CrossRef]
2. H. Guerboukha, K. Nallappan, and M. Skorobogatiy, “Toward real-time terahertz imaging,” Adv. Opt. Photonics 10(4), 843–938 (2018). [CrossRef]
3. S. C. Zhong, “Progress in terahertz nondestructive testing: A review,” Front. Mech. Eng. 14, 273–281 (2019). [CrossRef]
4. T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat Photonics 10(6), 371–379 (2016). [CrossRef]
5. T. Seifert, S. Jaiswal, U. Martens, J. Hannegan, L. Braun, P. Maldonado, F. Freimuth, A. Kronenberg, J. Henrizi, I. Radu, E. Beaurepaire, Y. Mokrousov, P. M. Oppeneer, M. Jourdan, G. Jakob, D. Turchinovich, L. M. Hayden, M. Wolf, M. Munzenberg, M. Klaui, and T. Kampfrath, “Efficient metallic spintronic emitters of ultrabroadband terahertz radiation,” Nat Photonics 10(7), 483–488 (2016). [CrossRef]
6. H. Y. Chen, H. Liu, Z. M. Zhang, K. Hu, and X. S. Fang, “Nanostructured Photodetectors: From Ultraviolet to Terahertz,” Adv. Mater. 28(3), 403–433 (2016). [CrossRef]
7. T. L. Wen, D. N. Zhang, Q. Y. Wen, Y. L. Liao, C. Zhang, J. Y. Li, W. Tian, Y. P. Li, H. W. Zhang, Y. X. Li, Q. H. Yang, and Z. Y. Zhong, “Enhanced Optical Modulation Depth of Terahertz Waves by Self-Assembled Monolayer of Plasmonic Gold Nanoparticles,” Adv. Opt. Mater. 4(12), 1974–1980 (2016). [CrossRef]
8. X. G. Zhao, Y. Wang, J. Schalch, G. W. Duan, K. Crernin, J. D. Zhang, C. X. Chen, R. D. Averitt, and X. Zhang, “Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers,” ACS Photonics 6(4), 830–837 (2019). [CrossRef]
9. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef]
10. N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D. S. Kim, and N. Park, “Colossal Terahertz Field Enhancement Using Split-Ring Resonators with a Sub-10 nm Gap,” ACS Photonics 5(2), 278–283 (2018). [CrossRef]
11. J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57(6), 37–43 (2004). [CrossRef]
12. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef]
13. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef]
14. H. T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat Photonics 3(3), 148–151 (2009). [CrossRef]
15. Q. Y. Wen, H. W. Zhang, Y. S. Xie, Q. H. Yang, and Y. L. Liu, “Dual band terahertz metamaterial absorber: Design, fabrication, and characterization,” Appl. Phys. Lett. 95(24), 241111 (2009). [CrossRef]
16. N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat Mater 11(11), 917–924 (2012). [CrossRef]
17. R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011). [CrossRef]
18. Y. C. Zhao, Y. X. Zhang, Q. W. Shi, S. X. Liang, W. X. Huang, W. Kou, and Z. Q. Yang, “Dynamic Photoinduced Controlling of the Large Phase Shift of Terahertz Waves via Vanadium Dioxide Coupling Nanostructures,” ACS Photonics 5(8), 3040–3050 (2018). [CrossRef]
19. R. Singh, C. Rockstuhl, F. Lederer, and W. L. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B. 79, 4 (2009). [CrossRef]
20. S. J. Kindness, N. W. Almond, B. B. Wei, R. Wallis, W. Michailow, V. S. Kamboj, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, D. A. Ritchie, and R. Degl’Innocenti, “Active Control of Electromagnetically Induced Transparency in a Terahertz Metamaterial Array with Graphene for Continuous Resonance Frequency Tuning,” Adv. Opt. Mater. 6(21), 1800570 (2018). [CrossRef]
21. J. Q. Gu, R. Singh, X. J. Liu, X. Q. Zhang, Y. F. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. G. Han, and W. L. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 6 (2012). [CrossRef]
22. P. Pitchappa, M. Manjappa, C. P. Ho, Y. Qian, R. Singh, N. Singh, and C. Lee, “Active control of near-field coupling in conductively coupled microelectromechanical system metamaterial devices,” Appl. Phys. Lett. 108(11), 111102 (2016). [CrossRef]
23. T. L. Wang, H. Y. Zhang, Y. Zhang, Y. P. Zhang, and M. Y. Cao, “Tunable bifunctional terahertz metamaterial device based on Dirac semimetals and vanadium dioxide,” Opt. Express 28(12), 17434–17448 (2020). [CrossRef]
24. T. L. Wang, Y. P. Zhang, H. Y. Zhang, and M. Y. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369–386 (2020). [CrossRef]
25. C. A. Coulson and M. J. Kearsley, “Colour centres in irradiated diamonds,” Proc. R. Soc. Lond. A 241, 433–454 (1957). [CrossRef]
26. M. S. Ma, Y. Wang, M. Navarro-Cia, F. Liu, F. Q. Zhang, Z. F. Li, Y. X. Li, S. M. Hanham, and Z. C. Hao, “The dielectric properties of some ceramic substrate materials at terahertz frequencies,” J. Eur. Ceram. Soc. 39(14), 4424–4428 (2019). [CrossRef]
27. G. L. Fu, X. Zhai, H. J. Li, S. X. Xia, and L. L. Wang, “Tunable plasmon-induced transparency based on bright-bright mode coupling between two parallel graphene nanostrips,” Plasmonics 11(6), 1597–1602 (2016). [CrossRef]
28. X. J. He, X. Y. Yang, G. J. Lu, W. L. Yang, F. M. Wu, Z. G. Yu, and J. X. Jiang, “Implementation of selective controlling electromagnetically induced transparency in terahertz graphene metamaterial,” Carbon 123, 668–675 (2017). [CrossRef]
29. H. L. Cai, Q. P. Huang, X. Hu, Y. Liu, Z. P. Fu, Y. Zhao, H. C. He, and Y. L. Lu, “All-Optical and Ultrafast Tuning of Terahertz Plasmonic Metasurfaces,” Adv. Opt. Mater. 6, 7 (2018). [CrossRef]
30. R. F. Pierret and P. Hall, Semiconductor Device Fundamentals: United States Edition (Addison Wesley, 1996).
31. M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Solar Energy Materials and Solar Cells 92(11), 1305–1310 (2008). [CrossRef]
32. H. C. He, Q. P. Huang, H. L. Cai, Y. Zhao, X. X. Lin, H. Cheng, T. Ma, J. L. Wang, H. L. Huang, M. Yin, Z. P. Fu, and Y. L. Lu, “Ultrafast and Broadband Terahertz Modulator With Polarization Selectivity,” IEEE Photonics J. 11, 1 (2019). [CrossRef]
33. O. Palais, J. Gervais, L. Clerc, and S. Martinuzzi, “High resolution lifetime scan maps of silicon wafers,” Materials Science and Engineering: B 71(1-3), 47–50 (2000). [CrossRef]
34. F. Gamiz, J. B. Roldan, P. Cartujo-Cassinello, J. E. Carceller, J. A. Lopez-Villanueva, and S. Rodriguez, “Electron mobility in extremely thin single-gate silicon-on-insulator inversion layers,” J Appl Phys 86(11), 6269–6275 (1999). [CrossRef]
