Open Access
Add to BibSonomy
Abstract
Mirror-asymmetric split-ring metamaterials with high quality factor in the terahertz (THz) band, consisting of patterned high magnetic permeability and low coercivity FeNHf films deposited on high resistivity silicon substrates, were studied for their magnetic field tunable response in frequency and transmission. Dynamic tuning of terahertz transmission and electromagnetic resonance modes were investigated theoretically and experimentally as a function of magnetization of the FeNHf film. Experimental results indicate that the metamaterial structure provides a giant tunability of resonance frequency (Δfr/fr=3.3%) and transmittivity (21%) at a frequency of 0.665 THz under a low magnetic field of H=100 Oe. Remarkable tuning coefficients of frequency and transmittivity, 0.23 GHz/Oe and 0.21%/Oe, respectively, were measured. Finite difference time domain simulations reveal that the incredible tunability stems predominately from the response of the THz dynamic magnetic field to magnetization. As a result, the metamaterial, consisting of a simple magnetic split-ring microstructure, provides previously unimagined paths to tunable devices for potential use in emerging THz technologies including 6G communication systems and networks.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
28 October 2020: A typographical correction was made to affiliation 3.
1. Introduction
Metamaterials have attracted extensive interest in research from the fundamental physics community for potential applications in RF engineering and optical communication because of their exotic electromagnetic properties that do not exist in naturally occurring materials [1–3]. In recent years, metamaterials research has gravitated to THz frequencies in areas such as THz modulators, resonators, filters, absorbers and sensors [4–8], in which the metamaterials are mainly composed of metallic Au and low dielectric loss substrate materials. It has been reported that traditional THz microstructures rely generally on metallic Au films. If the structure parameters are fixed, it is difficult to tune THz transmission in real time by the response of intrinsic properties of gold films to a tuning field [9,10]. Therefore, some new approaches based on the external magnetic field modulation of THz waves have been proposed. For example, the angular deflection of transmitted terahertz pulses could be modulated about 5° under a 780 Oe field by changing the anisotropic magneto-resistance in Co/sapphire particles [11]. A slight modulation of about 2% in magneto-terahertz conductivity was found in the semi-metal Mn3Sn film while a magnetic field is applied up to 7 T [12]. Additionally, damping of a modulated THz emission in Ta/Py/Ta multilayers was shown in the magnetodynamic response to ultrafast THz pulses [13]. Furthermore, a modulation in the transmissivity of about 70%, and the resonance frequency of about 80%, under a high magnetic field of H=8 T were reported in a semiconductor split-ring resonator, which is due to the change of the refractive index by the magnetic field [14]. Most recently, an investigation of magnetization dynamics driven by a high terahertz electric field of ∼ 20 MV/m has garnered much attention, which validates the great potential metamaterials have in THz bands in terms of nonlinear magnetization dynamics [15].
In this letter, metamaterials having magnetically tunable THz transmission were designed and demonstrated in both theory and experiment. The metastructure, with high quality factor, consists of magnetic split rings with mirror asymmetric configuration [9]. The split rings are made of soft magnetic FeNHf thin film having high magnetization and low coercivity in order to enable the tunability of permeability by a low external magnetic field. Owing to the response of the film’s magnetization to an applied magnetic field, the THz wave field can be effectively modulated in terms of the anisotropic permeability in the patterned structure of the FeNHf film. The proposed design has demonstrated a remarkable field tunability of transmittivity (>20%) in the THz frequency band, yielding a very high sensitivity of 0.23 GHz/Oe. These results provide previously unimagined paths to tunable devices for potential use in emerging THz technologies including 6G communication systems and networks.
2. Experiments
The proposed metamaterial consists of mirror asymmetric magnetic split-rings on a silicon substrate of high electrical resistivity ∼8000 Ω·cm. The dimension of the substrate was 10×10×0.5 mm3. To assemble the metastructure, magnetron sputtering was employed to deposit the patterned split-ring FeNHf film, along with semiconductor micro-nano processing. In the process, a 50 mm diameter Fe (99.99%) sputtering target embedded with three chips of hafnium (Hf) (2.5×2.5×0.5 mm3) was used during sputtering deposition. A static magnetic field of 150 Oe was applied parallel to the substrate surface during deposition in order to induce a magnetic anisotropy field along the film in-plane axis. The sputter deposition was accomplished at a working pressure of 0.3 Pa of mixed N2/Ar gas atmosphere for a duration of 10 minutes. Magnetic hysteresis loops of the FeNHf films were measured at room temperature using a physical property measurement system (PPMS, Quantum Design). The magnetic permeability of FeNHf films were measured by a shorted microstrip transmission-line over a frequency range of 0.5-4.5 GHz [16]. The compositional analysis of the FeNHf films were performed by energy dispersive X-ray spectroscopy (EDXS). The THz transmission properties of patterned magnetic metastructures were characterized by using a THz time-domain spectrometer (THz-TDS) with a power of 20 mW (under a positive nitrogen gas atmosphere to prevent THz absorption from humidity) [17]. A photograph of the experimental set-up and schematic of the THz-TDS measurement are illustrated in Figs. 1(a) and 1(b), where the sample is placed on the THz focal spot (∼2 mm2) in the measurement plane. The configuration of THz electric and magnetic fields in the metastructure was mapped by finite difference time domain (FDTD) simulation in terms of a frequency dependent Drude model for the magnetic metal layer with a conductivity of the FeNHf film, σ=4.2×105 S/m, where the conductivity was measured by the Van Der Pauw method.
Fig. 1. (a) Photograph of THz-TDS. (b) Schematic of the TDS measurement setup. (c) Schematic of the metastructure. (d) Photograph of sample s=30.
3. Analysis and numerical results
Figure 1(c) depicts the design of the mirror asymmetric split-ring metastructure. The square unit cell of the split rings has the dimensional parameters: length p=200 µm, m=30 µm, s=30 µm, width of wire: w=5 µm, distance between the split rings: d=20 µm, width of gap: g=5 µm, and the offset distance: δ=5 µm. A photograph of the fabricated metastructure is shown in Fig. 1(d).
The composition of the FeNHf film are determined by EDXS measurements as depicted in Fig. 2 and reported in the inset chart. It is clear that the FeNHf film contains Fe of 89.65 wt%, N of 5.32 wt% and Hf of 5.03 wt %, that is, Fe0.90N0.05Hf0.05. The bottom inset to Fig. 2 exhibits the cross section of the FeNHf film imaged by scanning electron microscopy (SEM) showing a ∼ 51.9 nm thickness. These data enable us to estimate a deposition rate of 5.19 nm/minute at a sputtering pressure of 0.3 Pa.
Fig. 2. EDXS spectrum and analysis results (top inset) with cross sectional SEM image (bottom inset) of FeNHf film.
Figure 3(a) shows magnetic hysteresis loops of the FeNHf film along easy and hard axes along the sample plane. Here, the magnetic anisotropy primarily stems from that induced by the applied field during the sputtering process [18]. The saturation magnetization and coercive field of the magnetic film were measured to be 4πM ∼16.7 kG and Hc = 5.1 Oe along the hard axis direction. Figure 3(b) plots a measurement of the complex permeability for FeNHf film samples. The real permeability µ’ is 610 along the hard axis, while the resonance frequency fr is 1.92 GHz. This surprisingly leads to a high Snoek’s limit of 1.17×1012 GHz. In contrast, the real permeability along the easy axis is very low and constant with frequency, which is consistent with previously reported results [19]. Furthermore, the Landau-Lifshitz-Gilbert (LLG) theory is utilized to describe the magnetic behavior of the soft magnetic film [18,20]:
Fig. 3. (a) M-H loops of the FeNHf film. (b) Permeability of the FeNHf film and best fit data from the LLG model.
Here, ω is the angular frequency. ωm=γ4πMs, ω0=γHeff, ωr2=ω02+ω0ωm and Δωr=α(2ω0+ωm) can be obtained by fitting to the experimental permeability spectrum. For the FeNHf film, it is estimated that the gyromagnetic ratio γ is 3.35×1011 Hz/T. The Lande g factor is γmee=1.91 where me=9.1×10−31 kg and e=1.6×10−19 C.
The effective anisotropy field, Heff, was estimated to be 19.7 Oe from fitting to the measured magnetic spectrum. Additionally, the dimensionless effective damping coefficient α is 0.014 and the relaxation time τ of precession is about 520 femtoseconds. Clearly, the film has very low intrinsic losses due to its low damping coefficient, which is favorable to reduce energy dissipation in practical devices. It is noteworthy that the film in-plane magnetic anisotropy provides anisotropy in permeability and consequently gives rise to tunability of THz transmission with respect to an applied magnetic field.
Figure 4 shows the THz transmissivity of magnetic and non-magnetic samples with geometric parameters, s=30 µm and s=36 µm, respectively. To compare, both magnetic FeNHf and non-magnetic Au patterned films have identical patterns and dimensions except for s. It is noted that increasing length s, leads to a shift of the resonance frequency fr to lower frequencies from 0.665 THz to 0.639 THz for the patterned FeNHf film metastructure. It is understandable that the frequency shift is attributed to the interaction between the incoming THz wave and metastructure in terms of the longer metallic wire dimension and the larger effective inductance based on transmission line theory [17],
Similarly, the resonance frequency of the Au metastructure shifts also from 0.695 THz to 0.656 THz when the parameter s increases from 30 µm to 36 µm. Nevertheless, either of them exhibits an identical frequency shift of about 0.03 THz with the change of structure parameters. It is conspicuous, however, that the operating frequency fr of the patterned FeNHf metastructure is distinctly lower than that of the Au metastructure if both have the same dimension. It stands to reason that the larger equivalent inductance of the FeNHf metastructure is responsible for the lower operating frequency, compared to the Au metastructure. Generally, the self-inductance of a planar spiral inductor with n-turns is described by [21]: where w is the line width and t is the thickness of the metal, l is the total length of the wire and µr is the relative permeability. The higher the permeability, the larger the inductance L. Therefore, the FeNHf metastructure exhibits the lower resonance frequency according to Eq. (3), compared to that of the non-magnetic Au metastructure. At the same time, the dip at T=0.70 in THz transmissivity of the FeNHf metastructure is also pronouncedly deeper than the dip at T=0.81 of the Au metastructure as depicted in Fig. 4(a). It is suggested that the metallic loss at the THz wave band has been effectively suppressed in the split-ring metastructures due to the low conductivity of σ=4.2×105 S/m of the FeNHf film. Figure 4(b) presents a simulation of transmissivity for both of the magnetic and non-magnetic metastructures with two geometric dimensions using the FDTD method. As a result, all of the simulations predict strong absorption for THz wave propagation through the patterned metastructures, which is also consistent with experimental results. Furthermore, the mirror-asymmetric magnetic split-ring metastructures exhibit a high-quality factor Q = fr/Δf=11.9 due to the sub-radiant LC resonant mode generated by the induced THz current, which results in a reduction of THz radiation losses. For most split-ring metamaterials, Q-values are low and usually not more than 10 because of THz radiation and eddy current losses [22–25]. In the unit with four mirror-asymmetry split-rings, the electric current direction in the upper two split-rings is counterclockwise, whereas in the lower two split-rings the electric current in clockwise, as shown in Fig. 1(c). This implies that the induced THz currents in the resonators oscillate out of phase, leading to the elimination of electromagnetic loss and ultimately the appearance of a sub-radiant LC resonance mode [9,25]. Therefore, this results in an enhanced tunability in frequency or transmittivity as is measured in the vicinity of the resonance frequency over a narrow THz band. Furthermore, The response frequency (response speed) f=(2πRC)-1 is an important parameter for a tunable modulator and is limited by RC constant in a resonant circuit [26]. In the present experiment, the resistance R of unit cell is estimated to be about 1100 Ω in terms of the conductivity 4.2×105 S/m and the dimensions of unit. The effective capacitance C=2.7 pF is estimated from the Eq. (3) and Eq. (4) based on the resonance frequency fr of 0.665 THz. Thus, the response frequency f is obtained to be 54 MHz.Fig. 4. THz transmissivity of samples with different parameters s as a function of the frequency. (a) Experiment and (b) Simulation.
To more accurately measure the field-tunability of the transmissivity avoiding any interference intrinsic to the setup from magnetic fields, an aluminum holder was used and first measured by the THz transmissivity testing system with and without an applied magnetic field H. This calibration step indicated that the variation in THz transmission of the aluminum holder was negligible (<0.1%) regardless of the applications of the 100 Oe magnetic field.
Figure 5(a) depicts a sketch of the geometric alignments of fields relative to the magnetic FeNHf-based split rings during measurements. When there is no magnetic field applied to the film elements, the permeability in the direction of the THz magnetic field $\tilde{H}$ (i.e., along the hard axis direction of the film) only relies on the induced anisotropy field along the easy axis. However, when an external magnetic field of 100 Oe is applied along the easy axis, an effective magnetic field is the sum of the induced anisotropy field and the applied field, which is responsible for the permeability in the $\tilde{H}$ direction, as illustrated in Fig. 5(a). As a result, an applied field will significantly reduce the permeability along the hard axis of the film, as depicted in Fig. 3(b). It is predicable that a change of permeability in the magnetic film would give rise to a change in the inductance and the THz resonance frequency and transmittivity in the high Q FeNHf magnetic split-ring metamaterials.
Fig. 5. (a) Sketch of the tunability measurement for FeNHf split-ring metamaterials. (b)-(c) Experimental and simulated THz transmissivity for sample s=30 µm with and without applied H, respectively. (d) Experimental and calculated tunability as a function of frequency.
Figures 5(b) and 5(c) shows the measured and simulated THz transmissivity of the metastructure sample s=30 µm when the external magnetic field H=100 Oe, is applied on or off along the direction perpendicular to the THz magnetic field $\tilde{H}$, respectively. It is found that the resonance frequency fr of the magnetic split-ring metastructure sensitively shifts to the higher frequency when the direction of the applied magnetic field is perpendicular to the THz field $\tilde{H}$, corresponding to the change (Δfr=0.023 THz) in resonance frequency from 0.665 THz to 0.688 THz. It is remarkable that such a high-Q metastructure can demonstrate frequency tunability Δfr/fr of 3.3% at the resonance frequency. Moreover, it is calculated that the frequency tuning coefficient, Δfr/ΔH is 0.23 GHz/Oe in the magnetic split-ring structure, which is nearly an order of the magnitude more than that observed (0.016 GHz/Oe) in semiconductor split-ring resonators [14].
Another interesting outcome in these experiments is the transmissivity tunability with magnetic field. Figure 5(d) illustrates experimental and calculated frequency dependence of the tunability of transmissivity (T), defined as (T(H)-T(0))/T(H) for the magnetic split-ring structure. Measurements reveal a maximum modulation in transmissivity of about 21% at the frequency of 0.665 THz, while a secondary peak appears at 0.691 THz, corresponding to -17% tunability in transmittivity. Correspondingly, the transmittivity tuning coefficient, ΔT/ΔH is calculated to be 0.21%/Oe, which is four orders of magnitude higher than that observed (0.000875%/Oe) in semiconductor split-ring resonators [14]. Figures 5(c) and 5(d) illustrate simulations of THz transmission and tunability when an applied field is on or off, respectively. The simulations of transmittivity and tunability with frequency are in good agreement with the experimental results. Furthermore, THz transmission in the thin film can be calculated by the equation [27],
where n is the effective refractive index, d is the thickness of the film, c is the speed of light and ω is the angular frequency. The effective refractive index n of the metastructures is calculated in terms of the measured transmissivity as shown in the inset of Fig. 5(b). Around the operating frequency of 0.65-75 THz, the effective refractive index n is about 50∼180, which is attributed to the effective permeability and permittivity of the metastructures.Table 1 presents a summary of transmittivity and resonance frequency tunability in THz bands for some materials under magnetic fields. To our knowledge, the tunability of these materials listed may arise from the tuning of refractive index, Fermi level or resistance by the applied magnetic field. It is no doubt that this work, based on the mirror-asymmetric magnetic split-ring metamaterials is most impressive by evidence of the demonstrated exceptionally high transmittivity tuning coefficient ΔT/ΔH of 0.21%/Oe and frequency tuning coefficient, Δfr/ΔH=0.23 GHz/Oe under a very low field of 100 Oe.
Table 1. Summary of tunability coefficients in magnetic field-controlled THz microstructures
In order to better understand the THz transmission and electromagnetic resonance behavior in the magnetic mirror-asymmetric split rings, Fig. 6 shows the mapping of THz electric $\tilde{E}$ and magnetic $\tilde{H}$ field distribution at the resonance frequency for the sample with s=30 µm, which is derived from FDTD simulations. Clearly, the resonance depression in the transmission curves stems from the electromagnetic resonance in the split gap of the open ring, where the strongest THz $\tilde{E}$-field is localized. Simultaneously, the excited current is mainly localized at the inside of the split-ring. When the external field H is applied in the X-direction, the THz $\tilde{E}$-field changes from 42.2 to 39.6 V/m, leading to about a 6.5% modulation. In this case, the THz $\tilde{H}$-field provides about 14% modulation from 176.5 to 151.2 mA/m. It is no doubt impossible for such an -field modulation to be observed in the non-magnetic Au metastructures. As a result $\tilde{H}$, the giant low-field tunability of THz transmissivity is verified to be $\tilde{H}$-field induced in the THz band in response to magnetization.
Fig. 6. Distribution of the magnitude of the $\tilde{E}$- and $\tilde{H}$-fields on the FeNHf metamaterials for sample s=30 µm at resonance frequencies: (a) and (c) fr=0.672 THz, (b) and (d) fr=0.694 THz.
4. Conclusion
THz wave transmission properties of magnetic FeNHf split-ring metamaterials have been investigated in theory and experiment. The design of unique magnetic split-ring metastructures have demonstrated a giant low-field tunability in the THz resonance frequency (Δfr/fr) of 3.3% and transmissivity of 21% under an applied field of 100 Oe. More importantly, the FeNHf split-ring metamaterial results in a high tuning coefficient of the resonance frequency (0.23 GHz/Oe) and transmittivity (0.21%/Oe), respectively. Theoretical analysis revealed that the remarkable tunability derives predominately from the THz $\tilde{H}$-field in response to changes in film magnetization.
The results presented here shed light on new magnetic field tunable THz metastructures with giant tunability in frequency and transmissivity that may hold practical importance for emerging THz technologies as modulators, resonators, filters, and sensors, including those for 6G communication systems and networks.
Funding
National Natural Science Foundation of China (61107093); Jiangsu Key Disciplines of Thirteen Five-Year Plan (20168765); Natural Science Research of Jiangsu Higher Education Institutions of China (19KJA140001, 17KJA140001).
Acknowledgments
The authors thank Prof. Biaobing Jin at Nanjing University for the THz-TDS measurements.
Disclosures
The authors declare no competing financial interests.
References
1. N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, “Optically implemented broadband blueshift switch in the terahertz regime,” Phys. Rev. Lett. 106(3), 037403 (2011). [CrossRef]
2. D. Schuring, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006). [CrossRef]
3. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305(5685), 788–792 (2004). [CrossRef]
4. A. Grebenchukov, M. Masyukov, A. Zaitsev, and M. Khodzitsky, “Asymmetric grapheme metamaterials for narrow band terahertz modulation,” Opt. Commun. 476, 126299 (2020). [CrossRef]
5. H. Song, L. Sun, and G. P. Wang, “Tunable perfect magnetic mirrors and retroreflectors in terahertz band,” Opt. Express 28(1), 753 (2020). [CrossRef]
6. M. Masyukov, A. N. Grebenchukov, E. A. Litvinov, A. Baldycheva, A. V. Vozianova, and M. K. Khodzitsky, “Photo-tunable terahertz absorber based on intercalated few-layer graphene,” J. Opt. 22(9), 095105 (2020). [CrossRef]
7. L. Cong, S. Tan, R. Yahiaoui, F. Yan, W. Zhang, and R. Singh, “Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: A comparison with the metasurfaces,” Appl. Phys. Lett. 106(3), 031107 (2015). [CrossRef]
8. X. Zhang, Y. Xing, Q. Zhang, Y. Gu, Y. Su, and C. Ma, “High speed terahertz modulator based on the single channel AlGaN/GaN high electron mobility transistor,” Solid-State Electron. 146, 9–12 (2018). [CrossRef]
9. Y. Gu, Y. Xing, X. Zhang, Y. Qian, X. Tian, W. Li, X. Lin, and C. Ma, “Enhancement of the electromagnetic energy in the asymmetric split rings with compensated microstructures,” Opt. Quantum Electron. 50(4), 168 (2018). [CrossRef]
10. Y. Xing, X. Zhang, Q. Zhang, Y. Gu, Y. Qian, X. Lin, Y. Tang, X. Cheng, C. Qin, J. Shen, T. Zang, and C. Ma, “Electromagnetic resonance in the asymmetric terahertz metamaterials with triangle microstructure,” Opt. Commun. 415, 115–120 (2018). [CrossRef]
11. C. A. Baron and A. Y. Elezzabi, “A magnetically active terahertz plasmonic artificial material,” Appl. Phys. Lett. 94(7), 071115 (2009). [CrossRef]
12. B. Cheng, Y. Wang, D. Barbalas, T. Higo, S. Nakatsuji, and N. P. Armitage, “Terahertz conductivity of the magnetic Weyl semimetal Mn3Sn films,” Appl. Phys. Lett. 115(1), 012405 (2019). [CrossRef]
13. J. Shen, X. Fan, Z. Chen, M. F. DeCamp, H. Zhang, and J. Q. Xiao, “Damping modulated terahertz emission of ferromagnetic films excited by ultrafast laser pulses,” Appl. Phys. Lett. 101(7), 072401 (2012). [CrossRef]
14. J. Han, A. Lakhtakia, and C. W. Qiu, “Terahertz metamaterials with semiconductor split-ring resonators for magnetostatic tunability,” Opt. Express 16(19), 14390 (2008). [CrossRef]
15. M. Hudl, M. d’Aquino, M. Pancaldi, S. H. Yang, M. G. Samant, S. S. P. Parkin, H. A. Dürr, C. Serpico, M. C. Hoffmann, and S. Bonetti, “Nonlinear magnetization dynamics driven by strong terahertz fields,” Phys. Rev. Lett. 123(19), 197204 (2019). [CrossRef]
16. Y. Liu, L. F. Chen, C. Y. Tan, H. J. Liu, and C. K. Ong, “Broadband complex permeability characterization of magnetic thin films using shorted microstrip transmission-line perturbation,” Rev. Sci. Instrum. 76(6), 063911 (2005). [CrossRef]
17. X. Zhang, R. Tan, Z. Zheng, X. Li, Z. Zhang, J. Sun, Y. Zhou, L. Lü, B. Zhang, and H. Qin, “Terahertz filters based on frequency selective surfaces for high-speed terahertz switch,” J. Appl. Phys. 113(1), 014504 (2013). [CrossRef]
18. F. Xu, N. N. Phuoc, X. Y. Zhang, Y. Ma, X. Chen, and C. K. Ong, “Tuning of the magnetization dynamics in as-sputtered FeCoSiN thin films by various sputtering gas pressures,” J. Appl. Phys. 104(9), 093903 (2008). [CrossRef]
19. U. Queitsch, J. McCord, A. Neudert, R. Schäfer, L. Schultz, K. Rott, and H. Brückl, “Domain wall induced modes of high-frequency response in ferromagnetic elements,” J. Appl. Phys. 100(9), 093911 (2006). [CrossRef]
20. S. Chikazumi, Physics of Magnetism (Krieger, Malabar, FL, 1964).
21. S. Jenei, B. K. J. C. Nauwelaers, and S. Decoutere, “Physics-based closed-form inductance expression for compact modeling of integrated spiral inductors,” IEEE J. Solid-State Circuits 37(1), 77–80 (2002). [CrossRef]
22. I. H. Libon, S. Baumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, “An optically controllable terahertz filter,” Appl. Phys. Lett. 76(20), 2821–2823 (2000). [CrossRef]
23. C. Li, C. Zhang, G. Hu, G. Zhou, S. Jiang, C. Jiang, G. Zhu, B. Jin, L. Kang, W. Xu, J. Chen, and P. Wu, “Electrically tunable superconducting terahertz metamaterial with low insertion loss and high switchable ratios,” Appl. Phys. Lett. 109(2), 022601 (2016). [CrossRef]
24. R. Yahiaoui, M. Manjappa, and Y. K. Srivastava, “Active control and switching of broadband electromagnetically induced transparency in symmetric metadevices,” Appl. Phys. Lett. 111(2), 021101 (2017). [CrossRef]
25. I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(7), 071108 (2012). [CrossRef]
26. H.-T. Chen, S. Palit, T. Tyler, C. M. Bingham, J Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, and N. M. Jokerst, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93(9), 091117 (2008). [CrossRef]
27. L. Duvillaret, F. Garet, and J.-L. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38(2), 409 (1999). [CrossRef]
28. R. Cheng, Y. Zhou, H. Liu, J. Liu, G. Sun, X. Zhou, H. Shen, Q. Wang, and Y. Zha, “Tunable graphene-based terahertz absorber via an external magnetic field,” Opt. Mater. Express 10(2), 501 (2020). [CrossRef]
