Open Access
Add to BibSonomy
Abstract
Slow wave and localized field are conducive to terahertz (THz) modulators with deep and fast modulation. Here we propose an electrically controlled THz modulator with slow wave effect and localized field composed of a high electron mobility transistor (HEMT) integrated metasurface. Unlike previously proposed schemes to realize slow wave effect electrically, this proposal controls the resonant modes directly through HEMT switches instead of the surrounding materials, leading to a modulation depth of 96% and a group delay of 10.4ps. The confined electric field where HEMT is embedded, and the slow wave effect, work together to pave a new mechanism for THz modulators with high performance.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of information technology, THz technology has attracted considerable attention owing to its advantages of ultra-broadband and fast transmission rate [1,2]. Realizing fast and efficient THz amplitude modulators is crucial for data transmission in THz systems [3]. The research of metasurfaces provides innovative ideas for designing novel THz modulation. Electromagnetic metasurfaces are artificially arranged composites with subwavelength structures, whose electromagnetic properties can be arbitrarily designed by changing their geometric parameters [4]. In order to achieve dynamical control, many approaches have been suggested by integrating metasurfaces with active materials [5], such as superconductors [6,7], semiconductors [8–10], phase-change materials [11,12] and microelectromechanical systems (MEMS) [13], each of which can be actively controlled by optical [14,15], electrical [16–18], or thermal methods [19]. Electrically controlled modulators have attracted great interest among these approaches since they provide a high degree of integration.
To improve the electrical modulation depth and rate, 2D materials with tunable conductivity and high carrier mobility like graphene [20], and two-dimensional electron gas(2-DEG) [21], have been loaded on THz metasurfaces. However, due to their two-dimensional characteristic, 2D materials have weak coupling with the incident THz wave. In order to enhance the coupling between 2D materials embedded metasurface and the THz wave, electromagnetic modes supporting electric field confinement are introduced to tightly confine the electric field with relatively low loss. As a result, the 2D materials can be more sensitive to the variation of the electrical doping intensity, which is expected to achieve high speed response and deep THz modulation [20]. R. Degl'Innocenti et al. reported a reflect-type amplitude modulator of a quantum cascade laser by exploiting the interplay between plasmonic modes on antenna arrays and monolayer graphene. A modulation cut-off frequency of 5MHz was exhibited in their work [22]. Later, the same group increased the cut-off frequency to 105MHz using a similar mechanism [23]. Y. Yao et al. demonstrated 100% modulation depth with a theoretical modulation speed of 20GHz by using a Fabry-Perot mode enhanced absorber [24]. Y. Zhao et al. realized 93% modulation depth and 3 GHz modulated sinusoidal signals by integrating 2-DEG onto a collective resonator [18]. In addition, waveguides are beneficial for achieving the desired field confinement as well [25]. P. K. Singh et al. presented an on-chip device, whose operation was based on the interaction of confined THz waves in a slot waveguide with electrically tunable 2-DEG [26]. Besides the confinement mode in Ref. [26], the long-term interaction between 2-DEG and the incident wave further prolonged their interaction length, achieving a cut-off frequency exceeding 14GHz. For a free-space-type metasurface-based modulator, the interaction length of THz wave propagating normally through the metasurface is quite small due to its low profile. Instead, it usually improves the modulation rate by reducing its footprint to reduce the total capacitance.
Employing slow wave effect is an alternate and feasible way to prolong the interaction length and improve the modulation performance for free-space-type modulators with low profiles [27]. Electromagnetically induced transparency-like (EIT-like) transmission is a typical way to realize slow wave [28,29]. Many kinds of electrically controlled EIT-like transmission in THz band have been reported [13,30,31]. Though there are transmission windows having significant slow waves in these approaches, their modulation depths are limited within 85% [32,33]. W. J. Wang et al. have proposed a p-Si hybrid plasmon-induced transparency metasurface to realize 99.9% modulation depth [34], but there was no discussion on its slow wave response.
Due to the complexity of the bias network and multi-coupling resonant modes in slow-wave metasurfaces, it is a challenge to tune the resonant modes themselves in EIT-like metasurfaces. Instead, most works chose to tune the electromagnetic characteristics of the surrounding materials, which is a drawback to improve modulation rate and depth. In this paper, we propose an electrically controlled metasurface THz amplitude modulator (MTAM) to realize slow waves and deep modulation simultaneously. By embedding HEMTs with 2-DEG in the gaps of the resonators, the resonant modes can be controlled directly by electrical doping, leading to a large modulation depth. Coupling between different modes results in a transmission window with significant slow waves. Meanwhile, the confined electric field in the gaps will further enhance the interaction between 2-DEG and electric field, which has positive significance for improving the modulation rate [35,36].
2. Model and simulation
2.1 Design
Unit cell of the MTAM consists of feeding lines, double L-shape wires (DLWs) and straight wires. HEMTs are integrated into the gaps of straight wires (SWs) to dynamically control the modulator by applying an external voltage across their gate electrodes, as shown in Fig. 1(a). 2-DEG with high carrier concentration and mobility are formed inside these HEMTs. When a negative voltage is applied to the gate, the energy band below the gate is raised up and the carrier concentration of 2-DEG decreases. When the absolute value of voltage is large to a certain extent, the electrons at the heterojunction are completely depleted to realize channel pinch-off. As a result, the SWs are divided into two parts by the gaps, called split short wires (SSWs). The structure of the metasurface modulator is shown in Fig. 1(b). The unit cell size is 200 µm × 200 µm and the width of the gold wire is w = 5 µm. The DLWs are symmetric, with length in y-direction a = 61µm and length in x-direction b = 85µm. The length and width of the gate are 1.5µm and 16µm respectively, while the source-drain spacing of HEMT is 4µm. Furthermore, the optimized dimension parameters of unit are listed as follows: l = 190 µm, g = 8 µm, c = 14 µm, s = 10 µm. As one of the third-generation semiconductors, GaN has a wider bandgap than GaAs does, which can support higher carrier mobility of 2-DEG. Therefore, the metal metamaterial structure is patterned on a GaN layer and a 160 µm SiC layer is attached below the GaN layer as a substrate. After preparing the GaN layer, AlGaN layer, HEMT active area and electrodes, the method of thinning substrate will be applied to reduce the thickness of SiC substrate to 160 µm by mechanical grinding process [17]. 3 nm 2-DEG nanostructures generated from the spontaneous polarization and piezoelectric polarization effect of the AlGaN/GaN heterostructure are nested in the gaps of the structure. The heterostructure consists of a 25 nm Al0.27Ga0.73N barrier layer and a 1.5 µm GaN layer. Both ends of the heterojunction are connected to the metal metamaterial through ohmic contacts to form the source and drain of the HEMT. The conductivity of ohmic contact is set at 412 Ω·µm, which is the measured ohmic contact resistivity tested by the transmission line model (TLM) method [18]. The gate is located in the center of the heterojunction and connected to the 2-DEG through a Schottky contact to form the electrical control. The 2-DEG has a good electronic characteristic with a sheet carrier concentration of 1.6×1014 cm-2 and electron mobility of 2170 cm2/(V·s) at room temperature [17,18]. The 2-DEG is connected to the source and drain as a dynamic switch. The source-drain spacing of HEMT is 4 µm, and the length of the 2DEG gated region is set to 1.8 µm, which is slightly longer than the gate length of 1.5 µm. The modulation voltage is loaded on the center gate grids, while the source and drain are connected to ground. Therefore, the effective resonance characteristics of the structure can be adjusted by the electrical control of the carrier distribution to the 2-DEG nanostructure, which could modulate the transmission of a normally incident THz wave which is incident along z-direction and with its polarization in the x-direction.
Fig. 1. (a) Schematic of the MTAM, TE polarized waves are incident normally. (b) x-y cross section of a unit of metasurface. The red area represents the HEMT control area.
2.2 Simulation
To illustrate the dynamic electrical-modulation mechanism, 3D fully electromagnetic simulation software CST Microwave Studio and dispersive Drude model are used. These tools analyze the electromagnetic characteristics of MTAM at different carrier concentrations to mimic different external voltages. Within the scope of THz frequency, Drude model can be written as [37]:
Without any applied voltage, the source and drain are connected by a high carrier concentration 2-DEG layer in the heterostructure via the ohmic contacts, which means current can flow through the source and drain. At that time, a transmission dip appears at 0.31THz, named Off-state. As the gate voltage increases, the carrier concentration 2-DEG layer in the conductive channel decreased until it is depleted. A remarkably transparent window appears around 0.31THz, named On-state, as shown in Fig. 2(a). A modulation depth of 96% between the On-state and Off-state is achieved. The loss tangent of SiC is about 0.0002 [38], which almost has no impact on the transmission coefficient. The GaN layer in our simulation is neglected since its dielectric constant 9.7 is very close to the one of SiC (9.8), and its thickness is much smaller than the one of SiC substrate.
Fig. 2. (a) Simulated magnitude of transmission coefficient S21 of MTAM at different states. Phase of the S21 (b) and group delay (c) of MTAM in the On-state. (d) Gaussian pulses pass through an air layer (upper) and the MTAM in the On-state (down)
Dispersion relation of the phase of S21 is shown in Fig. 2(b), where the blue area indicates strong dispersion characteristic between 0.3THz to 0.325THz. Group delay ${\tau _\textrm{d}}$ is applied to analyze the slow wave characteristics of the transparent window in On-state, and ${\tau _\textrm{d}}$ is defined by [15,39]:
where φ(ω) is the phase response of the transmission spectrum, ω is the angular frequency of the incident THz wave. The calculated group delay of MTAM in the On-state is shown in Fig. 2(c). We find that the group delay reaches 10.4ps at the frequency of the transmission window, indicating that the transparent window is an EIT-like window. A 430ps long Gaussian-shaped pulse centered at the transparency window is considered propagating through the metasurface in the On-state and an air layer with the same thickness of the metasurface respectively. The pulses can be seen in the Fig. 2(d) by applying Transient solver in CST, from which one can find that the center of envelop of the pulse passing through the metasurface will be delayed by about 12.6ps, indicating a slow wave with group delay of 12.6ps, which is a little different from the group delay of 10.4ps solved by the Frequency solver in CST. It essentially retains its Gaussian shape except a weak broadening.3. Analysis and discussion
To explore the mechanism of electrical modulation, we first conduct simulation analysis on the electromagnetic responses of the sub-resonators including DLW and SW/SSW, and then give a physical illustration of the Off/On-states of the MTAM respectively.
As shown in Fig. 3(a), the DLW is composed of L-shape wires, feeding lines and gate lines. With the same substrate and incident polarization described above, the transmission spectrum of DLW is shown in Fig. 3(b). There is a resonant dip at 0.31THz, named I. The electric field of DLW at I focused at the end of the L-shape wire and feeding lines, while the surface current is mainly distributed along wires in the y-direction, as shown in Fig. 3(c) and (d), indicating that a dipolar resonance is induced by the incident wave.
Fig. 3. (a) Schematic of the DLW. (b) The transmission spectrum of the DLW. (c) The electric field distribution at I. (d) The surface current direction at I.
The HEMT is integrated in the middle of the SW (straight wire), acting as a switch under the control of the gate voltage. An SW model on the same substrate is built and its electromagnetic response under different carrier concentrations is simulated, as shown in Fig. 4(a-b). With the increase of reversed gate bias voltage, the carrier concentration of 2-DEG decreases and a large resonant frequency blueshift from 0.112THz (II) to 0.342THz (III) is obtained. At II, the resonance in the SW results from the equivalent dipolar resonance, with fields focused at the upper and lower ends of each unit cell, as shown in Fig. 4(c). The high concentration 2-DEG layer connects the source and drain via the ohmic contacts, so the surface current can flow between the source and drain, oscillating in the long straight wire (SW), shown in Fig. 4(d). When a gate voltage is applied, the carrier concentration decreases with the increase of gate bias voltage, and the resonance at II gradually weakens. When the carrier concentration dropped to a certain critical point, the 2-DEG depletion in the split gap separated the source and drain, cutting the long straight wire into two identical splits short wires (SSWs). As a result, a new dipolar resonance appears in SSWs, with which the electric field concentrates on the feeding lines and the depletion gap, as shown in Fig. 4(e). The surface current can hardly pass through the gap, but oscillates on the two SSWs instead, shown in Fig. 4(f). This indicates that it is feasible to control the electromagnetic response of the metasurface dynamically by controlling the gate voltage.
Fig. 4. (a) Schematic of the SW. (b) Magnitude of the transmission coefficient S21 of the SW at different carrier concentrations. Electric field distribution of the SW at II (c) and III (e). Surface current distributions of the SW at II (d) and III (f).
Next, we analyze the electromagnetic response of the MTAM in the Off-state and compare it with that of the SW and DLW. In the Off-state, no voltage is applied to the gate, and the HEMT allows current to flow between the source and drain. As shown in Fig. 5(a), there are two resonant dips in the transmission spectrum of the MTAM at 0.31THz and 0.083THz, named I′ and II′ respectively. One can see that I′ and I almost overlap, and there is a redshift from II to II′. The electric field and current distributions of I′ and II′ are shown in Fig. 5(c-f). At I′, the electric field is mainly concentrated at the feeding lines and the end of L-shape wires, while the current flows mainly along the L-shape wires, with similar distributions as the ones at I in Fig. 3(c) and (d). This indicates that there is little coupling between the SW and DLW, and the resonance on the DLW serves as the dominant part of the resonance at I′. When considering mode at II′, one can find that the electric field distribution is similar to the one at II, but the intensity is much more enhanced. The current flowing on straight wires has the strongest intensity, indicating that the resonance on the SW plays the dominant role at II′. In general, the electromagnetic response mode of the MTAM appears as a combination of multiple dipole resonances in the Off-state.
Fig. 5. Characteristics of the MTAM. Transmission spectra of the MTAM, SW and DLW in the Off-state (a) and On-state (b). Electric field distributions of the MTAM at I′ (c) and II′ (e) in the Off-state. Surface current distributions of the MTAM at I′ (d) and II′ (f) in the On-state.
Next, the On-state refers to the MTAM when 2-DEG is exhausted in the gap. At this time, the current cannot flow through the HEMT, and the resonator SW turns into a pair of SSWs. Under the irradiation of the incident THz field, the MTAM demonstrates a strong response at 0.285THz (I′′) and 0.363THz (III′) respectively, and a transmission window shown in Fig. 5(b) with its central frequency at 0.31THz (IV) is obtained. Figure 6(a-f) show the electric field and surface current distributions at I′′, IV and III′. From Figs. 6(a) and (b) one can see that the electric field is mainly concentrated at the feeding lines and in the gaps between L-shaped wires, while the surface current oscillates along the vertical wires of the DLW at I′′, similar to the ones at I shown in Fig. 3. That is to say the resonance at I′′ results mainly from the resonant mode at I but is perturbed by the SSWs. At III′, the surface current oscillates along the two split short wires, showing a certain correspondence between III′ and III.
Fig. 6. Electric field and surface current distribution of MTAM at (a-b) I′′, (c-d) IV and (e-f) III′.
In particular, a transmission window appears at IV in the On-state. A new resonant mode arises inside this window originating from the coupling between the electric and magnetic responses of DLW and SSWs. As shown in Fig. 6(c) and (d), the electric field is confined in the middle of the two SSWs where the HEMT is embedded. Meanwhile the surface current forms a C-shape loop consisting of the right L-shape wires and SSWs, which is a typical inductance-capacitance (LC) resonance. It should be pointed out that the SSWs and the left L-shape wires in the adjacent cell also constitute a weaker C-shaped current loop.
To validate our deduction of the physical mechanism of the transmission window, a hybrid coupling model based on coupling mode theory is introduced to calculate and analyze the transmission spectrum of the metasurface [40,41]. There are two separately excited resonant modes ${\tilde{a}_1} = {a_1}{e^{i\omega t}}$ and ${\tilde{a}_2} = {a_2}{e^{i\omega t}}$, where ${\tilde{a}_1}$ corresponds to the resonance intensity of DLWs and ${\tilde{a}_2}$ corresponds to the resonance intensity of SSWs. The relationship between them is as follows [42]:
Fig. 7. (a) Fitting magnitude of transmission coefficient based on the hybrid coupling model. (b) Simulated magnitude of transmission coefficient of the MTAM at different carrier concentrations of 2-DEG.
Table 1. Parameters extracted based on hybrid coupling model (unit: THz)
The modulator we proposed can not only switch between On-state and Off-state, but can also achieve continuous regulation between the two states. With the increase of gate bias voltage, the concentration of 2-DEG carriers gradually decreases. The transmission coefficient of the MTAM at 0.31THz gradually increases until it reaches a peak, as shown in Fig. 7(b). This indicates that modulation depth of the MTAM can be adjusted by the gate bias voltage.
4. Summary
We proposed a novel electrically controlled THz modulator capable of achieving large modulation depth and slow wave effect by integrating HEMTs into a THz metasurface. The gate voltage is used to control the concentration of 2-DEG generated inside the HEMT leading to a resonant mode conversion in the metasurface. As a result, the metasurface can work in two different states, achieving a maximum modulation depth of 96%. In particular, an obvious EIT-like transmission window appears at 0.31THz in the On-state. A hybrid coupling model is introduced to explain the physical mechanism of this EIT-like phenomenon. There is a strong slow-wave effect at the transmission window, accompanied by a group delay of 10.4ps, which can prolong the interaction length between 2-DEG and incident wave effectively. Meanwhile, a confined electric field is formed in the gap of SSWs where 2-DEG is embedded in the On-state, which could further enhance the coupling between 2-DEG and incident wave, making it conducive to improve the THz modulation performance.
Funding
Wuhu and Xidian University Special Fund for Industry-university-research Cooperation (XWYCXY-012021018); National Natural Science Foundation of China (61871063); Science and Technology Research Program of Chongqing Municipal Education Commission of China (KJQN201900602, KJQN201900615, KJQN202000648); Natural Science Foundation of Chongqing (cstc2019jcyj-msxmX0639, cstc2020jcyj-msxm0605).
Acknowledgments
We thank Murali Shroff Kosgi from Northern Arizona University for revising our manuscript.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
1. Z. T. Ma, Z. X. Geng, Z. Y. Fan, J. Liu, and H. D. Chen, “Modulators for terahertz communication: the current state of the art,” Research 2019, 1–22 (2019). [CrossRef]
2. S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013). [CrossRef]
3. X. Q. Fan, Y. H. Li, S. H. Chen, Y. F. Xing, and T. S. Pan, “Mechanical terahertz modulation by skin-like ultrathin stretchable metasurface,” Small 16(37), 2002484 (2020). [CrossRef]
4. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef]
5. L. Wang, Y. X. Zhang, X. Q. Guo, T. Chen, H. J. Liang, X. L. Hao, X. Hou, W. Kou, Y. C. Zhao, T. C. Zhou, S. X. Liang, and Z. Q. Yang, “A review of THz modulators with dynamic tunable metasurfaces,” Nanomaterials 9(7), 965 (2019). [CrossRef]
6. Z. Vafapour, M. Dutta, and M. Stroscio, “Sensing, switching and modulating applications of a superconducting THz metamaterial,” IEEE Sens. J. 21(13), 15187–15195 (2021). [CrossRef]
7. C. H. Zhang, J. B. Wu, B. B. Jin, X. Q. Jia, L. Kang, W. W. Xu, H. B. Wang, J. Chen, M. Tonouchi, and P. H. Wu, “Tunable electromagnetically induced transparency from a superconducting terahertz metamaterial,” Appl. Phys. Lett. 110(24), 241105 (2017). [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. K. Lee, J. Son, J. Park, B. Kang, W. Jeon, F. Rotermund, and B. Min, “Linear frequency conversion via sudden merging of meta-atoms in time-variant metasurfaces,” Nat. Photonics 12(12), 765–773 (2018). [CrossRef]
10. X. Q. Su, C. M. Ouyang, N. N. Xu, S. Y. Tan, J. Q. Gu, Z. Tian, J. G. Han, F. P. Yan, and W. L. Zhang, “Broadband terahertz transparency in a switchable metasurface,” IEEE Photonics J. 7(1), 1–8 (2015). [CrossRef]
11. 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]
12. M. Z. Jiang, F. R. Hu, L. H. Zhang, B. G. Quan, W. L. Xu, H. T. Du, D. Xie, and Y. Chen, “Electrically triggered VO2 reconfigurable metasurface for amplitude and phase modulation of terahertz wave,” J. Lightwave Technol. 39(11), 3488–3494 (2021). [CrossRef]
13. P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016). [CrossRef]
14. E. Alvear-Cabezon, T. Taliercio, S. Blin, R. Smaali, F. Gonzalez-Posada, A. Baranov, R. Teissier, and E. Centeno, “Epsilon near-zero all-optical terahertz modulator,” Appl. Phys. Lett. 117(11), 111101 (2020). [CrossRef]
15. 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(1), 1151 (2012). [CrossRef]
16. M. T. Nouman, H. W. Kim, J. M. Woo, J. H. Hwang, D. Kim, and J. H. Jang, “Terahertz modulator based on metamaterials integrated with metal-semiconductor-metal varactors,” Sci. Rep. 6(1), 26452 (2016). [CrossRef]
17. Y. Zhang, S. Qiao, S. Liang, Z. Wu, Z. Yang, Z. Feng, H. Sun, Y. Zhou, L. Sun, Z. Chen, X. Zou, B. Zhang, J. Hu, S. Li, Q. Chen, L. Li, G. Xu, Y. Zhao, and S. Liu, “Gbps terahertz external modulator based on a composite metamaterial with a double-channel heterostructure,” Nano Lett. 15(5), 3501–3506 (2015). [CrossRef]
18. Y. C. Zhao, L. Wang, Y. X. Zhang, S. Qiao, S. X. Liang, T. C. Zhou, X. L. Zhang, X. Q. Guo, Z. H. Feng, F. Lan, Z. Chen, X. B. Yang, and Z. Q. Yang, “High-speed efficient terahertz modulation based on tunable collective-individual state conversion within an active 3 nm two-dimensional electron gas metasurface,” Nano Lett. 19(11), 7588–7597 (2019). [CrossRef]
19. J. Zhao, C. Ouyang, X. Chen, Y. Li, C. Zhang, L. Feng, B. Jin, J. Ma, Y. Liu, S. Zhang, Q. Xu, J. Han, and W. Zhang, “Temperature-controlled terahertz polarization conversion bandwidth,” Opt. Express 29(14), 21738–21748 (2021). [CrossRef]
20. M. Kim, S. Kim, and S. Kim, “Ultra-compact integrated terahertz modulator based on a graphene metasurface,” Opt. Lett. 46(3), 605–608 (2021). [CrossRef]
21. H. X. Zeng, H. J. Liang, Y. X. Zhang, L. Wang, S. X. Liang, S. Gong, Z. Li, Z. Q. Yang, X. L. Zhang, F. Lan, Z. H. Feng, Y. B. Gong, Z. Q. Yang, and D. M. Mittleman, “High-precision digital terahertz phase manipulation within a multichannel field perturbation coding chip,” Nat. Photonics 15(10), 751–757 (2021). [CrossRef]
22. R. Degl’Innocenti, D. S. Jessop, C. W. O. Sol, L. Xiao, S. J. Kindness, H. Lin, J. A. Zeitler, P. Braeuninger-Weimer, S. Hofmann, Y. Ren, V. S. Kamboj, J. P. Griffiths, H. E. Beere, and D. A. Ritchie, “Fast modulation of terahertz quantum cascade lasers using graphene loaded plasmonic antennas,” ACS Photonics 3(3), 464–470 (2016). [CrossRef]
23. D. S. Jessop, S. J. Kindness, L. Xiao, P. Braeuninger-Weimer, H. Lin, Y. Ren, C. X. Ren, S. Hofmann, J. A. Zeitler, H. E. Beere, D. A. Ritchie, and R. Degl’Innocenti, “Graphene based plasmonic terahertz amplitude modulator operating above 100 MHz,” Appl. Phys. Lett. 108(17), 171101 (2016). [CrossRef]
24. Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014). [CrossRef]
25. H. Zeng, S. Gong, L. Wang, T. Zhou, Y. Zhang, F. Lan, X. Cong, L. Wang, T. Song, Y. Zhao, Z. Yang, and D. Mittleman, “A review of terahertz phase modulation from free space to guided wave integrated devices,” Nanophotonics 11(3), 415–437 (2022). [CrossRef]
26. P. K. Singh and S. Sonkusale, “High speed terahertz modulator on the chip based on tunable terahertz slot waveguide,” Sci. Rep. 7(1), 40933 (2017). [CrossRef]
27. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]
28. Y. Z. Hu, M. Y. Tong, X. A. Cheng, J. Zhang, H. Hao, J. You, X. Zheng, and T. Jiang, “Bi2Se3-functionalized metasurfaces for ultrafast all-optical switching and efficient modulation of terahertz waves,” ACS Photonics 8(3), 771–780 (2021). [CrossRef]
29. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef]
30. S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018). [CrossRef]
31. C. Li, J. Wu, S. Jiang, R. Su, C. Zhang, C. Jiang, G. Zhou, B. Jin, L. Kang, W. Xu, J. Chen, and P. Wu, “Electrical dynamic modulation of THz radiation based on superconducting metamaterials,” Appl. Phys. Lett. 111(9), 092601 (2017). [CrossRef]
32. W. Cai, B. Xiao, J. Yu, and L. Xiao, “A compact graphene metamaterial based on electromagnetically induced transparency effect,” Opt. Commun. 475, 126266 (2020). [CrossRef]
33. B. Xiao, S. Tong, A. Fyffe, and Z. Shi, “Tunable electromagnetically induced transparency based on graphene metamaterials,” Opt. Express 28(3), 4048–4057 (2020). [CrossRef]
34. W. Wang, L. Du, J. Li, M. Hu, C. Sun, Y. Zhong, G. Zhao, Z. Li, L. G. Zhu, J. Yao, and F. Ling, “Active control of terahertz waves based on p-Si hybrid PIT metasurface device under avalanche breakdown,” Opt. Express 29(8), 12712–12722 (2021). [CrossRef]
35. L. Tao, Z. Chen, Z. Li, J. Wang, X. Xu, and J. Xu, “Enhancing light-matter interaction in 2D materials by optical micro/nano architectures for high-performance optoelectronic devices,” InfoMat 3(1), 36–60 (2021). [CrossRef]
36. Y. Hu, T. Jiang, J. Zhou, H. Hao, H. Sun, H. Ouyang, M. Tong, Y. Tang, H. Li, J. You, X. Zheng, Z. Xu, and X. Cheng, “Ultrafast terahertz transmission/group delay switching in photoactive WSe2-functionalized metaphotonic devices,” Nano Energy 68, 104280 (2020). [CrossRef]
37. D. Shrekenhamer, S. Rout, A. C. Strikwerda, C. Bingham, R. D. Averitt, S. Sonkusale, and W. J. Padilla, “High speed terahertz modulation from metamaterials with embedded high electron mobility transistors,” Opt. Express 19(10), 9968–9975 (2011). [CrossRef]
38. V. Parshin, E. Serov, G. Denisov, B. Garin, R. Denisyuk, V. V’Yuginov, V. Klevtsov, and N. Travin, “Silicon carbide for high-power applications at MM and THz ranges,” Diam. Relat. Mater 80, 1–4 (2017). [CrossRef]
39. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005). [CrossRef]
40. W. Tan, Y. Sun, Z.-G. Wang, and H. Chen, “Manipulating electromagnetic responses of metal wires at the deep subwavelength scale via both near- and far-field couplings,” Appl. Phys. Lett. 104(9), 091107 (2014). [CrossRef]
41. W. Tan, C. Zhang, C. Li, X. Zhou, X. Jia, Z. Feng, J. Su, and B. Jin, “Selective coherent perfect absorption of subradiant mode in ultrathin bi-layer metamaterials via antisymmetric excitation,” Appl. Phys. Lett. 110(18), 181111 (2017). [CrossRef]
42. 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]
43. C. Li, J. Wu, C. Zhang, W. Tan, B. Jin, L. Kang, W. Xu, J. Chen, and P. Wu, “Mode transition in cooperative metamaterials at terahertz frequencies,” J. Appl. Phys. 121(19), 193101 (2017). [CrossRef]
