Open Access
Add to BibSonomyAbstract
We propose a reconfigurable terahertz (THz) metamaterial that can control the transmittance by out-of-plane actuation with changing the sub-micron gap distance between electrically coupled metamaterial elements. By using the out-of-plane actuation, it was possible to avoid contact between the coupled metamaterial elements across the small initial gap during the adjustment of the gap size. THz spectroscopy was performed during actuation, and the transmission dip frequency was confirmed to be tunable from 0.82 to 0.92 THz for one linear polarization state and from 0.80 to 0.91 THz for the other linear polarization; the two polarizations were orthogonal. The proposed approach will contribute to the development of tunable metamaterials based on structural deformations.
© 2015 Optical Society of America
1. Introduction
Tunable metamaterials are one candidate for active optical components, particularly in the terahertz (THz) range, for which the variety of optical components is lacking. There are two typical metamaterial tuning methods: structural deformations [1–17 ] and tuning the properties of the surrounding material through external stimulation, such as light [18–21 ] and voltage [22–24 ]. Structural deformation methods achieved many kinds of functions, such as transmittance dip frequency modulating [7–16 ], intensity modulating [1,17 ] circular polarization modulating [2], multifunctional modulating [3], polarization sensitive [4] or insensitive [5], and wide range transmittance modulating [6], and so on. Recently, many studies have used structural deformation methods because of their potential for obtaining a large change in the transmittance property. In these studies, structural deformation was demonstrated by changing the configuration [1–13 ] or geometrical arrangements [14–17 ] of the metamaterial elements. C. Lee et al. changed the configuration of the metamaterial elements by controlling the gap size between a part of the element and the substrate using out-of-plane deformation [3,5,8,10 ]. A. Q. Liu et al. changed the geometrical arrangements of metamaterial elements by controlling the gap size between the elements using in-plane deformation [12,14 ]. For such deformations, smaller gap sizes between the movable and fixed elements are known to yield larger transmittance property changes [12,14 ]. In the THz range, strong electron coupling is induced at a sub-micron gap size because a sub-micron size is less than one-hundredth of the wavelength of THz light. Although such sub-micron size is able to be constructed using conventional semiconductor processes, previous studies have had difficulty in taking advantage of sub-micron gaps with smooth structural motion due to the following reason: it is difficult to simultaneously realize both a micron deformation and the sub-micron gap. That is, it is difficult to avoid contact between the movable and fixed elements if a narrow separation gap is located in the moving direction of the element [1].
In this paper, we propose a reconfigurable metamaterial whose small gap distance can be controlled without contact between the metamaterial elements. A unit of the proposed metamaterial consists of two closely patterned split-ring resonators (SRRs), which are typical metamaterial elements. We patterned one SRR on a movable MEMS (micro-electro-mechanical-systems) cantilever and the other SRR on a fixed membrane [Fig. 1(a-i) ]. These closely positioned SRRs induce an electrical-coupling effect [25,26 ] that changes the resonant frequency depending on the size of the gap. To enable smooth structural motion, the spring constant for the cantilever was designed to be considerably smaller in the out-of-plane direction (kz) than the spring constant in the in-plane direction (ky). This design forces the SRR to only move away from its initial narrow gap position [Fig. 1(a-ii)]. Therefore, we could design the minimum gap to be as small as possible without contact occurring.
Fig. 1 (a) Schematics of the configuration of the proposed metamaterial unit. An SRR is fixed to a cantilever, which can only move out-of-plane relative to the substrate. (b) An SEM image of the fabricated metamaterial and a schematic of the pneumatic actuation system. (c) The fabricated metamaterial unit (c-i) without and (c-ii) with the applied pneumatic force.
There have been similar out-of-plane deformation approaches that used, for example, the Lorentz force [27] or thermal force [28]. Instead of these forces, we employed a pneumatic force, which can generate a larger force than the electric force, magnetic force, and so on. Therefore, the pneumatic force is one of the promising candidates for the out-of-plane deformation of reconfigurable metamaterials for the THz range [Figs. 1(a)].
2. Device design
The proposed metamaterial unit consists of two SRRs with a designed gap of 0.2 μm. Figure 1(b-i) presents a scanning electron microscope (SEM) image of the fabricated metamaterial. The metamaterial units were arrayed on a 290-nm-thick Si diaphragm with an area of 10 mm × 10 mm. We actuated the metamaterial units by establishing a pressure differential between the upper and lower cantilever surfaces via the pneumatic force. The fabricated metamaterial was fixed to an air chamber to transmit pneumatic force to the metamaterial from the lower side of the cantilever, as shown in Fig. 1(b-ii), in which the hollow cavity in the chamber is covered by the metamaterial chip. Figures 1(c-i) and (c-ii) show the fabricated metamaterial unit without and with an applied pneumatic force, respectively. Applying a pneumatic force bends the cantilever and varies the gap between the SRRs from 0.2 μm to several microns.
Figure 2(a) shows the detailed design of the fabricated metamaterial unit. One SRR was formed on a membrane that did not deform, and the other SRR was formed on a 290-nm-thick cantilever with a zigzag support beam structure at its root to make it flexible in the out-of-plane direction. The width of the zigzag beam was 3 μm. Structural numerical simulations yielded spring constants for the designed cantilever of 9.75 × 10−3 and 3.94 N/m in the out-of-plane (kz) and in-plane (ky) directions, respectively. This approximately 400-fold difference in spring constants between kz and ky forced the cantilever to move only in the out-of-plane direction. Each SRR was a 40-μm × 40-μm square, and the width of the ring arm was 5 μm. The length of the split for each single SRR was 5 μm. The initial gap between the SRRs was 0.2 μm, which is approximately one-thousandth the wavelength of THz light. The pitches for the units in the longer and shorter directions were 107 and 60 μm, respectively. We designed the interspace distance between the cantilever and the fixed membrane to be approximately 1 μm to suppress leakage of the applied pneumatic force from the interspace such that the pressure differential between the upper and lower cantilever surfaces could be maintained. The structure was fabricated from a silicon-on-insulator wafer, which was composed of a 290-nm-thick device layer, a 400-nm-thick buried oxide (BOX) layer, and a 250-μm-thick handling layer. During the first fabrication step, the SRRs, which consisted of 45-nm-thick Au, were patterned using electron beam lithography and a lift-off process to obtain 200-nm gaps. The Si cantilever shapes were patterned using two subsequent electron beam lithography processes and deep reactive-ion etching (DRIE). Then, the handling layer was etched from the backside of the wafer with DRIE. The etching of the wafer was stopped at the place where the BOX layer existed because the BOX layer was worked as an etch stop layer for the DRIE. Finally, the BOX layers were etched using a vapor hydrogen fluoride (HF) etching to form free-standing cantilevers.
Fig. 2 (a) Design for SRRs fixed to the cantilever and membrane. (b) Pneumatic actuation setup. (c) Relation between the applied pressure and displacement. (d) The cantilevers smoothly moving without contacting with the fixed membrane. (d-i) Without applied pneumatic force. (d-ii) With applied pneumatic force (see Visualization 1).
3. Pneumatic actuation
The setup for actuating the fabricated metamaterial using a pneumatic force is shown in Fig. 2(b). The source of the pneumatic force was high-pressure nitrogen gas. The nitrogen gas was supplied to a Pneumatic PicoPump (PV830, World Precision Instruments Inc., USA) to control the pressure. The controlled pneumatic force was applied to the air chamber through a silicone tube. A pressure sensor (AP-C30, Keyence, Japan) was placed in the middle of the silicone tube to monitor the pneumatic force. The bottom of the air chamber was constructed from a 3-mm-thick THz window (Zeonex 480R, Nihon Zeon, Japan).
To evaluate the actuation property of the fabricated metamaterial, we measured the relation between the cantilever tip displacement and the applied pressure using a three-dimensional laser profiler [Fig. 2(c)]. A pneumatic force of zero yielded a gap size of 0.24 μm, whereas applying a pneumatic force bent the cantilever and increased the gap size. Although the initial interspace between the cantilever and the fixed membrane was designed to be sufficiently narrow to prevent nitrogen leakage, it was difficult to maintain a stable pressure differential of greater than 1 kPa between the upper and lower cantilever surfaces because of air leakage from the enlarged interspace between the cantilever and fixed membrane as the deformation increased. When a pneumatic force of over 1 kPa was applied, vibration of the cantilevers occurred. Therefore, we used less than 1 kPa for the stable deformation ranging from 0.24 to 5.44 μm without vibration. This controllable gap range corresponded to approximately 10% of the length of the movable cantilever. A movie that is attached as a supplementary shows the cantilevers smoothly moving in the out-of-plane direction with respect to the device surface without contacting with the fixed membrane [Fig. 2(d)].
4. Transmittance properties
The transmittance of the fabricated metamaterial was investigated using THz time-domain spectroscopy (THz-TDS) [29]. Figure 3(a) shows the transmission spectra normalized to the transmittance of the THz window of the air chamber, which had a transmittance of greater than 0.8 across the range from 0.3 to 1.7 THz. As shown in the inset of each graph, the measurements were performed for two mutually orthogonal polarization directions of the incident THz light [Figs. 3(a-i) and Fig.3 (a-ii)]. The transmittances were referred to as Txx and Tyy. Every spectrum exhibited a signature resonance (local minimum) of approximately 0.8-0.9 THz, and the resonant frequency increased as the gap size increased. These results indicate that the transmittance of the fabricated metamaterial was controllable by changing the gap using the pneumatic force. The resonant frequencies of the dips are plotted in Fig. 3(b). The frequencies for the 0.24- and 5.44-μm gaps shifted from 0.82 to 0.92 THz for Txx and from 0.80 to 0.91 THz for Tyy. These results demonstrate that small structural deformations in the fabricated metamaterial significantly changed the transmission property. Specifically, the deformation size of the gap, which was approximately 5 μm, corresponded to 12% of the typical size of a single SRR.
Fig. 3 (a) Transmittance spectra of the fabricated metamaterial. (b) Relation between the gap and resonant frequency.
To validate the experimental results of the tuning of the transmittance via the coupling of two close SRRs, we performed simulations using commercial finite element method (FEM) simulation software (COMSOL Multiphysics ver. 4.4, USA). A simulation model was designed as SRRs floating in the air, thus excluding the 290-nm-thick Si membrane. The SRRs were configured as follows: one SRR was lying on a horizontal plane, and the other was tilted around the x-axis, as shown in Fig. 4(c) , similar to the actual fabricated metamaterial. The gap in this simulation was determined based on the tilting angle. The conductivity of Au, which was used to construct the SRRs, was defined as 45.6 × 106 S/m. Figures 4(a-i) and (a-ii) present the simulated transmittance spectra. Two orthogonally different polarization directions for the incident light, which corresponded to the polarization directions in the experimental section, were introduced to the device and are described in the insets in Figs. 4(a-i) and (a-ii). Each spectrum had one transmission dip that shifted with the gap change, which agreed well with the experimental spectra. Compared with the experimental spectra, every resonant frequency was greater than the frequency in the corresponding experimental data by approximately 0.1 THz. This difference can be attributed to the Si substrate on which the actual SRRs were fixed and that was excluded in the simulation. The contribution of the Si substrate and air to this difference were estimated to be 0.13 and 0.87, respectively, by using the model function described in reference [30]. This result indicated that a contribution of the negligible thin Si substrate ( = 290 nm) was larger than that estimated only from the volume of the substrate.
Fig. 4 (a) Simulated transmittance spectra for the proposed metamaterial using SRRs floating in air. (b) Current distributions for a 0.2-μm-gap at the resonant frequency for Txx (i) and Tyy (ii). (c) A schematic figure of a view area of the (d) electric field distributions for the 0.2-μm (α = 0° (i)), 0.7-μm (α = 1° (ii)), and 1.4-μm (α = 2° (iii)) gaps at the resonant frequencies. (e) Enlarged images of the electric field distributions.
To investigate the cause of the transmission dip, we visualized the induced current for a 0.2-μm gap at the Txx and Tyy dip frequencies of 0.99 and 0.98 THz, respectively. The black arrows in Figs. 4(b-i) and 4(b-ii) represent the current direction, and the local distribution is indicated by the red cones. The current distribution for both Txx and Tyy confirmed that the transmission dip was induced by a circular current, which was attributed to the LC resonance. The asymmetric structure of the proposed metamaterial units, with respect to not only the x-axis but also the y-axis, contributed the induction of LC resonance not only for Txx but also for Tyy. The current direction indicates that opposite charges gathered between the start and end points of the black arrows for the left and right SRRs, respectively. This charge collection generated an electric field between the SRRs. The electric field indicated that capacitive coupling was induced at small gap sizes. To observe the dependence of the electric field amplitude on the gap size, we visualized the electric field distributions around the gaps between the SRRs, as shown in Fig. 4(c). We focused on electric field distributions of the proposed metamaterial only for x-polarized because those for x-polarized and y-polarized THz light were almost identical, as shown in Figs. 4(b-i) and (b-ii). Figures 4(d) and (e) show the electric field distributions on the yz plane located at the center of the SRRs at the resonant frequency for each gap size. The background color and the white arrows indicate the amplitude and the direction of the electric field, respectively. The lengths of the arrows in each figure were normalized. Figure 4(d-i), which corresponds to the 0.2-μm gap, shows that the electric field direction was circular and was centered at the gap. Additionally, the enlarged views in Fig. 4(e-i) confirm that a strong electric field was induced at the edge of the SRR that faced the gap. The maximum amplitude of this electric field was estimated to be approximately 400 times greater than that of the incident light. The amplitude of the electric field drastically decreased as the gap size was increased. For example, the maximum electric field amplitude of the 0.7-μm gap [Fig. 4(e-ii)] was one-third the electric field of the 0.2-μm gap [Fig. 4(e-i)]. For the 1.4-μm gap, the electric field amplitude was further decreased, as shown in Fig. 4(e-iii). This difference in the electric field caused changes in the coupling effect between the SRRs, which led to the spectral change observed in Fig. 4(a).
We have experimentally confirmed that changing the submicron gap enabled a large variation in the resonant frequency change. The proposed concept indicates that wider tuning range can be achieved if the initial gap is less than 200 nm, which is a potential advantage of this concept. To confirm this advantage of our concept for narrow gaps, we added simulations with 0.05-, 0.1-, 0.4- and 1.6-μm initial gaps using a simulation model, as shown in Figs. 5(a) . The simulations were performed (a-i) for the non-tilted SRRs, i.e., α = 0°, and for (a-ii) the 8°-tilted SRR, i.e., α = 8°. Figure 5(b) shows the relation between the initial gaps and resonant frequencies, including the result for the 0.2-μm initial gap, which was calculated in Fig. 4(a). It was confirmed that the resonant frequencies for the 8°-tilted SRR were almost independent of the initial gaps. This is because that the initial gaps were so small compared to the gap size between the fixed SRR and the tilted SRR. On the other hand, the resonant frequencies for non-tilted SRRs decreased as the initial gap decreased. In Fig. 4(c), we plotted the resonant frequencies as a function of tilting angle α. These simulated results confirm that a smaller initial gap yields a wider tuning range of the transmittance property changes because a smaller initial gap results in a decrease in the limit of the tunable resonant frequency range. In this paper, we designed the initial gap of the fabricated metamaterial to be 0.2 μm to achieve a stable and reproducible fabrication process. The fabricated metamaterial has the potential to achieve a large transmittance change through a slight structural change, provided that a finer fabrication process is adopted.
Fig. 5 (a) A schematic of the simulation model (a) for α = 0° and (b) for α = 8°. (b) The simulated relation between the initial gaps and resonant frequencies. (c) Correlation between the angle α and resonant frequency.
5. Conclusions
In conclusion, we achieved a tunable THz metamaterial with a controllable gap between SRRs that ranged from 0.24 to 5.44 μm. A pneumatic force was applied to generate a pressure differential between the upper and lower surfaces of the 290-nm-thick cantilever to which the SRR was fixed, and this force was used to control the size of the gap. The transmission properties measured using THz-TDS confirmed that the frequency at the transmission dip for the fabricated metamaterial was controllable from 0.82 to 0.92 THz for x-polarized light and from 0.80 to 0.91 THz for y-polarized light. The FEM simulations indicated that the transmission dip was induced by an LC resonance with a circular current. A slight deformation of as small as 12% of the size of a single SRR yielded an approximately 10% shift in the resonant frequency. Because the proposed design permits exploitation of an initial gap narrower than 0.24 μm without any contact between the structures by taking advantage of the finer fabrication MEMS process, it will contribute to the development of tunable filters that work across a wide frequency range using structurally tunable metamaterials.
Acknowledgments
The photolithography masks were fabricated using an electron-beam (EB) lithography apparatus (F5112 + VD01) donated by the Advantest Corporation at the VLSI Design and Education Center (VDEC) of the University of Tokyo. This work was supported by JSPS KAKENHI (15K17452). This work was also partially supported by the Murata Science Foundation. The measurements of THz transmittance properties were supported by Prof. Makoto Kuwata-Gonokami, Dr. Hiroharu Tamaru, Dr. Kuniaki Konishi, Dr. Natsuki Kanda, and Mr. Natsuki Nemoto. We also greatly appreciate discussions with these individuals regarding the data obtained from these measurements.
References and links
1. Z. Han, K. Kohno, H. Fujita, K. Hirakawa, and H. Toshiyoshi, “MEMS reconfigurable metamaterial for terahertz switchable filter and modulator,” Opt. Express 22(18), 21326–21339 (2014). [CrossRef] [PubMed]
2. T. Kan, A. Isozaki, N. Kanda, N. Nemoto, K. Konishi, M. Kuwata-Gonokami, K. Matsumoto, and I. Shimoyama, “Spiral metamaterial for active tuning of optical activity,” Appl. Phys. Lett. 102(22), 221906 (2013). [CrossRef]
3. P. Pitchappa, C. P. Ho, L. Dhakar, and C. Lee, “Microelectromechanically reconfigurable interpixelated metamaterial for independent tuning of multiple resonances at terahertz spectral region,” Optica 2(6), 571–578 (2015). [CrossRef]
4. F. Ma, Y. Qian, Y.-S. Lin, H. Liu, X. Zhang, Z. Liu, J. M. L. Tsai, and C. Lee, “Polarization-sensitive microelectromechanical systems based tunable terahertz metamaterials using three dimensional electric split-ring resonator arrays,” Appl. Phys. Lett. 102(16), 161912 (2013). [CrossRef]
5. P. Pitchappa, C. P. Ho, Y. Qian, L. Dhakar, N. Singh, and C. Lee, “Microelectromechanically tunable multiband metamaterial with preserved isotropy,” Sci. Rep. 5, 11678 (2015). [CrossRef] [PubMed]
6. M. Unlu, M. R. Hashemi, C. W. Berry, S. Li, S. H. Yang, and M. Jarrahi, “Switchable scattering meta-surfaces for broadband terahertz modulation,” Sci. Rep. 4, 5708 (2014). [CrossRef] [PubMed]
7. W. M. Zhu, A. Q. Liu, X. M. Zhang, D. P. Tsai, T. Bourouina, J. H. Teng, X. H. Zhang, H. C. Guo, H. Tanoto, T. Mei, G. Q. Lo, and D. L. Kwong, “Switchable magnetic metamaterials using micromachining processes,” Adv. Mater. 23(15), 1792–1796 (2011). [CrossRef] [PubMed]
8. C. P. Ho, P. Pitchappa, Y.-S. Lin, C.-Y. Huang, P. Kropelnicki, and C. Lee, “Electrothermally actuated microelectromechanical systems based omega-ring terahertz metamaterial with polarization dependent characteristics,” Appl. Phys. Lett. 104(16), 161104 (2014). [CrossRef]
9. P. Pitchappa, C. Pei Ho, Y.-S. Lin, P. Kropelnicki, C.-Y. Huang, N. Singh, and C. Lee, “Micro-electro-mechanically tunable metamaterial with enhanced electro-optic performance,” Appl. Phys. Lett. 104(15), 151104 (2014). [CrossRef]
10. P. Pitchappa, C. P. Ho, L. Dhakar, Y. Qian, N. Singh, and C. Lee, “Periodic array of subwavelength MEMS cantilevers for dynamic manipulation of terahertz waves,” J. Microelectromech. Syst. Lett. 24(3), 525–527 (2015). [CrossRef]
11. A. Lalas, N. Kantartzis, and T. Tsiboukis, “Tunable terahertz metamaterials by means of piezoelectric MEMS actuators,” Europhys. Lett. 107(5), 58004 (2014). [CrossRef]
12. W. M. Zhu, A. Q. Liu, T. Bourouina, D. P. Tsai, J. H. Teng, X. H. Zhang, G. Q. Lo, D. L. Kwong, and N. I. Zheludev, “Microelectromechanical Maltese-cross metamaterial with tunable terahertz anisotropy,” Nat. Commun. 3, 1274 (2012). [CrossRef] [PubMed]
13. Y.-S. Lin and C. Lee, “Tuning characteristics of mirrorlike T-shape terahertz metamaterial using out-of-plane actuated cantilevers,” Appl. Phys. Lett. 104(25), 251914 (2014). [CrossRef]
14. Y. H. Fu, A. Q. Liu, W. M. Zhu, X. M. Zhang, D. P. Tsai, J. B. Zhang, T. Mei, J. F. Tao, H. C. Guo, X. H. Zhang, J. H. Teng, N. I. Zheludev, G. Q. Lo, and D. L. Kwong, “A micromachined reconfigurable metamaterial via reconfiguration of asymmetric split-ring resonators,” Adv. Funct. Mater. 21(18), 3589–3594 (2011). [CrossRef]
15. W. Zhang, A. Q. Liu, W. M. Zhu, E. P. Li, H. Tanoto, Q. Y. Wu, J. H. Teng, X. H. Zhang, M. L. J. Tsai, G. Q. Lo, and D. L. Kwong, “Micromachined switchable metamaterial with dual resonance,” Appl. Phys. Lett. 101(15), 151902 (2012). [CrossRef]
16. W. M. Zhu, A. Q. Liu, W. Zhang, J. F. Tao, T. Bourouina, J. H. Teng, X. H. Zhang, Q. Y. Wu, H. Tanoto, H. C. Guo, G. Q. Lo, and D. L. Kwong, “Polarization dependent state to polarization independent state change in THz metamaterials,” Appl. Phys. Lett. 99(22), 221102 (2011). [CrossRef]
17. H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “MEMS Based Structurally Tunable Metamaterials at Terahertz Frequencies,” J. Infrared Millim. Terahertz Waves 32(5), 580–595 (2011). [CrossRef]
18. N. Kanda, K. Konishi, and M. Kuwata-Gonokami, “Dynamics of photo-induced terahertz optical activity in metal chiral gratings,” Opt. Lett. 37(17), 3510–3512 (2012). [CrossRef] [PubMed]
19. J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012). [CrossRef] [PubMed]
20. H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008). [CrossRef]
21. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006). [CrossRef] [PubMed]
22. 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] [PubMed]
23. W. L. Chan, H. T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 213511 (2009). [CrossRef]
24. O. Paul, C. Imhof, B. Lägel, S. Wolff, J. Heinrich, S. Höfling, A. Forchel, R. Zengerle, R. Beigang, and M. Rahm, “Polarization-independent active metamaterial for high-frequency terahertz modulation,” Opt. Express 17(2), 819–827 (2009). [CrossRef] [PubMed]
25. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010). [CrossRef] [PubMed]
26. E. Tatartschuk, N. Gneiding, F. Hesmer, A. Radkovskaya, and E. Shamonina, “Mapping inter-element coupling in metamaterials: Scaling down to infrared,” J. Appl. Phys. 111(9), 094904 (2012). [CrossRef]
27. J. Valente, J.-Y. Ou, E. Plum, I. J. Youngs, and N. I. Zheludev, “A magneto-electro-optical effect in a plasmonic nanowire material,” Nat. Commun. 6, 7021 (2015). [CrossRef] [PubMed]
28. J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11(5), 2142–2144 (2011). [CrossRef] [PubMed]
29. K. E. Peiponen, A. Zeitler, and M. Kuwata-Gonokami, Terahertz Spectroscopy and Imaging (Springer Berlin Heidelberg, 2012).
30. D. J. Park, S. J. Park, I. Park, and Y. H. Ahn, “Dielectric substrate effect on the metamaterial resonances in terahertz frequency range,” Curr. Appl. Phys. 14(4), 570–574 (2014). [CrossRef]
