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We present terahertz (THz) transmission control by several uniquely designed patterns of nano-slot antenna array. Collinearly aligned slot antenna arrays have been usually applied to THz filters with frequency band tunability by their geometry. Normally the amplitude in transmission (reflection) in the collinear alignment case can be varied via rotating the azimuthal angle with a sinusoidal trend, which can limit their utilization and performance only at fixed angle between the alignment of the resonant antennas and incident beam polarization. To pursue a variety of metamaterial uses, here, we present polarization-independent THz filters using variously aligned antenna array (asterisk, chlorophyll, and honeycomb patterns) in such counter-intuitive aspects. Besides, unprecedented multi resonance behaviors were observed in chlorophyll and honeycomb patterns, which can be explained with interferences by adjacent structures. The measured spectra were analyzed by harmonic oscillator model with simplified coupling between slots and their adjacent.
© 2017 Optical Society of America
1. Introduction
Terahertz (THz) electromagnetic wave has attracted great attention in many applications including spectroscopy and imaging for chemical and biomedical sensing purposes, since it can convey vast information on optical properties of target analytes over a broad spectrum. The most representative advantage using THz electromagnetic wave (with its typical photon energy of few meV) can be attributed to its non-ionizing and non-destructive features [1–3]. Considering that interesting spectral features of many bio- and chemical-molecules are observed in the broad THz band such as intra- and inter-molecular vibrational modes, THz wave is a proper choice for sensing purposes in those applications [4–9]. Earlier works on the THz based sensing techniques, therefore, made their effort to improve THz device performance in term of frequency tuning and transmission/reflection control. Antenna structures can be a good candidate for enhancement and localization of the THz field, allowing the field control over the resonance characteristics [10]. For high performance, THz antenna consists of subwavelength structures on the order of λ/10 - λ/10,000, with one to three orders of magnitude enhancement [11,12]. THz antenna based metamaterials can be applied for variable THz filters using insulator-to-metal phase transition [13, 14], boosting a nonlinear optical process [15], and sensing of extremely small amount of chemical compounds using absorption cross-section increment [16–18]. Design of THz metamaterial and alignment of antenna structures have been still of interest in improving their performances. Bandwidth was controlled in various ways such as composition of several geometries providing multi-resonance [19–23]. And rotation symmetric structures were applied to suppress the change of transmission/reflection [24–30]. In most of the antenna based THz metamaterials, the antennas are aligned collinearly to maximize the transmission (reflection) efficiency, because polarization responses of elementary slots are quite different between vertical and horizontal directions [31–35]. In particular, for the purpose of molecular sensing, the rotation dependence of the metamaterial based sensor on the polarization of the incident THz waves can be issued with unexpected decreasing of efficiency in experiment. The polarization angle mismatch between the incident wave and the most efficient orientation of the sample could make a variation in signal intensity. Normally this variation can be modified by rotating the sample itself, however, it is hardly applicable to directly attached samples such as thin film. The rotation-free metamaterial can be easily applied to any type of sample, without unnecessarily repeated detaching and attaching the sample onto the metamaterials.
Here, we report several types of rotation-free patterns of nano-slot antenna array improving performance of THz metamaterials. Conventional collinearly patterned antennas and three kinds of rotation-free antennas inspired by asterisk, honeycomb and chlorophyll shapes from nature were fabricated and the THz transmission behaviors through those samples were compared. Unlike collinear and asterisk-shape cases having single sharp resonance based on an elementary slot, honeycomb- and chlorophyll-shape cases show not only a fundamental resonance related to the elementary slot, but also a secondary resonance by slot-to-slot coupling. To understand measured spectral features, a coupled harmonic oscillator model was introduced. The spectral changes depending on coupling strength were calculated using the coupled harmonic oscillator model and fitting parameters were extracted from the transmission spectra.
2. Design and experiment
2.1 Nano-slot antenna design
We designed nano-slot antennas in collinear and three different shapes patterned alignments as shown in Fig. 1(a). The suggested antennas are composed of nano-slot antenna structures fabricated onto a thin gold film (150 nm in thickness) on a high resistivity Si substrate (500 μm in thickness, 20,000 Ωcm in resistivity). Each elementary nano-slot antenna has a length of 64 μm and a width of 500 nm with a resonance at 0.92 THz, determined by the relation fres = c/(2neffL), where neff is an effective refractive index of the substrate and L is a length of the slot antenna [10]. The collinearly patterned antenna array is composed of unidirectional slots with a period of 80 μm in y direction, and a period of 56.5 μm in the x direction. Also, honeycomb-, asterisk- and chlorophyll- shape patterned arrays have the same elementary nano-slot antenna designed for a resonance at 0.92 THz. The asterisk-shape patterned array is made of slots with rotation symmetry. The honeycomb-shape patterned array has continuous hexagonal patterns consisted of three slots which are periodically rotated with angles; 0, 120, and 240 degree, respectively. The chlorophyll-shape patterned array is designed to mimic a molecular structure of green pigments related to photosynthesis because the molecular structure except the side chain has rotation symmetry.
Fig. 1 (a) Various types of THz filters for rotation-free performance. Optical microscopic images of nano-slot antenna array fabricated in collinear alignment, asterisk-, honeycomb-, and chlorophyll-shape alignments onto thin gold films. (b) Experimental setup for THz transmission measurements on samples with azimuthal rotation angle dependence is described.
2.2 Experimental setup
THz-time domain spectroscopy (TDS) system was used to obtain transmittance through various shape patterned slot antenna array samples at 0.2-2.0 THz frequency range. A schematic of measurement system is shown in Fig. 1(b). In the experiment, a Ti:sapphire pulsed laser which has 800 nm center wavelength, 100 fs pulse duration, and 80 MHz repetition rate was used to drive the THz-TDS system. The laser beam was split into two parts: a strong pump beam and a weak reference beam. Photoconductive antenna was driven by the pump beam to generate a THz wave, then a collimated THz wave by off-axis parabolic mirrors was normally irradiated onto a nano-slot antenna with a focus size (0.9 mm) by polymethylpentene (TPX) lens. Then, the THz wave passing through the nano-slot antenna was detected by electro-optic sampling using ZnTe crystal leading high signal-to-ratio up to 10,000:1. THz polarization was linear and horizontally fixed. The system was placed in a closed box with relative humidity of less than 1% to reduce absorption by water vapor.
2.3 Results and discussion
THz transmission spectra through various types of nano-slot antennas are shown in Fig. 2. Basically, all patterns consist of identical slot antennas implying the same fundamental resonance. In the collinear alignment, the nano-slot antenna shows a transmission maximum at 0.92 THz and the transmittance decreases according to the incident azimuthal angle, ϕ, between the direction of the long axis of the slot antenna and the polarization of the incident THz waves (Fig. 2(a)). It can be explained according to the Malus’ law, T(ϕ) = T(0)cos2ϕ. Here, the transmittance can be defined as, , where Esample and Eref are transmitted electric fields through the nano-slot antenna and a bare Si substrate, respectively [25].
Fig. 2 (a-d) Transmission spectra for nano-slot antenna arrays with respect to azimuthal rotation angle. The different absolute values of transmittance are owing to different opening coverage. The collinearly aligned antenna array shows that transmittance decreases by the rotation angle, however, other patterns are rotation-free as shown in (e). The transmission efficiency can be considered with the field enhancement factor for each sample as shown in (f). Red axis on left side is for collinear pattern, and green axis on right side is for rotation-free patterns.
However, interestingly, the measured transmission spectra for asterisk-, honeycomb- and chlorophyll-shape patterned arrays do not have such strong rotation dependence as shown in Fig. 2(b-d). Normalized spectra in transmittance for four patterns are plotted in terms of the incident angle between 0 and 90 degree, which show clear different behaviors in Fig. 2(e). Except the collinear pattern, three nano-slot antennas show excellent rotation-free performances with the standard deviation less than 0.02. To evaluate the efficiency of the individual nano-slot antennas, as an excellent THz filter, the transmission enhancement factor can be also considered in Fig. 2(f). The transmission enhancement factor is determined by the relation as, Enhancement factor = Tmax/β, and β = Aslot/Aaperture, where Aslot and Aaperture are coverage area of slots and aperture area of the sample holder (here it is 1.6x1.6 mm2) [17]. The field enhancement for the collinear patterned array is the highest among four samples where the polarization is perpendicular to the long axis, however it is drastically decreasing according to the incident azimuthal angle as mentioned above. Meanwhile three other shape patterned arrays have similar values regardless of the azimuthal angle. Especially, honeycomb has relatively higher enhancement factor keeping same value in terms of the incident angle. It can be inferred that there is a tradeoff between the enhancement factor and the rotation angle independence.
On the other hand, it is also noted that there are additional resonance peaks in the spectra at the lower frequency regime in addition to the fundamental resonance frequency for rotation-free patterns: 0.71 THz for the honeycomb pattern and 0.76 THz for the chlorophyll pattern, respectively. The origin of sub-resonance peaks near 0.7~0.75 THz can be deduced from the spectral change due to the near-field coupling by placing elementary resonators closer [21, 36, 37]. These unique spectral features can be interpreted using a coupled harmonic oscillator model, to get more details of spectral characteristics and origin of multi resonance behaviors.
3. Modeling for dual resonance
To understand the measured transmission, both the fundamental resonance of the elementary slots and coupled resonances with neighbor slots should be considered. Each slot antenna can be treated as a single harmonic oscillator with a resonance frequency, ω0, and a damping rate, γ. The coupling strength is determined by the coupling coefficient, g. Three harmonic oscillators consist of one independent oscillator and two coupled oscillators, are then excited by the incident THz field with an efficiency, αi (i = 1, 2 and 3). The coupling with neighbor slots has an excitation efficiency, α1. Assuming that the independent oscillator, α3 and one of the coupled oscillator, α1 have an equivalent excitation efficiency, depicting the fundamental resonance, the equation of motion can be described as following:
, where xi = Xi e-iωt for each harmonic oscillator and the incident THz field amplitude is E. The set of equation of motion can be simplified using a matrix form as the following:,where ci = (ωi2-ω2)-iγiω. The THz transmission through the subwavelength slots is attributed to the re-radiation of the resonance mode with the efficiency proportional to the second derivative of the displacement of the harmonic oscillator. In the far-field regime, the transmission can be then measured as sum of individual transmissions at each resonance mode [37].We applied Eq. (3) to describe the measured transmittance spectra for various types of nano-slot antenna arrays by fitting.The fitted spectra (light blue in Fig. 3) are in excellent agreement with the measured data set. In the collinear patterned array, the maximum transmittance in Fig. 3(a) at the azimuthal angle 0° was analyzed with single harmonic oscillator. The list of extracted parameters are in Table 1. The excitation efficiencies α1, and α2, and the coupling coefficient, g, can be negligible in the single harmonic oscillator model, especially for collinear and asterisk-shape patterns in Fig. 3(a-b). In other cases, however, the excitation efficiencies α1, α2 and α3 depend on the pattern types because nano-slot antennas have different transmission efficiencies. Especially, for honeycomb- in Fig. 3(c) and chlorophyll-patterns in Fig. 3(d), two excitation efficiencies, α1 and α2, were extracted from the model. Because the red shift of the secondary resonance is affected by the coupling strength, the honeycomb-shape patterned array has the higher coupling constant of g = 13.1 than the chlorophyll-shape patterned array (g = 10.5). From this, it can be inferred that the coupling coefficient is related to the separation of slots between neighbors in a pattern geometry [19]. Further studies about coupling constants with systematically changed parameters will give more insight on spectral characteristics and frequency tunability of designed filters for THz waves.
Fig. 3 Transmission spectra with fitting curves. (a, b) The spectra for the collinearly aligned array and asterisk-shape patterned array fitted with a single harmonic oscillator show a single fundamental resonance near 0.9 THz corresponding to their length of the slot antenna and effective refractive index. (c, d) The spectra for the honeycomb- and the chlorophyll-shape patterned antenna array fitted with a coupled harmonic oscillator model have two resonances, near 0.9 THz as a fundamental resonance and near 0.7 THz as a coupled resonance.
Table 1. Extracted parameters for fitted transmission spectra in Fig. 3.
For investigating spectral changes by resonance couplings, we calculated transmission spectra depending on the coupling strength with a coupled harmonic oscillator model, as introduced above. The calculated transmission spectra for the honeycomb-shape in Fig. 4(a) and the chlorophyll-shape in Fig. 4(b) represent similar behaviors in spectrum, but different amplitudes due to their different transmission efficiency. If each single nano-slot antennas are sufficiently separated, the coupling coefficient, g, approaches to zero, and thus the transmission has only the single fundamental resonance, as shown in the spectra for the collinear and the asterisk cases. As the coupling becomes stronger, single resonance spectrum gets split and turns into the dual resonance form as appeared in experimental results for honeycomb and chlorophyll cases. The resonances are slightly redshifted from the fundamental resonance frequencies, while transmission amplitudes are decreasing, until clear resonance peak separations at g = 6.1 for honeycomb and g = 7 for chlorophyll cases, respectively, are appeared. When the resonance peak separation comes up, the primary resonance is slightly blue-shifted to recover the fundamental resonance, meanwhile the secondary resonance is linearly redshifted in terms of the coupling constant. By changing the parameters, the transmission and resonance characteristics can be efficiently controlled and tuned at even multiple resonance frequencies.
Fig. 4 Calculated transmission spectra for (a) honeycomb- and (b) chlorophyll-shape patterned antenna array depending on their coupling constants. The resonance peak is split into two resonance modes while transmission amplitude becomes decreasing as coupling strength is increasing.
4. Conclusion
In conclusion, we present unique designs of the nano-slot antenna array with asterisk-, honeycomb- and chlorophyll-shape patterns to archive rotation-free performance, unlike conventional collinearly patterned array having the transmission property under the Malus’ law. THz transmission spectra of the antenna array were interpreted with respect to the resonance frequency and the transmission efficiency. In particular, honeycomb- and chlorophyll-shape patterned array show the secondary resonance features by strong coupling with adjacent slots. To explain the secondary resonance, the coupled harmonic oscillator model was applied with identical resonance condition and different excitation efficiencies for each neighbor slot. This gives spectral change depending on the coupling strength, providing analytical information for the resonance tunability. Finally, our results have shown great potential in further applications including optical sensors as rotation-free and controllable multi resonance THz filters
Funding
National Research Foundation of Korea (NRF-2016M3A6B3936653, NRF-2016R1A2B2010858); the University of Seoul (201604271100); KIST institutional funding (2E27270 and 2V05550)
References and links
1. J.-H. Son, “Principle and applications of terahertz molecular imaging,” Nanotechnology 24(21), 214001 (2013). [CrossRef] [PubMed]
2. S. J. Oh, Y.-M. Huh, J.-S. Suh, J. Choi, S. Haam, and J.-H. Son, “Cancer Diagnosis by Terahertz Molecular Imaging Technique,” J. Infrared Millim. Terahertz Waves 33(1), 74–81 (2012). [CrossRef]
3. K. W. Kim, K.-S. Kim, H. Kim, S. H. Lee, J.-H. Park, J.-H. Han, S.-H. Seok, J. Park, Y. Choi, Y. I. Kim, J. K. Han, and J.-H. Son, “Terahertz dynamic imaging of skin drug absorption,” Opt. Express 20(9), 9476–9484 (2012). [CrossRef] [PubMed]
4. N. Nagai, R. Kumazawa, and R. Fukasawa, “Direct evidence of inter-molecular vibrations by THz spectroscopy,” Chem. Phys. Lett. 413(4–6), 495–500 (2005). [CrossRef]
5. M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, and R. Büttner, “Label-free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77(24), 4049–4051 (2000). [CrossRef]
6. M. Walther, B. M. Fischer, A. Ortner, A. Bitzer, A. Thoman, and H. Helm, “Chemical sensing and imaging with pulsed terahertz radiation,” Anal. Bioanal. Chem. 397(3), 1009–1017 (2010). [CrossRef] [PubMed]
7. Y. C. Sim, J. Y. Park, K.-M. Ahn, C. Park, and J.-H. Son, “Terahertz imaging of excised oral cancer at frozen temperature,” Biomed. Opt. Express 4(8), 1413–1421 (2013). [CrossRef] [PubMed]
8. J. Y. Park, H. J. Choi, G.-E. Nam, K.-S. Cho, and J.-H. Son, “In Vivo Dual-Modality Terahertz/Magnetic Resonance Imaging Using Superparamagnetic Iron Oxide Nanoparticles as a Dual Contrast Agent,” IEEE Trans. Terahertz Sci. Technol. 2(1), 93–98 (2012). [CrossRef]
9. S. J. Oh, S.-H. Kim, K. Jeong, Y. Park, Y.-M. Huh, J.-H. Son, and J.-S. Suh, “Measurement depth enhancement in terahertz imaging of biological tissues,” Opt. Express 21(18), 21299–21305 (2013). [CrossRef] [PubMed]
10. J. H. Kang, J.-H. Choe, D.-S. Kim, and Q.-H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17(18), 15652–15658 (2009). [CrossRef] [PubMed]
11. M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors,” Opt. Express 15(19), 11781–11789 (2007). [CrossRef] [PubMed]
12. M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009). [CrossRef]
13. M. Seo, J. Kyoung, H. Park, S. Koo, H. S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H. T. Kim, N. Park, Q. H. Park, K. Ahn, and D. S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett. 10(6), 2064–2068 (2010). [CrossRef] [PubMed]
14. M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012). [CrossRef] [PubMed]
15. S. Han, J.-Y. Kim, T. Kang, Y.-M. Bahk, J. Rhie, B. J. Kang, Y. S. Kim, J. Park, W. T. Kim, H. Jeon, F. Rotermund, and D.-S. Kim, “Colossal Terahertz Nonlinearity in Angstrom- and Nanometer-Sized Gaps,” ACS Photonics 3(8), 1440–1445 (2016). [CrossRef]
16. D.-K. Lee, J.-H. Kang, J.-S. Lee, H.-S. Kim, C. Kim, J. Hun Kim, T. Lee, J.-H. Son, Q.-H. Park, and M. Seo, “Highly sensitive and selective sugar detection by terahertz nano-antennas,” Sci. Rep. 5, 15459 (2015). [CrossRef] [PubMed]
17. H. R. Park, K. J. Ahn, S. Han, Y. M. Bahk, N. Park, and D. S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13(4), 1782–1786 (2013). [CrossRef] [PubMed]
18. D.-K. Lee, G. Kim, C. Kim, Y. M. Jhon, J. H. Kim, T. Lee, J. Son, and M. Seo, “Ultrasensitive Detection of Residual Pesticides Using THz Near-Field Enhancement,” IEEE Trans. Terahertz Sci. Technol. 6(3), 389–395 (2016). [CrossRef]
19. A. Artar, A. A. Yanik, and H. Altug, “Multispectral Plasmon Induced Transparency in Coupled Meta-Atoms,” Nano Lett. 11(4), 1685–1689 (2011). [CrossRef] [PubMed]
20. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]
21. 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] [PubMed]
22. W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3368 (2012). [CrossRef] [PubMed]
23. R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014). [CrossRef]
24. X. Li, H. Liu, Q. Sun, and N. Huang, “Ultra-broadband and polarization-insensitive wide-angle terahertz metamaterial absorber,” Photon. Nanostructures 15, 81–88 (2015). [CrossRef]
25. J.-W. Lee, J.-K. Yang, I.-B. Sohn, H.-K. Choi, C. Kang, and C.-S. Kee, “Relationship between the order of rotation symmetry in perforated apertures and terahertz transmission characteristics,” Opt. Eng. 51(11), 119002 (2012). [CrossRef]
26. L. Qi, “Broadband and Polarization Independent Terahertz Metamaterial Filters Using Metal-Dielectric-Metal Complementary Ring Structure,” J. Opt. Soc. Korea 20(2), 263–268 (2016). [CrossRef]
27. I. A. I. Al-Naib, C. Jansen, N. Born, and M. Koch, “Polarization and angle independent terahertz metamaterials with high Q-factors,” Appl. Phys. Lett. 98(9), 091107 (2011). [CrossRef]
28. X. Zhang, Q. Li, W. Cao, J. Gu, R. Singh, Z. Tian, J. Han, and W. Zhang, “Polarization-Independent Plasmon-Induced Transparency in a Fourfold Symmetric Terahertz Metamaterial,” IEEE J. Sel. Top. Quantum Electron. 19(1), 8400707 (2013). [CrossRef]
29. Y. Ma, Q. Chen, J. Grant, S. C. Saha, A. Khalid, and D. R. S. Cumming, “A terahertz polarization insensitive dual band metamaterial absorber,” Opt. Lett. 36(6), 945–947 (2011). [CrossRef] [PubMed]
30. H. Tao, C. M. Bingham, A. C. Strikwerda, D. Pilon, D. Shrekenhamer, N. I. Landy, K. Fan, X. Zhang, W. J. Padilla, and R. D. Averitt, “Highly flexible wide angle of incidence terahertz metamaterial absorber: Design, fabrication, and characterization,” Phys. Rev. B 78(24), 241103 (2008). [CrossRef]
31. J. R. Dimaio and J. Ballato, “Polarization-dependent transmission through subwavelength anisotropic aperture arrays,” Opt. Express 14(6), 2380–2384 (2006). [CrossRef] [PubMed]
32. M. Sarrazin and J. P. Vigneron, “Polarization effects in metallic films perforated with a bidimensional array of subwavelength rectangular holes,” Opt. Commun. 240(1–3), 89–97 (2004). [CrossRef]
33. A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239(1–3), 61–66 (2004). [CrossRef]
34. J. Yang and J. Zhang, “Nano-polarization-converter based on magnetic plasmon resonance excitation in an L-shaped slot antenna,” Opt. Express 21(7), 7934–7942 (2013). [CrossRef] [PubMed]
35. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]
36. C. Sun, J. Si, Z. Dong, and X. Deng, “Tunable multispectral plasmon induced transparency based on graphene metamaterials,” Opt. Express 24(11), 11466–11474 (2016). [CrossRef] [PubMed]
37. S. Yin, X. Lu, N. Xu, S. Wang, Y. e, X. Pan, X. Xu, H. Liu, L. Chen, W. Zhang, and L. Wang, “Spoof surface plasmon polaritons in terahertz transmission through subwavelength hole arrays analyzed by coupled oscillator model,” Sci. Rep. 5(1), 16440 (2015). [CrossRef] [PubMed]
