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Abstract
Development of continuous wave (CW) sources has recently advanced in various frequencies of the terahertz waveband. However, there are few materials suitable for the terahertz waveband, and attractive materials are eagerly awaited. Metamaterials with artificial sub-wavelength structures would enable designs with an arbitrary refractive index including negative values providing simultaneous control of dielectric and magnetic properties. Here, measurements demonstrate that a simple metasurface, a two-dimensional metamaterial, consisting of asymmetrical metal patches on the front and back of a dielectric substrate has a negative refractive index of −3.03 + j0.29, transmission of 56.4%, and reflection of 3.51% at 1.96 THz. The metasurface would offer attractive optical components such as super lenses, ultrathin collimators, and cloaking.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Technology involving electromagnetic waves in unexplored frequency bands has progressively advanced with interactions between the development of optical sources and creation of unprecedented materials. The terahertz waveband is a promising candidate for high speed wireless communication [1] and imaging [2], with terahertz continuous wave (CW) sources having been reported in a wide range of terahertz wavebands. A continuous wave in the 0.3-THz band has been reported by a resonant-tunneling diode (RTD) at room temperature [3], with RTD radiating continuous terahertz waves at 1.86 [4] and 1.92 [5] THz, also reported at room temperature in the higher frequencies. A quantum cascade laser (QCL) is also an attractive terahertz CW source in industrial terahertz applications, and in very recent years results at room temperature has frequently been reported from approximately 1.0 to 5.0 THz [6–10]. This has increased the demand for materials that are able to manipulate terahertz waves and for development of sophisticated optical components. There are much fewer materials suitable for the terahertz waveband than for the visible light region and microwaves. The basic properties of materials such as the refractive index, transmission, and reflection are correlated in the Fresnel equations, and the control of both dielectric and magnetic properties is necessary for unconstrained designs of such materials. However, control of the magnetic as well as the dielectric properties are commonly challenging in the high frequency bands. Metamaterials consisting of meta-atoms with sub wavelength structures enable the direct control of dielectric and magnetic properties and designs with arbitrary refractive indices, transmission, and reflection properties. Such a design would make it possible to produce an unprecedented material suitable for the terahertz waveband, a material that could also be applied to optical components for terahertz sources. A negative refractive index was reported in 2000 in the microwave band [11] as a remarkable result in metamaterials, and negative magnetic responses were reported in 2004 [12] and 2005 [13]. Terahertz metamaterials have been applied to attractive terahertz components such as absorbers [14], antireflection coatings [15], and polarization conversion components [16]. Metadevices [17] evolved from metamaterials can actively control terahertz waves using external modulations of various kinds [18–24] for game-changing industrial applications. Materials are at the center of elements in applications and devices, and metamaterials with a negative refractive index has been reported in the terahertz waveband for pairs of crossbars [25], short-slab pairs and wires [26], bi-layer S-strings [27], H-shaped wire-pairs [28], close-ring pairs [29], cut wire pairs [30], Mie resonance [31], fishnets [32–34], and asymmetrically aligned cut wire pairs [35]. Metamaterials with a negative refractive index would be able to restore an evanescent wave and demonstrate imaging beyond the diffraction limit. The work in [36] reported near-perfect imaging by a metamaterial with a negative refractive index consisting of steric structures integrated on a source in the microwave band. A complicated structure is commonly needed to achieve a negative refractive index, and a simple structure is necessary to avoid difficulties when integrated on terahertz sources. Further, wavelengths are on the order of microns in the terahertz waveband, and it is not easy to integrate three-dimensional metamaterials on sources in the terahertz waveband. The work in [25,29] has demonstrated a three-dimensional metamaterial in the terahertz waveband. A two-dimensional metamaterial with a simple structure, a metasurface, could be simply integrated on terahertz sources and would be very useful.
Here, we demonstrate a metasurface with a negative refractive index in the 2.0-THz band with a simple structure. This metasurface has metal patches arranged asymmetrically with a periodic shift on the front and back of a dielectric substrate. The dielectric substrate is a cyclo-olefin polymer film with low dielectric loss in the terahertz waveband. Both sides of the cyclo-olefin polymer film are coated with copper, and the coated film is etched for the fabrication. Terahertz time-domain spectroscopy (THz-TDS) is used to measure the material properties of such a fabricated metasurface with a negative refractive index. The measurements demonstrate a negative refractive index of −3.03 + j0.29, transmission of 56.4%, and reflection of 3.51% at 1.96 THz. The metasurface offers applications in various attractive terahertz components operating beyond the conventional performance and will help accelerate the development of path-breaking terahertz applications. The structure is flexible and could be applied to nonplanar optical components in the terahertz waveband [37]. Further, the control of the magnetic properties as well as the dielectric properties in the higher frequency bands would contribute as a useful material in a wide range of fields such as radiative cooling [38] and a transparent near-infrared reflector [39] in the infrared region.
2. Operating principle
Figure 1(a) shows a metasurface with a negative refractive index consisting of metal patches. The metal patches are asymmetrically aligned with the shift of one periodicity along the y-direction on the front and back of a dielectric substrate as in Fig. 1(b). Dielectric and magnetic resonances are caused by an E-field and H-field of terahertz waves, respectively. Parameters of the metal patches in Table 1 can simultaneously control the dielectric and magnetic resonances. Figure 2 shows equivalent circuits of symmetrical and asymmetrical structures to effectively suggest the dielectric and magnetic resonances. The resonance frequency f is expressed with the inductance L and capacitance C of the metasurface as in the following Eq. (1). This approach using the equation for a standard LC circuit is still phenomenological [35], but the method in [40] could quantify the effective inductance L and capacitance C for the development of a high-quality terahertz metamaterial with a negative refractive index.
The dielectric resonance for the symmetrical structure is determined by the inductance of a metal patch and the capacitance of a metal patch gap along the y-axis as shown in the left figure of Fig. 2(a). The dielectric resonance for the asymmetrical structure is determined by the inductance of a metal patch and the capacitance of the front and back metal patches as well as the capacitance of a metal patch gap along the y-axis as shown in the right figure of Fig. 2(a). The capacitance components are enlarged for the asymmetrical structure when compared with that of the symmetrical structure. The phenomena in Fig. 2(a) cause that a dielectric resonance frequency of an asymmetrical structure is lower than that of a symmetrical one in Eq. (1). The magnetic resonance for the asymmetrical structure is determined by the inductance of metal patches on the front and back and the capacitance of the metal patches on the front and back as shown in the left figure of Fig. 2(b). The magnetic resonance for the asymmetrical structure is determined by the inductance of a metal patch on one side of the front and back and the capacitance of metal patches on front and back as shown in the right figure of Fig. 2(b). The inductance and capacitance components are reduced for the asymmetrical structure when compared with that of the symmetrical structure. The phenomena in Fig. 2(b) cause that a magnetic resonance frequency of an asymmetrical structure is higher than that of a symmetrical one in Eq. (1). The frequency of the dielectric resonance overlaps that of the magnetic resonance of an asymmetrical structure. The negative refractive index is caused by the negative permittivity and permeability at the resonance frequency.
Fig. 1 (a) Metasurface with a negative refractive index consisting of meta-atoms on the front and back of a dielectric substrate. (b) Enlarged view of a metasurface consisting of asymmetrically aligned metal patches.
Table 1. Parameters of the metal patches
Fig. 2 (a) Equivalent circuits of symmetrically and asymmetrically aligned metal patches at a dielectric resonance frequency. (b) Equivalent circuits of symmetrically and asymmetrically aligned metal patches at a magnetic resonance frequency.
Figures 3(a)-3(c) show the frequency characteristics of the refractive index, relative permittivity, and permeability for a symmetrical structure, respectively. Figures 3(d), (e), and (f) show the frequency characteristics of the refractive index, relative permittivity, and permeability for an asymmetrical structure, respectively. The red and blue regions show frequency bands with negative permittivity and permeability, respectively. The frequency bands with negative relative permittivities do not overlap with those of the negative relative permeabilities of the symmetrical structure. The frequency bands with negative relative permittivities shift to lower frequencies with an asymmetrical structure when compared with a symmetrical structure. This phenomenon is predicted by the equivalent circuits. The frequency bands with negative relative permeabilities shift to higher frequencies with an asymmetrical structure. This phenomenon is also predicted by the equivalent circuits. The relative permittivity and permeability have negative values from 1.89 to 2.25 THz, and a negative refractive index can be designed for the frequency waveband.
Fig. 3 Frequency characteristics of (a) refractive index, (b) relative permittivity, and (c) relative permeability for the metasurface consisting of the symmetrically aligned metal patches. Frequency characteristics of (d) refractive index, (e) relative permittivity, and (f) relative permeability for the metasurface consisting of the asymmetrically aligned metal patches.
3. Design procedure
Figure 4 shows a unit-cell model of a metasurface consisting of meta-atoms on the front and back of a dielectric substrate to derive the optimized parameters. The full model has a periodic structure consisting of asymmetrically aligned metal patches. The unit-cell model is one period of asymmetrical metal patches extracted from the full model using periodic boundary conditions at the exterior region. The metal is copper with low loss and conductivity σ = 5.8 × 107 S/m, and the dielectric substrate is cyclo-olefin polymer with a refractive index nCOP = 1.53 + j0.0012 measured in the terahertz waveband [41]. The design is performed by the finite element method with an ANSYS HFSS simulator. An effective refractive index is derived from scattering matrices of a design model with the following Eqs. (2), (3), and (4),
where k0 is the wave number in free space and m is an integer [42]. Figures 5(a)–5(d) show contour maps of the real part of the refractive index, the imaginary part of the refractive index, the transmission, and the reflection with the length l of metal patches varied from 40 to 70 um and a gap g between metal patches from 40 to 70 um at 1.96 THz. The half-wavelength inside the metasurface is smaller than the thickness in the Bragg regime, and the effective optical constants cannot be expected to be accurate [43]. Refractive indices can be controlled from −3.18 to 3.18 for a 24 μm thick metasurface. Figures 5(a)–5(d) derive optimized parameters of a length l and gap g for a metasurface with a negative refractive index, a low imaginary part of the refractive index, high transmission, and low reflection. The X marks in the contour maps show the parameters in Table 1. The other parameters of the metal patches are also fixed as in Table 1. The metasurface with the parameters of the X marks designs a refractive index of −2.81 + j0.049, a transmission of 80.2%, and the reflection of 14.1% at 1.96 THz. The parameters are chosen to obtain high transmission and low reflection taking into consideration impedance matching between the metasurface and vacuum. The relative permittivity, permeability, and relative impedance are −1.04 - j0.089, −7.52 + j0.91, and 2.68 - j0.28 at 1.96 THz respectively.Fig. 5 Contour maps of (a) the real part of the refractive index, (b) the imaginary part of the refractive index, (c) the transmission, and (d) the reflection at 1.96 THz.
4. Fabrication and measurement
Figure 6(a) shows a fabricated metasurface with a negative refractive index in the 2.0-THz band. Figure 6(b) shows the fabricated asymmetrically aligned paired metal patches which perform as meta-atoms. The cyclo-olefin polymer film is coated with copper on the front and back, and the coated film is etched to provide the properties described below. Figures 7(a)–7(c) show the frequency characteristics of the measurements and simulations for the refractive index, relative permittivity, and relative permeability, respectively. The measurements are developed by THz-TDS Toptica TeraFlash, and the frequency resolution of the measurements is 0.005 THz. A photoconductive antenna radiates the terahertz wave, and a lens focuses the terahertz wave at the sample and a reference. The reference is used to derive optical constants by the comparison of the data of the sample and reference. The reference is transmission data measured without the fabricated metasurface in dry air. The spot size and focal depth of the focused beam at the sample and reference are approximately 0.54 mm and 3.0 mm at 1.96 THz for the transmission measurements, respectively. The angle of reflection is 0 degrees for the reflection measurements. The spot size and focal depth of the focused beam at the sample and reference are approximately 0.83 mm and 7.1 mm at 1.96 THz for the reflection measurements, respectively. Differences in the optical path lengths of the sample and a mirror as a reference are caused by bending of the metasurface and experimental errors in the reflection measurements. The refractive index is derived after reflection phases of measurements is compensated for on the condition that the reflected phases of the measurements are ideally the same as those of the simulations. The compensation predicts that the optical path length of the reflection measurements for the sample is 62 μm shorter than that of the reference. The measurements demonstrate a negative refractive index of −3.03 + j0.29, transmission of 56.4%, and reflection of 3.51% at 1.96 THz. The relative permittivity, permeability, and relative impedance are −1.57 – j0.55, −4.83 + j2.80, and 1.67 – j0.76 at 1.96 THz. Figure 8(a) shows energy losses due to the dielectric and magnetic properties which are expressed as |μr|Im(εr) and |εr|Im(μr), respectively. The dielectric and magnetic losses have negative values at the respective frequency bands. Figure 8(b) shows that the sum of the dielectric and magnetic losses are positive, and that conservation of energy is satisfied in the metasurface. The discrepancies between the measurements and simulations could be caused by other experimental errors in optical systems for transmission and reflection measurements and fabrication errors.
Fig. 6 (a) Photograph of the fabricated metasurface with a negative refractive index consisting of asymmetrically aligned paired metal patches. (b) Laser microscopic image of the fabricated asymmetrically aligned paired metal patches.
Fig. 7 Measurements and simulations of frequency characteristics for (a) the real and imaginary parts of the refractive indices, (b) the real and imaginary parts of the relative permittivity, and (c) the real and imaginary parts of the relative permeability.
Fig. 8 Frequency characteristics of (a) dielectric energy loss and magnetic energy loss and (b) the sum of the dielectric and magnetic energy losses.
5. Conclusions
A metasurface with a negative refractive index in the 2.0-THz band is simply designed by asymmetrical metal patches which simultaneously control both the negative permittivity and permeability. The designed metasurface has a refractive index of −2.81 + j0.049, transmission of 80.2%, and the reflection of 14.1% at 1.96 THz, the base is a cyclo-olefin polymer coated with etched copper on the front and back. Measurements by THz-TDS demonstrate the material properties of the metasurface with a negative refractive index of −3.03 + j0.29, transmission of 56.4%, and reflection of 3.51% at 1.96 THz. Such metasurfaces with a negative refractive index can open the way to attractive terahertz components and contribute to game-changing applications with terahertz CW sources.
Funding
Grant-in-Aid for Young Scientists (A) (No. 26706017), Japan Society for the Promotion of Science (JSPS); Support Center for Advanced Telecommunications Technology Research Foundation (SCAT); Japan Association for Chemical Innovation; TEPCO Memorial Foundation; TUAT president’s discretionary funding.
References and links
1. T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10(6), 371–379 (2016). [CrossRef]
2. C. G. Wade, N. Šibalić, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017). [CrossRef]
3. T. Miyamoto, A. Yamaguchi, and T. Mukai, “Terahertz imaging system with resonant tunneling diodes,” Jpn. J. Appl. Phys. 55(3), 032201 (2016). [CrossRef]
4. H. Kanaya, T. Maekawa, S. Suzuki, and M. Asada, “Structure dependence of oscillation characteristics of resonant-tunneling-diode terahertz oscillators associated with intrinsic and extrinsic delay times,” Jpn. J. Appl. Phys. 54(9), 094103 (2015). [CrossRef]
5. T. Maekawa, H. Kanaya, S. Suzuki, and M. Asada, “Oscillation up to 1.92 THz in resonant tunneling diode by reduced conduction loss,” Appl. Phys. Express 9(2), 024101 (2016). [CrossRef]
6. K. Vijayraghavan, Y. Jiang, M. Jang, A. Jiang, K. Choutagunta, A. Vizbaras, F. Demmerle, G. Boehm, M. C. Amann, and M. A. Belkin, “Broadly tunable terahertz generation in mid-infrared quantum cascade lasers,” Nat. Commun. 4(2021), 2021 (2013). [PubMed]
7. M. Razeghi, Q. Y. Lu, N. Bandyopadhyay, W. Zhou, D. Heydari, Y. Bai, and S. Slivken, “Quantum cascade lasers: from tool to product,” Opt. Express 23(7), 8462–8475 (2015). [CrossRef] [PubMed]
8. K. Fujita, M. Hitaka, A. Ito, T. Edamura, M. Yamanishi, S. Jung, and M. A. Belkin, “Terahertz generation in mid-infrared quantum cascade lasers with a dual-upper-state active region,” Appl. Phys. Lett. 106(25), 251104 (2015). [CrossRef]
9. K. Fujita, M. Hitaka, A. Ito, M. Yamanishi, T. Dougakiuchi, and T. Edamura, “Ultra-broadband room-temperature terahertz quantum cascade laser sources based on difference frequency generation,” Opt. Express 24(15), 16357–16365 (2016). [CrossRef] [PubMed]
10. K. Fujita, A. Ito, M. Hitaka, T. Dougakiuchi, and T. Edamura, “Low-threshold room-temperature continuous-wave operation of a terahertz difference-frequency quantum cascade laser source,” Appl. Phys. Express 10(8), 082102 (2017). [CrossRef]
11. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]
12. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]
13. N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the far-infrared frequency regime,” Opt. Lett. 30(11), 1348–1350 (2005). [CrossRef] [PubMed]
14. H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 16(10), 7181–7188 (2008). [CrossRef] [PubMed]
15. H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010). [CrossRef] [PubMed]
16. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef] [PubMed]
17. N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012). [CrossRef] [PubMed]
18. 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]
19. 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]
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. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009). [CrossRef]
22. H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable Terahertz Metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009). [CrossRef] [PubMed]
23. 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), 1151 (2012). [CrossRef] [PubMed]
24. T. Kan, A. Isozaki, N. Kanda, N. Nemoto, K. Konishi, H. Takahashi, M. K. -Gonokami, K. Matsumoto, and I. Shimoyama, “Enantiomeric switching of chiral metamaterial for terahertz polarization modulation employing vertically deformable MEMS spirals,” Nat. Commun. 6(8422), 1–7 (2015).
25. O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, “Negative index bulk metamaterial at terahertz frequencies,” Opt. Express 16(9), 6736–6744 (2008). [CrossRef] [PubMed]
26. T. F. Gundogdu, N. Katsarakis, M. Kafesaki, R. S. Penciu, G. Konstantinidis, A. Kostopoulos, E. N. Economou, and C. M. Soukoulis, “Negative index short-slab pair and continuous wires metamaterials in the far infrared regime,” Opt. Express 16(12), 9173–9180 (2008). [CrossRef] [PubMed]
27. H. O. Moser, J. A. Kong, L. K. Jian, H. S. Chen, G. Liu, M. Bahou, S. M. P. Kalaiselvi, S. M. Maniam, X. X. Cheng, B. I. Wu, P. D. Gu, A. Chen, S. P. Heussler, S. Mahmood, and L. Wen, “Free-standing THz electromagnetic metamaterials,” Opt. Express 16(18), 13773–13780 (2008). [CrossRef] [PubMed]
28. M. Awad, M. Nagel, and H. Kurz, “Negative-index metamaterial with polymer-embedded wire-pair structures at terahertz frequencies,” Opt. Lett. 33(22), 2683–2685 (2008). [CrossRef] [PubMed]
29. J. Gu, J. Han, X. Lu, R. Singh, Z. Tian, Q. Xing, and W. Zhang, “A close-ring pair terahertz metamaterial resonating at normal incidence,” Opt. Express 17(22), 20307–20312 (2009). [CrossRef] [PubMed]
30. P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, “Strongly birefringent metamaterials as negative index terahertz wave plates,” Appl. Phys. Lett. 95(17), 171104 (2009). [CrossRef]
31. K. Takano, Y. Yakiyama, K. Shibuya, K. Izumi, H. Miyazaki, Y. Jimba, F. Miyamaru, H. Kitahara, and M. Hangyo, “Fabrication and performance of TiO2-ceramic-based metamaterials for terahertz frequency range,” IEEE Trans. THz Sci. Technol. 3(6), 812–819 (2013).
32. C.-L. Chang, W.-C. Wang, H.-R. Lin, F. Ju Hsieh, Y.-B. Pun, and C.-H. Chan, “Tunable terahertz fishnet metamaterial,” Appl. Phys. Lett. 102(15), 151903 (2013). [CrossRef]
33. W. Zhu, F. Xiao, M. Kang, D. Sikdar, and M. Premaratne, “Tunable terahertz left-handed metamaterial based on multi-layer graphene-dielectric composite,” Appl. Phys. Lett. 104(5), 051902 (2014). [CrossRef]
34. Q.-L. Zhang, L.-M. Si, Y. Huang, X. Lv, and W. Zhu, “Low-index-metamaterial for gain enhancement of planar terahertz antenna,” AIP Adv. 4(3), 037103 (2014). [CrossRef]
35. T. Suzuki, M. Sekiya, T. Sato, and Y. Takebayashi, “Negative Refractive Index Metamaterial with High Transmission, Low Reflection, and Low Loss in the Terahertz Waveband,” Opt. Express 26(7), 8314–8324 (2018). [CrossRef] [PubMed]
36. A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed-material plate,” Phys. Rev. Lett. 92(7), 077401 (2004). [CrossRef] [PubMed]
37. K. Fan, X. Zhao, J. Zhang, K. Geng, G. R. Keiser, H. R. Seren, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically tunable terahertz metamaterials on highly flexible substrates,” IEEE Trans. THz Sci. Technol. 3(6), 702–708 (2013).
38. Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017). [CrossRef] [PubMed]
39. T. Tani, S. Hakuta, N. Kiyoto, and M. Naya, “Transparent near-infrared reflector metasurface with randomly dispersed silver nanodisks,” Opt. Express 22(8), 9262–9270 (2014). [CrossRef] [PubMed]
40. S. Tan, F. Yan, L. Singh, W. Cao, N. Xu, X. Hu, R. Singh, M. Wang, and W. Zhang, “Terahertz metasurfaces with a high refractive index enhanced by the strong nearest neighbor coupling,” Opt. Express 23(22), 29222–29230 (2015). [CrossRef] [PubMed]
41. Y. Kishi, M. Nagai, J. C. Young, K. Takano, M. Hangyo, and T. Suzuki, “Terahertz laminated-structure polarizer with high extinction ratio and transmission power,” Appl. Phys. Express 8(3), 032201 (2015). [CrossRef]
42. X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004). [CrossRef] [PubMed]
43. O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, “Gradient index metamaterial based on slot elements,” Appl. Phys. Lett. 96(24), 241110 (2010). [CrossRef]
