Abstract

An optically tunable terahertz negative-refractive index metamaterial (NIM) is proposed. The NIMs are composed of two aluminum rings and two photosensitive ring-shaped silicon apertures coaxially coated on the both sides of Teflon substrate. The NIMS are also designed to realize wide incident angle, polarization insensitivity, and tunability. Similar to the real atom, the unit cell of NIMs is equivalent to the Teflon nucleus surrounded by top and bottom resonator electrons, which indicates that the equivalent-energy level of NIMs can be dynamically controlled by the resonator electrons, once the scale of substrate nucleus is fixed. Using the LC-circuit model, the dynamic control of the equivalent-energy level of NIMs is studied in detail. Simulation results indicate that the transmission of NIMs is tuned from lowpass to highpass when the conductivity of silicon is increased, and the corresponding phase at lower frequency can be continually tuned. Correspondingly, the negative refractive index of NIMs represents dynamically tunable property, and the tunable negative refraction is simulated by classical wedge prism model. Besides, the phase flow indicates that the direction of phase velocity of NIMs is negative for the single-negative index.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (8)

L. La Spada and L. Vegni, “Electromagnetic Nanoparticles for Sensing and Medical Diagnostic Applications,” Materials (Basel) 11(4), 603 (2018).
[Crossref] [PubMed]

A. M. Shaltout, J. Kim, A. Boltasseva, V. M. Shalaev, and A. V. Kildishev, “Ultrathin and multicolour optical cavities with embedded metasurfaces,” Nat. Commun. 9(1), 2673 (2018).
[Crossref] [PubMed]

D. Wu, Y. Liu, L. Chen, R. Ma, C. Liu, C. Xiang, R. Li, and H. Ye, “Broadband mid-infrared dual-band double-negative metamaterial: realized using a simple geometry,” Plasmonics 13(4) 1287–1295 (2018).

K. Sun, R. Fan, X. Zhang, Z. Zhang, Z. Shi, N. Wang, P. Xie, Z. Wang, G. Fan, H. Liu, C. Liu, T. Li, C. Yan, and Z. Guo, “An overview of metamaterials and their achievements in wireless power transfer,” J. Mater. Chem. C Mater. Opt. Electron. Devices 6(12), 2925–2943 (2018).
[Crossref]

J. Zi, Q. Xu, Q. Wang, C. Tian, Y. Li, X. Zhang, J. Han, and W. Zhang, “Terahertz polarization converter based on all-dielectric high birefringence metamaterial with elliptical air holes,” Opt. Commun. 416, 130–136 (2018).
[Crossref]

F. Ling, Z. Zhong, R. Huang, and B. Zhang, “A broadband tunable terahertz negative refractive index metamaterial,” Sci. Rep. 8(1), 9843 (2018).
[Crossref] [PubMed]

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]

T. Suzuki and S. Kondoh, “Negative refractive index metasurface in the 2.0-THz band,” Opt. Mater. Express 8(7), 1916–1925 (2018).
[Crossref]

2017 (6)

L. La Spada and L. Vegni, “Near-zero-index wires,” Opt. Express 25(20), 23699–23708 (2017).
[Crossref] [PubMed]

Y. J. Lin, Y. H. Chang, W. C. Chien, and W. Kuo, “Transmission line metamaterials based on strongly coupled split ring/complementary split ring resonators,” Opt. Express 25(24), 30395–30405 (2017).
[Crossref] [PubMed]

T. T. Yeh, T. Y. Huang, T. Tanaka, and T. J. Yen, “Demonstration of a three-dimensional negative Index medium operated at multiple-angle incidences by monolithic metallic hemispherical shells,” Sci. Rep. 7(1), 45549 (2017).
[Crossref] [PubMed]

C. Liu, Y. Bai, L. Jing, Y. Yang, H. Chen, J. Zhou, Q. Zhao, and L. Qiao, “Equivalent energy level hybridization approach for high-performance metamaterials design,” Acta Mater. 135, 144–149 (2017).
[Crossref]

L. La Spada, S. Haq, and Y. Hao, “Modeling and design for electromagnetic surface wave devices,” Radio Sci. 52(9), 1049–1057 (2017).
[Crossref]

Y. Lee, S. J. Kim, H. Park, and B. Lee, “Metamaterials and metasurfaces for sensor applications,” Sensors (Basel) 17(8), 1726 (2017).
[Crossref] [PubMed]

2016 (4)

Y. Liu, Y. Hao, K. Li, and S. Gong, “Radar cross section reduction of a microstrip antenna based on polarization conversion metamaterial,” IEEE Antenn. Wirel. Pr. 15, 80–83 (2016).
[Crossref]

K. J. Wang, Y. X. Peng, L. Wang, M. D. He, Z. J. Li, L. H. Liu, J. B. Li, X. J. Wang, J. Q. Liu, L. Xu, W. D. Hu, and X. Chen, “Plasmon resonances in a periodic square coaxial hole array in a graphene sheet,” Plasmonics 11(4), 1129–1137 (2016).
[Crossref]

S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C. W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[Crossref] [PubMed]

L. La Spada and L. Vegni, “Metamaterial-based wideband electromagnetic wave absorber,” Opt. Express 24(6), 5763–5772 (2016).
[Crossref] [PubMed]

2015 (4)

T. T. Kim, S. S. Oh, H. S. Park, R. Zhao, S. H. Kim, W. Choi, B. Min, and O. Hess, “Optical activity enhanced by strong inter-molecular coupling in planar chiral metamaterials,” Sci. Rep. 4(1), 5864 (2015).
[Crossref] [PubMed]

T. Cao, C. Wei, and L. Mao, “Ultrafast tunable chirped phase-change metamaterial with a low power,” Opt. Express 23(4), 4092–4105 (2015).
[Crossref] [PubMed]

C. Liu, Y. Bai, J. Zhou, Q. Zhao, Y. Yan, J. Li, Y. Su, and L. Qiao, “Equivalent energy-level structures in stacked metamaterials,” J. Mater. Chem. C Mater. Opt. Electron. Devices 3(45), 11827–11832 (2015).
[Crossref]

Q. Wang and B. Li, “Electronic transport characterization of silicon wafers by spatially resolved steady-state photocarrier radiometric imaging,” J. Appl. Phys. 118(12), 125705 (2015).
[Crossref]

2014 (3)

F. Monticone and A. Alu, “Metamaterials and plasmonics: From nanoparticles to nanoantenna arrays, metasurfaces, and metamaterials,” Chin. Phys. B 23(4), 047809 (2014).
[Crossref]

K. Wang and H. Kampwerth, “Separation algorithm for bulk lifetime and surface recombination velocity of thick silicon wafers and bricks via time-resolved photoluminescence decay,” J. Appl. Phys. 115(17), 173103 (2014).
[Crossref]

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]

2013 (2)

K. Fan, A. C. Strikwerda, X. Zhang, and R. D. Averitt, “Three-dimensional broadband tunable terahertz metamaterials,” Phys. Rev. B Condens. Matter Mater. Phys. 87(16), 161104 (2013).
[Crossref]

Z. Li and Y. J. Ding, “Terahertz broadband-stop filters,” IEEE J. Sel. Top. Quant. 19(1), 8500705 (2013).
[Crossref]

2012 (2)

Y. R. Padooru, A. B. Yakovlev, C. S. R. Kaipa, G. W. Hanson, F. Medina, F. Mesa, and A. W. Glisson, “New absorbing boundary conditions and analytical model for multilayered mushroom-type metamaterials: Applications to wideband absorbers,” IEEE Trans. Antenn. Propag. 60(12), 5727–5742 (2012).
[Crossref]

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] [PubMed]

2011 (5)

T. Okada and K. Tanaka, “Photo-designed terahertz devices,” Sci. Rep. 1(1), 121 (2011).
[Crossref] [PubMed]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B Condens. Matter Mater. Phys. 83(24), 245119 (2011).
[Crossref]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

T. Kleine-Ostmann and T. Nagatsuma, “A review on terahertz communications research,” J. Infrared Millim. Te. 32(2), 143–171 (2011).
[Crossref]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. J. Brueck, “Ultrafast nonlinear optical spectroscopy of a dual-band negative index metamaterial all-optical switching device,” Opt. Express 19(5), 3973–3983 (2011).
[Crossref] [PubMed]

2010 (2)

Y. Q. Ye, Y. Jin, and S. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in the terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010).
[Crossref]

J. Wang, S. Qu, Z. Xu, H. Ma, S. Xia, Y. Yang, X. Wu, Q. Wang, and C. Chen, “Normal-incidence left-handed metamaterials based on symmetrically connected split-ring resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(3), 036601 (2010).
[Crossref] [PubMed]

2009 (4)

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]

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]

N. T. Tung, V. D. Lam, J. W. Park, M. H. Cho, J. Y. Rhee, W. H. Jang, and Y. P. Lee, “Single-and double-negative refractive indices of combined metamaterial structure,” J. Appl. Phys. 106(5), 053109 (2009).
[Crossref]

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94(7), 073506 (2009).
[Crossref]

2008 (4)

Y. J. Bao, R. W. Peng, D. J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N. B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[Crossref] [PubMed]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[Crossref]

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).
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R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94(7), 073506 (2009).
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Y. Liu, Y. Hao, K. Li, and S. Gong, “Radar cross section reduction of a microstrip antenna based on polarization conversion metamaterial,” IEEE Antenn. Wirel. Pr. 15, 80–83 (2016).
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Gu, J.

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Han, J.

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Y. R. Padooru, A. B. Yakovlev, C. S. R. Kaipa, G. W. Hanson, F. Medina, F. Mesa, and A. W. Glisson, “New absorbing boundary conditions and analytical model for multilayered mushroom-type metamaterials: Applications to wideband absorbers,” IEEE Trans. Antenn. Propag. 60(12), 5727–5742 (2012).
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N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
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N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
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A. M. Shaltout, J. Kim, A. Boltasseva, V. M. Shalaev, and A. V. Kildishev, “Ultrathin and multicolour optical cavities with embedded metasurfaces,” Nat. Commun. 9(1), 2673 (2018).
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Kuo, W.

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L. La Spada and L. Vegni, “Electromagnetic Nanoparticles for Sensing and Medical Diagnostic Applications,” Materials (Basel) 11(4), 603 (2018).
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L. La Spada, S. Haq, and Y. Hao, “Modeling and design for electromagnetic surface wave devices,” Radio Sci. 52(9), 1049–1057 (2017).
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T. T. Yeh, T. Y. Huang, T. Tanaka, and T. J. Yen, “Demonstration of a three-dimensional negative Index medium operated at multiple-angle incidences by monolithic metallic hemispherical shells,” Sci. Rep. 7(1), 45549 (2017).
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Figures (9)

Fig. 1
Fig. 1 The three-dimensional distributions of (a) photoexcited carrier density and (b) conductivity of Si with different exciting time and penetrating depth. The inset is conductivity of Si with different photoexcitation powers.
Fig. 2
Fig. 2 (a) Schematic illustration of a unit cell structure of the tunable NIMs, (b) the principle of the photoexcitation.
Fig. 3
Fig. 3 (a) The normalized transmissions and (b) phase spectra of monolayer and bilayer MMs. The brown-dashed and pink-dashed curves represent the analytic transmissions of S1 and S2, respectively.
Fig. 4
Fig. 4 (a) The surface current distributions of S1 and S2. (b) Schematics of equivalent-energy level of S1, B1, S2 and B2. (c) The surface current distributions of B1 and B2. (d) LC-circuit models and (e) magnetic field distributions of B1 and B2. The solid and dashed single arrows represent current direction of the top and bottom resonators, respectively. The blue single arrow line indicates the current direction of ring, while the green and red single arrow lines represent the current directions of inner and outer parts of ring aperture, respectively. The black double arrow represents the coupling between different parts of MMs.
Fig. 5
Fig. 5 (a) The normalized transmission and (b) the transmission phase with different σ of Si. (c) The electric field and (d) the magnetic field distributions of NIMs with different states at 1.1 THz.
Fig. 6
Fig. 6 The transmission contour of the NIMs with different polarization angles (a) without photoexcitation and (b) with σ = 6 × 104 S/m. The transmission contour of the NIMs with different incident angles (c) without photoexcitation and (d) with σ = 6 × 104 S/m.
Fig. 7
Fig. 7 The constitutive parameter of NIMs (a) without photoexcitation, (b) with conductivity σ = 1 × 103 S/m, (c) with conductivity σ = 1 × 104 S/m and (b) with conductivity σ = 6 × 104 S/m. The gray and pink regions represent the DNR band and SNR band, respectively.
Fig. 8
Fig. 8 Negative refraction of NIMs in the wedge sample.
Fig. 9
Fig. 9 (a) The transmission spectra of NIMs with different layers. Phase flows with free space and five-layered NIMs with σ = 6 × 104 S/m under normal incidence (b) at 1.25 THz with a constant phase step of 60 degrees.

Equations (18)

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I(t)= I 0 2π σ e ( t t 0 2 σ ) 2
ΔN t =D 2 ΔN z 2 +G(z,t) ΔN τ f
G(z,t)=I(t) (1R)αβ LWhf e αz
ΔN τ f = B r ΔN τ Auger
{ ΔN(0,t)= D S ΔN z | z=0 ΔN(,t)=0
ΔN(z,0)=0
σ=q μ p ΔN
f r = 1 2π ( l m +Ω)C
P r =NP=Nex= N e 2 m 0 1 ( ω r 2 ω 2 iγω ) E
ε r (ω)=1+ N e 2 m 0 ε 0 1 ( ω r 2 ω 2 iγω )
lim d0 t(f)=real| c(1+ n sub ) c(1+ n sub )if χ e |
lim d0 t(f)=1real| c(1+ n sub ) c(1+ n sub )if χ e |
L I-M = L eff +M
L I-E = L eff M
L 1eff = 1 1 L exter + 1 L inter + M 1 + M 2 = L exter L inter L exter + L inter + M 1 + M 2
L 2eff = 1 1 L exter + 1 L inter + M 1 + M 2 = L exter L inter L exter + L inter + M 1 + M 2
L II-M = L 1eff + L 2eff + M 3 + M 4
L II-E = L 1eff + L 2eff M 3 M 4