Abstract

In general, there is a fundamental trade-off between the operational bandwidth and the attainable absorption. So, obtaining broadband wave absorption of a low reference standard such as 90% is not very difficult. However, when trying to obtain higher absorption such as 99%, the bandwidth will drop dramatically. Here, we demonstrate that broadband near-perfect absorption of over 99% absorption with a 60% relative bandwidth can be obtained utilizing single-layered and nonstructured graphene loaded with periodical dielectric wires. The absorption mechanism originates from the coupling of Mie resonances in dielectric wires excited by the incident wave to the graphene plasmon resonances, which introduces two absorption contributions: direct near-field absorption in the graphene and radiative emission into the graphene.

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

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2018 (1)

J. Yang, Z. Zhu, J. Zhang, C. Guo, W. Xu, K. Liu, X. Yuan, and S. Qin, “Broadband terahertz absorber based on multi-band continuous plasmon resonances in geometrically gradient dielectric-loaded graphene plasmon structure,” Sci. Rep. 8(1), 3239 (2018).
[Crossref] [PubMed]

2017 (11)

F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017).
[Crossref] [PubMed]

Y. L. Liao and Y. Zhao, “Graphene-based tunable ultra-narrowband mid-infrared TE-polarization absorber,” Opt. Express 25(25), 32080–32089 (2017).
[Crossref] [PubMed]

L. Ye, Y. Chen, G. Cai, N. Liu, J. Zhu, Z. Song, and Q. H. Liu, “Broadband absorber with periodically sinusoidally-patterned graphene layer in terahertz range,” Opt. Express 25(10), 11223–11232 (2017).
[Crossref] [PubMed]

K. Arik, S. Abdollahramezani, and A. Khavasi, “Polarization Insensitive and Broadband Terahertz Absorber Using Graphene Disks,” Plasmonics 12(2), 393 (2017).
[Crossref]

W. Xu, L. Xie, and Y. Ying, “Mechanisms and applications of terahertz metamaterial sensing: a review,” Nanoscale 9(37), 13864–13878 (2017).
[Crossref] [PubMed]

J. A. Montoya, Z. B. Tian, S. Krishna, and W. J. Padilla, “Ultra-thin infrared metamaterial detector for multicolor imaging applications,” Opt. Express 25(19), 23343–23355 (2017).
[Crossref] [PubMed]

X. Zhang, H. Li, Z. Wei, and L. Qi, “Metamaterial for polarization-incident angle independent broadband perfect absorption in the terahertz range,” Opt. Mater. Express 7(9), 3294–3302 (2017).
[Crossref]

B. X. Wang, G. Z. Wang, T. Sang, and L. L. Wang, “Six-band terahertz metamaterial absorber based on the combination of multiple-order responses of metallic patches in a dual-layer stacked resonance structure,” Sci. Rep. 7(1), 41373 (2017).
[Crossref] [PubMed]

D. M. Nguyen, D. Lee, and J. Rho, “Control of light absorbance using plasmonic grating based perfect absorber at visible and near-infrared wavelengths,” Sci. Rep. 7(1), 2611 (2017).
[Crossref] [PubMed]

J. Chen, Y. Jin, P. Chen, Y. Shan, J. Xu, F. Kong, and J. Shao, “Polarization-independent almost-perfect absorber controlled from narrowband to broadband,” Opt. Express 25(12), 13916–13922 (2017).
[Crossref] [PubMed]

Y. Liu, J. Qiu, J. Zhao, and L. Liu, “General design method of ultra-broadband perfect absorbers based on magnetic polaritons,” Opt. Express 25(20), A980–A989 (2017).
[Crossref] [PubMed]

2016 (5)

2015 (7)

S. Yi, M. Zhou, X. Shi, Q. Gan, J. Zi, and Z. Yu, “A multiple-resonator approach for broadband light absorption in a single layer of nanostructured graphene,” Opt. Express 23(8), 10081–10090 (2015).
[Crossref] [PubMed]

A. Khavasi, “Design of ultra-broadband graphene absorber using circuit theory,” J. Opt. Soc. Am. B 32(9), 1941–1946 (2015).
[Crossref]

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterial,” AIP Adv. 5(6), 067106 (2015).
[Crossref]

Z. Zhu, C. Guo, J. Zhang, K. Liu, X. Yuan, and S. Qin, “Broadband single-layered graphene absorber using periodic arrays of graphene ribbons with gradient width,” Appl. Phys. Express 8(1), 015102 (2015).
[Crossref]

Y. Bai, L. Zhao, D. Ju, Y. Jiang, and L. Liu, “Wide-angle, polarization-independent and dual-band infrared perfect absorber based on L-shaped metamaterial,” Opt. Express 23(7), 8670–8680 (2015).
[Crossref] [PubMed]

Y. Shan, L. Chen, C. Shi, Z. Cheng, X. Zang, B. Xu, and Y. Zhu, “Ultrathin flexible dual band terahertz absorber,” Opt. Commun. 350, 63–70 (2015).
[Crossref]

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91(19), 195444 (2015).
[Crossref]

2014 (6)

Y. Wen, W. Ma, J. Bailey, G. Matmon, X. Yu, and G. Aeppli, “Planar broadband and high absorption metamaterial using single nested resonator at terahertz frequencies,” Opt. Lett. 39(6), 1589–1592 (2014).
[Crossref] [PubMed]

X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, and J. Tian, “Polarization-insensitive and wide-angle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime,” J. Opt. 16(12), 125107 (2014).
[Crossref]

Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752 (2014).
[Crossref] [PubMed]

B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4(2), 4130 (2014).
[PubMed]

R. Yahiaoui, U. C. Chung, S. N. Burokur, A. D. Lustrac, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Broadband effective magnetic response of inorganic dielectric resonator-based metamaterial for microwave applications,” Appl. Phys., A Mater. Sci. Process. 114(3), 997–1002 (2014).
[Crossref]

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (5)

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
[Crossref] [PubMed]

Z. H. Zhu, C. C. Guo, K. Liu, W. M. Ye, X. D. Yuan, B. Yang, and T. Ma, “Metallic nanofilm half-wave plate based on magnetic plasmon resonance,” Opt. Lett. 37(4), 698–700 (2012).
[Crossref] [PubMed]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref] [PubMed]

L. Shi, T. U. Tuzer, R. Fenollosa, and F. Meseguer, “A New Dielectric Metamaterial Building Block with a Strong Magnetic Response in the Sub-1.5-Micrometer Region: Silicon Colloid Nanocavities,” Adv. Mater. 24(44), 5934–5938 (2012).
[Crossref] [PubMed]

2011 (2)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

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

2010 (1)

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
[Crossref] [PubMed]

2009 (1)

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

2008 (1)

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]

2007 (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Abdollahramezani, S.

K. Arik, S. Abdollahramezani, and A. Khavasi, “Polarization Insensitive and Broadband Terahertz Absorber Using Graphene Disks,” Plasmonics 12(2), 393 (2017).
[Crossref]

Aeppli, G.

Alù, A.

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91(19), 195444 (2015).
[Crossref]

Amin, M.

Arik, K.

K. Arik, S. Abdollahramezani, and A. Khavasi, “Polarization Insensitive and Broadband Terahertz Absorber Using Graphene Disks,” Plasmonics 12(2), 393 (2017).
[Crossref]

Bagci, H.

Bai, Y.

Bailey, J.

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Beruete, M.

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91(19), 195444 (2015).
[Crossref]

Bozhevolnyi, S. I.

F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
[Crossref] [PubMed]

Brongersma, M. L.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
[Crossref] [PubMed]

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

Burokur, S. N.

R. Yahiaoui, U. C. Chung, S. N. Burokur, A. D. Lustrac, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Broadband effective magnetic response of inorganic dielectric resonator-based metamaterial for microwave applications,” Appl. Phys., A Mater. Sci. Process. 114(3), 997–1002 (2014).
[Crossref]

Cai, G.

Cai, W.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
[Crossref] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Cao, L.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
[Crossref] [PubMed]

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

Capasso, F.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref] [PubMed]

Chen, J.

Chen, L.

Y. Shan, L. Chen, C. Shi, Z. Cheng, X. Zang, B. Xu, and Y. Zhu, “Ultrathin flexible dual band terahertz absorber,” Opt. Commun. 350, 63–70 (2015).
[Crossref]

Chen, P.

Chen, S.

X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, and J. Tian, “Polarization-insensitive and wide-angle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime,” J. Opt. 16(12), 125107 (2014).
[Crossref]

Chen, Y.

L. Ye, Y. Chen, G. Cai, N. Liu, J. Zhu, Z. Song, and Q. H. Liu, “Broadband absorber with periodically sinusoidally-patterned graphene layer in terahertz range,” Opt. Express 25(10), 11223–11232 (2017).
[Crossref] [PubMed]

F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
[Crossref] [PubMed]

Cheng, H.

X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, and J. Tian, “Polarization-insensitive and wide-angle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime,” J. Opt. 16(12), 125107 (2014).
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Y. Pang, H. Cheng, Y. Zhou, and J. Wang, “Analysis and design of wire-based metamaterial absorbers using equivalent circuit approach,” J. Appl. Phys. 113(11), 114902 (2013).
[Crossref]

Cheng, Z.

Y. Shan, L. Chen, C. Shi, Z. Cheng, X. Zang, B. Xu, and Y. Zhu, “Ultrathin flexible dual band terahertz absorber,” Opt. Commun. 350, 63–70 (2015).
[Crossref]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
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R. Yahiaoui, U. C. Chung, S. N. Burokur, A. D. Lustrac, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Broadband effective magnetic response of inorganic dielectric resonator-based metamaterial for microwave applications,” Appl. Phys., A Mater. Sci. Process. 114(3), 997–1002 (2014).
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L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

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B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4(2), 4130 (2014).
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F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
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Ding, F.

F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
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X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, and J. Tian, “Polarization-insensitive and wide-angle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime,” J. Opt. 16(12), 125107 (2014).
[Crossref]

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R. Yahiaoui, U. C. Chung, S. N. Burokur, A. D. Lustrac, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Broadband effective magnetic response of inorganic dielectric resonator-based metamaterial for microwave applications,” Appl. Phys., A Mater. Sci. Process. 114(3), 997–1002 (2014).
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A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
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L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
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L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
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Feng, Y.

Fenollosa, R.

L. Shi, T. U. Tuzer, R. Fenollosa, and F. Meseguer, “A New Dielectric Metamaterial Building Block with a Strong Magnetic Response in the Sub-1.5-Micrometer Region: Silicon Colloid Nanocavities,” Adv. Mater. 24(44), 5934–5938 (2012).
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Gao, F.

Gao, R. M.

Ge, L.

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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Guo, C.

J. Yang, Z. Zhu, J. Zhang, C. Guo, W. Xu, K. Liu, X. Yuan, and S. Qin, “Broadband terahertz absorber based on multi-band continuous plasmon resonances in geometrically gradient dielectric-loaded graphene plasmon structure,” Sci. Rep. 8(1), 3239 (2018).
[Crossref] [PubMed]

F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017).
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Z. Zhu, C. Guo, J. Zhang, K. Liu, X. Yuan, and S. Qin, “Broadband single-layered graphene absorber using periodic arrays of graphene ribbons with gradient width,” Appl. Phys. Express 8(1), 015102 (2015).
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Guo, C. C.

Han, D.

Hao, Y.

B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4(2), 4130 (2014).
[PubMed]

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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He, Y.

Horng, J.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Jiang, T.

Jiang, Y.

Jiao, Z.

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterial,” AIP Adv. 5(6), 067106 (2015).
[Crossref]

Jin, Y.

J. Chen, Y. Jin, P. Chen, Y. Shan, J. Xu, F. Kong, and J. Shao, “Polarization-independent almost-perfect absorber controlled from narrowband to broadband,” Opt. Express 25(12), 13916–13922 (2017).
[Crossref] [PubMed]

F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
[Crossref] [PubMed]

Ju, D.

Ju, L.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
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K. Arik, S. Abdollahramezani, and A. Khavasi, “Polarization Insensitive and Broadband Terahertz Absorber Using Graphene Disks,” Plasmonics 12(2), 393 (2017).
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A. Khavasi, “Design of ultra-broadband graphene absorber using circuit theory,” J. Opt. Soc. Am. B 32(9), 1941–1946 (2015).
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W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Kong, F.

Kong, J.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
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Kotakoski, J.

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
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Krasheninnikov, A. V.

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
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Krishna, S.

Landy, N. I.

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).
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Lee, D.

D. M. Nguyen, D. Lee, and J. Rho, “Control of light absorbance using plasmonic grating based perfect absorber at visible and near-infrared wavelengths,” Sci. Rep. 7(1), 2611 (2017).
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X. Zhang, H. Li, Z. Wei, and L. Qi, “Metamaterial for polarization-incident angle independent broadband perfect absorption in the terahertz range,” Opt. Mater. Express 7(9), 3294–3302 (2017).
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H. Li, L. Wang, and X. Zhai, “Tunable graphene-based mid-infrared plasmonic wide-angle narrowband perfect absorber,” Sci. Rep. 6(1), 36651 (2016).
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X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, and J. Tian, “Polarization-insensitive and wide-angle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime,” J. Opt. 16(12), 125107 (2014).
[Crossref]

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Liao, Y. L.

Ling, F.

Liu, K.

J. Yang, Z. Zhu, J. Zhang, C. Guo, W. Xu, K. Liu, X. Yuan, and S. Qin, “Broadband terahertz absorber based on multi-band continuous plasmon resonances in geometrically gradient dielectric-loaded graphene plasmon structure,” Sci. Rep. 8(1), 3239 (2018).
[Crossref] [PubMed]

F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017).
[Crossref] [PubMed]

Z. Zhu, C. Guo, J. Zhang, K. Liu, X. Yuan, and S. Qin, “Broadband single-layered graphene absorber using periodic arrays of graphene ribbons with gradient width,” Appl. Phys. Express 8(1), 015102 (2015).
[Crossref]

Z. H. Zhu, C. C. Guo, K. Liu, W. M. Ye, X. D. Yuan, B. Yang, and T. Ma, “Metallic nanofilm half-wave plate based on magnetic plasmon resonance,” Opt. Lett. 37(4), 698–700 (2012).
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Liu, L.

Liu, N.

Liu, Q. H.

Liu, S.

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterial,” AIP Adv. 5(6), 067106 (2015).
[Crossref]

Liu, W.

X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, and J. Tian, “Polarization-insensitive and wide-angle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime,” J. Opt. 16(12), 125107 (2014).
[Crossref]

Liu, Y.

Loncar, M.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref] [PubMed]

Luo, C.

Lustrac, A. D.

R. Yahiaoui, U. C. Chung, S. N. Burokur, A. D. Lustrac, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Broadband effective magnetic response of inorganic dielectric resonator-based metamaterial for microwave applications,” Appl. Phys., A Mater. Sci. Process. 114(3), 997–1002 (2014).
[Crossref]

Ma, T.

Ma, W.

Maglione, M.

R. Yahiaoui, U. C. Chung, S. N. Burokur, A. D. Lustrac, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Broadband effective magnetic response of inorganic dielectric resonator-based metamaterial for microwave applications,” Appl. Phys., A Mater. Sci. Process. 114(3), 997–1002 (2014).
[Crossref]

Martin, M.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Matmon, G.

Meseguer, F.

L. Shi, T. U. Tuzer, R. Fenollosa, and F. Meseguer, “A New Dielectric Metamaterial Building Block with a Strong Magnetic Response in the Sub-1.5-Micrometer Region: Silicon Colloid Nanocavities,” Adv. Mater. 24(44), 5934–5938 (2012).
[Crossref] [PubMed]

Milne, W. I.

B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4(2), 4130 (2014).
[PubMed]

Mock, J. J.

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]

Mohammadi Estakhri, N.

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91(19), 195444 (2015).
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Montoya, J. A.

Mounaix, P.

R. Yahiaoui, U. C. Chung, S. N. Burokur, A. D. Lustrac, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Broadband effective magnetic response of inorganic dielectric resonator-based metamaterial for microwave applications,” Appl. Phys., A Mater. Sci. Process. 114(3), 997–1002 (2014).
[Crossref]

Naeem, M.

B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4(2), 4130 (2014).
[PubMed]

Nguyen, D. M.

D. M. Nguyen, D. Lee, and J. Rho, “Control of light absorbance using plasmonic grating based perfect absorber at visible and near-infrared wavelengths,” Sci. Rep. 7(1), 2611 (2017).
[Crossref] [PubMed]

Ning, R.

R. Ning, S. Liu, H. Zhang, and Z. Jiao, “Dual-gated tunable absorption in graphene-based hyperbolic metamaterial,” AIP Adv. 5(6), 067106 (2015).
[Crossref]

Novoselov, K. S.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Orazbayev, B.

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91(19), 195444 (2015).
[Crossref]

Padilla, W. J.

J. A. Montoya, Z. B. Tian, S. Krishna, and W. J. Padilla, “Ultra-thin infrared metamaterial detector for multicolor imaging applications,” Opt. Express 25(19), 23343–23355 (2017).
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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]

Pang, Y.

Y. Pang, H. Cheng, Y. Zhou, and J. Wang, “Analysis and design of wire-based metamaterial absorbers using equivalent circuit approach,” J. Appl. Phys. 113(11), 114902 (2013).
[Crossref]

Park, J. S.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Polman, A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref] [PubMed]

Qi, L.

Qin, S.

J. Yang, Z. Zhu, J. Zhang, C. Guo, W. Xu, K. Liu, X. Yuan, and S. Qin, “Broadband terahertz absorber based on multi-band continuous plasmon resonances in geometrically gradient dielectric-loaded graphene plasmon structure,” Sci. Rep. 8(1), 3239 (2018).
[Crossref] [PubMed]

F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017).
[Crossref] [PubMed]

Z. Zhu, C. Guo, J. Zhang, K. Liu, X. Yuan, and S. Qin, “Broadband single-layered graphene absorber using periodic arrays of graphene ribbons with gradient width,” Appl. Phys. Express 8(1), 015102 (2015).
[Crossref]

Qiu, J.

Rho, J.

D. M. Nguyen, D. Lee, and J. Rho, “Control of light absorbance using plasmonic grating based perfect absorber at visible and near-infrared wavelengths,” Sci. Rep. 7(1), 2611 (2017).
[Crossref] [PubMed]

Sajuyigbe, S.

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]

Sang, T.

B. X. Wang, G. Z. Wang, T. Sang, and L. L. Wang, “Six-band terahertz metamaterial absorber based on the combination of multiple-order responses of metallic patches in a dual-layer stacked resonance structure,” Sci. Rep. 7(1), 41373 (2017).
[Crossref] [PubMed]

Santos-Cottin, D.

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
[Crossref] [PubMed]

Schuller, J. A.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
[Crossref] [PubMed]

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[Crossref] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Shan, Y.

J. Chen, Y. Jin, P. Chen, Y. Shan, J. Xu, F. Kong, and J. Shao, “Polarization-independent almost-perfect absorber controlled from narrowband to broadband,” Opt. Express 25(12), 13916–13922 (2017).
[Crossref] [PubMed]

Y. Shan, L. Chen, C. Shi, Z. Cheng, X. Zang, B. Xu, and Y. Zhu, “Ultrathin flexible dual band terahertz absorber,” Opt. Commun. 350, 63–70 (2015).
[Crossref]

Shankar, R.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref] [PubMed]

Shao, J.

Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Shi, C.

Y. Shan, L. Chen, C. Shi, Z. Cheng, X. Zang, B. Xu, and Y. Zhu, “Ultrathin flexible dual band terahertz absorber,” Opt. Commun. 350, 63–70 (2015).
[Crossref]

Shi, L.

L. Shi, T. U. Tuzer, R. Fenollosa, and F. Meseguer, “A New Dielectric Metamaterial Building Block with a Strong Magnetic Response in the Sub-1.5-Micrometer Region: Silicon Colloid Nanocavities,” Adv. Mater. 24(44), 5934–5938 (2012).
[Crossref] [PubMed]

Shi, X.

Smith, D. R.

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]

Song, Y.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref] [PubMed]

Song, Z.

Spinelli, P.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
[Crossref] [PubMed]

Tian, J.

X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, and J. Tian, “Polarization-insensitive and wide-angle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime,” J. Opt. 16(12), 125107 (2014).
[Crossref]

Tian, Z. B.

Tuncer, H. M.

B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4(2), 4130 (2014).
[PubMed]

Tuzer, T. U.

L. Shi, T. U. Tuzer, R. Fenollosa, and F. Meseguer, “A New Dielectric Metamaterial Building Block with a Strong Magnetic Response in the Sub-1.5-Micrometer Region: Silicon Colloid Nanocavities,” Adv. Mater. 24(44), 5934–5938 (2012).
[Crossref] [PubMed]

Vakil, A.

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

Vasudev, A. P.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
[Crossref] [PubMed]

Verschuuren, M. A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3(1), 692 (2012).
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Vigneras, V.

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B. X. Wang, G. Z. Wang, T. Sang, and L. L. Wang, “Six-band terahertz metamaterial absorber based on the combination of multiple-order responses of metallic patches in a dual-layer stacked resonance structure,” Sci. Rep. 7(1), 41373 (2017).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Wang, G. Z.

B. X. Wang, G. Z. Wang, T. Sang, and L. L. Wang, “Six-band terahertz metamaterial absorber based on the combination of multiple-order responses of metallic patches in a dual-layer stacked resonance structure,” Sci. Rep. 7(1), 41373 (2017).
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Wang, J.

Y. Pang, H. Cheng, Y. Zhou, and J. Wang, “Analysis and design of wire-based metamaterial absorbers using equivalent circuit approach,” J. Appl. Phys. 113(11), 114902 (2013).
[Crossref]

Wang, L.

H. Li, L. Wang, and X. Zhai, “Tunable graphene-based mid-infrared plasmonic wide-angle narrowband perfect absorber,” Sci. Rep. 6(1), 36651 (2016).
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Wang, L. L.

B. X. Wang, G. Z. Wang, T. Sang, and L. L. Wang, “Six-band terahertz metamaterial absorber based on the combination of multiple-order responses of metallic patches in a dual-layer stacked resonance structure,” Sci. Rep. 7(1), 41373 (2017).
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L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
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Y. Shan, L. Chen, C. Shi, Z. Cheng, X. Zang, B. Xu, and Y. Zhu, “Ultrathin flexible dual band terahertz absorber,” Opt. Commun. 350, 63–70 (2015).
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Xu, W.

J. Yang, Z. Zhu, J. Zhang, C. Guo, W. Xu, K. Liu, X. Yuan, and S. Qin, “Broadband terahertz absorber based on multi-band continuous plasmon resonances in geometrically gradient dielectric-loaded graphene plasmon structure,” Sci. Rep. 8(1), 3239 (2018).
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W. Xu, L. Xie, and Y. Ying, “Mechanisms and applications of terahertz metamaterial sensing: a review,” Nanoscale 9(37), 13864–13878 (2017).
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F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017).
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B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4(2), 4130 (2014).
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L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor Nanowire Optical Antenna Solar Absorbers,” Nano Lett. 10(2), 439–445 (2010).
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J. Yang, Z. Zhu, J. Zhang, C. Guo, W. Xu, K. Liu, X. Yuan, and S. Qin, “Broadband terahertz absorber based on multi-band continuous plasmon resonances in geometrically gradient dielectric-loaded graphene plasmon structure,” Sci. Rep. 8(1), 3239 (2018).
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F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017).
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Yue, J.

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F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017).
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Z. Zhu, C. Guo, J. Zhang, K. Liu, X. Yuan, and S. Qin, “Broadband single-layered graphene absorber using periodic arrays of graphene ribbons with gradient width,” Appl. Phys. Express 8(1), 015102 (2015).
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Y. Pang, H. Cheng, Y. Zhou, and J. Wang, “Analysis and design of wire-based metamaterial absorbers using equivalent circuit approach,” J. Appl. Phys. 113(11), 114902 (2013).
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F. Ding, J. Dai, Y. Chen, J. Zhu, Y. Jin, and S. I. Bozhevolnyi, “Broadband near-infrared metamaterial absorbers utilizing highly lossy metals,” Sci. Rep. 6(1), 39445 (2016).
[Crossref] [PubMed]

Zhu, Y.

Y. Shan, L. Chen, C. Shi, Z. Cheng, X. Zang, B. Xu, and Y. Zhu, “Ultrathin flexible dual band terahertz absorber,” Opt. Commun. 350, 63–70 (2015).
[Crossref]

Zhu, Z.

J. Yang, Z. Zhu, J. Zhang, C. Guo, W. Xu, K. Liu, X. Yuan, and S. Qin, “Broadband terahertz absorber based on multi-band continuous plasmon resonances in geometrically gradient dielectric-loaded graphene plasmon structure,” Sci. Rep. 8(1), 3239 (2018).
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F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017).
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Z. Zhu, C. Guo, J. Zhang, K. Liu, X. Yuan, and S. Qin, “Broadband single-layered graphene absorber using periodic arrays of graphene ribbons with gradient width,” Appl. Phys. Express 8(1), 015102 (2015).
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R. Yahiaoui, U. C. Chung, S. N. Burokur, A. D. Lustrac, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Broadband effective magnetic response of inorganic dielectric resonator-based metamaterial for microwave applications,” Appl. Phys., A Mater. Sci. Process. 114(3), 997–1002 (2014).
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B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4(2), 4130 (2014).
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Supplementary Material (1)

NameDescription
» Visualization 1       The animate field of 1.1 THz shows that the high-frequency absorption stems from the coupling of Mie resonance to graphene plasmon resonance.

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Figures (5)

Fig. 1
Fig. 1 Schematic representation of the broadband near-perfect absorber, consisting of monolayer graphene loaded with periodical dielectric wires supported by a piece of dielectric substrate on a metallic film.
Fig. 2
Fig. 2 (a) The absorption spectrum under normal incident wave with the electric field parallel to x-axis. (b) The ratio of the input impedance of the absorber to the impedance of the free space in the 99% absorption band. (c) Magnetic field amplitude patterns on the x-z plane for six representational frequencies in the 99% absorption band.
Fig. 3
Fig. 3 The absorption curves with varying Fermi level.
Fig. 4
Fig. 4 (a) The absorption curves with varying bottom width of the dielectric wire. (b) The absorption curves with varying tilt angle of the dielectric wire. (c) The absorption curves with varying height of the dielectric wire.
Fig. 5
Fig. 5 Calculated absorption as a function of frequency and incident angle θ.

Equations (9)

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Re( Z in / Z 0 )=1
Im( Z in / Z 0 )=0,
1/α Re( Z in / Z 0 )| f α
Im( Z in / Z 0 )| f 0,
A m =1 ( 1α 1+α ) 2 .
σ( ω ) 2 e 2 k B T π 2 i ω+i τ 1 ln( 2cosh E F 2 k B T ),
A1 | S 11 | 2 .
F= ( Z in Z 0 )/ ( Z in + Z 0 ) ,
Z in Z 0 = 1+ S 11 1 S 11 .

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