Abstract

In this paper, a bulk Dirac semimetals (BDSs) based tunable narrowband absorber at terahertz frequencies is proposed and it has the attractive property of being polarization-independent at normal incidence because of its 90° rotational symmetry. Numerical results show that the absorption bandwidth is about 1.469e-2 THz and the total quality factor Q, defined as Q = f0f, reaches about 94.6, which can be attributed to the low power loss of the guided mode resonance in the dielectric layer. The simulation results are analyzed with coupled mode theory. Interestingly, on the premise of maintaining the absorbance at a level greater than 0.95, the absorption frequency can be tuned from 1.381 to 1.395 THz by varying the Fermi energy of BDSs from 50 to 80 meV. Our results may also provide potential applications in optical filter and bio-chemical sensing.

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

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2018 (3)

G. D. Liu, X. Zhai, L. L. Wang, Q. Lin, S. X. Xia, X. Luo, and C. J. Zhao, “A High-Performance Refractive Index Sensor Based on Fano Resonance in Si Split-Ring Metasurface,” Plasmonics 13(1), 15–19 (2018).
[Crossref]

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

Z. Song, K. Wang, J. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018).
[Crossref] [PubMed]

2017 (10)

W. Zhu, F. Xiao, I. D. Rukhlenko, J. Geng, X. Liang, M. Premaratne, and R. Jin, “Wideband visible-light absorption in an ultrathin silicon nanostructure,” Opt. Express 25(5), 5781–5786 (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]

M. Luo, S. Shen, L. Zhou, S. Wu, Y. Zhou, and L. Chen, “Broadband, wide-angle, and polarization-independent metamaterial absorber for the visible regime,” Opt. Express 25(14), 16715–16724 (2017).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017).
[Crossref] [PubMed]

H. Chen, H. Zhang, M. Liu, Y. Zhao, X. Guo, and Y. Zhang, “Realization of tunable plasmon-induced transparency by bright-bright mode coupling in Dirac semimetals,” Opt. Mater. Express 7(9), 3397 (2017).
[Crossref]

J. Hwang and J. W. Roh, “Electrically tunable two-dimensional metasurfaces at near-infrared wavelengths,” Opt. Express 25(21), 25071–25078 (2017).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Graphene Surface Plasmons with Dielectric Metasurfaces,” J. Lightwave Technol. 35(20), 4553–4558 (2017).
[Crossref]

X. Jiang, T. Wang, S. Xiao, X. Yan, and L. Cheng, “Tunable ultra-high-efficiency light absorption of monolayer graphene using critical coupling with guided resonance,” Opt. Express 25(22), 27028–27036 (2017).
[Crossref] [PubMed]

H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (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]

2016 (9)

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

O. V. Kotov and Y. E. Lozovik, “Dielectric response and novel electromagnetic modes in three-dimensional Dirac semimetal films,” Phys. Rev. B 93(23), 235417 (2016).
[Crossref]

L. Zhang, S. Zhang, Z. Song, Y. Liu, L. Ye, and Q. H. Liu, “Adaptive Decoupling Using Tunable Metamaterials,” IEEE Trans. Microw. Theory 64(9), 2730–2739 (2016).
[Crossref]

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Z. Liu, G. Liu, G. Fu, X. Liu, and Y. Wang, “Multi-band light perfect absorption by a metal layer-coupled dielectric metamaterial,” Opt. Express 24(5), 5020–5025 (2016).
[Crossref] [PubMed]

C. Zou, P. Gutruf, W. Withayachumnankul, L. Zou, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Nanoscale TiO2 dielectric resonator absorbers,” Opt. Lett. 41(15), 3391–3394 (2016).
[Crossref] [PubMed]

Y. Chen, J. Yao, Z. Song, L. Ye, G. Cai, and Q. H. Liu, “Independent tuning of double plasmonic waves in a free-standing graphene-spacer-grating-spacer-graphene hybrid slab,” Opt. Express 24(15), 16961–16972 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, B. Sun, J. Q. Liu, and S. C. Wen, “Dynamically tunable plasmonically induced transparency in sinusoidally curved and planar graphene layers,” Opt. Express 24(16), 17886–17899 (2016).
[Crossref] [PubMed]

J. Xu, Z. Zhao, H. Yu, L. Yang, P. Gou, J. Cao, Y. Zou, J. Qian, T. Shi, Q. Ren, and Z. An, “Design of triple-band metamaterial absorbers with refractive index sensitivity at infrared frequencies,” Opt. Express 24(22), 25742–25751 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (6)

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1(4), 347–353 (2014).
[Crossref]

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (2014).
[Crossref]

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

B. X. Wang, L. L. Wang, G. Z. Wang, W. Q. Huang, X. F. Li, and X. Zhai, “Frequency continuous tunable terahertz metamaterial absorber,” J. Lightwave Technol. 32(6), 1183–1189 (2014).
[Crossref]

Z. Song and B. Zhang, “Wide-angle polarization-insensitive transparency of a continuous opaque metal film for near-infrared light,” Opt. Express 22(6), 6519–6525 (2014).
[Crossref] [PubMed]

2013 (4)

T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B 87(23), 235121 (2013).
[Crossref]

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Z. Li and N. Yu, “Modulation of mid-infrared light using graphene-metal plasmonic antennas,” Appl. Phys. Lett. 102(13), 131108 (2013).
[Crossref]

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

2012 (1)

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

2011 (3)

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

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]

B. Zhang, Y. Zhao, Q. Hao, B. Kiraly, I. C. Khoo, S. Chen, and T. J. Huang, “Polarization-independent dual-band infrared perfect absorber based on a metal-dielectric-metal elliptical nanodisk array,” Opt. Express 19(16), 15221–15228 (2011).
[Crossref] [PubMed]

2010 (2)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

2008 (2)

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]

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]

2002 (1)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[Crossref]

An, Z.

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Averitt, R. D.

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]

Bai, S.

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Basov, D. N.

T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B 87(23), 235121 (2013).
[Crossref]

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]

Bhaskaran, M.

Bian, R. B.

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (2014).
[Crossref]

Bingham, C. M.

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]

Cai, G.

Cao, J.

Capasso, F.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Carbotte, J. P.

T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B 87(23), 235121 (2013).
[Crossref]

Carver, S.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Chen, H.

Chen, L.

M. Luo, S. Shen, L. Zhou, S. Wu, Y. Zhou, and L. Chen, “Broadband, wide-angle, and polarization-independent metamaterial absorber for the visible regime,” Opt. Express 25(14), 16715–16724 (2017).
[Crossref] [PubMed]

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (2014).
[Crossref]

Chen, S.

Chen, X.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Chen, Y.

Chen, Y. L.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Cheng, L.

Copner, N.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Dai, X.

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Ding, P.

Du, K.

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Duan, T.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Dudin, P.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Fan, C.

Fan, K.

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]

Fan, S.

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1(4), 347–353 (2014).
[Crossref]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[Crossref]

Fang, Z.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Feng, D. L.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Fu, G.

Fumeaux, C.

Genevet, P.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Geng, J.

Giessen, H.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Girit, C.

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]

Gong, H.

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Gong, Y.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Gou, P.

Guo, X.

Gutruf, P.

Hao, Q.

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).
[Crossref] [PubMed]

He, J.

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Hoesch, M.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Homes, C. C.

T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B 87(23), 235121 (2013).
[Crossref]

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).
[Crossref] [PubMed]

Hu, J.

Hu, W.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Huang, J.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Huang, L.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Huang, T. J.

Huang, W. Q.

Huang, Y.

Hussain, Z.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Hwang, J.

Jiang, J.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Jiang, X.

Jiang, Y.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Jin, R.

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[Crossref]

Jokerst, N. M.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Kats, M. A.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Khoo, I. C.

Kim, T.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Kiraly, B.

Kong, J.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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Kotov, O. V.

O. V. Kotov and Y. E. Lozovik, “Dielectric response and novel electromagnetic modes in three-dimensional Dirac semimetal films,” Phys. Rev. B 93(23), 235417 (2016).
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Landy, N. I.

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]

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]

Li, G.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Li, H.

Li, J.

Li, K.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Li, O.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Li, Q.

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Li, X. F.

Li, Z.

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

Z. Li and N. Yu, “Modulation of mid-infrared light using graphene-metal plasmonic antennas,” Appl. Phys. Lett. 102(13), 131108 (2013).
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Liang, E.

Liang, X.

W. Zhu, F. Xiao, I. D. Rukhlenko, J. Geng, X. Liang, M. Premaratne, and R. Jin, “Wideband visible-light absorption in an ultrathin silicon nanostructure,” Opt. Express 25(5), 5781–5786 (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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Liao, Y. L.

Lin, Q.

G. D. Liu, X. Zhai, L. L. Wang, Q. Lin, S. X. Xia, X. Luo, and C. J. Zhao, “A High-Performance Refractive Index Sensor Based on Fano Resonance in Si Split-Ring Metasurface,” Plasmonics 13(1), 15–19 (2018).
[Crossref]

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

Liu, B. S.

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (2014).
[Crossref]

Liu, C. X.

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (2014).
[Crossref]

Liu, G.

Liu, G. D.

G. D. Liu, X. Zhai, L. L. Wang, Q. Lin, S. X. Xia, X. Luo, and C. J. Zhao, “A High-Performance Refractive Index Sensor Based on Fano Resonance in Si Split-Ring Metasurface,” Plasmonics 13(1), 15–19 (2018).
[Crossref]

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

Liu, J. Q.

Liu, M.

Liu, N.

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]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Liu, Q. H.

Liu, T.

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

Liu, X.

Z. Liu, G. Liu, G. Fu, X. Liu, and Y. Wang, “Multi-band light perfect absorption by a metal layer-coupled dielectric metamaterial,” Opt. Express 24(5), 5020–5025 (2016).
[Crossref] [PubMed]

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Liu, Y.

L. Zhang, S. Zhang, Z. Song, Y. Liu, L. Ye, and Q. H. Liu, “Adaptive Decoupling Using Tunable Metamaterials,” IEEE Trans. Microw. Theory 64(9), 2730–2739 (2016).
[Crossref]

Liu, Z.

Liu, Z. K.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Lozovik, Y. E.

O. V. Kotov and Y. E. Lozovik, “Dielectric response and novel electromagnetic modes in three-dimensional Dirac semimetal films,” Phys. Rev. B 93(23), 235417 (2016).
[Crossref]

Lu, W.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Lu, X.

Luo, M.

Luo, X.

G. D. Liu, X. Zhai, L. L. Wang, Q. Lin, S. X. Xia, X. Luo, and C. J. Zhao, “A High-Performance Refractive Index Sensor Based on Fano Resonance in Si Split-Ring Metasurface,” Plasmonics 13(1), 15–19 (2018).
[Crossref]

Ma, B.

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (2014).
[Crossref]

Mao, W. Z.

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (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]

Martinez, J. J.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Mesch, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Mo, S.-K.

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [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]

Ni, B.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Padilla, W. J.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

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]

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]

Peng, H.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Pilon, D.

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]

Piper, J. R.

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1(4), 347–353 (2014).
[Crossref]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Prabhakaran, D.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Premaratne, M.

Qian, J.

Qin, M.

Qiu, M.

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Qu, Y.

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Rees-Whippey, D.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Ren, Q.

Ren, R.

Roh, J. W.

Rukhlenko, I. D.

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]

Shang, X. J.

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

Shao, C.

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Sharapov, S. G.

T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B 87(23), 235121 (2013).
[Crossref]

Shen, S.

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]

Shen, Z. X.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Shi, T.

Shrekenhamer, D.

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]

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, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Song, Z.

Sriram, S.

Starr, A. F.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Starr, T.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Strikwerda, A. C.

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]

Sun, B.

Tao, H.

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]

Timusk, T.

T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B 87(23), 235121 (2013).
[Crossref]

Tyler, T.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Wang, B. X.

G. D. Liu, X. Zhai, L. L. Wang, B. X. Wang, Q. Lin, and X. J. Shang, “Actively tunable Fano resonance based on a T-shaped graphene nanodimer,” Plasmonics 11(2), 381–387 (2016).
[Crossref]

B. X. Wang, L. L. Wang, G. Z. Wang, W. Q. Huang, X. F. Li, and X. Zhai, “Frequency continuous tunable terahertz metamaterial absorber,” J. Lightwave Technol. 32(6), 1183–1189 (2014).
[Crossref]

Wang, F.

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]

Wang, G. Z.

Wang, J.

Wang, K.

Wang, L.

H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (2017).
[Crossref] [PubMed]

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Wang, L. L.

Wang, T.

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

X. Jiang, T. Wang, S. Xiao, X. Yan, and L. Cheng, “Tunable ultra-high-efficiency light absorption of monolayer graphene using critical coupling with guided resonance,” Opt. Express 25(22), 27028–27036 (2017).
[Crossref] [PubMed]

Wang, Y.

Z. Liu, G. Liu, G. Fu, X. Liu, and Y. Wang, “Multi-band light perfect absorption by a metal layer-coupled dielectric metamaterial,” Opt. Express 24(5), 5020–5025 (2016).
[Crossref] [PubMed]

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (2014).
[Crossref]

Wang, Z. J.

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Weiss, T.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Wen, S. C.

Weng, H. M.

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Withayachumnankul, W.

Wu, S.

Xia, S. X.

Xiao, F.

Xiao, S.

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

X. Jiang, T. Wang, S. Xiao, X. Yan, and L. Cheng, “Tunable ultra-high-efficiency light absorption of monolayer graphene using critical coupling with guided resonance,” Opt. Express 25(22), 27028–27036 (2017).
[Crossref] [PubMed]

Xu, C.

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

Xu, J.

Yan, X.

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

X. Jiang, T. Wang, S. Xiao, X. Yan, and L. Cheng, “Tunable ultra-high-efficiency light absorption of monolayer graphene using critical coupling with guided resonance,” Opt. Express 25(22), 27028–27036 (2017).
[Crossref] [PubMed]

Yang, L.

Yao, J.

Yao, Y.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Ye, H.

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Ye, L.

Yu, H.

Yu, N.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Z. Li and N. Yu, “Modulation of mid-infrared light using graphene-metal plasmonic antennas,” Appl. Phys. Lett. 102(13), 131108 (2013).
[Crossref]

Zettl, 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]

Zhai, X.

Zhang, B.

Zhang, H.

Zhang, L.

L. Zhang, S. Zhang, Z. Song, Y. Liu, L. Ye, and Q. H. Liu, “Adaptive Decoupling Using Tunable Metamaterials,” IEEE Trans. Microw. Theory 64(9), 2730–2739 (2016).
[Crossref]

X. Lu, L. Zhang, and T. Zhang, “Nanoslit-microcavity-based narrow band absorber for sensing applications,” Opt. Express 23(16), 20715–20720 (2015).
[Crossref] [PubMed]

Zhang, S.

L. Zhang, S. Zhang, Z. Song, Y. Liu, L. Ye, and Q. H. Liu, “Adaptive Decoupling Using Tunable Metamaterials,” IEEE Trans. Microw. Theory 64(9), 2730–2739 (2016).
[Crossref]

Zhang, T.

Zhang, W.

Y. Gong, X. Liu, K. Li, J. Huang, J. J. Martinez, D. Rees-Whippey, S. Carver, L. Wang, W. Zhang, T. Duan, and N. Copner, “Coherent emission of light using stacked gratings,” Phys. Rev. B 87(20), 205121 (2013).
[Crossref]

Zhang, X.

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]

Zhang, Y.

H. Chen, H. Zhang, M. Liu, Y. Zhao, X. Guo, and Y. Zhang, “Realization of tunable plasmon-induced transparency by bright-bright mode coupling in Dirac semimetals,” Opt. Mater. Express 7(9), 3397 (2017).
[Crossref]

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Zhao, C. J.

G. D. Liu, X. Zhai, L. L. Wang, Q. Lin, S. X. Xia, X. Luo, and C. J. Zhao, “A High-Performance Refractive Index Sensor Based on Fano Resonance in Si Split-Ring Metasurface,” Plasmonics 13(1), 15–19 (2018).
[Crossref]

Zhao, D.

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Zhao, Y.

Zhao, Z.

Zhou, B.

Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014).
[Crossref] [PubMed]

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Zhou, L.

Zhou, Y.

Zhu, J.

Zhu, W.

Zou, C.

Zou, L.

Zou, Y.

ACS Photonics (1)

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1(4), 347–353 (2014).
[Crossref]

Adv. Opt. Mater. (1)

Y. Qu, Q. Li, H. Gong, K. Du, S. Bai, D. Zhao, H. Ye, and M. Qiu, “Spatially and spectrally resolved narrowband optical absorber based on 2D grating nanostructures on metallic films,” Adv. Opt. Mater. 4(3), 480–486 (2016).
[Crossref]

Appl. Phys. Lett. (1)

Z. Li and N. Yu, “Modulation of mid-infrared light using graphene-metal plasmonic antennas,” Appl. Phys. Lett. 102(13), 131108 (2013).
[Crossref]

Carbon (1)

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

IEEE Trans. Microw. Theory (1)

L. Zhang, S. Zhang, Z. Song, Y. Liu, L. Ye, and Q. H. Liu, “Adaptive Decoupling Using Tunable Metamaterials,” IEEE Trans. Microw. Theory 64(9), 2730–2739 (2016).
[Crossref]

J. Appl. Phys. (1)

Y. Wang, B. S. Liu, R. B. Bian, W. Z. Mao, C. X. Liu, B. Ma, and L. Chen, “A novel ultrathin and broadband microwave metamaterial absorber,” J. Appl. Phys. 116(9), 094504 (2014).
[Crossref]

J. Lightwave Technol. (2)

J. Phys. D Appl. Phys. (1)

G. Li, X. Chen, O. Li, C. Shao, Y. Jiang, L. Huang, B. Ni, W. Hu, and W. Lu, “A novel plasmonic resonance sensor based on an infrared perfect absorber,” J. Phys. D Appl. Phys. 45(20), 2202 (2012).
[Crossref]

Nano Lett. (2)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref] [PubMed]

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Nat. Mater. (2)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

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]

Opt. Express (16)

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]

Z. Song and B. Zhang, “Wide-angle polarization-insensitive transparency of a continuous opaque metal film for near-infrared light,” Opt. Express 22(6), 6519–6525 (2014).
[Crossref] [PubMed]

Z. Liu, G. Liu, G. Fu, X. Liu, and Y. Wang, “Multi-band light perfect absorption by a metal layer-coupled dielectric metamaterial,” Opt. Express 24(5), 5020–5025 (2016).
[Crossref] [PubMed]

Y. Chen, J. Yao, Z. Song, L. Ye, G. Cai, and Q. H. Liu, “Independent tuning of double plasmonic waves in a free-standing graphene-spacer-grating-spacer-graphene hybrid slab,” Opt. Express 24(15), 16961–16972 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, B. Sun, J. Q. Liu, and S. C. Wen, “Dynamically tunable plasmonically induced transparency in sinusoidally curved and planar graphene layers,” Opt. Express 24(16), 17886–17899 (2016).
[Crossref] [PubMed]

X. Lu, L. Zhang, and T. Zhang, “Nanoslit-microcavity-based narrow band absorber for sensing applications,” Opt. Express 23(16), 20715–20720 (2015).
[Crossref] [PubMed]

J. He, P. Ding, J. Wang, C. Fan, and E. Liang, “Ultra-narrow band perfect absorbers based on plasmonic analog of electromagnetically induced absorption,” Opt. Express 23(5), 6083–6091 (2015).
[Crossref] [PubMed]

Z. Song, K. Wang, J. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018).
[Crossref] [PubMed]

J. Xu, Z. Zhao, H. Yu, L. Yang, P. Gou, J. Cao, Y. Zou, J. Qian, T. Shi, Q. Ren, and Z. An, “Design of triple-band metamaterial absorbers with refractive index sensitivity at infrared frequencies,” Opt. Express 24(22), 25742–25751 (2016).
[Crossref] [PubMed]

B. Zhang, Y. Zhao, Q. Hao, B. Kiraly, I. C. Khoo, S. Chen, and T. J. Huang, “Polarization-independent dual-band infrared perfect absorber based on a metal-dielectric-metal elliptical nanodisk array,” Opt. Express 19(16), 15221–15228 (2011).
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W. Zhu, F. Xiao, I. D. Rukhlenko, J. Geng, X. Liang, M. Premaratne, and R. Jin, “Wideband visible-light absorption in an ultrathin silicon nanostructure,” Opt. Express 25(5), 5781–5786 (2017).
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M. Luo, S. Shen, L. Zhou, S. Wu, Y. Zhou, and L. Chen, “Broadband, wide-angle, and polarization-independent metamaterial absorber for the visible regime,” Opt. Express 25(14), 16715–16724 (2017).
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X. Jiang, T. Wang, S. Xiao, X. Yan, and L. Cheng, “Tunable ultra-high-efficiency light absorption of monolayer graphene using critical coupling with guided resonance,” Opt. Express 25(22), 27028–27036 (2017).
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Opt. Lett. (2)

Opt. Mater. Express (1)

Phys. Rev. B (5)

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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G. D. Liu, X. Zhai, L. L. Wang, Q. Lin, S. X. Xia, X. Luo, and C. J. Zhao, “A High-Performance Refractive Index Sensor Based on Fano Resonance in Si Split-Ring Metasurface,” Plasmonics 13(1), 15–19 (2018).
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Science (1)

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[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 Schematic of the proposed metasurface composed of the upper photonic crystal slab with circular air holes and the lower thick BDSs films. Corresponding electromagnetic excitation configuration (with polarization direction along the x axis) and geometric parameters are denoted by black letters in Fig. 1.
Fig. 2
Fig. 2 (a) The real and (b) imaginary parts of the dynamic conductivity for BDSs (normalized to 1 nm of the thickness) at zero temperature in units e2/ℏ as a function of the normalized frequency ℏω/EF. The parameters of BDSs are set as g = 40, εc = 3, τ = 4.5 × 10−13 s.
Fig. 3
Fig. 3 (a) The absorption spectra of the proposed absorber. The red curve (blue point) is the numerical (theoretical) result achieved by the FDTD (coupled mode theory) method. (b) Electric field |EZ|2 distributions of the proposed absorber at the resonance frequency of f0 = 1.3898 THz. (c) Electric field |EZ|2 distributions of the cross section of the proposed absorber at the resonance frequency of f0 = 1.3898 THz. The air hole and the slab boundaries are indicated by the white lines.
Fig. 4
Fig. 4 Absorption spectra for different EF of the BDSs.
Fig. 5
Fig. 5 (a) The real and (b) imaginary parts of the permittivity of BDSs.
Fig. 6
Fig. 6 Absorption spectra for (a) different diameter D, (b) different height H, (c) different period P, and (d) surrounding medium with different refractive index n, respectively.
Fig. 7
Fig. 7 The schematic diagrams of oblique incidence plane wave for (a) TE polarizations and (b) TM polarizations, respectively. Absorption spectra for different incident angle with (c) TE polarizations and (d) TM polarizations, respectively. The magnetic field HZ distributions are shown at the resonance frequency of (e) R2 mode (fR2 ≈1.31 THz) and (f) R1 mode (fR1 ≈1.40 THz) for the absorber illuminated by TM-polarized plane wave with the incidence angle θ = 15°. The air hole boundaries are indicated by the white lines.

Equations (6)

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Re( σ( Ω ) )= e 2 g k F 24π Ωθ( Ω2 )
Im( σ( Ω ) )= e 2 g k F 24 π 2 [ 4 Ω ΩIn( 4 ε c 2 | Ω 2 4 | ) ]
ε= ε b +iσ/ω ε 0
r= s s + = j( ω  ω 0 )+ δ γ e   j( ω  ω 0 )+ δ+ γ e
A=  4δ γ e ( ω  ω 0 ) 2 +  ( δ+ γ e ) 2
Δω   ω 0 =  ω- ω 0 ω 0   V dV[ ( Δ ε   E )  E 0 * + ( Δ μ    H )   H 0 * ] dV( ε | E 0 | 2 + μ | H 0 | 2 )

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