Abstract

A novel multilayer photonic structure is proposed to achieve the strong enhancement of light absorption in monolayer molybdenum disulfide (MoS2). Both numerical and analytical results illustrate that the absolute absorption of light in this atomically thin layer can approach as high as 96% at the visible wavelengths due to the excitation of Tamm plasmon mode. It is also found that the operating wavelength and height of sharp absorption peak are particularly dependent on the layer thicknesses and period number of dielectric grating, MoS2 position in the spacer, and incident angle of light, which contribute to the tunability and selectivity of light-MoS2 interaction. These results would provide a new pathway for the improvement of MoS2 photoluminescence and photodetection.

© 2017 Optical Society of America

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    [Crossref]

2017 (2)

2016 (4)

H. Lu, X. Gan, B. Jia, D. Mao, and J. Zhao, “Tunable high-efficiency light absorption of monolayer graphene via Tamm plasmon polaritons,” Opt. Lett. 41(20), 4743–4746 (2016).
[Crossref] [PubMed]

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

S. Bahauddin, H. Robatjazi, and I. Thomann, “Broadband absorption engineering to enhance light absorption in monolayer MoS2,” ACS Photonics 3(5), 853–862 (2016).
[Crossref]

J. Piper and S. Fan, “Broadband absorption enhancement in solar cells with an atomically thin active layer,” ACS Photonics 3(4), 571–577 (2016).
[Crossref]

2015 (5)

S. Butun, S. Tongay, and K. Aydin, “Enhanced light emission from large-area monolayer MoS2 using plasmonic nanodisc arrays,” Nano Lett. 15(4), 2700–2704 (2015).
[Crossref] [PubMed]

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

H. Wang, C. Zhang, W. Chan, S. Tiwari, and F. Rana, “Ultrafast response of monolayer molybdenum disulfide photodetectors,” Nat. Commun. 6, 8831 (2015).
[Crossref] [PubMed]

H. Lu, B. P. Cumming, and M. Gu, “Highly efficient plasmonic enhancement of graphene absorption at telecommunication wavelengths,” Opt. Lett. 40(15), 3647–3650 (2015).
[Crossref] [PubMed]

2014 (7)

J. 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. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

B. Zhao, J. M. Zhao, and Z. M. Zhang, “Enhancement of near-infrared absorption in graphene with metal gratings,” Appl. Phys. Lett. 105(3), 031905 (2014).
[Crossref]

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

Z. Sun and H. Chang, “Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology,” ACS Nano 8(5), 4133–4156 (2014).
[Crossref] [PubMed]

J. Zheng, R. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1(9), 768–774 (2014).
[Crossref]

2013 (2)

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2.,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref] [PubMed]

M. Bernardi, M. Palummo, and J. C. Grossman, “Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials,” Nano Lett. 13(8), 3664–3670 (2013).
[Crossref] [PubMed]

2012 (1)

X. Zhang, J. Song, X. Li, J. Feng, and H. Sun, “Optical Tamm states enhanced broad-band absorption of organic solar cells,” Appl. Phys. Lett. 101(24), 243901 (2012).
[Crossref]

2011 (2)

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Opt. Express 19(19), 18393–18398 (2011).
[Crossref] [PubMed]

2010 (1)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

2007 (1)

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

1972 (1)

P. Johnson and R. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Abram, R.

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

Aydin, K.

S. Butun, S. Tongay, and K. Aydin, “Enhanced light emission from large-area monolayer MoS2 using plasmonic nanodisc arrays,” Nano Lett. 15(4), 2700–2704 (2015).
[Crossref] [PubMed]

Bahauddin, S.

S. Bahauddin, H. Robatjazi, and I. Thomann, “Broadband absorption engineering to enhance light absorption in monolayer MoS2,” ACS Photonics 3(5), 853–862 (2016).
[Crossref]

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Barton, R.

J. Zheng, R. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1(9), 768–774 (2014).
[Crossref]

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Bernardi, M.

M. Bernardi, M. Palummo, and J. C. Grossman, “Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials,” Nano Lett. 13(8), 3664–3670 (2013).
[Crossref] [PubMed]

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Brand, S.

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

Butun, S.

S. Butun, S. Tongay, and K. Aydin, “Enhanced light emission from large-area monolayer MoS2 using plasmonic nanodisc arrays,” Nano Lett. 15(4), 2700–2704 (2015).
[Crossref] [PubMed]

Chamberlain, J.

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

Chan, W.

H. Wang, C. Zhang, W. Chan, S. Tiwari, and F. Rana, “Ultrafast response of monolayer molybdenum disulfide photodetectors,” Nat. Commun. 6, 8831 (2015).
[Crossref] [PubMed]

Chang, H.

Z. Sun and H. Chang, “Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology,” ACS Nano 8(5), 4133–4156 (2014).
[Crossref] [PubMed]

Chen, X.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Chenet, D.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Cheng, J.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Chernikov, A.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Christy, R.

P. Johnson and R. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Chu, S.

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Cumming, B. P.

Deng, H.

Dubey, M.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

Englund, D.

J. Zheng, R. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1(9), 768–774 (2014).
[Crossref]

Fan, S.

J. Piper and S. Fan, “Broadband absorption enhancement in solar cells with an atomically thin active layer,” ACS Photonics 3(4), 571–577 (2016).
[Crossref]

J. 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]

Feng, J.

X. Zhang, J. Song, X. Li, J. Feng, and H. Sun, “Optical Tamm states enhanced broad-band absorption of organic solar cells,” Appl. Phys. Lett. 101(24), 243901 (2012).
[Crossref]

Ferrari, A. C.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Gan, X.

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photonics Res. 5(3), 162–167 (2017).
[Crossref]

H. Lu, X. Gan, B. Jia, D. Mao, and J. Zhao, “Tunable high-efficiency light absorption of monolayer graphene via Tamm plasmon polaritons,” Opt. Lett. 41(20), 4743–4746 (2016).
[Crossref] [PubMed]

Gong, Q.

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Gong, Y.

Grossman, J. C.

M. Bernardi, M. Palummo, and J. C. Grossman, “Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials,” Nano Lett. 13(8), 3664–3670 (2013).
[Crossref] [PubMed]

Gu, M.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

H. Lu, B. P. Cumming, and M. Gu, “Highly efficient plasmonic enhancement of graphene absorption at telecommunication wavelengths,” Opt. Lett. 40(15), 3647–3650 (2015).
[Crossref] [PubMed]

Guo, C.

Guo, W.

Halas, N.

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

Hasan, T.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Heinz, T.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Hill, H.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Hone, J.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Hossain, M. M.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Hu, W.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Huang, W.

Iorsh, I.

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

Ji, Q.

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Jia, B.

Jing, Y.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Johnson, P.

P. Johnson and R. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kaliteevski, M.

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

Kavokin, A.

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

Kayci, M.

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2.,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref] [PubMed]

Kis, A.

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2.,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref] [PubMed]

Lauchner, A.

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

Lembke, D.

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2.,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref] [PubMed]

Li, J.

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Li, L.

Li, X.

X. Zhang, J. Song, X. Li, J. Feng, and H. Sun, “Optical Tamm states enhanced broad-band absorption of organic solar cells,” Appl. Phys. Lett. 101(24), 243901 (2012).
[Crossref]

Li, Y.

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Liao, L.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Lim, C.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Lin, H.

Liu, C.

Liu, K.

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Liu, X.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Opt. Express 19(19), 18393–18398 (2011).
[Crossref] [PubMed]

Loh, K.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Long, Y.

Lopez-Sanchez, O.

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2.,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref] [PubMed]

Lou, J.

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

Lu, H.

Lu, W.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Luo, W.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Mao, D.

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photonics Res. 5(3), 162–167 (2017).
[Crossref]

H. Lu, X. Gan, B. Jia, D. Mao, and J. Zhao, “Tunable high-efficiency light absorption of monolayer graphene via Tamm plasmon polaritons,” Opt. Lett. 41(20), 4743–4746 (2016).
[Crossref] [PubMed]

Miao, J.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Najmaei, S.

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

Ni, Z.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Orozco, C.

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

Palummo, M.

M. Bernardi, M. Palummo, and J. C. Grossman, “Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials,” Nano Lett. 13(8), 3664–3670 (2013).
[Crossref] [PubMed]

Pan, A.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Peng, W.

Piper, J.

J. Piper and S. Fan, “Broadband absorption enhancement in solar cells with an atomically thin active layer,” ACS Photonics 3(4), 571–577 (2016).
[Crossref]

J. 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]

Popa, D.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Privitera, G.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Radenovic, A.

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2.,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref] [PubMed]

Ramasubramaniam, A.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

Rana, F.

H. Wang, C. Zhang, W. Chan, S. Tiwari, and F. Rana, “Ultrafast response of monolayer molybdenum disulfide photodetectors,” Nat. Commun. 6, 8831 (2015).
[Crossref] [PubMed]

Reineck, P.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Rigosi, A.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Robatjazi, H.

S. Bahauddin, H. Robatjazi, and I. Thomann, “Broadband absorption engineering to enhance light absorption in monolayer MoS2,” ACS Photonics 3(5), 853–862 (2016).
[Crossref]

Shelykh, I.

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

Shen, L.

Shi, K.

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Shih, E.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Sobhani, A.

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

Song, J.

X. Zhang, J. Song, X. Li, J. Feng, and H. Sun, “Optical Tamm states enhanced broad-band absorption of organic solar cells,” Appl. Phys. Lett. 101(24), 243901 (2012).
[Crossref]

Sun, H.

X. Zhang, J. Song, X. Li, J. Feng, and H. Sun, “Optical Tamm states enhanced broad-band absorption of organic solar cells,” Appl. Phys. Lett. 101(24), 243901 (2012).
[Crossref]

Sun, Z.

Z. Sun and H. Chang, “Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology,” ACS Nano 8(5), 4133–4156 (2014).
[Crossref] [PubMed]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Tang, D.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Thomann, I.

S. Bahauddin, H. Robatjazi, and I. Thomann, “Broadband absorption engineering to enhance light absorption in monolayer MoS2,” ACS Photonics 3(5), 853–862 (2016).
[Crossref]

Tiwari, S.

H. Wang, C. Zhang, W. Chan, S. Tiwari, and F. Rana, “Ultrafast response of monolayer molybdenum disulfide photodetectors,” Nat. Commun. 6, 8831 (2015).
[Crossref] [PubMed]

Tongay, S.

S. Butun, S. Tongay, and K. Aydin, “Enhanced light emission from large-area monolayer MoS2 using plasmonic nanodisc arrays,” Nano Lett. 15(4), 2700–2704 (2015).
[Crossref] [PubMed]

Torrisi, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Wang, B.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Wang, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Wang, G.

Wang, H.

H. Wang, C. Zhang, W. Chan, S. Tiwari, and F. Rana, “Ultrafast response of monolayer molybdenum disulfide photodetectors,” Nat. Commun. 6, 8831 (2015).
[Crossref] [PubMed]

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

Wang, L.

Wang, Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Wen, F.

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

Wu, S.

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Xia, F.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

Xiao, D.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

Xu, H.

Zande, A.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

Zeng, C.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Zhang, C.

H. Wang, C. Zhang, W. Chan, S. Tiwari, and F. Rana, “Ultrafast response of monolayer molybdenum disulfide photodetectors,” Nat. Commun. 6, 8831 (2015).
[Crossref] [PubMed]

Zhang, H.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Zhang, Q.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Zhang, X.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

X. Zhang, J. Song, X. Li, J. Feng, and H. Sun, “Optical Tamm states enhanced broad-band absorption of organic solar cells,” Appl. Phys. Lett. 101(24), 243901 (2012).
[Crossref]

Zhang, Y.

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Zhang, Z. M.

B. Zhao, J. M. Zhao, and Z. M. Zhang, “Enhancement of near-infrared absorption in graphene with metal gratings,” Appl. Phys. Lett. 105(3), 031905 (2014).
[Crossref]

Zhao, B.

B. Zhao, J. M. Zhao, and Z. M. Zhang, “Enhancement of near-infrared absorption in graphene with metal gratings,” Appl. Phys. Lett. 105(3), 031905 (2014).
[Crossref]

Zhao, J.

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photonics Res. 5(3), 162–167 (2017).
[Crossref]

H. Lu, X. Gan, B. Jia, D. Mao, and J. Zhao, “Tunable high-efficiency light absorption of monolayer graphene via Tamm plasmon polaritons,” Opt. Lett. 41(20), 4743–4746 (2016).
[Crossref] [PubMed]

Zhao, J. M.

B. Zhao, J. M. Zhao, and Z. M. Zhang, “Enhancement of near-infrared absorption in graphene with metal gratings,” Appl. Phys. Lett. 105(3), 031905 (2014).
[Crossref]

Zheng, J.

J. Zheng, R. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1(9), 768–774 (2014).
[Crossref]

ACS Nano (2)

Z. Sun and H. Chang, “Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology,” ACS Nano 8(5), 4133–4156 (2014).
[Crossref] [PubMed]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

ACS Photonics (4)

S. Bahauddin, H. Robatjazi, and I. Thomann, “Broadband absorption engineering to enhance light absorption in monolayer MoS2,” ACS Photonics 3(5), 853–862 (2016).
[Crossref]

J. Piper and S. Fan, “Broadband absorption enhancement in solar cells with an atomically thin active layer,” ACS Photonics 3(4), 571–577 (2016).
[Crossref]

J. Zheng, R. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1(9), 768–774 (2014).
[Crossref]

J. 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]

Appl. Phys. Lett. (3)

A. Sobhani, A. Lauchner, S. Najmaei, C. Orozco, F. Wen, J. Lou, and N. Halas, “Enhancing the photocurrent and photoluminescence of single crystal monolayer MoS2 with resonant plasmonic nanoshells,” Appl. Phys. Lett. 104(3), 031112 (2014).
[Crossref]

X. Zhang, J. Song, X. Li, J. Feng, and H. Sun, “Optical Tamm states enhanced broad-band absorption of organic solar cells,” Appl. Phys. Lett. 101(24), 243901 (2012).
[Crossref]

B. Zhao, J. M. Zhao, and Z. M. Zhang, “Enhancement of near-infrared absorption in graphene with metal gratings,” Appl. Phys. Lett. 105(3), 031905 (2014).
[Crossref]

Nano Lett. (2)

M. Bernardi, M. Palummo, and J. C. Grossman, “Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials,” Nano Lett. 13(8), 3664–3670 (2013).
[Crossref] [PubMed]

S. Butun, S. Tongay, and K. Aydin, “Enhanced light emission from large-area monolayer MoS2 using plasmonic nanodisc arrays,” Nano Lett. 15(4), 2700–2704 (2015).
[Crossref] [PubMed]

Nat. Commun. (1)

H. Wang, C. Zhang, W. Chan, S. Tiwari, and F. Rana, “Ultrafast response of monolayer molybdenum disulfide photodetectors,” Nat. Commun. 6, 8831 (2015).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2.,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref] [PubMed]

Nat. Photonics (2)

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Opt. Mater. Express (1)

Photonics Res. (1)

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photonics Res. 5(3), 162–167 (2017).
[Crossref]

Phys. Rev. B (3)

P. Johnson and R. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. Hill, A. Zande, D. Chenet, E. Shih, J. Hone, and T. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90(20), 205422 (2014).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, and I. Shelykh, “Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B 76(16), 165415 (2007).
[Crossref]

Sci. Rep. (2)

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

J. Li, Q. Ji, S. Chu, Y. Zhang, Y. Li, Q. Gong, K. Liu, and K. Shi, “Tuning the photo-response in monolayer MoS2 by plasmonic nano-antenna,” Sci. Rep. 6(1), 23626 (2016).
[Crossref] [PubMed]

Small (1)

J. Miao, W. Hu, Y. Jing, W. Luo, L. Liao, A. Pan, S. Wu, J. Cheng, X. Chen, and W. Lu, “Surface plasmon-enhanced photodetection in few layer MoS2 phototransistors with Au nanostructure arrays,” Small 11(20), 2392–2398 (2015).
[Crossref] [PubMed]

Other (1)

C. Janisch, H. Song, C. Zhou, Z. Lin, A. Elías, D. Ji, M. Terrones, Q. Gan, and Z. Liu, “MoS2 monolayers on nanocavities: enhancement in light-matter interaction,” 2D Mater. 3(2), 025017 (2016).

Supplementary Material (1)

NameDescription
» Visualization 1       Electric fields

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of the multilayer configuration consisting of a Bragg grating with stacked SiO2 and TiO2 layers, a metal (silver) film, a spacer between the grating and metal film, a monolayer MoS2 in the spacer, and substrate. Here, the thicknesses of SiO2 and TiO2 layers in Bragg grating are ds and dt, respectively. The thicknesses of spacer and metal film are dc, and da, respectively. The distance between the metal and MoS2 is dm. The light is incident on the left of the structure with angle θ. The period number of Bragg grating is N. (b) Light absorption of the structure with ds = 110 nm, dt = 60 nm, dc = 250 nm, da = 200 nm, dm = 100 nm, and N = 8. The circles and curve denote the TMM theoretical and FDTD simulation results, respectively.
Fig. 2
Fig. 2 (a) Light absorption of monolayer MoS2 with and without the photonic multilayer. The curves stand for the FDTD results. The ring and rectangular circles are the PDD analytical and TMM theoretical results. (b) Field distribution (see Visualization 1) and profile of |E|2 in the structure at 662 nm. The electric field Ein of incident light is set as 1 V/m.
Fig. 3
Fig. 3 (a) Light absorption spectrum of monolayer MoS2 in the structures with different ds. (b) Wavelength and height of MoS2 absorption peak as a function of ds. The curves represent the FDTD results. The blue and red circles denote the TMM theoretical and PDD analytical results, respectively. (c) Electric field intensities at the absorption peaks of MoS2 in the structures with different ds. (d) Imaginary parts of relative permittivity of monolayer MoS2 and electric field intensities in MoS2 at the absorption peaks with different ds. (e) Peak values of the light absorption of monolayer MoS2 as a function of both ds and dt. The arrow denotes the position of ds = 110 nm and dt = 60 nm. (f) Peak values of light absorption of MoS2 layer in the structure with different grating period number N when ds = 110 nm and dt = 60 nm.
Fig. 4
Fig. 4 (a) Light absorption of monolayer MoS2 at the absorption peaks in the structure with different dm. The inset shows electric field intensities around MoS2 (dashed lines) when dm is 40, 100, and 140 nm. (b) Electric field intensity along the multilayer with dm = 200 nm. The inset shows the corresponding electric field distribution.
Fig. 5
Fig. 5 Wavelength of light absorption peak of monolayer MoS2 in the multilayer structure with different incident angles θ for s- and p-polarized light. The curves and circles denote the FDTD numerical and TMM theoretical results.

Equations (3)

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M i = 1 2 n i 1 cos θ i 1 ( n i 1 cos θ i + n i cos θ i 1 n i 1 cos θ i n i cos θ i 1 n i 1 cos θ i n i cos θ i 1 n i 1 cos θ i + n i cos θ i 1 ) ,
P i = ( exp ( j 2 π d i n i cos θ i / λ ) 0 0 exp ( j 2 π d i n i cos θ i / λ ) ) ,
α = V w ( x , y ) d V 0.5 c ε 0 | E i n | 2 S cos θ ,

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