Abstract

A tunable polarization-independent coherent perfect absorber (CPA) is proposed based on the metal-graphene hollowed-out cross array nanostructure at the mid-infrared region. By adjusting the phase difference between the incident beams, the coherent absorption at 9969nm is all-optically modulated from 99.97% to nearly 0 with the modulation depth over 80dB. The absorption resonance of the CPA is tuned by the gate-controlled Fermi energy with the coherent absorption remaining nearly 100%. The CPA is also found to be angular insensitive to incident beams within the range of −12° to 12°. The central-symmetry nanostructure leads to the polarization independence and the introduced graphene layer results in the electrical tunability of the CPA at the absorption resonance, which have prospects in applications such as for tunable mid-infrared detectors, transducers, modulators, and optical switches.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

K. Arik, S. Abdollahramezani, and A. Khavasi, “Polarization insensitive and broadband terahertz absorber using graphene disks,” Plasmonics 12, 1–6 (2017).
[Crossref]

X. Zhang and Y. Wu, “Scheme for achieving coherent perfect absorption by anisotropic metamaterials,” Opt. Express 25, 4860–4874 (2017).
[Crossref] [PubMed]

2016 (2)

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photonics 3, 1531–1535 (2016).
[Crossref]

S. Mukherjee and S. D. Gupta, “Coherent perfect absorption mediated enhancement of transverse spin in a gap plasmon guide,” Eur. Phys. J. Appl. Phys. 76, 30001 (2016).
[Crossref]

2015 (6)

2014 (4)

J. Zhang, C. Guo, K. Liu, Z. Zhu, W. Ye, X. Yuan, and S. Qin, “Coherent perfect absorption and transparency in a nanostructured graphene film,” Opt. Express 22, 12524–12532 (2014).
[Crossref] [PubMed]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

X. Kong, S. B. Liu, H. Zhang, B. Bian, and C. Chen, “Incident angle insensitive tunable multichannel perfect absorber consisting of nonlinear plasma and matching metamaterials,” Phys. Plasmas 21, 207402 (2014).
[Crossref]

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

2012 (5)

2011 (2)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889 (2011).
[Crossref] [PubMed]

S. Longhi, “Coherent perfect absorption in a homogeneously-broadened two-level medium,” Phys. Rev. A 83, 911–915 (2011).
[Crossref]

2010 (1)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

2008 (1)

G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 19912 (2008).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Abdollahramezani, S.

Agarwal, G. S.

Altan, H.

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photonics 3, 1531–1535 (2016).
[Crossref]

Anwar, S.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Arik, K.

Balci, O.

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photonics 3, 1531–1535 (2016).
[Crossref]

Bao, Y.

Y. Bao, S. Zu, Y. Zhang, and Z. Fang, “Active control of graphene-based unidirectional surface plasmon launcher,” Acs Photonics 2, 1335 (2015).
[Crossref]

Bian, B.

X. Kong, S. B. Liu, H. Zhang, B. Bian, and C. Chen, “Incident angle insensitive tunable multichannel perfect absorber consisting of nonlinear plasma and matching metamaterials,” Phys. Plasmas 21, 207402 (2014).
[Crossref]

Cao, H.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Chen, C.

X. Kong, S. B. Liu, H. Zhang, B. Bian, and C. Chen, “Incident angle insensitive tunable multichannel perfect absorber consisting of nonlinear plasma and matching metamaterials,” Phys. Plasmas 21, 207402 (2014).
[Crossref]

Chong, Y.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889 (2011).
[Crossref] [PubMed]

Chong, Y. D.

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

De Abajo, F. J. G.

S. Thongrattanasiri, F. H. Koppens, and F. J. G. De Abajo, and , “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref]

Deshmukh, R.

Dutta-Gupta, S.

Fan, Y.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Fang, Z.

Y. Bao, S. Zu, Y. Zhang, and Z. Fang, “Active control of graphene-based unidirectional surface plasmon launcher,” Acs Photonics 2, 1335 (2015).
[Crossref]

Farajollahi, S.

Feng, Q.

Fu, Q.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Ge, L.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Gopal, A. V.

Gu, C.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Guo, C.

Gupta, S. D.

Hang, Z. H.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Hanson, G. W.

G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 19912 (2008).
[Crossref]

Hou, B.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Hu, C.

Hu, X.

Huang, C.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Kakenov, N.

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photonics 3, 1531–1535 (2016).
[Crossref]

Kavehvash, Z.

Khavasi, A.

Kocabas, C.

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photonics 3, 1531–1535 (2016).
[Crossref]

Kong, X.

X. Kong, S. B. Liu, H. Zhang, B. Bian, and C. Chen, “Incident angle insensitive tunable multichannel perfect absorber consisting of nonlinear plasma and matching metamaterials,” Phys. Plasmas 21, 207402 (2014).
[Crossref]

Koppens, F. H.

S. Thongrattanasiri, F. H. Koppens, and F. J. G. De Abajo, and , “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref]

Lai, Y.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Li, H.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Li, J.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Li, S.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Liu, K.

Liu, S. B.

X. Kong, S. B. Liu, H. Zhang, B. Bian, and C. Chen, “Incident angle insensitive tunable multichannel perfect absorber consisting of nonlinear plasma and matching metamaterials,” Phys. Plasmas 21, 207402 (2014).
[Crossref]

Liu, Z.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Longhi, S.

S. Longhi, “Non-reciprocal transmission in photonic lattices based on unidirectional coherent perfect absorption,” Opt. Lett. 40, 1278–1281 (2015).
[Crossref] [PubMed]

S. Longhi and G. D. Valle, “Coherent perfect absorbers for transient, periodic or chaotic optical fields: time-reversed lasers beyond threshold,” Phys. Rev. A 85, 5272–5291 (2012).
[Crossref]

S. Longhi, “Coherent perfect absorption in a homogeneously-broadened two-level medium,” Phys. Rev. A 83, 911–915 (2011).
[Crossref]

Lu, W.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Luo, J.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Luo, X.

Ma, X.

Martin, O. J.

Martin, O. J. F.

Mukherjee, S.

S. Mukherjee and S. D. Gupta, “Coherent perfect absorption mediated enhancement of transverse spin in a gap plasmon guide,” Eur. Phys. J. Appl. Phys. 76, 30001 (2016).
[Crossref]

Noh, H.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889 (2011).
[Crossref] [PubMed]

Ozkan, V. A.

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photonics 3, 1531–1535 (2016).
[Crossref]

Pu, M.

Qin, S.

Shen, M.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Stone, A. D.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Takan, T.

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photonics 3, 1531–1535 (2016).
[Crossref]

Thongrattanasiri, S.

S. Thongrattanasiri, F. H. Koppens, and F. J. G. De Abajo, and , “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref]

Valle, G. D.

S. Longhi and G. D. Valle, “Coherent perfect absorbers for transient, periodic or chaotic optical fields: time-reversed lasers beyond threshold,” Phys. Rev. A 85, 5272–5291 (2012).
[Crossref]

Wan, W.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889 (2011).
[Crossref] [PubMed]

Wang, C.

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

C. Wang, C. Huang, C. Hu, M. Wang, M. Pu, Q. Feng, X. Luo, X. Ma, and Z. Zhao, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express 20, 2246 (2012).
[Crossref] [PubMed]

Wang, J.

Wang, M.

Wei, Z.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Wu, Y.

Ye, W.

Yuan, X.

Zhang, F.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Zhang, H.

X. Kong, S. B. Liu, H. Zhang, B. Bian, and C. Chen, “Incident angle insensitive tunable multichannel perfect absorber consisting of nonlinear plasma and matching metamaterials,” Phys. Plasmas 21, 207402 (2014).
[Crossref]

Zhang, J.

Zhang, X.

Zhang, Y.

Y. Bao, S. Zu, Y. Zhang, and Z. Fang, “Active control of graphene-based unidirectional surface plasmon launcher,” Acs Photonics 2, 1335 (2015).
[Crossref]

Zhao, Q.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Zhao, Z.

Zhu, Z.

Zu, S.

Y. Bao, S. Zu, Y. Zhang, and Z. Fang, “Active control of graphene-based unidirectional surface plasmon launcher,” Acs Photonics 2, 1335 (2015).
[Crossref]

ACS Photonics (1)

N. Kakenov, O. Balci, T. Takan, V. A. Ozkan, H. Altan, and C. Kocabas, “Observation of gate-tunable coherent perfect absorption of terahertz radiation in graphene,” ACS Photonics 3, 1531–1535 (2016).
[Crossref]

Y. Bao, S. Zu, Y. Zhang, and Z. Fang, “Active control of graphene-based unidirectional surface plasmon launcher,” Acs Photonics 2, 1335 (2015).
[Crossref]

Eur. Phys. J. Appl. Phys. (1)

S. Mukherjee and S. D. Gupta, “Coherent perfect absorption mediated enhancement of transverse spin in a gap plasmon guide,” Eur. Phys. J. Appl. Phys. 76, 30001 (2016).
[Crossref]

J. Appl. Phys. (1)

G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 19912 (2008).
[Crossref]

Opt. Express (4)

Opt. Lett. (6)

Phys. Plasmas (1)

X. Kong, S. B. Liu, H. Zhang, B. Bian, and C. Chen, “Incident angle insensitive tunable multichannel perfect absorber consisting of nonlinear plasma and matching metamaterials,” Phys. Plasmas 21, 207402 (2014).
[Crossref]

Phys. Rev. A (2)

S. Longhi, “Coherent perfect absorption in a homogeneously-broadened two-level medium,” Phys. Rev. A 83, 911–915 (2011).
[Crossref]

S. Longhi and G. D. Valle, “Coherent perfect absorbers for transient, periodic or chaotic optical fields: time-reversed lasers beyond threshold,” Phys. Rev. A 85, 5272–5291 (2012).
[Crossref]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Phys. Rev. Lett. (2)

S. Thongrattanasiri, F. H. Koppens, and F. J. G. De Abajo, and , “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Plasmonics (1)

K. Arik, S. Abdollahramezani, and A. Khavasi, “Polarization insensitive and broadband terahertz absorber using graphene disks,” Plasmonics 12, 1–6 (2017).
[Crossref]

Sci. Rep. (2)

S. Li, J. Luo, S. Anwar, S. Li, W. Lu, Z. H. Hang, Y. Lai, B. Hou, M. Shen, and C. Wang, “An equivalent realization of coherent perfect absorption under single beam illumination,” Sci. Rep. 4, 7369 (2014).
[Crossref] [PubMed]

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Science (1)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889 (2011).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) The schematic of the tunable polarization-independent metal-graphene coherent perfect absorber. (b) The unit cell of the metal-graphene CPA nanostructure
Fig. 2
Fig. 2 (a)The simulated transmission, reflection and absorption spectra with the p polarization under the incoherent illumination. (b) The simulated transmission, reflection and absorption spectra with the p polarization under the coherent illumination and the absorption spectrum with the s polarization under the coherent illumination. (c) The simulated electric filed distribution at the absorption resonance of the coherent illumination under the p and s polarization, respectively.
Fig. 3
Fig. 3 The simulated coherent absorption, transmission and reflection versus the phase difference between two incident beams at the absorption resonance wavelength λ = 9969nm. The inset is the simulated modulation depth D of the metal-graphene CPA.
Fig. 4
Fig. 4 The simulated coherent absorption spectra of the metal-graphene CPA with (a) different hollowed-out cross structure length a1, (b) different hollowed-out cross structure width a2, (c) different Fermi energies. And (d) is the effective circuit model of the CPA.
Fig. 5
Fig. 5 (a) The coherent absorption spectra of the metal-graphene CPA with the different incident angles θ. (b) The coherent absorption of the metal-graphene CPA versus the phase difference between the incident beams with different incident angles θ.

Equations (6)

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A = 1 ( | r | 2 + | t | 2 ) = 1 R T
r = η , t = 1 + η
[ O 1 O 2 ] = S [ I 1 I 2 ] = [ r 1   t 2   t 1   r 2   ] [ I 1 I 2 ]
A c o = 1 | O 1 | 2 + | O 2 | 2 | I 1 | 2 + | I 2 | 2 = 1 | r 1   I 1 + t 2   I 2 | 2 + | r 2   I 2 + t 1   I 1 | 2 | I 1 | 2 + | I 2 | 2 = 1 | r + t α e i β | 2 + | t + r α e i β | 2 1 + α 2
A c o = 1 1 / 2 1 + α 2 2 α c o s β 1 + α 2
σ ( ω ) = i e 2 ( ω 2 i Γ ) π 2 [ 1 ( ω 2 i Γ ) 2 0 ϵ ( f d ( ϵ ) ϵ f d ( ϵ ) ϵ ) d ϵ 0 f d ( ϵ ) f d ( ϵ ) ( ω 2 i Γ ) 2 4 ( ϵ / ) 2 d ϵ ]

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