Abstract

We theoretically study the absorption property of graphene manipulated by a dielectric cylinder through an analytical method. The distinctive absorption properties of incident waves with different polarizations (TM and TE) are analyzed and they are strongly correlated with the structure resonance and material dispersion. Besides, the characteristics of graphene absorption tuned by the cylinder radius and refractive index as well as the chemical potential of graphene are systematically investigated. It is found that enhancement and continuous tunability of graphene absorption can be achieved by utilizing the whispering gallery mode produced in the dielectric cylinder and harnessing the graphene optical conductivity via tuning its chemical potential by exterior electrical grating. The theoretical studies open up a simple while efficient means to manipulate the absorption of graphene in a broad frequency range via the geometric and physical configuration of hybrid graphene-microstructures.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
  2. Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
    [Crossref] [PubMed]
  3. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
    [Crossref]
  4. L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
    [Crossref] [PubMed]
  5. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
    [Crossref] [PubMed]
  6. W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
    [Crossref] [PubMed]
  7. Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
    [Crossref]
  8. J. T. Kim, K. H. Chung, and C. G. Choi, “Thermo-optic mode extinction modulator based on graphene plasmonic waveguide,” Opt. Express 21(13), 15280–15286 (2013).
    [Crossref] [PubMed]
  9. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
    [Crossref] [PubMed]
  10. J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  13. 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]
  14. Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  20. J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
    [Crossref]
  21. M. Mariano, F. J. Rodriguez, P. Romero-Gomez, G. Kozyreff, and J. Martorell, “Light coupling into the whispering gallery modes of a fiber array thin film solar cell for fixed partial sun tracking,” Sci. Rep. 4, 4959 (2014).
    [Crossref]
  22. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
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2015 (1)

Z. Y. Li, “Optics and photonics at nanoscale: principles and perspectives,” Europhys. Lett. 110(1), 14001 (2015).
[Crossref]

2014 (4)

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]

J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: a brief review,” Chin. Phys. B 23(4), 047305 (2014).
[Crossref]

M. Mariano, F. J. Rodriguez, P. Romero-Gomez, G. Kozyreff, and J. Martorell, “Light coupling into the whispering gallery modes of a fiber array thin film solar cell for fixed partial sun tracking,” Sci. Rep. 4, 4959 (2014).
[Crossref]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

2013 (4)

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

J. Li, H. Guo, and Z.-Y. Li, “Microscopic and macroscopic manipulation of gold nanorod and its hybrid nanostructures [Invited],” Photon. Res. 1(1), 28–41 (2013).
[Crossref]

J. T. Kim, K. H. Chung, and C. G. Choi, “Thermo-optic mode extinction modulator based on graphene plasmonic waveguide,” Opt. Express 21(13), 15280–15286 (2013).
[Crossref] [PubMed]

M. Hashemi, M. H. Farzad, N. A. Mortensen, and S. S. Xiao, “Enhanced absorption of graphene in the visible region by use of plasmonic nanostructures,” J Optics-UK 15(5), 055003 (2013).
[Crossref]

2012 (6)

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
[Crossref]

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref] [PubMed]

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

A. Ferreira, N. M. R. Peres, R. M. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

2011 (2)

J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

2010 (2)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

2007 (2)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

2006 (1)

B. J. Wiley, S. H. Im, Z. Y. Li, J. McLellan, A. Siekkinen, and Y. Xia, “Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis,” J. Phys. Chem. B 110(32), 15666–15675 (2006).
[Crossref] [PubMed]

Ajayan, P. M.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Bai, J.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Bao, J.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Bao, M.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Bao, Q.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref] [PubMed]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Chen, B.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Chen, Z. H.

J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
[Crossref]

Cheng, R.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Choi, C. G.

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Chung, K. H.

Dai, J.

J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
[Crossref]

de Abajo, F. J. G.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Duan, X.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

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]

Fang, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Fang, Z.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Farzad, M. H.

M. Hashemi, M. H. Farzad, N. A. Mortensen, and S. S. Xiao, “Enhanced absorption of graphene in the visible region by use of plasmonic nanostructures,” J Optics-UK 15(5), 055003 (2013).
[Crossref]

Feng, M.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Ferreira, A.

A. Ferreira, N. M. R. Peres, R. M. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

García de Abajo, F. J.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Guo, H.

Guo, J. Y.

J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
[Crossref]

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Halas, N. J.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Hasan, T.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Hashemi, M.

M. Hashemi, M. H. Farzad, N. A. Mortensen, and S. S. Xiao, “Enhanced absorption of graphene in the visible region by use of plasmonic nanostructures,” J Optics-UK 15(5), 055003 (2013).
[Crossref]

Hu, X. H.

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
[Crossref]

Hu, Z.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Huang, Y.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Im, S. H.

B. J. Wiley, S. H. Im, Z. Y. Li, J. McLellan, A. Siekkinen, and Y. Xia, “Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis,” J. Phys. Chem. B 110(32), 15666–15675 (2006).
[Crossref] [PubMed]

Jiang, W. S.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Kim, J. T.

Koppens, F. H. L.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Kozyreff, G.

M. Mariano, F. J. Rodriguez, P. Romero-Gomez, G. Kozyreff, and J. Martorell, “Light coupling into the whispering gallery modes of a fiber array thin film solar cell for fixed partial sun tracking,” Sci. Rep. 4, 4959 (2014).
[Crossref]

Li, J.

Li, J. F.

J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: a brief review,” Chin. Phys. B 23(4), 047305 (2014).
[Crossref]

Li, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Li, X.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Li, Z. H.

J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
[Crossref]

Li, Z. Y.

Z. Y. Li, “Optics and photonics at nanoscale: principles and perspectives,” Europhys. Lett. 110(1), 14001 (2015).
[Crossref]

J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: a brief review,” Chin. Phys. B 23(4), 047305 (2014).
[Crossref]

B. J. Wiley, S. H. Im, Z. Y. Li, J. McLellan, A. Siekkinen, and Y. Xia, “Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis,” J. Phys. Chem. B 110(32), 15666–15675 (2006).
[Crossref] [PubMed]

Li, Z.-Y.

Liao, L.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Lin, Y. C.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Liu, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Liu, X. H.

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
[Crossref]

Liu, Y.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Liu, Y. G.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Liu, Z.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Liu, Z. B.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Loh, K. P.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref] [PubMed]

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Mariano, M.

M. Mariano, F. J. Rodriguez, P. Romero-Gomez, G. Kozyreff, and J. Martorell, “Light coupling into the whispering gallery modes of a fiber array thin film solar cell for fixed partial sun tracking,” Sci. Rep. 4, 4959 (2014).
[Crossref]

Martorell, J.

M. Mariano, F. J. Rodriguez, P. Romero-Gomez, G. Kozyreff, and J. Martorell, “Light coupling into the whispering gallery modes of a fiber array thin film solar cell for fixed partial sun tracking,” Sci. Rep. 4, 4959 (2014).
[Crossref]

McLellan, J.

B. J. Wiley, S. H. Im, Z. Y. Li, J. McLellan, A. Siekkinen, and Y. Xia, “Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis,” J. Phys. Chem. B 110(32), 15666–15675 (2006).
[Crossref] [PubMed]

Meng, C.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Mortensen, N. A.

M. Hashemi, M. H. Farzad, N. A. Mortensen, and S. S. Xiao, “Enhanced absorption of graphene in the visible region by use of plasmonic nanostructures,” J Optics-UK 15(5), 055003 (2013).
[Crossref]

Nordlander, P.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Novoselov, K. S.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Peres, N. M. R.

A. Ferreira, N. M. R. Peres, R. M. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[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]

Qu, Y.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Ribeiro, R. M.

A. Ferreira, N. M. R. Peres, R. M. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

Rodriguez, F. J.

M. Mariano, F. J. Rodriguez, P. Romero-Gomez, G. Kozyreff, and J. Martorell, “Light coupling into the whispering gallery modes of a fiber array thin film solar cell for fixed partial sun tracking,” Sci. Rep. 4, 4959 (2014).
[Crossref]

Romero-Gomez, P.

M. Mariano, F. J. Rodriguez, P. Romero-Gomez, G. Kozyreff, and J. Martorell, “Light coupling into the whispering gallery modes of a fiber array thin film solar cell for fixed partial sun tracking,” Sci. Rep. 4, 4959 (2014).
[Crossref]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Shen, Y. R.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Sheng, Q. W.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Siekkinen, A.

B. J. Wiley, S. H. Im, Z. Y. Li, J. McLellan, A. Siekkinen, and Y. Xia, “Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis,” J. Phys. Chem. B 110(32), 15666–15675 (2006).
[Crossref] [PubMed]

Stauber, T.

A. Ferreira, N. M. R. Peres, R. M. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

Sun, L. X.

J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
[Crossref]

Sun, Z.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Thongrattanasiri, S.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

Tian, J. G.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Tong, L.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Wang, D. N.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Wang, H.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Wang, K. L.

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

Wang, P.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Wang, Y.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Wiley, B. J.

B. J. Wiley, S. H. Im, Z. Y. Li, J. McLellan, A. Siekkinen, and Y. Xia, “Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis,” J. Phys. Chem. B 110(32), 15666–15675 (2006).
[Crossref] [PubMed]

Xia, Y.

B. J. Wiley, S. H. Im, Z. Y. Li, J. McLellan, A. Siekkinen, and Y. Xia, “Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis,” J. Phys. Chem. B 110(32), 15666–15675 (2006).
[Crossref] [PubMed]

Xiao, S. S.

M. Hashemi, M. H. Farzad, N. A. Mortensen, and S. S. Xiao, “Enhanced absorption of graphene in the visible region by use of plasmonic nanostructures,” J Optics-UK 15(5), 055003 (2013).
[Crossref]

Xiao, Y.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Xin, W.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Xu, C. X.

J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
[Crossref]

Xu, Y.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhan, T. R.

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
[Crossref]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhao, F. Y.

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
[Crossref]

Zhou, W. Y.

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Zi, J.

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
[Crossref]

ACS Nano (2)

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

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]

Chin. Phys. B (1)

J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: a brief review,” Chin. Phys. B 23(4), 047305 (2014).
[Crossref]

Europhys. Lett. (1)

Z. Y. Li, “Optics and photonics at nanoscale: principles and perspectives,” Europhys. Lett. 110(1), 14001 (2015).
[Crossref]

J Optics-UK (1)

M. Hashemi, M. H. Farzad, N. A. Mortensen, and S. S. Xiao, “Enhanced absorption of graphene in the visible region by use of plasmonic nanostructures,” J Optics-UK 15(5), 055003 (2013).
[Crossref]

J. Phys. Chem. B (1)

B. J. Wiley, S. H. Im, Z. Y. Li, J. McLellan, A. Siekkinen, and Y. Xia, “Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis,” J. Phys. Chem. B 110(32), 15666–15675 (2006).
[Crossref] [PubMed]

J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

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

J. Dai, C. X. Xu, L. X. Sun, Z. H. Chen, J. Y. Guo, and Z. H. Li, “Multiphoton absorption-induced optical whispering-gallery modes in ZnO microcavities at room temperature,” J. Phys. D Appl. Phys. 44(2), 025404 (2011).
[Crossref]

Laser Phys. Lett. (1)

Z. B. Liu, M. Feng, W. S. Jiang, W. Xin, P. Wang, Q. W. Sheng, Y. G. Liu, D. N. Wang, W. Y. Zhou, and J. G. Tian, “Broadband all-optical modulation using a graphene-covered-microfiber,” Laser Phys. Lett. 10(6), 065901 (2013).
[Crossref]

Nano Lett. (2)

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Nat. Photonics (1)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Nature (2)

L. Liao, Y. C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467(7313), 305–308 (2010).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Opt. Express (1)

Photon. Res. (1)

Phys. Rev. B (2)

A. Ferreira, N. M. R. Peres, R. M. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

T. R. Zhan, F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
[Crossref]

Phys. Rev. Lett. (1)

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[Crossref] [PubMed]

Sci. Rep. (1)

M. Mariano, F. J. Rodriguez, P. Romero-Gomez, G. Kozyreff, and J. Martorell, “Light coupling into the whispering gallery modes of a fiber array thin film solar cell for fixed partial sun tracking,” Sci. Rep. 4, 4959 (2014).
[Crossref]

Other (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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Figures (7)

Fig. 1
Fig. 1 Schematic of light incident on a graphene coated dielectric cylinder embedded in the air.
Fig. 2
Fig. 2 (a) Calculated absorption cross section as a function of the radius of graphene coated cylinder at the wavelength of 1.55 μm at the incidence of TM wave. (b)-(d) Calculated magnetic field ( H z ) distributions of different cylinders with radius of (b) 4.140 μm, (c) 4.325 μm and (d) 4.510 μm, corresponding to the absorption peaks in (a).
Fig. 3
Fig. 3 Calculated absorption cross sections and peak values at different radius [(a) and (b)], refractive index [(c) and (d)] and chemical potential [(e) and (f)] of the graphene coated cylinder at the incidence of TM wave.
Fig. 4
Fig. 4 Calculated magnetic field ( H z ) distributions at the incident wavelength of (a) 1.55 μm and (b) 1.5 μm (b) for TM wave. The radius of cylinder is 4.14 μm.
Fig. 5
Fig. 5 Calculated absorption cross section as a function of the radius of the graphene coated cylinder at the wavelength of 1.55 μm for TE wave.
Fig. 6
Fig. 6 Calculated absorption cross sections and peak values at different radius [(a) and (b)], refractive index [(c) and (d)] and chemical potential [(e) and (f)] of the graphene coated cylinder for TE wave.
Fig. 7
Fig. 7 Calculated electric field ( E z ) distributions at the incident wavelength of (a) 2.5 μm and (b) 1.5 μm for TE wave. The radius of cylinder is 4.14 μm.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

× H = i ω ε E ,
× E = i ω μ H ,
1 r r ( r H ϕ ) 1 r H r ϕ = i ω ε E z ,
1 r E z ϕ = i ω μ H r , E z r = i ω μ H ϕ .
2 E z r 2 + 1 r E z r + 1 r 2 2 E z ϕ 2 + k 2 E z = 0 ,
E z = n = B e s s e l ( n , k r ) e i n ϕ ,
E i z = E 0 e i k 0 r cos ϕ ,
E i z = n = A n J n ( k 0 r ) e i n ϕ ,
H i r = 1 i ω μ r E i z ϕ = n ω μ r n = A n J n ( k 0 r ) e i n ϕ , H i ϕ = 1 i ω μ E i z r = k 0 i ω μ n = A n J n ' ( k 0 r ) e i n ϕ .
E c z = n = C n J n ( m k 0 r ) e i n ϕ , H c r = 1 i ω μ r E c z ϕ = n ω μ r n = C n J n ( m k 0 r ) e i n ϕ , H c ϕ = 1 i ω μ E c z r = m k 0 i ω μ n = C n J n ' ( m k 0 r ) e i n ϕ ,
E s z = n = B n H n ( k 0 r ) e i n ϕ , H s r = 1 i ω μ r E s z ϕ = n ω μ r n = B n H n ( k 0 r ) e i n ϕ , H s ϕ = 1 i ω μ E s z r = k 0 i ω μ n = B n H n ' ( k 0 r ) e i n ϕ ,
e ^ r × ( E i z + E s z E c z ) = 0 , e ^ r × ( H ^ i ϕ + H ^ s ϕ H ^ c ϕ ) = σ E c z ,
R t e n = B n A n = J n ( m k 0 a ) J n ' ( k 0 a ) m J n ( k 0 a ) J n ' ( m k 0 a ) i ω μ σ J n ( m k 0 a ) J n ( k 0 a ) J n ( m k 0 a ) H n ' ( k 0 a ) m H n ( k 0 a ) J n ' ( m k 0 a ) i ω μ σ J n ( m k 0 a ) H n ( k 0 a ) .
1 r r ( r E ϕ ) 1 r E r ϕ = i ω μ H z ,
1 r H z ϕ = i ω ε E r , H z r = i ω ε E ϕ .
2 H z r 2 + 1 r H z r + 1 r 2 2 H z ϕ 2 + k 2 H z = 0 ,
H i z = H 0 e i k 0 r cos ϕ .
H i z = n = D n J n ( k 0 r ) e i n ϕ ,
E i r = 1 i ω ε 0 r H i z ϕ = n ω ε 0 r n = D n J n ( k 0 r ) e i n ϕ , E i ϕ = 1 i ω ε 0 H i z r = k 0 i ω ε 0 n = D n J n ' ( k 0 r ) e i n ϕ .
H c z = m n = G n J n ( m k 0 r ) e i n ϕ , E c r = 1 i ω ε m r H c z ϕ = n m ω ε m r n = G n J n ( m k 0 r ) e i n ϕ , E c ϕ = 1 i ω ε m H c z r = k 0 i ω ε 0 n = G n J n ' ( m k 0 r ) e i n ϕ ,
H s z = n = F n H n ( k 0 r ) e i n ϕ , E s r = 1 i ω ε 0 r H s z ϕ = n ω ε 0 r n = F n H n ( k 0 r ) e i n ϕ , E s ϕ = 1 i ω ε 0 H s z r = k 0 i ω ε 0 n = F n H n ' ( k 0 r ) e i n ϕ ,
e ^ r × ( E i ϕ + E s ϕ E c ϕ ) = 0 , e ^ r × ( H ^ i z + H ^ s z H ^ c z ) = σ E c ϕ ,
R t m n = F n D n = J n ' ( m k 0 a ) J n ( k 0 a ) m J n ' ( k 0 a ) J n ( m k 0 a ) i σ k 0 ω ε 0 J n ' ( m k 0 a ) J n ' ( k 0 a ) J n ' ( m k 0 a ) H n ( k 0 a ) m H n ' ( k 0 a ) J n ( m k 0 a ) i σ k 0 ω ε 0 J n ' ( m k 0 a ) H n ' ( k 0 a ) .
C s c a = 4 k 0 [ | R 0 | 2 + 2 n = 1 ( | R n | 2 ) ] , C e x t = 4 k 0 Re { R 0 + 2 n = 1 R n } ,
C a b s = C e x t C s c a .

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