Abstract

The complex refractive index (CRI) of graphene waveguide (GW) is of great importance for modeling and developing graphene-based photonic or optoelectronic devices. In this paper, the CRI of the GW is investigated theoretically and experimentally, it is found that the CRI of the GW will modulate the intensity and phase of transmitting light. The phase alterations are obtained spectrally by a Microfiber-based Mach–Zehnder interferometer (MMZI), experimental results demonstrate that the CRIs of the GW vary from 2.91-i13.92 to 3.81-i14.64 for transmitting wavelengths ranging from 1510 to 1590 nm. This method cannot only be used to determine the CRI of the GW optically and provide one of the fundamental parameters for designing graphene-based optic devices for communication and sensing applications, but also is adoptable in graphene-based transformation optics for determination of the CRI of the GW at other wavelengths.

© 2013 Optical Society of America

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2013

Y. Wu, B. Yao, Y. Cheng, X. Liu, Y. Gong, and Y. Rao, “Hybrid graphene-microfiber waveguide for chemical gas sensing,” J. Sel. Top. Quantum Electron.20(1), 4400206 (2013).
[CrossRef]

2012

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012).
[CrossRef]

M. Oya, H. Kishikawa, N. Goto, and S. Yanagiya, “All-optical switch consisting of two-stage interferometers controlled by using saturable absorption of monolayer graphene,” Opt. Express20(24), 27322–27330 (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]

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

X. He, Z. B. Liu, and D. N. Wang, “Wavelength-tunable, passively mode-locked fiber laser based on graphene and chirped fiber Bragg grating,” Opt. Lett.37(12), 2394–2396 (2012).
[CrossRef] [PubMed]

B. Yao, Y. Wu, L. Jia, Y. Rao, Y. Gong, and C. Jiang, “Mode field distribution of optical transmission along micro fiber affected by CNTs films with complex refraction index,” J. Opt. Soc. Am. B29(5), 891–895 (2012).
[CrossRef]

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett.101(11), 111110 (2012).
[CrossRef]

2011

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[CrossRef] [PubMed]

J. T. Kim and S.-Y. Choi, “Graphene-based plasmonic waveguides for photonic integrated circuits,” Opt. Express19(24), 24557–24562 (2011).
[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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

L. Yuan, “Recent progress of in-fiber integrated interferometers,” Photonic Sens.1(1), 1–5 (2011).
[CrossRef]

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

B. V. Cunning, C. L. Brown, and D. Kielpinski, “Low-loss flake-graphene saturable absorber mirror for laser mode-locking at sub-200-fs pulse duration,” Appl. Phys. Lett.99(26), 261109 (2011).
[CrossRef]

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

2009

M. Bruna and S. Borini, “Optical constants of graphene layers in the visible range,” Appl. Phys. Lett.94(3), 031901 (2009).
[CrossRef]

N. J. Horing, “Coupling of graphene and surface plasmons,” Phys. Rev. B80(19), 193401 (2009).
[CrossRef]

2008

X. Wang, Y. P. Chen, and D. D. Nolte, “Strong anomalous optical dispersion of graphene: complex refractive index measured by Picometrology,” Opt. Express16(26), 22105–22112 (2008).
[CrossRef] [PubMed]

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys.103(6), 064302 (2008).
[CrossRef]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

2007

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

E. H. Hwang and S. D. Sarma, “Dielectric function, screening, and plasmons in two-dimensional grapheme,” Phys. Rev. B75(20), 205418 (2007).
[CrossRef]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett.99(1), 016803 (2007).
[CrossRef] [PubMed]

2006

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of Dirac quasiparticles in graphene,” Phys. Rev. Lett.96(25), 256802 (2006).
[CrossRef] [PubMed]

2003

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Ahn, J. H.

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

Anugrah, Y.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett.101(11), 111110 (2012).
[CrossRef]

Ashcom, J. B.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Bae, S. H.

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

Basov, D. N.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

Borini, S.

M. Bruna and S. Borini, “Optical constants of graphene layers in the visible range,” Appl. Phys. Lett.94(3), 031901 (2009).
[CrossRef]

Breusing, M.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Brown, C. L.

B. V. Cunning, C. L. Brown, and D. Kielpinski, “Low-loss flake-graphene saturable absorber mirror for laser mode-locking at sub-200-fs pulse duration,” Appl. Phys. Lett.99(26), 261109 (2011).
[CrossRef]

Bruna, M.

M. Bruna and S. Borini, “Optical constants of graphene layers in the visible range,” Appl. Phys. Lett.94(3), 031901 (2009).
[CrossRef]

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of Dirac quasiparticles in graphene,” Phys. Rev. Lett.96(25), 256802 (2006).
[CrossRef] [PubMed]

Chen, Y. F.

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[CrossRef] [PubMed]

Chen, Y. P.

Chen, Z. L.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

Cheng, Y.

Y. Wu, B. Yao, Y. Cheng, X. Liu, Y. Gong, and Y. Rao, “Hybrid graphene-microfiber waveguide for chemical gas sensing,” J. Sel. Top. Quantum Electron.20(1), 4400206 (2013).
[CrossRef]

Choi, M. R.

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

Choi, S.-Y.

Chua, L. L.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

Clark, J.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

Cunning, B. V.

B. V. Cunning, C. L. Brown, and D. Kielpinski, “Low-loss flake-graphene saturable absorber mirror for laser mode-locking at sub-200-fs pulse duration,” Appl. Phys. Lett.99(26), 261109 (2011).
[CrossRef]

Elsaesser, T.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

Friend, R. H.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[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]

Gattass, R. R.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Geim, A. K.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Goh, R. G. S.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

Gong, Y.

Y. Wu, B. Yao, Y. Cheng, X. Liu, Y. Gong, and Y. Rao, “Hybrid graphene-microfiber waveguide for chemical gas sensing,” J. Sel. Top. Quantum Electron.20(1), 4400206 (2013).
[CrossRef]

B. Yao, Y. Wu, L. Jia, Y. Rao, Y. Gong, and C. Jiang, “Mode field distribution of optical transmission along micro fiber affected by CNTs films with complex refraction index,” J. Opt. Soc. Am. B29(5), 891–895 (2012).
[CrossRef]

Goto, N.

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012).
[CrossRef]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of Dirac quasiparticles in graphene,” Phys. Rev. Lett.96(25), 256802 (2006).
[CrossRef] [PubMed]

Han, T. H.

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

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(6), 064302 (2008).
[CrossRef]

Hao, X.

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[CrossRef] [PubMed]

Hao, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

He, S. L.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

He, X.

Henriksen, E. A.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

Ho, P. K. H.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

Hong, B. H.

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

Horing, N. J.

N. J. Horing, “Coupling of graphene and surface plasmons,” Phys. Rev. B80(19), 193401 (2009).
[CrossRef]

Huang, R.

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[CrossRef] [PubMed]

Hwang, E. H.

E. H. Hwang and S. D. Sarma, “Dielectric function, screening, and plasmons in two-dimensional grapheme,” Phys. Rev. B75(20), 205418 (2007).
[CrossRef]

Jia, L.

Jiang, C.

Jiang, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Kielpinski, D.

B. V. Cunning, C. L. Brown, and D. Kielpinski, “Low-loss flake-graphene saturable absorber mirror for laser mode-locking at sub-200-fs pulse duration,” Appl. Phys. Lett.99(26), 261109 (2011).
[CrossRef]

Kim, J. T.

Kim, P.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

Kishikawa, H.

Knorr, A.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Koester, S. J.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett.101(11), 111110 (2012).
[CrossRef]

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]

Kuehn, S.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Lee, T. W.

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

Lee, Y.

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

Li, H.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett.101(11), 111110 (2012).
[CrossRef]

Li, M.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett.101(11), 111110 (2012).
[CrossRef]

Li, P. J.

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[CrossRef] [PubMed]

Li, Y. R.

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[CrossRef] [PubMed]

Li, Z. Q.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

Lim, C. H. Y. X.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

Lim, G. K.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

Liu, J. B.

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Liu, X.

Y. Wu, B. Yao, Y. Cheng, X. Liu, Y. Gong, and Y. Rao, “Hybrid graphene-microfiber waveguide for chemical gas sensing,” J. Sel. Top. Quantum Electron.20(1), 4400206 (2013).
[CrossRef]

Liu, Z. B.

Loh, K. P.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

Lou, J. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Malic, E.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Martin, M. C.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

Maxwell, I.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Mikhailov, S. A.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett.99(1), 016803 (2007).
[CrossRef] [PubMed]

Milde, F.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Nair, R. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

Ng, W. H.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

Ni, Z.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

Nolte, D. D.

Novoselov, K. S.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012).
[CrossRef]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

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

Oya, M.

Peres, N. M. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012).
[CrossRef]

Rabe, J. P.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Rao, Y.

Y. Wu, B. Yao, Y. Cheng, X. Liu, Y. Gong, and Y. Rao, “Hybrid graphene-microfiber waveguide for chemical gas sensing,” J. Sel. Top. Quantum Electron.20(1), 4400206 (2013).
[CrossRef]

B. Yao, Y. Wu, L. Jia, Y. Rao, Y. Gong, and C. Jiang, “Mode field distribution of optical transmission along micro fiber affected by CNTs films with complex refraction index,” J. Opt. Soc. Am. B29(5), 891–895 (2012).
[CrossRef]

Ropers, C.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Sarma, S. D.

E. H. Hwang and S. D. Sarma, “Dielectric function, screening, and plasmons in two-dimensional grapheme,” Phys. Rev. B75(20), 205418 (2007).
[CrossRef]

Severin, N.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of Dirac quasiparticles in graphene,” Phys. Rev. Lett.96(25), 256802 (2006).
[CrossRef] [PubMed]

Shen, M. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Stauber, T.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

Stormer, H. L.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

Tan, H. W.

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

Tang, D. Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

Thongrattanasiri, S.

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]

Tong, L. M.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

Wang, B.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

Wang, D. N.

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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Wang, X.

Wang, Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

Wang, Z. G.

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[CrossRef] [PubMed]

Winzer, T.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

Woo, S. H.

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

Wu, Y.

Y. Wu, B. Yao, Y. Cheng, X. Liu, Y. Gong, and Y. Rao, “Hybrid graphene-microfiber waveguide for chemical gas sensing,” J. Sel. Top. Quantum Electron.20(1), 4400206 (2013).
[CrossRef]

B. Yao, Y. Wu, L. Jia, Y. Rao, Y. Gong, and C. Jiang, “Mode field distribution of optical transmission along micro fiber affected by CNTs films with complex refraction index,” J. Opt. Soc. Am. B29(5), 891–895 (2012).
[CrossRef]

Yanagiya, S.

Yao, B.

Y. Wu, B. Yao, Y. Cheng, X. Liu, Y. Gong, and Y. Rao, “Hybrid graphene-microfiber waveguide for chemical gas sensing,” J. Sel. Top. Quantum Electron.20(1), 4400206 (2013).
[CrossRef]

B. Yao, Y. Wu, L. Jia, Y. Rao, Y. Gong, and C. Jiang, “Mode field distribution of optical transmission along micro fiber affected by CNTs films with complex refraction index,” J. Opt. Soc. Am. B29(5), 891–895 (2012).
[CrossRef]

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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Yuan, L.

L. Yuan, “Recent progress of in-fiber integrated interferometers,” Photonic Sens.1(1), 1–5 (2011).
[CrossRef]

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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Zhang, H.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett.99(1), 016803 (2007).
[CrossRef] [PubMed]

ACS Nano

Z. G. Wang, Y. F. Chen, P. J. Li, X. Hao, J. B. Liu, R. Huang, and Y. R. Li, “Flexible graphene-based electroluminescent devices,” ACS Nano5(9), 7149–7154 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett.101(11), 111110 (2012).
[CrossRef]

B. V. Cunning, C. L. Brown, and D. Kielpinski, “Low-loss flake-graphene saturable absorber mirror for laser mode-locking at sub-200-fs pulse duration,” Appl. Phys. Lett.99(26), 261109 (2011).
[CrossRef]

M. Bruna and S. Borini, “Optical constants of graphene layers in the visible range,” Appl. Phys. Lett.94(3), 031901 (2009).
[CrossRef]

J. Appl. Phys.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys.103(6), 064302 (2008).
[CrossRef]

J. Opt. Soc. Am. B

J. Sel. Top. Quantum Electron.

Y. Wu, B. Yao, Y. Cheng, X. Liu, Y. Gong, and Y. Rao, “Hybrid graphene-microfiber waveguide for chemical gas sensing,” J. Sel. Top. Quantum Electron.20(1), 4400206 (2013).
[CrossRef]

Nat. Mater.

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

Nat. Photonics

G. K. Lim, Z. L. Chen, J. Clark, R. G. S. Goh, W. H. Ng, H. W. Tan, R. H. Friend, P. K. H. Ho, and L. L. Chua, “Giant broadband nonlinear optical absorption response in dispersed graphene single sheets,” Nat. Photonics5(9), 554–560 (2011).
[CrossRef]

T. H. Han, Y. Lee, M. R. Choi, S. H. Woo, S. H. Bae, B. H. Hong, J. H. Ahn, and T. W. Lee, “Extremely efficient flexible organic light-emitting diodes with modified graphene anode,” Nat. Photonics6(2), 105–110 (2012).
[CrossRef]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011).
[CrossRef]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012).
[CrossRef]

Nat. Phys.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008).
[CrossRef]

Nature

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Photonic Sens.

L. Yuan, “Recent progress of in-fiber integrated interferometers,” Photonic Sens.1(1), 1–5 (2011).
[CrossRef]

Phys. Rev. B

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B83(15), 153410 (2011).
[CrossRef]

N. J. Horing, “Coupling of graphene and surface plasmons,” Phys. Rev. B80(19), 193401 (2009).
[CrossRef]

E. H. Hwang and S. D. Sarma, “Dielectric function, screening, and plasmons in two-dimensional grapheme,” Phys. Rev. B75(20), 205418 (2007).
[CrossRef]

Phys. Rev. Lett.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of Dirac quasiparticles in graphene,” Phys. Rev. Lett.96(25), 256802 (2006).
[CrossRef] [PubMed]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett.99(1), 016803 (2007).
[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]

Science

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308 (2008).
[CrossRef] [PubMed]

Other

http://refractiveindex.info/?group=CRYSTALS&material=MgF2 .

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic diagram of the structure for the light propagating along the GMFW (Red: SMF, White: Monolayer graphene, Cyan: MgF2 substrate). The orange arrows show the transmitting direction of the evanescent waves. (b) Geometry of the cross-section of the GMHW. (c) The theoretical CRI of the GW. (d) The effective CRI of the GMHW (Blue curve: real part, red dashed: imaginary part). (e) Simulated field intensity distribution of the GMHW. (f) The field intensity of the Microfiber/GW distributed along y-axis according to (e).

Fig. 2
Fig. 2

For λ = 1550nm: (a) Correlation between neffRE and transmitting phase at z = 20μm. (b) Correlation between neffIM and attenuation at z = 20μm. (c) (d) (e): The 3-D distributes of the electric field intensity along the microfiber, the microfiber/MgF2 and the GMHW, respectively.

Fig. 3
Fig. 3

(a) Setup of the GMHW-based MMZI. (b) The experimental details of the GMHW (c) SEM of the GMHW. (d) Raman spectrum of the GW on the MgF2 substrate, the blue curve indicates the G/MgF2 and the red line indicates the MgF2 substrate only.

Fig. 4
Fig. 4

(a) The correlation of wavelength and |△nRE|. (b) The correlation of wavelength and |△φ|. (c) The simulated results of the |Λ|(λ, LG).

Fig. 5
Fig. 5

Micro-console is used to adjust the interacting length between the GW and the microfiber precisely. The GW is not attached to the microfiber (a). By continuously lifting the MgF2, the GW is attached to the microfiber with a length of (b) 2mm and (c) 5mm. (e), (f), and (g) are the experimental photographs for the interacting length of ~1mm, ~2mm and ~5mm, respectively.

Fig. 6
Fig. 6

(a) neffRE of the microfiber (blue solid) and the microfiber on MgF2 (red dashed). The spectral shifts for the band of (b)1510nm-1511nm, (c) 1549.5nm-1550.nm, and (d) 1589nm-1590nm.

Fig. 7
Fig. 7

Spectral shifts for the band of (a) 1510nm-1511nm, (b) 1549.5nm-1550.nm, and (c) 1589nm-1590nm. (d) The Λ-λ relationships for different LG and (e) The attenuations correspond to λ for different LG. In (d) and (e), blue rhombuses, red cubes and green triangles present LG = 1mm, 2mm and 5mm respectively.

Fig. 8
Fig. 8

(a) Experimentally measured effective refractive index of the GMHW (Real part: Blue cubes; Imaginary part: Red dots) verifies the simulated results (blue and red dashed). (b) Calculated CRI of the GW based on experimental results (Real part: Blue cubes; Imaginary part: Red dots) corresponds to the theoretical results (blue and red dashed).

Equations (4)

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2πc λ d ( L 2 ν f L 1 ν f )=(2N+1)π
2πc λ d ' ( L 2 L G ν f + L G ν G L 1 ν f )=(2N+1)π
Λ= 2 L G 2N+1 Δ n RE
n g ={ 3.02 ( n eff RE ) 2 32.80( n eff RE )+42.44 }+i{ 0.29 ( 10 4 n eff IM ) 2 +0.65( 10 4 n eff IM )13.20 }

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