Abstract

The effective mode index (EMI) of a graphene-coated side-polished fiber (GSPF) is calculated numerically. Whereby, the influences of graphene atom layer number, residual radius of SPF, light frequency, scattering rate of graphene, and temperature on the EMI are investigated comprehensively. Two types of mechanisms for the electro-optical absorption modulation are found for such GSPF-based modulator. One mechanism is Pauli blocking effect (PBE) and the other is plasmonic attenuation effect (PAE). With the optimal design parameters, a PBE-based modulator is theoretically predicted to have a 0.0072 dB/μm modulation depth, 2.92 V driving voltage swing, 6.35 nJ/bit power consumption, and 56.2 THz optical modulation bandwidth. It is also predicted that a PAE-based modulator could have a 0.0056 dB/μm modulation depth, 0.6 V driving voltage swing, 0.27 nJ/bit power consumption, and 2.5 THz optical modulation bandwidth. By further optimization, the modulator performance such as the relatively high power consumption and the narrow operation bandwidth can be improved. Owing to their seamless connection to optical fiber networks, the GSPF-based modulators have great potential to be used in fast and high-capacity optical communication systems.

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

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2017 (10)

C. Gao, L. Gao, T. Zhu, and G. Yin, “Incoherent optical modulation of graphene based on an in-line fiber Mach-Zehnder interferometer,” Opt. Lett. 42(9), 1708–1711 (2017).
[Crossref] [PubMed]

X. Hu and J. Wang, “Design and modeling of compact phase shifter based on graphene electro-refraction effects,” J. Appl. Phys. 121(11), 113108 (2017).
[Crossref]

B. J. Park, M. K. Kim, and J. T. Kim, “Analysis of a graphene-based silicon electro-absorption modulator in isotropic and anisotropic graphene models,” J. Korean Phys. Soc. 70(11), 967–972 (2017).
[Crossref]

S. W. Ye, F. Yuan, X. H. Zou, M. K. Shah, R. G. Lu, and Y. Liu, “High-speed optical phase modulator based on graphene-silicon waveguide,” IEEE J. Sel. Top. Quantum Electron. 23(1), 3400105 (2017).
[Crossref]

L. A. Shiramin and D. V. Thourhout, “Graphene modulators and switches integrated on silicon and silicon nitride waveguide,” IEEE J. Sel. Top. Quantum Electron. 23(1), 3600107 (2017).

M. Fan, H. Yang, P. Zheng, G. Hu, B. Yun, and Y. Cui, “Multilayer graphene electro-absorption optical modulator based on double-stripe silicon nitride waveguide,” Opt. Express 25(18), 21619–21629 (2017).
[Crossref] [PubMed]

L. Wu, H. X. Liu, J. B. Li, S. L. Wang, S. Qu, and L. Dong, “A 130 GHz electro-optic ring modulator with double-layer graphene,” Crystals 7(3), 65 (2017).
[Crossref]

Z. Z. Ma, M. H. Tahersima, S. Khan, and V. J. Sorger, “Two-dimensional material-based mode confinement engineering in electro-optic modulators,” IEEE J. Sel. Top. Quantum Electron. 23(1), 3400208 (2017).
[Crossref]

Y. Wang, T. Li, and S. Zhu, “Graphene-based plasmonic modulator on a groove-structured metasurface,” Opt. Lett. 42(12), 2247–2250 (2017).
[Crossref] [PubMed]

S. Qu, C. Ma, and H. Liu, “Tunable graphene-based hybrid plasmonic modulators for subwavelength confinement,” Sci. Rep. 7(1), 5190 (2017).
[Crossref] [PubMed]

2016 (10)

X. Y. He, M. Xu, and X. C. Zhang, “Theoretical investigation of a broadband all-optical graphene-microfiber modulator,” J. Opt. Soc. Am. B 33(12), 2588–2595 (2016).
[Crossref]

A. Phatak, Z. Cheng, C. Qin, and K. Goda, “Design of electro-optic modulators based on graphene-on-silicon slot waveguides,” Opt. Lett. 41(11), 2501–2504 (2016).
[Crossref] [PubMed]

X. Chen, Y. Wang, Y. J. Xiang, G. B. Jiang, L. L. Wang, Q. L. Bao, H. Zhang, Y. Liu, S. C. Wen, and D. Y. Fan, “A broadband optical modulator based on a graphene hybrid plasmonic waveguide,” J. Lightwave Technol. 34(21), 4948–4953 (2016).
[Crossref]

J. S. Kim and J. T. Kim, “Silicon electro-absorption modulator based on graphene-hexagonal boron nitride heterostructure,” J. Lightwave Technol. 34(22), 5293–5299 (2016).
[Crossref]

S. L. Yu, X. Q. Wu, K. R. Chen, B. G. Chen, X. Guo, D. X. Dai, L. M. Tong, W. T. Liu, and Y. R. Shen, “All- optical graphene modulator based on optical kerr phase shift,” Optica 3(6), 541–544 (2016).
[Crossref]

H. Zhang, N. Healy, L. Shen, C. C. Huang, D. W. Hewak, and A. C. Peacock, “Enhanced all-optical modulation in a graphene-coated fibre with low insertion loss,” Sci. Rep. 6(1), 23512 (2016).
[Crossref] [PubMed]

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal broadband graphene optical modulator with 35 GHz speed,” ACS Photonics 3(9), 1564–1568 (2016).
[Crossref]

K. J. A. Ooi, J. L. Cheng, J. E. Sipe, L. K. Ang, and D. T. H. Tan, “Ultrafast, broadband, and configurable midinfrared all-optical switching in nonlinear graphene plasmonic waveguide,” APL Photonics 1(4), 046101 (2016).
[Crossref]

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “all-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–128 (2016).
[Crossref]

2015 (11)

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
[Crossref] [PubMed]

R. Hao, W. Du, E. P. Li, and H. S. Chen, “Graphene assisted TE/TM-independent polarizer based on Mach- Zehnder interferometer,” IEEE Photonics Technol. Lett. 27(10), 1112–1115 (2015).
[Crossref]

M. Mohsin, D. Neumaier, D. Schall, M. Otto, C. Matheisen, A. L. Giesecke, A. A. Sagade, and H. Kurz, “Experimental verification of electro-refractive phase modulation in graphene,” Sci. Rep. 5(1), 10967 (2015).
[Crossref] [PubMed]

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro- optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref] [PubMed]

J. H. Chen, B. C. Zheng, G. H. Shao, S. J. Ge, F. Xu, and Y. Q. Lu, “An all-optical modulator based on a stereo graphene-microfiber structure,” Light Sci. Appl. 4(12), e360 (2015).
[Crossref]

C. Meng, S. L. Yu, H. Q. Wang, Y. Cao, L. M. Tong, W. T. Liu, and Y. S. Shen, “Graphene-doped polymer nanofibers for low-threshold nonlinear optical waveguiding,” Light Sci. Appl. 4(11), e348 (2015).
[Crossref]

S. Yu, C. Meng, B. Chen, H. Wang, X. Wu, W. Liu, S. Zhang, Y. Liu, Y. Su, and L. Tong, “Graphene decorated microfiber for ultrafast optical modulation,” Opt. Express 23(8), 10764–10770 (2015).
[Crossref] [PubMed]

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J. K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J. Y. Park, F. Rotermund, and D. I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

S. Das, A. Salandrino, J. Z. Wu, and R. Hui, “Near-infrared electro-optic modulator based on plasmonic graphene,” Opt. Lett. 40(7), 1516–1519 (2015).
[Crossref] [PubMed]

2014 (6)

W. Du, E. P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photonics Technol. Lett. 26(20), 2008–2011 (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]

S. Ye, Z. Wang, L. Tang, Y. Zhang, R. Lu, and Y. Liu, “Electro-absorption optical modulator using dual-graphene-on-graphene configuration,” Opt. Express 22(21), 26173–26180 (2014).
[Crossref] [PubMed]

N. Youngblood, Y. Anugrah, R. Ma, S. J. Koester, and M. Li, “Multifunctional graphene optical modulator and photodetector integrated on silicon waveguides,” Nano Lett. 14(5), 2741–2746 (2014).
[Crossref] [PubMed]

F. Xing, G. X. Meng, Q. Zhang, L. T. Pan, P. Wang, Z. B. Liu, W. S. Jiang, Y. Chen, and J. G. Tian, “Ultrasensitive flow sensing of a single cell using graphene-based optical sensors,” Nano Lett. 14(6), 3563–3569 (2014).
[Crossref] [PubMed]

Q. Y. Wen, W. Tian, Q. Mao, Z. Chen, W. W. Liu, Q. H. Yang, M. Sanderson, and H. W. Zhang, “Graphene based all-optical spatial terahertz modulator,” Sci. Rep. 4(1), 7409 (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. Gosciniak and D. T. H. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci. Rep. 3(1), 1897 (2013).
[Crossref] [PubMed]

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

J. S. Gómez-Díaz, M. Esquius-Morote, and J. Perruisseau-Carrier, “Plane wave excitation-detection of non-resonant plasmons along finite-width graphene strips,” Opt. Express 21(21), 24856–24872 (2013).
[Crossref] [PubMed]

2012 (5)

M. Midrio, S. Boscolo, M. Moresco, M. Romagnoli, C. De Angelis, A. Locatelli, and A. D. Capobianco, “Graphene-assisted critically-coupled optical ring modulator,” Opt. Express 20(21), 23144–23155 (2012).
[Crossref] [PubMed]

Z. L. Lu and W. S. Zhao, “Nanoscale electro-optic modulators based on graphene-slot waveguides,” J. Opt. Soc. Am. B 29(6), 1490–1496 (2012).
[Crossref]

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref] [PubMed]

P. Weis, J. L. Garcia-Pomar, M. Höh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref] [PubMed]

2011 (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]

D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

B. Sensale-Rodriguez, T. Fang, R. S. Yan, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett. 99, 113104 (2011).
[Crossref]

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

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref] [PubMed]

2010 (2)

M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145, (2010).
[Crossref] [PubMed]

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

2009 (1)

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

2008 (2)

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]

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,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

2007 (1)

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

2005 (1)

T. Ozel, A. Gaur, J. A. Rogers, and M. Shim, “Polymer electrolyte gating of carbon nanotube network transistors,” Nano Lett. 5(5), 905–911 (2005).
[Crossref] [PubMed]

Ahn, K. J.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J. K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J. Y. Park, F. Rotermund, and D. I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

Ahn, Y. H.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J. K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J. Y. Park, F. Rotermund, and D. I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

Allen, M. J.

M. J. Allen, V. C. Tung, and R. B. Kaner, “Honeycomb carbon: a review of graphene,” Chem. Rev. 110(1), 132–145, (2010).
[Crossref] [PubMed]

Altug, H.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
[Crossref] [PubMed]

Ang, L. K.

K. J. A. Ooi, J. L. Cheng, J. E. Sipe, L. K. Ang, and D. T. H. Tan, “Ultrafast, broadband, and configurable midinfrared all-optical switching in nonlinear graphene plasmonic waveguide,” APL Photonics 1(4), 046101 (2016).
[Crossref]

Ansell, D.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref] [PubMed]

Anugrah, Y.

N. Youngblood, Y. Anugrah, R. Ma, S. J. Koester, and M. Li, “Multifunctional graphene optical modulator and photodetector integrated on silicon waveguides,” Nano Lett. 14(5), 2741–2746 (2014).
[Crossref] [PubMed]

Avouris, P.

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

Bae, S.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J. K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J. Y. Park, F. Rotermund, and D. I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[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, Q. L.

Basko, D. M.

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

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,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Bonaccorso, F.

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

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,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Boscolo, S.

Bozhevolnyi, S. I.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref] [PubMed]

Britnell, L.

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref] [PubMed]

Brodyanski, A.

P. Weis, J. L. Garcia-Pomar, M. Höh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref] [PubMed]

Cao, Y.

C. Meng, S. L. Yu, H. Q. Wang, Y. Cao, L. M. Tong, W. T. Liu, and Y. S. Shen, “Graphene-doped polymer nanofibers for low-threshold nonlinear optical waveguiding,” Light Sci. Appl. 4(11), e348 (2015).
[Crossref]

Capobianco, A. D.

Cardenas, J.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

Chang, D. E.

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “all-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–128 (2016).
[Crossref]

Chen, B.

S. Yu, C. Meng, B. Chen, H. Wang, X. Wu, W. Liu, S. Zhang, Y. Liu, Y. Su, and L. Tong, “Graphene decorated microfiber for ultrafast optical modulation,” Opt. Express 23(8), 10764–10770 (2015).
[Crossref] [PubMed]

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, B. G.

Chen, H. S.

R. Hao, W. Du, E. P. Li, and H. S. Chen, “Graphene assisted TE/TM-independent polarizer based on Mach- Zehnder interferometer,” IEEE Photonics Technol. Lett. 27(10), 1112–1115 (2015).
[Crossref]

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

Chen, J. H.

J. H. Chen, B. C. Zheng, G. H. Shao, S. J. Ge, F. Xu, and Y. Q. Lu, “An all-optical modulator based on a stereo graphene-microfiber structure,” Light Sci. Appl. 4(12), e360 (2015).
[Crossref]

Chen, K. R.

Chen, X.

Chen, Y.

F. Xing, G. X. Meng, Q. Zhang, L. T. Pan, P. Wang, Z. B. Liu, W. S. Jiang, Y. Chen, and J. G. Tian, “Ultrasensitive flow sensing of a single cell using graphene-based optical sensors,” Nano Lett. 14(6), 3563–3569 (2014).
[Crossref] [PubMed]

Chen, Z.

Q. Y. Wen, W. Tian, Q. Mao, Z. Chen, W. W. Liu, Q. H. Yang, M. Sanderson, and H. W. Zhang, “Graphene based all-optical spatial terahertz modulator,” Sci. Rep. 4(1), 7409 (2014).
[Crossref] [PubMed]

Cheng, J. L.

K. J. A. Ooi, J. L. Cheng, J. E. Sipe, L. K. Ang, and D. T. H. Tan, “Ultrafast, broadband, and configurable midinfrared all-optical switching in nonlinear graphene plasmonic waveguide,” APL Photonics 1(4), 046101 (2016).
[Crossref]

Cheng, Z.

Choi, S. Y.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J. K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J. Y. Park, F. Rotermund, and D. I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

Constant, T. J.

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “all-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–128 (2016).
[Crossref]

Cui, Y.

Dai, D. X.

Dalir, H.

H. Dalir, Y. Xia, Y. Wang, and X. Zhang, “Athermal broadband graphene optical modulator with 35 GHz speed,” ACS Photonics 3(9), 1564–1568 (2016).
[Crossref]

Das, S.

De Angelis, C.

Ding, Y.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro- optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Dong, L.

L. Wu, H. X. Liu, J. B. Li, S. L. Wang, S. Qu, and L. Dong, “A 130 GHz electro-optic ring modulator with double-layer graphene,” Crystals 7(3), 65 (2017).
[Crossref]

Du, W.

R. Hao, W. Du, E. P. Li, and H. S. Chen, “Graphene assisted TE/TM-independent polarizer based on Mach- Zehnder interferometer,” IEEE Photonics Technol. Lett. 27(10), 1112–1115 (2015).
[Crossref]

W. Du, E. P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photonics Technol. Lett. 26(20), 2008–2011 (2014).
[Crossref]

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

Echtermeyer, T. J.

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref] [PubMed]

Esquius-Morote, M.

Etezadi, D.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
[Crossref] [PubMed]

Fan, D. Y.

Fan, M.

Fang, T.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref] [PubMed]

B. Sensale-Rodriguez, T. Fang, R. S. Yan, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett. 99, 113104 (2011).
[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]

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.

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref] [PubMed]

D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

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

Frandsen, L. H.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro- optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Gao, C.

Gao, L.

García de Abajo, F. J.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015).
[Crossref] [PubMed]

Garcia-Pomar, J. L.

P. Weis, J. L. Garcia-Pomar, M. Höh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref] [PubMed]

Gaur, A.

T. Ozel, A. Gaur, J. A. Rogers, and M. Shim, “Polymer electrolyte gating of carbon nanotube network transistors,” Nano Lett. 5(5), 905–911 (2005).
[Crossref] [PubMed]

Ge, S. J.

J. H. Chen, B. C. Zheng, G. H. Shao, S. J. Ge, F. Xu, and Y. Q. Lu, “An all-optical modulator based on a stereo graphene-microfiber structure,” Light Sci. Appl. 4(12), e360 (2015).
[Crossref]

Geim, A. K.

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (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,” Science 320(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,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Giesecke, A. L.

M. Mohsin, D. Neumaier, D. Schall, M. Otto, C. Matheisen, A. L. Giesecke, A. A. Sagade, and H. Kurz, “Experimental verification of electro-refractive phase modulation in graphene,” Sci. Rep. 5(1), 10967 (2015).
[Crossref] [PubMed]

Goda, K.

Gómez-Díaz, J. S.

Gorbachev, R. V.

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[Crossref] [PubMed]

Gosciniak, J.

J. Gosciniak and D. T. H. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci. Rep. 3(1), 1897 (2013).
[Crossref] [PubMed]

Grigorenko, A. N.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref] [PubMed]

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (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,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Guo, X.

Han, Z.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[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(6), 064302 (2008).
[Crossref]

Hao, R.

R. Hao, W. Du, E. P. Li, and H. S. Chen, “Graphene assisted TE/TM-independent polarizer based on Mach- Zehnder interferometer,” IEEE Photonics Technol. Lett. 27(10), 1112–1115 (2015).
[Crossref]

W. Du, E. P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photonics Technol. Lett. 26(20), 2008–2011 (2014).
[Crossref]

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

Harada, Y.

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
[Crossref]

Hasan, T.

D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

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

He, X. Y.

Healy, N.

H. Zhang, N. Healy, L. Shen, C. C. Huang, D. W. Hewak, and A. C. Peacock, “Enhanced all-optical modulation in a graphene-coated fibre with low insertion loss,” Sci. Rep. 6(1), 23512 (2016).
[Crossref] [PubMed]

Hendry, E.

T. J. Constant, S. M. Hornett, D. E. Chang, and E. Hendry, “all-optical generation of surface plasmons in graphene,” Nat. Phys. 12(2), 124–128 (2016).
[Crossref]

Hewak, D. W.

H. Zhang, N. Healy, L. Shen, C. C. Huang, D. W. Hewak, and A. C. Peacock, “Enhanced all-optical modulation in a graphene-coated fibre with low insertion loss,” Sci. Rep. 6(1), 23512 (2016).
[Crossref] [PubMed]

Hibino, H.

R. Kou, Y. Hori, T. Tsuchizawa, K. Warabi, Y. Kobayashi, Y. Harada, H. Hibino, T. Yamamoto, H. Nakajima, and K. Yamada, “Ultra-fine metal gate operated graphene optical intensity modulator,” Appl. Phys. Lett. 109(25), 251101 (2016).
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B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
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Yan, R. S.

B. Sensale-Rodriguez, T. Fang, R. S. Yan, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett. 99, 113104 (2011).
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Yang, H.

Yang, L. Z.

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
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Yang, Q. H.

Q. Y. Wen, W. Tian, Q. Mao, Z. Chen, W. W. Liu, Q. H. Yang, M. Sanderson, and H. W. Zhang, “Graphene based all-optical spatial terahertz modulator,” Sci. Rep. 4(1), 7409 (2014).
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Ye, S.

Ye, S. W.

S. W. Ye, F. Yuan, X. H. Zou, M. K. Shah, R. G. Lu, and Y. Liu, “High-speed optical phase modulator based on graphene-silicon waveguide,” IEEE J. Sel. Top. Quantum Electron. 23(1), 3400105 (2017).
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N. Youngblood, Y. Anugrah, R. Ma, S. J. Koester, and M. Li, “Multifunctional graphene optical modulator and photodetector integrated on silicon waveguides,” Nano Lett. 14(5), 2741–2746 (2014).
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S. W. Ye, F. Yuan, X. H. Zou, M. K. Shah, R. G. Lu, and Y. Liu, “High-speed optical phase modulator based on graphene-silicon waveguide,” IEEE J. Sel. Top. Quantum Electron. 23(1), 3400105 (2017).
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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).
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H. Zhang, N. Healy, L. Shen, C. C. Huang, D. W. Hewak, and A. C. Peacock, “Enhanced all-optical modulation in a graphene-coated fibre with low insertion loss,” Sci. Rep. 6(1), 23512 (2016).
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F. Xing, G. X. Meng, Q. Zhang, L. T. Pan, P. Wang, Z. B. Liu, W. S. Jiang, Y. Chen, and J. G. Tian, “Ultrasensitive flow sensing of a single cell using graphene-based optical sensors,” Nano Lett. 14(6), 3563–3569 (2014).
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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).
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C. Meng, S. L. Yu, H. Q. Wang, Y. Cao, L. M. Tong, W. T. Liu, and Y. S. Shen, “Graphene-doped polymer nanofibers for low-threshold nonlinear optical waveguiding,” Light Sci. Appl. 4(11), e348 (2015).
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Figures (11)

Fig. 1
Fig. 1 Relationships between σ (solid line for real part and dashed lines for imaginary part) and μc: (a) with different ω for T = 298 K, Γ = 1e12 Hz; (b) with different Γ for T = 298 K, ω/2π = 1.94e14 Hz; (c) with different T for Γ = 1e12 Hz, ω/2π = 1.94e14 Hz; (d) relative permittivity of graphene εg as a function of chemical potential for ω/2π = 1.94e14 Hz, T = 298 K, Γ = 1e12 Hz
Fig. 2
Fig. 2 Sketch map of GSPF and its cross-sectional view.
Fig. 3
Fig. 3 Imaginary and real part of neff as functions of chemical potential with different N for R = 1.5 μm, T = 298 k, Γ = 1e12 Hz, and ω/2π = 1.94e14 Hz.
Fig. 4
Fig. 4 (a) ΔIm(neff) of both TE- and TM-mode and (b) AENZ of TM-mode as functions of R under the condition of N = 10, T = 298 K, Γ = 1e12 Hz, and ω/2π = 1.94e14 Hz. (c) Field distribution of TE-mode with the change of R.
Fig. 5
Fig. 5 Im(neff) of (a) TE- and (c) TM-mode as functions of chemical potential with different ω for R = 1.5 μm, T = 298 K, Γ = 1e12 Hz, and N = 10; (b) ΔIm(neff) of TE-mode as a function of wavelength; (d) AENZ as a function of wavelength.
Fig. 6
Fig. 6 Im(neff) of (a) TE- and (c) TM-mode as functions of chemical potential with different Γ for R = 1.5 μm, T = 298 K, N = 10, and ω/2π = 1.94e14 Hz; (b) ΔIm(neff) of TE-mode as a function of scattering rate; (d) AENZ as a function of scattering rate.
Fig. 7
Fig. 7 Im(neff) of (a) TE- and (c) TM-mode as functions of chemical potential with different T for R = 1.5 μm, N = 10, Γ = 1e12 Hz, and ω/2π = 1.94e14 Hz; (b) ΔIm(neff) of TE-mode as a function of temperature; (d) AENZ as a function of temperature.
Fig. 8
Fig. 8 ΔIm(neff) of TE-mode for N = 4 with ion liquid overlapping as well as N = 10 with air overlapping as functions of residual radius of SPF.
Fig. 9
Fig. 9 Sketch map of the modulator based on GSPF.
Fig. 10
Fig. 10 (a) TE-mode power for different wavelength as functions of chemical potential; (b) TM-mode power for different wavelength as functions of chemical potential.
Fig. 11
Fig. 11 (a) Im(neff) of TE-mode with both wavelength and chemical potential in unit of hω/2π;(b) Im(neff) of TE-mode with both wavelength and chemical potential in unit of eV; (c) Im(neff) of TM-mode with both wavelength and chemical potential in unit of hω/2π; (d) Im(neff) of TM-mode with both wavelength and chemical potential in unit of eV.

Equations (5)

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n s = 2 π 2 v F 2 0 ε[ f d ( ε ) f d ( ε+2 μ c ) ]dε
σ( ω, μ c ,Γ,T )= j e 2 ( ω+j2Γ ) π 2 [ 0 ε( f d ( ε ) ε f d ( ε ) ε ) dε 0 f d ( ε ) f d ( ε ) ( ω+j2Γ ) 2 4 ( ε/ ) 2 dε]
n g = ( ε g ) 1/2 = ( 1+ jσ ε 0 ω t g ) 1/2
power=10lg P P 0 =10lg{ | exp( j k 0 n eff L ) | 2 }
C 0 ( V D V Dirac )=e n s

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