Abstract

We investigate the electrically controlled light propagation in the metal–dielectric–metal plasmonic waveguide with a sandwiched graphene monolayer. The theoretical and simulation results show that the propagation loss exhibits an obvious peak when the permittivity of graphene approaches an epsilon-near-zero point when adjusting the gate voltage on graphene. The analog of electromagnetically induced transparency (EIT) can be generated by introducing side-coupled stubs into the waveguide. Based on the EIT-like effect, the hybrid plasmonic waveguide with a length of only 1.5 μm can work as a modulator with an extinction ratio of 15.8  dB, which is 2.3 times larger than the case without the stubs. The active modulation of surface plasmon polariton propagation can be further improved by tuning the carrier mobility of graphene. The graphene-supported plasmonic waveguide system could find applications for the nanoscale manipulation of light and chip-integrated modulation.

© 2017 Chinese Laser Press

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    [Crossref]
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    [Crossref]
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    [Crossref]
  46. J. Gosciniak and D. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24, 185202 (2013).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (9)

H. Ren, X. Li, Q. Zhang, and M. Gu, “On-chip noninterference angular momentum multiplexing of broadband light,” Science 352, 805–809 (2016).
[Crossref]

C. Zhang, C. Min, L. Du, and X. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108, 201601 (2016).
[Crossref]

Z. Chen, H. Li, S. Zhan, B. Li, Z. He, H. Xu, and M. Zheng, “Tunable high quality factor in two multimode plasmonic stubs waveguide,” Sci. Rep. 6, 24446 (2016).
[Crossref]

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmons based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
[Crossref]

R. Yu, V. Pruneri, and F. Abajo, “Active modulation of visible light with graphene-loaded ultrathin metal plasmonic antennas,” Sci. Rep. 6, 32144 (2016).
[Crossref]

H. Jussila, H. Yang, N. Granqvist, and Z. Sun, “Surface plasmon resonance for characterization of large-area atomic-layer graphene film,” Optica 3, 151–158 (2016).
[Crossref]

W. Liu, B. Wang, S. Ke, C. Qin, H. Long, K. Wang, and P. Lu, “Enhanced plasmonic nanofocusing of terahertz waves in tapered graphene multilayers,” Opt. Express 24, 14765–14780 (2016).
[Crossref]

Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “Tunable dual-band asymmetric transmission for circularly polarized waves with graphene planar chiral metasurfaces,” Opt. Lett. 41, 3142–3145 (2016).
[Crossref]

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

2015 (6)

J. Shin and J. Kim, “Broadband silicon optical modulator using a graphene-integrated hybrid plasmonic waveguide,” Nanotechnology 26, 365201 (2015).
[Crossref]

J. Liu, Y. Zhou, L. Li, P. Wang, and A. V. Zayats, “Controlling plasmon-induced transparency of graphene metamolecules with external magnetic field,” Opt. Express 23, 12524–12532 (2015).
[Crossref]

R. Yu, V. Pruneri, and F. J. G. de Abajo, “Resonant visible light modulation with graphene,” ACS Photon. 2, 550–558 (2015).
[Crossref]

J. Shin, J. Kim, and J. Kim, “Graphene-based hybrid plasmonic modulator,” J. Opt. 17, 125801 (2015).
[Crossref]

R. Hao, X. Peng, E. Li, Y. Xu, J. Jin, X. Zhang, and H. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5, 15335 (2015).
[Crossref]

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

2014 (6)

V. Apalkov and M. Stockman, “Proposed graphene nanospasers,” Light Sci. Appl. 3, e191 (2014).
[Crossref]

X. He and H. X. Lu, “Graphene-supported tunable extraordinary transmission,” Nanotechnology 25, 325201 (2014).
[Crossref]

R. McCarron, W. Dickson, A. Krasavin, G. Wurtz, and A. Zayats, “Dipolar emission in trench metal-insulator-metal waveguides for short-scale plasmonic communications: numerical optimization,” J. Opt. 16, 114006 (2014).
[Crossref]

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8, 229–233 (2014).
[Crossref]

M. S. Kwon, “Discussion of the epsilon-near-zero effect of graphene in a horizontal slot waveguide,” IEEE Photon. J. 6, 1–9 (2014).
[Crossref]

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, 347–353 (2014).
[Crossref]

2013 (7)

J. Gosciniak and D. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24, 185202 (2013).
[Crossref]

J. Gosciniak and D. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci. Rep. 3, 01897 (2013).
[Crossref]

L. Yang, T. Hu, R. Hao, C. Qiu, C. Xu, H. Yu, Y. Xu, X. Jiang, Y. Li, and J. Yang, “Low-chirp high-extinction-ratio modulator based on graphene-silicon waveguide,” Opt. Lett. 38, 2512–2515 (2013).
[Crossref]

B. Fan, F. Liu, X. Wang, Y. Li, K. Cui, X. Feng, and Y. Huang, “Integrated sensor for ultra-thin layer sensing based on hybrid coupler with short-range surface plasmon polariton and dielectric waveguide,” Appl. Phys. Lett. 102, 061109 (2013).
[Crossref]

J. Chen, Z. Li, X. Zhang, J. Xiao, and Q. Gong, “Submicron bidirectional all-optical plasmonic switches,” Sci. Rep. 3, 1451 (2013).
[Crossref]

X. Gan, R. Shiue, Y. Gao, K. Mak, X. Yao, L. Li, A. Szep, D. Walker, J. Hone, T. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13, 691–696 (2013).
[Crossref]

X. Gan, R. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
[Crossref]

2012 (11)

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

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

H. Choo, M. Kim, M. Staffaroni, T. Seok, J. Bokor, S. Cabrini, P. Schuck, M. Wu, and E. Yablonovitch, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6, 838–844 (2012).
[Crossref]

P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23, 444011 (2012).
[Crossref]

V. Sorger, R. Oulton, R. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37, 728–738 (2012).
[Crossref]

P. Neutens, L. Lagae, G. Borghs, and P. Dorpe, “Plasmon filters and resonators in metal-insulator-metal waveguides,” Opt. Express 20, 3408–3423 (2012).
[Crossref]

X. Kong, W. Yan, Z. Li, and J. Tian, “Optical properties of metal-multi-insulator-metal plasmonic waveguides,” Opt. Express 20, 12133–12146 (2012).
[Crossref]

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

G. Wang, H. Lu, and X. Liu, “Dispersionless slow light in MIM waveguide based on a plasmonic analogue of electromagnetically induced transparency,” Opt. Express 20, 20902–20907 (2012).
[Crossref]

H. Lu, X. Liu, and D. Mao, “Plasmonic analog of electromagnetically induced transparency in multi-nanoresonator-coupled waveguide systems,” Phys. Rev. A 85, 053803 (2012).
[Crossref]

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photon. J. 4, 735–740 (2012).
[Crossref]

2011 (5)

F. Hu, H. Yi, and Z. Zhou, “Wavelength demultiplexing structure based on arrayed plasmonic slot cavities,” Opt. Lett. 36, 1500–1502 (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, 64–67 (2011).
[Crossref]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref]

P. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5, 5855–5863 (2011).
[Crossref]

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

2010 (2)

2009 (4)

C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express 17, 10757–10766 (2009).
[Crossref]

M. Hill, M. Marell, E. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. Veldhoven, E. Geluk, F. Karouta, Y. Oei, R. Nötzel, C. Ning, and M. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[Crossref]

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3, 283–286 (2009).
[Crossref]

Q. Gan, Y. J. Ding, and F. J. Bartoli, “‘Rainbow’ trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

2008 (1)

J. Chen, C. Jang, S. Xiao, M. Ishigami, and M. Fuhrer, “Intrinsic and extrinsic performance limits of graphene devices on SiO2,” Nat. Nanotechnol. 3, 206–209 (2008).
[Crossref]

2007 (1)

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

2006 (1)

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength scale localization,” Phys. Rev. B 73, 035407 (2006).
[Crossref]

2005 (1)

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[Crossref]

2003 (1)

W. Barnes, A. Dereux, and T. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref]

1972 (1)

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

Abajo, F.

R. Yu, V. Pruneri, and F. Abajo, “Active modulation of visible light with graphene-loaded ultrathin metal plasmonic antennas,” Sci. Rep. 6, 32144 (2016).
[Crossref]

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

Alloatti, L.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8, 229–233 (2014).
[Crossref]

Alù, A.

P. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5, 5855–5863 (2011).
[Crossref]

Apalkov, V.

V. Apalkov and M. Stockman, “Proposed graphene nanospasers,” Light Sci. Appl. 3, e191 (2014).
[Crossref]

Assefa, S.

X. Gan, R. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
[Crossref]

Atwater, H.

J. Dionne, L. Sweatlock, H. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength scale localization,” Phys. Rev. B 73, 035407 (2006).
[Crossref]

Bao, Q.

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

Barnes, W.

W. Barnes, A. Dereux, and T. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref]

Bartoli, F. J.

Q. Gan, Y. J. Ding, and F. J. Bartoli, “‘Rainbow’ trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

Berini, P.

P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23, 444011 (2012).
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J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
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ACS Photon. (1)

R. Yu, V. Pruneri, and F. J. G. de Abajo, “Resonant visible light modulation with graphene,” ACS Photon. 2, 550–558 (2015).
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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, 347–353 (2014).
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Appl. Phys. Lett. (3)

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
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B. Fan, F. Liu, X. Wang, Y. Li, K. Cui, X. Feng, and Y. Huang, “Integrated sensor for ultra-thin layer sensing based on hybrid coupler with short-range surface plasmon polariton and dielectric waveguide,” Appl. Phys. Lett. 102, 061109 (2013).
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C. Zhang, C. Min, L. Du, and X. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108, 201601 (2016).
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IEEE Photon. J. (2)

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photon. J. 4, 735–740 (2012).
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M. S. Kwon, “Discussion of the epsilon-near-zero effect of graphene in a horizontal slot waveguide,” IEEE Photon. J. 6, 1–9 (2014).
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J. Opt. (2)

R. McCarron, W. Dickson, A. Krasavin, G. Wurtz, and A. Zayats, “Dipolar emission in trench metal-insulator-metal waveguides for short-scale plasmonic communications: numerical optimization,” J. Opt. 16, 114006 (2014).
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J. Shin, J. Kim, and J. Kim, “Graphene-based hybrid plasmonic modulator,” J. Opt. 17, 125801 (2015).
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J. Opt. Soc. Am. B (1)

Light Sci. Appl. (1)

V. Apalkov and M. Stockman, “Proposed graphene nanospasers,” Light Sci. Appl. 3, e191 (2014).
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MRS Bull. (1)

V. Sorger, R. Oulton, R. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS Bull. 37, 728–738 (2012).
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Nano Lett. (1)

X. Gan, R. Shiue, Y. Gao, K. Mak, X. Yao, L. Li, A. Szep, D. Walker, J. Hone, T. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13, 691–696 (2013).
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Nanotechnology (4)

J. Gosciniak and D. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24, 185202 (2013).
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P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23, 444011 (2012).
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X. He and H. X. Lu, “Graphene-supported tunable extraordinary transmission,” Nanotechnology 25, 325201 (2014).
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J. Shin and J. Kim, “Broadband silicon optical modulator using a graphene-integrated hybrid plasmonic waveguide,” Nanotechnology 26, 365201 (2015).
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Nat. Mater. (1)

A. Geim and K. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
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Nat. Nanotechnol. (1)

J. Chen, C. Jang, S. Xiao, M. Ishigami, and M. Fuhrer, “Intrinsic and extrinsic performance limits of graphene devices on SiO2,” Nat. Nanotechnol. 3, 206–209 (2008).
[Crossref]

Nat. Photonics (6)

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Figures (7)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the graphene-supported MDM plasmonic waveguide. An external gate voltage Vg is exerted on the graphene. The inset shows the section-cross profile of the waveguide with graphene. Here, d1 (d3) represents the distance between the graphene and metal film below (above) the dielectric layer (silica, ϵd=2.25). d2 and L are the thickness and length of graphene, respectively. (b) Real and imaginary parts of the relative permittivity ϵg of graphene with the different bias voltages |Vb| at the wavelength of 1.49 μm in the waveguide with d1=45  nm and d3=5  nm.

Fig. 2.
Fig. 2.

(a) Real and (b) imaginary parts of ERI (neff) of the plasmonic mode at λ=1.49  μm as a function of the bias voltage of graphene in the MDM plasmonic waveguide with d1=45  nm and d3=5  nm. The curves and circles denote the theoretical and simulation results obtained by the equations and FEM, respectively.

Fig. 3.
Fig. 3.

(a)–(d) Normalized electric field and magnetic field profiles in the MDM waveguide at λ=1.49  μm when |Vb|=6 and 7.76 V.

Fig. 4.
Fig. 4.

Transmission spectra in the graphene-supported MDM plasmonic waveguide [shown in Fig. 1(a)] when |Vb|=6 and 7.76 V. The inset shows the transmission as a function of the bias voltage in the waveguide with d1=45  nm, d3=5  nm, and L=670  nm.

Fig. 5.
Fig. 5.

(a) Schematic diagram of the graphene-supported MDM plasmonic waveguide with the double side-coupled stubs. The inset shows the cross-section diagram of the plasmonic waveguide. l1 and w1 (l2 and w2) stand for the height and width of the stub 1 (stub 2), respectively. (b) Transmission spectra in the graphene-supported MDM plasmonic waveguide with the stub 1, stub 2, and double stubs when |Vb|=6  V. (c) Transmission spectra in the waveguide with the double stubs when |Vb|=7.76  V. The inset shows the ER of the modulation at different wavelengths. Here, d1=45  nm, d3=5  nm, l1=130  nm, w1=50  nm, l2=190  nm, w2=50  nm, and L=670  nm.

Fig. 6.
Fig. 6.

(a)–(d) Normalized electric field and magnetic field distributions at λ=1.49  μm in the MDM plasmonic waveguide when |Vb|=6 and 7.76 V.

Fig. 7.
Fig. 7.

ER of the EOM as a function of the carrier mobility μ of graphene in the MDM plasmonic waveguide without and with the double side-coupled stubs.

Equations (5)

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

σintra=ie2kBTπ2(ω+iτ1){μckBT+2ln[exp(μckBT)+1]},
σinter=ie24πln[2|μc|(ω+iτ1)2|μc|+(ω+iτ1)],
(1+X04)+(X01+X14)Y1+(X02+X24)Y2+(X03+X34)Y3+(X12+X01X24)Y1Y2+(X13+X01X34)Y1Y3+(X23+X02X34)Y2Y3+(X01X23+X12X34)Y1Y2Y3=0,
Xln=ϵlk0(neff2ϵn)ϵnk0(neff2ϵl)(l,n=0,1,2,3,4),
Yl=tanh[dlk0(neff2ϵl)](l=1,2,3).

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