Abstract

We give the effective refractive index of graphene plasmonic waveguides with both linear and nonlinear effects based on the nonlinear cross-phase modulation, and address the effects of photo-induced refractive index change and absorption change. A non-resonant all-optical nonlinear graphene plasmonic switch with an ultra-compact size of 0.25 μm2 is proposed and numerically analyzed based on the dynamics of the photo-induced absorption change. The results show that the all-optical graphene plasmonic switch can realize a broad bandwidth over 5 THz, a potentially very high switching speed and an extinction ratio of 18.14 dB with the electric amplitude of the pump light of 1.5 × 107 V/m at the signal frequency of 28 THz. Our study could provide a possibility for future all-optical highly integrated optical components.

© 2016 Optical Society of America

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  4. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
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    [Crossref] [PubMed]
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    [Crossref]
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  32. A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
    [Crossref]
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    [Crossref]

2016 (2)

2015 (4)

X. He, Z. Y. Zhao, and W. Shi, “Graphene-supported tunable near-IR metamaterials,” Opt. Lett. 40(2), 178–181 (2015).
[Crossref] [PubMed]

L. Jiang, J. Guo, L. Wu, X. Dai, and Y. Xiang, “Manipulating the optical bistability at terahertz frequency in the Fabry-Perot cavity with graphene,” Opt. Express 23(24), 31181–31191 (2015).
[Crossref] [PubMed]

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

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

2014 (7)

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
[Crossref]

Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (2014).
[Crossref] [PubMed]

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
[Crossref]

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, 7409 (2014).
[Crossref] [PubMed]

J. Wang, W. B. Lu, X. B. Li, Z. H. Ni, and T. Qiu, “Graphene plasmon guided along a nanoribbon coupled with a nanoring,” J. Phys. D Appl. Phys. 47(13), 135106 (2014).
[Crossref]

J. Tao, X. Yu, B. Hu, A. Dubrovkin, and Q. J. Wang, “Graphene-based tunable plasmonic Bragg reflector with a broad bandwidth,” Opt. Lett. 39(2), 271–274 (2014).
[Crossref] [PubMed]

H. Nasari and M. S. Abrishamian, “All-optical tunable notch filter by use of Kerr nonlinearity in the graphene microribbon array,” J. Opt. Soc. Am. B 31(7), 1691–1697 (2014).
[Crossref]

2013 (3)

F. J. García de Abajo, “Applied physics. Graphene nanophotonics,” Science 339(6122), 917–918 (2013).
[Crossref] [PubMed]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

2012 (3)

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

Y. J. Zhu, X. G. Huang, and X. Mei, “A surface plasmon polarition electro-optic switch based on a metal-insulator-metal structure with a strip waveguide and two side-coupled cavities,” Chin. Phys. Lett. 29(6), 64214 (2012).
[Crossref]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

2011 (6)

A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (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,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

2010 (2)

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

2009 (3)

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

2007 (2)

S. A. Mikhailov, “Non-linear electromagnetic response of graphene,” EPL 79(2), 417–429 (2007).
[Crossref]

L. A. Falkovsky and C. C. Persheguba, “Optical far-infrafred properties of a garphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Abrishamian, M. S.

Avouris, P.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

Bai, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Bao, Q.

Y. Lu, J. Song, J. Yuan, L. Zhang, S. Q. Yang Wu, W. Yu, M. Zhao, C. W. Qiu, J. Teng, K. P. Loh, C. Zhang, and Q. Bao, “Highly efficient plasmon excitation in graphene-Bi2Te3 heterostructure,” J. Opt. Soc. Am. B 33(9), 1842–1846 (2016).
[Crossref]

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (2014).
[Crossref] [PubMed]

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

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Bian, F.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Bludov, Y. V.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
[Crossref]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
[Crossref]

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Capasso, F.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Carroll, D.

I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Chen, J.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
[Crossref]

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, 7409 (2014).
[Crossref] [PubMed]

Cormode, D.

A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
[Crossref]

Dai, X.

Dubrovkin, A.

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Falkovsky, L. A.

L. A. Falkovsky and C. C. Persheguba, “Optical far-infrafred properties of a garphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Fan, S.

Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (2014).
[Crossref] [PubMed]

Freitag, M.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

García de Abajo, F. J.

F. J. García de Abajo, “Applied physics. Graphene nanophotonics,” Science 339(6122), 917–918 (2013).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Genevet, P.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (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,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Godbout, N.

Gu, M.

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

Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (2014).
[Crossref] [PubMed]

Guinea, F.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

Guo, J.

Hale, P. J.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

He, X.

Hendry, E.

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

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
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Y. J. Zhu, X. G. Huang, and X. Mei, “A surface plasmon polarition electro-optic switch based on a metal-insulator-metal structure with a strip waveguide and two side-coupled cavities,” Chin. Phys. Lett. 29(6), 64214 (2012).
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I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

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M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
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M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
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N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
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Jiang, X.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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Kockaert, P.

Kong, J.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
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A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
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Li, S.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
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Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (2014).
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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
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J. Wang, W. B. Lu, X. B. Li, Z. H. Ni, and T. Qiu, “Graphene plasmon guided along a nanoribbon coupled with a nanoring,” J. Phys. D Appl. Phys. 47(13), 135106 (2014).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
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Liu, J.

Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (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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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, 7409 (2014).
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Liu, X.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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Y. Lu, J. Song, J. Yuan, L. Zhang, S. Q. Yang Wu, W. Yu, M. Zhao, C. W. Qiu, J. Teng, K. P. Loh, C. Zhang, and Q. Bao, “Highly efficient plasmon excitation in graphene-Bi2Te3 heterostructure,” J. Opt. Soc. Am. B 33(9), 1842–1846 (2016).
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Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
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Lu, H.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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J. Wang, W. B. Lu, X. B. Li, Z. H. Ni, and T. Qiu, “Graphene plasmon guided along a nanoribbon coupled with a nanoring,” J. Phys. D Appl. Phys. 47(13), 135106 (2014).
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R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
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Lu, Y.

Mao, Q.

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, 7409 (2014).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Y. J. Zhu, X. G. Huang, and X. Mei, “A surface plasmon polarition electro-optic switch based on a metal-insulator-metal structure with a strip waveguide and two side-coupled cavities,” Chin. Phys. Lett. 29(6), 64214 (2012).
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E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

Nasari, H.

Neely, D.

I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

Ni, Z. H.

J. Wang, W. B. Lu, X. B. Li, Z. H. Ni, and T. Qiu, “Graphene plasmon guided along a nanoribbon coupled with a nanoring,” J. Phys. D Appl. Phys. 47(13), 135106 (2014).
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A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
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Pogorelsky, I. V.

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Polyanskiy, M.

I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

Qiu, C. W.

Qiu, T.

J. Wang, W. B. Lu, X. B. Li, Z. H. Ni, and T. Qiu, “Graphene plasmon guided along a nanoribbon coupled with a nanoring,” J. Phys. D Appl. Phys. 47(13), 135106 (2014).
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H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
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Roberts, A.

A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
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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, 7409 (2014).
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A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
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N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
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Savchenko, A. K.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Shkolnikov, P.

I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

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M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
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M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 308–310 (2009).
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Y. Lu, J. Song, J. Yuan, L. Zhang, S. Q. Yang Wu, W. Yu, M. Zhao, C. W. Qiu, J. Teng, K. P. Loh, C. Zhang, and Q. Bao, “Highly efficient plasmon excitation in graphene-Bi2Te3 heterostructure,” J. Opt. Soc. Am. B 33(9), 1842–1846 (2016).
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Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (2014).
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Song, Y.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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Tao, J.

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
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J. Tao, X. Yu, B. Hu, A. Dubrovkin, and Q. J. Wang, “Graphene-based tunable plasmonic Bragg reflector with a broad bandwidth,” Opt. Lett. 39(2), 271–274 (2014).
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Teng, J.

Tian, W.

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, 7409 (2014).
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Turner, M. D.

Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (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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N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
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Venkatesan, T.

Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
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Virally, S.

Wang, E.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

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).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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J. Wang, W. B. Lu, X. B. Li, Z. H. Ni, and T. Qiu, “Graphene plasmon guided along a nanoribbon coupled with a nanoring,” J. Phys. D Appl. Phys. 47(13), 135106 (2014).
[Crossref]

Wang, Q. J.

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
[Crossref]

J. Tao, X. Yu, B. Hu, A. Dubrovkin, and Q. J. Wang, “Graphene-based tunable plasmonic Bragg reflector with a broad bandwidth,” Opt. Lett. 39(2), 271–274 (2014).
[Crossref] [PubMed]

Wang, W.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
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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, 7409 (2014).
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I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

Wu, L.

Wu, R.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
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Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
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Q. Bao, J. Chen, Y. Xiang, K. Zhang, S. Li, X. Jiang, Q. H. Xu, K. P. Loh, and T. Venkatesan, “Graphene nanobubbles: a new optical nonlinear material,” Adv. Opt. Mater. 3(6), 744–749 (2015).
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Xue, Y.

Q. Zhang, X. Li, M. M. Hossain, Y. Xue, J. Zhang, J. Song, J. Liu, M. D. Turner, S. Fan, Q. Bao, and M. Gu, “Graphene surface plasmons at the near-infrared optical regime,” Sci. Rep. 4, 6559 (2014).
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I. V. Pogorelsky, V. Yakimenko, M. Polyanskiy, P. Shkolnikov, M. Ispiryan, D. Neely, P. McKenna, D. Carroll, Z. Najmudin, and L. Willingale, “Ultrafast CO2 laser technology: Application in ion acceleration,” Nucl. Instrum. Methods Phys. Res. 620(1), 67–70 (2010).

Yan, H.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
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Figures (5)

Fig. 1
Fig. 1 The Real(neff) and the Imag(neff) of graphene deposited on a silica substrate as a function of the signal frequency at different field amplitudes of the pump light with ω' = 28.3 THz.
Fig. 2
Fig. 2 Schematic of the all-optical nonlinear graphene plasmonic switch. The length and the width of the switch are L = 500 nm and W = 500 nm, respectively. The width of graphene is Wg = 50 nm, and the thickness of each buffer is H1 = H2 = 200 nm. The pump light with the electric field direction in the xz-plane is applied on the switch.
Fig. 3
Fig. 3 Transmittance spectra of the all-optical nonlinear graphene plasmonic switch under the electric field amplitudes of the pump light of E = 0 and E = 1.5 × 107 V/m.
Fig. 4
Fig. 4 The Ey field profiles of the all-optical nonlinear graphene plasmonic switch. (a) and (b) signify respectively the “ON” and “OFF” states at the signal frequency of 23 THz, (c) and (d) indicate the “ON” and “OFF” states at the signal frequency of 28 THz, respectively.
Fig. 5
Fig. 5 (a). The extinction ratio of the all-optical nonlinear plasmonic graphene switch as a function of the electric field amplitude of the pump light with the signal frequency of 26 THz. Figure 5(b). The extinction ratio of the switch as a function of the widths of the graphene nanoribbon for different plasmonic modes.

Equations (10)

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σ(ω)= σ intra (ω)+ σ inter (ω)
σ intra = 2i e 2 k B T π 2 (ω+i τ 1 ) ln[ 2cosh( E f 2 k B T ) ]
σ inter = e 2 4 { 1 2 + 1 π arctan( ω2 E f 2 k B T ) i 2π ln[ (ω+2 E f ) 2 (ω2 E f ) 2 + (2 k B T) 2 ] }
ε=1+ iσ( ω ) ε 0 ω t G
J = J L + J NL =[ σ(ω)+ σ 3 (ω) | E | 2 ] E
σ 3 (ω)=-i 9 8 e 2 π 2 (e v F ) 2 E f ω 3
σ 3 '(ω')=-i 9 4 e 2 π 2 (e v F ) 2 E f ω ' 3
σ total (ω,ω')= σ intra (ω)+ σ 3 '(ω') | E | 2
σ total (ω,ω')= σ intra (ω)+σ ' 3, inter (ω') | E | 2
n eff = k sp / k 0 = ε 0 ε 1 + ε 2 2 2iω σ total (ω,ω')

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