Abstract

We investigate the surface vector plasmonic lattice solitons (PLSs) in semi-infinite graphene-pair arrays (GPAs). The surface vector PLSs are composed of two components which are associated with different band gaps. Both components undergo mutual self-trapping at the boundary of the semi-infinite structure when the self-focusing nonlinearity of graphene and the light diffraction reach a balance. Thanks to the strong confinement of SPPs, the surface vector PLSs can be squeezed into a deep-subwavelength width of ~0.003λ. By comparing with bulk solitons, the surface PLSs are more readily to excite by external waves and more sensitive to the surrounding environment. The study may develop promising applications in all-optical switching devices and optical sensors on deep-subwavelength scale.

© 2017 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]

2017 (6)

S. A. Mikhailov, “Nonperturbative quasiclassical theory of the nonlinear electrodynamic response of graphene,” Phys. Rev. B 95(8), 085432 (2017).
[Crossref]

A. Marini, J. D. Cox, and F. J. Garcia de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95(12), 125408 (2017).
[Crossref]

P. Lan, M. Ruhmann, L. He, C. Zhai, F. Wang, X. Zhu, Q. Zhang, Y. Zhou, M. Li, M. Lein, and P. Lu, “Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy,” Phys. Rev. Lett. 119(3), 033201 (2017).
[Crossref] [PubMed]

Z. Wang, B. Wang, H. Long, K. Wang, and P. Lu, “Surface plasmonic lattice solitons in semi-infinite graphene sheet arrays,” J. Lightwave Technol. 35(14), 2960–2965 (2017).
[Crossref]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of Plasmonic Supermodes in Graphene Multilayer Arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

H. Huang, S. Ke, B. Wang, H. Long, K. Wang, and P. Lu, “Numerical study on plasmonic absorption enhancement by a rippled grapheme sheet,” J. Lightwave Technol. 35(2), 320–324 (2017).
[Crossref]

2016 (5)

2015 (6)

Z. Li, K. Yao, F. Xia, S. Shen, J. Tian, and Y. Liu, “Graphene Plasmonic Metasurfaces to Steer Infrared Light,” Sci. Rep. 5(1), 12423 (2015).
[Crossref] [PubMed]

Y. Fan, B. Wang, H. Huang, K. Wang, H. Long, and P. Lu, “Plasmonic Zitterbewegung in binary graphene sheet arrays,” Opt. Lett. 40(13), 2945–2948 (2015).
[Crossref] [PubMed]

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic Plasmons and Topological Transitions Over Uniaxial Metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
[Crossref] [PubMed]

Z. Wang, B. Wang, H. Long, K. Wang, and P. Lu, “Plasmonic lattice solitons in nonlinear graphene sheet arrays,” Opt. Express 23(25), 32679–32689 (2015).
[Crossref] [PubMed]

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Bloch mode engineering in graphene modulated periodic waveguides and cavities,” J. Opt. Soc. Am. B 32(8), 1748–1753 (2015).
[Crossref]

2014 (3)

2013 (5)

A. V. Gorbach, “Nonlinear graphene plasmonics: Amplitude equation for surface plasmons,” Phys. Rev. A 87(1), 013830 (2013).
[Crossref]

D. A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. Garcia-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical solitons,” Laser Photonics Rev. 7(2), L7–L11 (2013).
[Crossref]

S. Hong, J. I. Dadap, N. Petrone, P. Yeh, J. Hone, and R. M. Osgood., “Optical third-harmonic generation in graphene,” Phys. Rev. X 3(2), 021014 (2013).
[Crossref]

Y. Kou, F. Ye, and X. Chen, “Multiband vector plasmonic lattice solitons,” Opt. Lett. 38(8), 1271–1273 (2013).
[Crossref] [PubMed]

2012 (4)

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B 86(12), 121108 (2012).
[Crossref]

2011 (1)

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

2010 (2)

N. M. R. Peres, “Colloquium: The transport properties of graphene: an introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (2010).
[Crossref]

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

2009 (1)

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

2008 (1)

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008).
[Crossref] [PubMed]

2007 (2)

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

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (2)

J. Hudock, S. Suntsov, D. Christodoulides, and G. Stegeman, “Vector discrete nonlinear surface waves,” Opt. Express 13(20), 7720–7725 (2005).
[Crossref] [PubMed]

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

2003 (1)

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

1997 (1)

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[Crossref]

Alù, A.

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic Plasmons and Topological Transitions Over Uniaxial Metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
[Crossref] [PubMed]

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Andryieuski, A.

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B 86(12), 121108 (2012).
[Crossref]

Avouris, P.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Bludov, Y. V.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

Bonaccorso, F.

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

Bravo-Abad, J.

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. Garcia-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical solitons,” Laser Photonics Rev. 7(2), L7–L11 (2013).
[Crossref]

Chandra, B.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Chen, P. Y.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Chen, X.

Chigrin, D. N.

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B 86(12), 121108 (2012).
[Crossref]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Christodoulides, D.

Christodoulides, D. N.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[Crossref]

Cohen, O.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

Coskun, T. H.

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[Crossref]

Cox, J. D.

A. Marini, J. D. Cox, and F. J. Garcia de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95(12), 125408 (2017).
[Crossref]

Dadap, J. I.

S. Hong, J. I. Dadap, N. Petrone, P. Yeh, J. Hone, and R. M. Osgood., “Optical third-harmonic generation in graphene,” Phys. Rev. X 3(2), 021014 (2013).
[Crossref]

de Abajo, F. J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Fan, Y.

Ferrari, A. C.

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

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Fleischer, J. W.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

Freitag, M.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Garanovich, I.

Garcia de Abajo, F. J.

A. Marini, J. D. Cox, and F. J. Garcia de Abajo, “Theory of graphene saturable absorption,” Phys. Rev. B 95(12), 125408 (2017).
[Crossref]

Garcia-Vidal, F. J.

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. Garcia-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical solitons,” Laser Photonics Rev. 7(2), L7–L11 (2013).
[Crossref]

García-Vidal, F. J.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Geim, A. K.

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

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

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Genov, D. A.

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S. Ke, B. Wang, C. Qin, H. Long, K. Wang, and P. Lu, “Exceptional Points and Asymmetric Mode Switching in Plasmonic Waveguides,” J. Lightwave Technol. 34(22), 5258–5262 (2016).
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D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multilayer graphene,” Laser Photonics Rev. 8(2), 291–296 (2014).
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Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
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Z. Wang, B. Wang, H. Long, K. Wang, and P. Lu, “Surface plasmonic lattice solitons in semi-infinite graphene sheet arrays,” J. Lightwave Technol. 35(14), 2960–2965 (2017).
[Crossref]

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[Crossref]

C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Non-reciprocal Phase Shift and Mode Modulation in Dynamic Graphene Waveguides,” J. Lightwave Technol. 34(16), 3877–3883 (2016).

S. Ke, B. Wang, C. Qin, H. Long, K. Wang, and P. Lu, “Exceptional Points and Asymmetric Mode Switching in Plasmonic Waveguides,” J. Lightwave Technol. 34(22), 5258–5262 (2016).
[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref]

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[Crossref] [PubMed]

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P. Lan, M. Ruhmann, L. He, C. Zhai, F. Wang, X. Zhu, Q. Zhang, Y. Zhou, M. Li, M. Lein, and P. Lu, “Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy,” Phys. Rev. Lett. 119(3), 033201 (2017).
[Crossref] [PubMed]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of Plasmonic Supermodes in Graphene Multilayer Arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
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F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of Plasmonic Supermodes in Graphene Multilayer Arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

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[Crossref]

Z. Wang, B. Wang, H. Long, K. Wang, and P. Lu, “Surface plasmonic lattice solitons in semi-infinite graphene sheet arrays,” J. Lightwave Technol. 35(14), 2960–2965 (2017).
[Crossref]

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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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Zhu, X.

P. Lan, M. Ruhmann, L. He, C. Zhai, F. Wang, X. Zhu, Q. Zhang, Y. Zhou, M. Li, M. Lein, and P. Lu, “Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy,” Phys. Rev. Lett. 119(3), 033201 (2017).
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ACS Nano (2)

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Nature (1)

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
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P. Lan, M. Ruhmann, L. He, C. Zhai, F. Wang, X. Zhu, Q. Zhang, Y. Zhou, M. Li, M. Lein, and P. Lu, “Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy,” Phys. Rev. Lett. 119(3), 033201 (2017).
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Z. Li, K. Yao, F. Xia, S. Shen, J. Tian, and Y. Liu, “Graphene Plasmonic Metasurfaces to Steer Infrared Light,” Sci. Rep. 5(1), 12423 (2015).
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Science (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the semi-infinite graphene-pair arrays. (b), (c) Dispersion relation of SPPs in GPAs for the wavelength λ1 = 9.8 μm and λ2 = 10 μm respectively. The first component (λ1 = 9.8 μm) and the second component (λ2 = 10 μm) are associated with semi-infinite band gap and finite gap, respectively. The propagation bands are signed by shade and the two components are represented by the solid dots.
Fig. 2
Fig. 2 (a), (b) The normalized tangential electric field (Ez) and the normalized intensity distribution (|E|2) of the surface PLSs for the first component of the surface vector PLSs λ1 = 9.8 μm. (c), (d) For the second component λ2 = 10 μm, the normalized tangential electric field (Ez) and the normalized intensity distribution (|E|2) of the surface PLSs. The black lines stand for the graphene sheets and the red dash lines represent the PLSs in the infinite graphene-pair arrays.
Fig. 3
Fig. 3 (a), (b) The propagation constants of both components vary with the peak intensities of the first and second components respectively. (c), (d) The widths and propagation lengths of the surface vector PLS vary with the peak intensity of the first component while the peak intensity of the second one is fixed at I2 = 220 V2/μm2.
Fig. 4
Fig. 4 (a), (b) The stable propagation of the first and second components without considering graphene loss. (c), (d) The single propagation of arbitrary component when the other one is removed. (e), (f) The stable propagation of two components in lossy semi-infinite GPAs.
Fig. 5
Fig. 5 (a) For the scalar soliton of the first component, the relation between the power and propagation constant. (b) The propagation constants of the linear guided modes for the second component vary with that of the scalar soliton of the first component. (c) For the scalar soliton of the second component, the relation between the power and propagation constant. (d) The propagation constants of the linear guided modes for the first component vary with that of the scalar soliton of the second component. (The dot a1 stands for the scalar soliton for the first component with the peak intensity I1 = 180 V2/μm2, and a2 refers to the mode for the second component guided by the soliton from a1).
Fig. 6
Fig. 6 (a) The profile of the scalar soliton reprensented by a1 in Fig. 5(a). (b) The profile of the guided mode for the second component corresponding to a2 in Fig. 5(b).
Fig. 7
Fig. 7 For arbitrary single component, (a), (b) the threshold power increases as the chemical potential of graphene is enhanced.

Equations (5)

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

( 0 k 0 ε r ( x ) η 0 η 0 k 0 x 1 ε r ( x ) x + k 0 η 0 0 ) ( H y E x ) = k z ( H y E x ) ,
σ N L = σ 0 ( 3 ) ( S ( 3 / 0 ) + S ( 2 / 1 ) + S ( 1 / 2 ) + S ( 0 / 3 ) ) ,
E z , m = i η 0 k 0 ε r H y , m x
P = 1 2 Re ( E x H y * ) d x ,
w = x 2 | E | 2 d x / | E | 2 d x .

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