Abstract

We study the optical bistability of graphene-wrapped dielectric cylinders with Kerr-type nonlinear response within the framework of both nonlinear full-wave scattering theory and nonlinear quasistatic theory. Typical optical bistable properties are observed in both near-field and far-field spectra with the excitation of electric dipolar modes. Moreover, when high electromagnetic field is applied, nonlinear full wave theory yields new bistable region, indicating the existence of an artificial tunable magnetic dipole. The switching threshold fields are found to be tunable by changing either the size, permittivity of the nanocylinder or the chemical potential of graphene. Our results offer insight into the interaction between Kerr-type nonlinearity and graphene plasmonics, and may promise the graphene-wrapped nanowire a candidate for all-optical switching and nano-memories in terahertz region.

© 2017 Optical Society of America

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Tunable optical bistability of dielectric/nonlinear graphene/dielectric heterostructures

Xiaoyu Dai, Leyong Jiang, and Yuanjiang Xiang
Opt. Express 23(5) 6497-6508 (2015)

References

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    [Crossref] [PubMed]
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    [Crossref]
  42. W. M. V. Wan, H. C. Lee, P. M. Hui, and K. W. Yu, “Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior,” Phys. Rev. B Condens. Matter 54(6), 3946–3953 (1996).
    [Crossref] [PubMed]
  43. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  45. V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4(8), 1535–1539 (2004).
    [Crossref]
  46. K. Vynck, D. Felbacq, E. Centeno, A. I. Căbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102(13), 133901 (2009).
    [Crossref] [PubMed]
  47. W. Liu, A. E. Miroshnichenko, R. F. Oulton, D. N. Neshev, O. Hess, and Y. S. Kivshar, “Scattering of core-shell nanowires with the interference of electric and magnetic resonances,” Opt. Lett. 38(14), 2621–2624 (2013).
    [Crossref] [PubMed]
  48. D. Gao, L. Gao, A. Novitsky, H. Chen, and B. Luk’yanchuk, “Topological effects in anisotropy-induced nano-fano resonance of a cylinder,” Opt. Lett. 40(17), 4162–4165 (2015).
    [Crossref] [PubMed]
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  51. R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108(9), 093901 (2012).
    [Crossref] [PubMed]
  52. D. A. Smirnova, R. E. Noskov, L. A. Smirnov, and Y. S. Kivshar, “Dissipative plasmon solitons in graphene nanodisk arrays,” Phys. Rev. B 91(7), 075409 (2015).
    [Crossref]

2016 (7)

H. Chen, Y. Zhang, B. Zhang, and L. Gao, “Optical bistability in a nonlinear-shell-coated metallic nanoparticle,” Sci. Rep. 6(1), 21741 (2016).
[Crossref] [PubMed]

H. L. Chen, D. L. Gao, and L. Gao, “Effective nonlinear optical properties and optical bistability in composite media containing spherical particles with different sizes,” Opt. Express 24(5), 5334–5345 (2016).
[Crossref]

M. M. Jadidi, J. C. König-Otto, S. Winnerl, A. B. Sushkov, H. D. Drew, T. E. Murphy, and M. Mittendorff, “Nonlinear Terahertz absorption of graphene plasmons,” Nano Lett. 16(4), 2734–2738 (2016).
[Crossref] [PubMed]

R. Yu, J. D. Cox, and F. J. G. de Abajo, “Nonlinear plasmonic sensing with nanographene,” Phys. Rev. Lett. 117(12), 123904 (2016).
[Crossref] [PubMed]

R. J. Li, X. Lin, S. S. Lin, X. M. Zhang, E. P. Li, and H. S. Chen, “Graphene induced mode bifurcation at low input power,” Carbon 98, 463–467 (2016).
[Crossref]

Y. Huang, A. E. Miroshnichenko, and L. Gao, “Low-threshold optical bistability of graphene-wrapped dielectric composite,” Sci. Rep. 6(1), 23354 (2016).
[Crossref] [PubMed]

Y. Huang and L. Gao, “Tunable Fano resonances and enhanced optical bistability in composites of coated cylinders due to nonlocality,” Phys. Rev. B 93(23), 235439 (2016).
[Crossref]

2015 (9)

D. Gao, L. Gao, A. Novitsky, H. Chen, and B. Luk’yanchuk, “Topological effects in anisotropy-induced nano-fano resonance of a cylinder,” Opt. Lett. 40(17), 4162–4165 (2015).
[Crossref] [PubMed]

A. Fallahi, T. Low, M. Tamagnone, and J. Perruisseau-Carrier, “Nonlocal electromagnetic response of graphene nanostructures,” Phys. Rev. B 91(12), 121405 (2015).
[Crossref]

D. A. Smirnova, R. E. Noskov, L. A. Smirnov, and Y. S. Kivshar, “Dissipative plasmon solitons in graphene nanodisk arrays,” Phys. Rev. B 91(7), 075409 (2015).
[Crossref]

R. J. Li, X. Lin, S. S. Lin, X. Liu, and H. S. Chen, “Tunable deep-subwavelength superscattering using graphene monolayers,” Opt. Lett. 40(8), 1651–1654 (2015).
[Crossref] [PubMed]

T.-H. Xiao, L. Gan, and Z.-Y. Li, “Efficient manipulation of graphene absorption by a simple dielectric cylinder,” Opt. Express 23(15), 18975–18987 (2015).
[Crossref] [PubMed]

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5(1), 12271 (2015).
[Crossref] [PubMed]

S. Gong, T. Zhao, M. Sanderson, M. Hu, R. B. Zhong, X. X. Chen, P. Zhang, C. Zhang, and S. G. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
[Crossref]

A. Ciattoni and C. Rizza, “Graphene-nonlinearity unleashing at lasing threshold in graphene-assisted cavities,” Phys. Rev. A 91(5), 053833 (2015).
[Crossref]

T. Christensen, W. Yan, A. P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

2014 (6)

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]

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]

D. A. Smirnova, I. V. Shadrivov, A. E. Miroshnichenko, A. I. Smirnov, and Y. S. Kivshar, “Second-harmonic generation by a graphene nanoparticle,” Phys. Rev. B 90(3), 035412 (2014).
[Crossref]

J. D. Cox and F. Javier García de Abajo, “Electrically tunable nonlinear plasmonics in graphene nanoislands,” Nat. Commun. 5, 5725 (2014).
[Crossref] [PubMed]

A. Mirzaei, A. E. Miroshnichenko, N. A. Zharova, and I. V. Shadrivov, “Light scattering by nonlinear cylindrical multilayer structures,” J. Opt. Soc. Am. B 31(7), 1595–1599 (2014).
[Crossref]

Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014).
[Crossref] [PubMed]

2013 (3)

W. Liu, A. E. Miroshnichenko, R. F. Oulton, D. N. Neshev, O. Hess, and Y. S. Kivshar, “Scattering of core-shell nanowires with the interference of electric and magnetic resonances,” Opt. Lett. 38(14), 2621–2624 (2013).
[Crossref] [PubMed]

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

P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for Terahertz applications,” Science 341(6146), 620–621 (2013).
[Crossref] [PubMed]

2012 (4)

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12(2), 992–996 (2012).
[Crossref] [PubMed]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[Crossref] [PubMed]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108(9), 093901 (2012).
[Crossref] [PubMed]

2011 (2)

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

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

2010 (3)

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

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]

Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

2009 (2)

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

K. Vynck, D. Felbacq, E. Centeno, A. I. Căbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102(13), 133901 (2009).
[Crossref] [PubMed]

2005 (1)

2004 (3)

L. Gao, L. Gu, and Y. Huang, “Effective medium approximation for optical bistability in nonlinear metal-dielectric composites,” Solid State Commun. 129(9), 593–598 (2004).
[Crossref]

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]

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4(8), 1535–1539 (2004).
[Crossref]

2003 (1)

L. Gao, L. Gu, and Z. Li, “Optical bistability and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6), 066601 (2003).
[Crossref] [PubMed]

2001 (1)

L. Gao, K. W. Yu, Z. Y. Li, and B. Hu, “Effective nonlinear optical properties of metal-dielectric composite media with shape distribution,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036615 (2001).
[Crossref] [PubMed]

2000 (1)

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335(6), 276–371 (2000).
[Crossref]

1996 (2)

L. Gao and Z. Y. Li, “Self-consistent formalism for a strongly nonlinear composite: Comparison with variational approach,” Phys. Lett. A 219(5–6), 324–328 (1996).
[Crossref]

W. M. V. Wan, H. C. Lee, P. M. Hui, and K. W. Yu, “Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior,” Phys. Rev. B Condens. Matter 54(6), 3946–3953 (1996).
[Crossref] [PubMed]

1994 (1)

D. J. Bergman, O. Levy, and D. Stroud, “Theory of optical bistability in a weakly nonlinear composite medium,” Phys. Rev. B Condens. Matter 49(1), 129–134 (1994).
[Crossref] [PubMed]

1982 (1)

Y. R. Shen, “Recent advances in optical bistability,” Nature 299(5886), 779–780 (1982).
[Crossref]

1979 (1)

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35(11), 846–848 (1979).
[Crossref]

1976 (1)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).
[Crossref]

Alù, A.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[Crossref] [PubMed]

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

Argyropoulos, C.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[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.

Belov, P. A.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108(9), 093901 (2012).
[Crossref] [PubMed]

Bergman, D. J.

D. J. Bergman, O. Levy, and D. Stroud, “Theory of optical bistability in a weakly nonlinear composite medium,” Phys. Rev. B Condens. Matter 49(1), 129–134 (1994).
[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]

Bonaccorso, F.

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

Bratschitsch, R.

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12(2), 992–996 (2012).
[Crossref] [PubMed]

Buin, A. K.

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4(8), 1535–1539 (2004).
[Crossref]

Cabuz, A. I.

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Y. Huang, A. E. Miroshnichenko, and L. Gao, “Low-threshold optical bistability of graphene-wrapped dielectric composite,” Sci. Rep. 6(1), 23354 (2016).
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D. A. Smirnova, I. V. Shadrivov, A. E. Miroshnichenko, A. I. Smirnov, and Y. S. Kivshar, “Second-harmonic generation by a graphene nanoparticle,” Phys. Rev. B 90(3), 035412 (2014).
[Crossref]

A. Mirzaei, A. E. Miroshnichenko, N. A. Zharova, and I. V. Shadrivov, “Light scattering by nonlinear cylindrical multilayer structures,” J. Opt. Soc. Am. B 31(7), 1595–1599 (2014).
[Crossref]

W. Liu, A. E. Miroshnichenko, R. F. Oulton, D. N. Neshev, O. Hess, and Y. S. Kivshar, “Scattering of core-shell nanowires with the interference of electric and magnetic resonances,” Opt. Lett. 38(14), 2621–2624 (2013).
[Crossref] [PubMed]

Mirzaei, A.

Mittendorff, M.

M. M. Jadidi, J. C. König-Otto, S. Winnerl, A. B. Sushkov, H. D. Drew, T. E. Murphy, and M. Mittendorff, “Nonlinear Terahertz absorption of graphene plasmons,” Nano Lett. 16(4), 2734–2738 (2016).
[Crossref] [PubMed]

Moger, 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]

Monticone, F.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[Crossref] [PubMed]

Morozov, 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]

Mortensen, N. A.

T. Christensen, W. Yan, A. P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Murphy, T. E.

M. M. Jadidi, J. C. König-Otto, S. Winnerl, A. B. Sushkov, H. D. Drew, T. E. Murphy, and M. Mittendorff, “Nonlinear Terahertz absorption of graphene plasmons,” Nano Lett. 16(4), 2734–2738 (2016).
[Crossref] [PubMed]

Nakotte, H.

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4(8), 1535–1539 (2004).
[Crossref]

Neshev, D. N.

Noskov, R. E.

D. A. Smirnova, R. E. Noskov, L. A. Smirnov, and Y. S. Kivshar, “Dissipative plasmon solitons in graphene nanodisk arrays,” Phys. Rev. B 91(7), 075409 (2015).
[Crossref]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108(9), 093901 (2012).
[Crossref] [PubMed]

Novitsky, A.

Novoselov, K. S.

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]

Osgood, R. M.

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

Oulton, R. F.

Peres, N. M. R.

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]

Perruisseau-Carrier, J.

A. Fallahi, T. Low, M. Tamagnone, and J. Perruisseau-Carrier, “Nonlocal electromagnetic response of graphene nanostructures,” Phys. Rev. B 91(12), 121405 (2015).
[Crossref]

Petrone, N.

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

Psaltis, D.

Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

Pu, Y.

Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

Ren, G.

Rizza, C.

A. Ciattoni and C. Rizza, “Graphene-nonlinearity unleashing at lasing threshold in graphene-assisted cavities,” Phys. Rev. A 91(5), 053833 (2015).
[Crossref]

Sanderson, M.

S. Gong, T. Zhao, M. Sanderson, M. Hu, R. B. Zhong, X. X. Chen, P. Zhang, C. Zhang, and S. G. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
[Crossref]

Santos, J. E.

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]

Sarychev, A. K.

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335(6), 276–371 (2000).
[Crossref]

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).
[Crossref] [PubMed]

Shadrivov, I. V.

D. A. Smirnova, I. V. Shadrivov, A. E. Miroshnichenko, A. I. Smirnov, and Y. S. Kivshar, “Second-harmonic generation by a graphene nanoparticle,” Phys. Rev. B 90(3), 035412 (2014).
[Crossref]

A. Mirzaei, A. E. Miroshnichenko, N. A. Zharova, and I. V. Shadrivov, “Light scattering by nonlinear cylindrical multilayer structures,” J. Opt. Soc. Am. B 31(7), 1595–1599 (2014).
[Crossref]

Shalaev, V. M.

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4(8), 1535–1539 (2004).
[Crossref]

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335(6), 276–371 (2000).
[Crossref]

Shen, Y. R.

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]

Y. R. Shen, “Recent advances in optical bistability,” Nature 299(5886), 779–780 (1982).
[Crossref]

Smirnov, A. I.

D. A. Smirnova, I. V. Shadrivov, A. E. Miroshnichenko, A. I. Smirnov, and Y. S. Kivshar, “Second-harmonic generation by a graphene nanoparticle,” Phys. Rev. B 90(3), 035412 (2014).
[Crossref]

Smirnov, L. A.

D. A. Smirnova, R. E. Noskov, L. A. Smirnov, and Y. S. Kivshar, “Dissipative plasmon solitons in graphene nanodisk arrays,” Phys. Rev. B 91(7), 075409 (2015).
[Crossref]

Smirnova, D. A.

D. A. Smirnova, R. E. Noskov, L. A. Smirnov, and Y. S. Kivshar, “Dissipative plasmon solitons in graphene nanodisk arrays,” Phys. Rev. B 91(7), 075409 (2015).
[Crossref]

D. A. Smirnova, I. V. Shadrivov, A. E. Miroshnichenko, A. I. Smirnov, and Y. S. Kivshar, “Second-harmonic generation by a graphene nanoparticle,” Phys. Rev. B 90(3), 035412 (2014).
[Crossref]

Smith, P. W.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35(11), 846–848 (1979).
[Crossref]

Soukoulis, C. M.

P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for Terahertz applications,” Science 341(6146), 620–621 (2013).
[Crossref] [PubMed]

Stroud, D.

D. J. Bergman, O. Levy, and D. Stroud, “Theory of optical bistability in a weakly nonlinear composite medium,” Phys. Rev. B Condens. Matter 49(1), 129–134 (1994).
[Crossref] [PubMed]

Sun, Z.

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

Sushkov, A. B.

M. M. Jadidi, J. C. König-Otto, S. Winnerl, A. B. Sushkov, H. D. Drew, T. E. Murphy, and M. Mittendorff, “Nonlinear Terahertz absorption of graphene plasmons,” Nano Lett. 16(4), 2734–2738 (2016).
[Crossref] [PubMed]

Tamagnone, M.

A. Fallahi, T. Low, M. Tamagnone, and J. Perruisseau-Carrier, “Nonlocal electromagnetic response of graphene nanostructures,” Phys. Rev. B 91(12), 121405 (2015).
[Crossref]

Tang, D. Y.

Tassin, P.

P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for Terahertz applications,” Science 341(6146), 620–621 (2013).
[Crossref] [PubMed]

Tomlinson, W. J.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35(11), 846–848 (1979).
[Crossref]

Tong, L.

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]

Trügler, A.

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12(2), 992–996 (2012).
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Vakil, A.

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

Vasilevskiy, M. I.

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]

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).
[Crossref]

Vynck, K.

K. Vynck, D. Felbacq, E. Centeno, A. I. Căbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102(13), 133901 (2009).
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Wan, W. M. V.

W. M. V. Wan, H. C. Lee, P. M. Hui, and K. W. Yu, “Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior,” Phys. Rev. B Condens. Matter 54(6), 3946–3953 (1996).
[Crossref] [PubMed]

Wang, H.

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]

Winnerl, S.

M. M. Jadidi, J. C. König-Otto, S. Winnerl, A. B. Sushkov, H. D. Drew, T. E. Murphy, and M. Mittendorff, “Nonlinear Terahertz absorption of graphene plasmons,” Nano Lett. 16(4), 2734–2738 (2016).
[Crossref] [PubMed]

Wubs, M.

T. Christensen, W. Yan, A. P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Xiang, Y.

X. Dai, L. Jiang, and Y. Xiang, “Low threshold optical bistability at terahertz frequencies with graphene surface plasmons,” Sci. Rep. 5(1), 12271 (2015).
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Xiao, T.-H.

Xiao, Y.

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]

Xu, Y.

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]

Yan, W.

T. Christensen, W. Yan, A. P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Yeh, P.-C.

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

Yu, K. W.

J. P. Huang and K. W. Yu, “Effective nonlinear optical properties of graded metal-dielectric composite films of anisotropic particles,” J. Opt. Soc. Am. B 22(8), 1640–1647 (2005).
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L. Gao, K. W. Yu, Z. Y. Li, and B. Hu, “Effective nonlinear optical properties of metal-dielectric composite media with shape distribution,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036615 (2001).
[Crossref] [PubMed]

W. M. V. Wan, H. C. Lee, P. M. Hui, and K. W. Yu, “Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior,” Phys. Rev. B Condens. Matter 54(6), 3946–3953 (1996).
[Crossref] [PubMed]

Yu, R.

R. Yu, J. D. Cox, and F. J. G. de Abajo, “Nonlinear plasmonic sensing with nanographene,” Phys. Rev. Lett. 117(12), 123904 (2016).
[Crossref] [PubMed]

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Zhang, B.

H. Chen, Y. Zhang, B. Zhang, and L. Gao, “Optical bistability in a nonlinear-shell-coated metallic nanoparticle,” Sci. Rep. 6(1), 21741 (2016).
[Crossref] [PubMed]

Zhang, C.

S. Gong, T. Zhao, M. Sanderson, M. Hu, R. B. Zhong, X. X. Chen, P. Zhang, C. Zhang, and S. G. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
[Crossref]

Zhang, H.

Zhang, P.

S. Gong, T. Zhao, M. Sanderson, M. Hu, R. B. Zhong, X. X. Chen, P. Zhang, C. Zhang, and S. G. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
[Crossref]

Zhang, X. M.

R. J. Li, X. Lin, S. S. Lin, X. M. Zhang, E. P. Li, and H. S. Chen, “Graphene induced mode bifurcation at low input power,” Carbon 98, 463–467 (2016).
[Crossref]

Zhang, Y.

H. Chen, Y. Zhang, B. Zhang, and L. Gao, “Optical bistability in a nonlinear-shell-coated metallic nanoparticle,” Sci. Rep. 6(1), 21741 (2016).
[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]

Zhao, L. M.

Zhao, T.

S. Gong, T. Zhao, M. Sanderson, M. Hu, R. B. Zhong, X. X. Chen, P. Zhang, C. Zhang, and S. G. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
[Crossref]

Zharova, N. A.

Zhong, R. B.

S. Gong, T. Zhao, M. Sanderson, M. Hu, R. B. Zhong, X. X. Chen, P. Zhang, C. Zhang, and S. G. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
[Crossref]

Zhu, B.

ACS Nano (1)

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

Appl. Phys. Lett. (2)

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35(11), 846–848 (1979).
[Crossref]

S. Gong, T. Zhao, M. Sanderson, M. Hu, R. B. Zhong, X. X. Chen, P. Zhang, C. Zhang, and S. G. Liu, “Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime,” Appl. Phys. Lett. 106(22), 223107 (2015).
[Crossref]

Carbon (1)

R. J. Li, X. Lin, S. S. Lin, X. M. Zhang, E. P. Li, and H. S. Chen, “Graphene induced mode bifurcation at low input power,” Carbon 98, 463–467 (2016).
[Crossref]

J. Opt. Soc. Am. B (2)

Nano Lett. (4)

T. Hanke, J. Cesar, V. Knittel, A. Trügler, U. Hohenester, A. Leitenstorfer, and R. Bratschitsch, “Tailoring spatiotemporal light confinement in single plasmonic nanoantennas,” Nano Lett. 12(2), 992–996 (2012).
[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]

M. M. Jadidi, J. C. König-Otto, S. Winnerl, A. B. Sushkov, H. D. Drew, T. E. Murphy, and M. Mittendorff, “Nonlinear Terahertz absorption of graphene plasmons,” Nano Lett. 16(4), 2734–2738 (2016).
[Crossref] [PubMed]

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4(8), 1535–1539 (2004).
[Crossref]

Nat. Commun. (1)

J. D. Cox and F. Javier García de Abajo, “Electrically tunable nonlinear plasmonics in graphene nanoislands,” Nat. Commun. 5, 5725 (2014).
[Crossref] [PubMed]

Nat. Photonics (2)

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

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Nature (1)

Y. R. Shen, “Recent advances in optical bistability,” Nature 299(5886), 779–780 (1982).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Phys. Lett. A (1)

L. Gao and Z. Y. Li, “Self-consistent formalism for a strongly nonlinear composite: Comparison with variational approach,” Phys. Lett. A 219(5–6), 324–328 (1996).
[Crossref]

Phys. Rep. (1)

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335(6), 276–371 (2000).
[Crossref]

Phys. Rev. A (1)

A. Ciattoni and C. Rizza, “Graphene-nonlinearity unleashing at lasing threshold in graphene-assisted cavities,” Phys. Rev. A 91(5), 053833 (2015).
[Crossref]

Phys. Rev. B (6)

T. Christensen, W. Yan, A. P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

D. A. Smirnova, I. V. Shadrivov, A. E. Miroshnichenko, A. I. Smirnov, and Y. S. Kivshar, “Second-harmonic generation by a graphene nanoparticle,” Phys. Rev. B 90(3), 035412 (2014).
[Crossref]

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]

A. Fallahi, T. Low, M. Tamagnone, and J. Perruisseau-Carrier, “Nonlocal electromagnetic response of graphene nanostructures,” Phys. Rev. B 91(12), 121405 (2015).
[Crossref]

Y. Huang and L. Gao, “Tunable Fano resonances and enhanced optical bistability in composites of coated cylinders due to nonlocality,” Phys. Rev. B 93(23), 235439 (2016).
[Crossref]

D. A. Smirnova, R. E. Noskov, L. A. Smirnov, and Y. S. Kivshar, “Dissipative plasmon solitons in graphene nanodisk arrays,” Phys. Rev. B 91(7), 075409 (2015).
[Crossref]

Phys. Rev. B Condens. Matter (2)

W. M. V. Wan, H. C. Lee, P. M. Hui, and K. W. Yu, “Mean-field theory of strongly nonlinear random composites: Strong power-law nonlinearity and scaling behavior,” Phys. Rev. B Condens. Matter 54(6), 3946–3953 (1996).
[Crossref] [PubMed]

D. J. Bergman, O. Levy, and D. Stroud, “Theory of optical bistability in a weakly nonlinear composite medium,” Phys. Rev. B Condens. Matter 49(1), 129–134 (1994).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

L. Gao, L. Gu, and Z. Li, “Optical bistability and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6), 066601 (2003).
[Crossref] [PubMed]

L. Gao, K. W. Yu, Z. Y. Li, and B. Hu, “Effective nonlinear optical properties of metal-dielectric composite media with shape distribution,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036615 (2001).
[Crossref] [PubMed]

Phys. Rev. Lett. (7)

Y. Pu, R. Grange, C.-L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36(19), 1135–1138 (1976).
[Crossref]

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
[Crossref] [PubMed]

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]

R. Yu, J. D. Cox, and F. J. G. de Abajo, “Nonlinear plasmonic sensing with nanographene,” Phys. Rev. Lett. 117(12), 123904 (2016).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of the model
Fig. 2
Fig. 2 The linear scattering efficiency for various incident wavelength, chemical potential, and nanowire radius with parameters (a) ε=2.25 , μ c =0.3eV , (b) ε=1.5 , a=100nm , and (c) ε=2.25 , a=100nm . Other parameters are ε h =2.25 and τ=0.1ps
Fig. 3
Fig. 3 The modulus of the nonlinear local field E non,g as a function of the incident field E 0 for varied (a) chemical potentials; (b) sizes and (c) permittivity. Other parameters are ε h =2.25 and τ=0.1ps .
Fig. 4
Fig. 4 Same as those in Fig. 3, but for TE case.
Fig. 5
Fig. 5 (a) Dependence of the modulus of the nonlinear field E non,g inside the graphene on the incident wavelength at different chemical potentials; (b) and (c) illustrate the nonlinear far-field spectra versus incident wavelength at different chemical potentials.
Fig. 6
Fig. 6 The modulus of nonlinear local field E non,g as a function of E 0 , (a) undethe FWST and QL with a=100nm , μ c =0.3eV ; (b) different terms within the FWST;(c) with different chemical potentials. Other parameters are ε= ε h =2.25 .
Fig. 7
Fig. 7 Curves of the dimensionless field x as a function of y,for different values of the chemical potentials.

Equations (16)

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E i = i k n= E n M n (1) , H i = 1 ωμ n= E n N n (1) E s = i k n= A n E n M n (3) , H s = 1 ωμ n= A n E n N n (3) , E c = i k 1 n= F n E n M n (1) , H c = 1 ω μ 1 n= F n E n N n (1)
n ^ ( E i + E s E c )=0, n ^ ×( H c H i H s )= σ 0 E t .
A n = J n (x) J n ' (mx)m J n ' (x) J n (mx)i σ 0 α J n ' (x) J n ' (mx) H n (x) J n ' (mx)m H n ' (x) J n (mx)i σ 0 α H n ' (x) J n ' (mx) F n = H n (x) J n ' (x) H n ' (x) J n (x) H n (x) J n ' (mx)m H n ' (x) J n (mx)i σ 0 α H n ' (x) J n ' (mx) ,
E c,local = E 0 n= i n+1 F n ( in J n ( k 1 a) k 1 a e ^ r J n ' ( k 1 a) e ^ φ ) e inφ | E c,local | 2 = | E 0 | 2 | n= i n+1 F n ( in J n ( k 1 a) k 1 a e ^ r J n ' ( k 1 a) e ^ φ ) e inφ | 2 ,
| E lin,g | 2 = | E 0 | 2 | n= i n+1 F n J n ' ( k 1 a) e ^ φ e inφ | 2 .
Q sca = 2 x ( | A 0 | 2 +2 n=1 | A n | 2 ), Q ext = 2 x Re( A 0 +2 n=1 A n ),
ϕ c =B E 0 rcosφ, ϕ h =( E 0 r+ C E 0 r )cosφ.
n ^ ×[ E h E c ] | r=a =0, n ^ [ D h D c ] | r=a =ρ,
B= 2 ε h ε+ ε h +γ ,C= a 2 (ε ε h +γ) ε+ ε h +γ ,
| E lin,g | QL 2 = | E c | 2 = | B | 2 | E 0 | 2 ,
Q sca,QL = π 2 (ka) 3 4 | C a 2 | 2 , Q ext,QL =π(ka) Im(C) a 2 .
| E non,g | FWST 2 = | E 0 | 2 | n= i n+1 F ˜ n J n ' ( k 1 a) e ^ φ e inφ | 2 , F ˜ n = H n (x) J n ' (x) H n ' (x) J n (x) H n (x) J n ' (mx)m H n ' (x) J n (mx)i σ ˜ g α H n ' (x) J n ' (mx) ,
| E non,g | QL 2 = | B ˜ | 2 | E 0 | 2 , B ˜ = 2 ε h ε+ ε h +i σ ˜ g /( ωa ε 0 ) .
y(x)=x P 2 [ x 2 +2Qx+ Q 2 + R 2 ],
Q ˜ sca = 2 x ( | A ˜ 0 | 2 +2 n=1 | A ˜ n | 2 ), Q ˜ ext = 2 x Re( A ˜ 0 +2 n=1 A ˜ n )
Q ˜ sca,QL = π 2 (ka) 3 4 | C ˜ a 2 | 2 , Q ˜ ext,QL =π(ka) Im( C ˜ ) a 2 .

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