Abstract

We study the effective nonlinear optical properties of composite media in which identical nonlinear nanospheres are randomly embedded in the linear host medium. In the weakly-nonlinear case, we aim at the effective linear permittivity and effective third-order nonlinear susceptibility with effective medium theory combined with the linear Mie theory. We show that large enhancement of optical nonlinear susceptibility can be achieved at the surface plasmon resonant wavelength, which can be tuned by changing the size of nanoparticles. Our numerical results are compared with those in the quasistatic limit or/and from Comsol simulations, good agreement is found. In the strong-nonlinear case, based on nonlinear Mie theory and self-consistent mean-field method, we study the optical bistability of the composite media. The optical bistability and tristability are found, and the bistable threshold fields are found to be strongly dependent on the sizes of nanoparticles and the incident wavelength. Such nonlinear nanocomposites with large optical nonlinearity and tunable bistable behavior are envisioned for use as nonlinear optical nanodevices such as optical nanoswitches, optical nanomemories and so on.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Linear and nonlinear optical characteristics of composites containing metal nanoparticles with different sizes and shapes

Kwang-Hyon Kim, Anton Husakou, and Joachim Herrmann
Opt. Express 18(7) 7488-7496 (2010)

Optical bistability in graphene-wrapped dielectric nanowires

K. Zhang and L. Gao
Opt. Express 25(12) 13747-13759 (2017)

Optical bistability in core-shell magnetoplasmonic nanoparticles with magnetocontrollability

W. J. Yu, H. Sun, and L. Gao
Opt. Express 24(19) 22272-22281 (2016)

References

  • View by:
  • |
  • |
  • |

  1. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
    [Crossref]
  2. L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (2014).
    [Crossref] [PubMed]
  3. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nature Phonton. 6, 737–748 (2012).
    [Crossref]
  4. D. Stroud and V. E. Wood, “Decoupling approximation for the nonlinear-optical response of composite media,” J. Opt. Soc. Am. B 6(4), 778–786 (1989).
    [Crossref]
  5. M. F. Law, Y. Gu, and K. W. Yu, “Optical nonlinearity enhancment through correlated microstructure,” Phys. Rev. B 58(19), 12536–12539 (1998).
    [Crossref]
  6. A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal/dielectric composites,” Phys. Report 335(6), 275–371 (2000).
    [Crossref]
  7. L. Gao, K. W. Yu, Z. Y. Li, and B. Hu, “Effective nonlinear optical properties of metal/dielctric composite media with shape distribution,” Phys. Rev. E 64(3), 036615 (2001).
    [Crossref]
  8. L. Gao, J. P. Huang, and K. W. Yu, “Effective nonlinear optical properties of composite media of graded spherical particles,” Phys. Rev. B 69(7), 075105 (2004).
    [Crossref]
  9. K. H. Kim, A. Husakou, and J. Herrmann, “Linear and nonlinear optical characteristics of composites containing metal nanoparticles with different sizes and shapes,” Opt. Express 18(7), 7488–7496 (2010).
    [Crossref] [PubMed]
  10. 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]
  11. 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, 035412 (2014).
    [Crossref]
  12. Y. R. Shen, “Recent advances in optical bistability,” Nature 299(5886), 779–780 (1982).
    [Crossref]
  13. K. M. Leung, “Optical bistability in the scattering and absorption of light from nonlinear microparticles,” Phys. Rev. A 33(4), 2461–2464 (1986).
    [Crossref] [PubMed]
  14. R. Neuendorf, M. Quinten, and U. Kreibig, “Optical bistability of small heterogeneous clusters,” J. Chem. Phys. 104(16), 6348–6354 (1996).
    [Crossref]
  15. D. J. Bergman, O. Levy, and D. Stroud, “Theory of optical bistability in a weakly nonlinear composite medium,” Phys. Rev. B 49(1), 129–134 (1994).
    [Crossref]
  16. L. Gao, L. P. Gu, and Z. Y. Li, “Optical bistability and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E 68(6), 066601 (2003).
    [Crossref]
  17. L. Gao, L. P. Gu, and Y. Y. Huang, “Effective medium approximation for optical bistability in nonlinear metaldielectric composites,” Solid State Commun. 129(9), 593–598 (2004).
    [Crossref]
  18. R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108, 093901 (2012).
    [Crossref] [PubMed]
  19. R. Noskov, P. Belov, and Y. Kivshar, “Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
    [Crossref] [PubMed]
  20. R. E. Noskov, A. E. Krasnok, and Y. S. Kivshar, “Nonlinear metal-dielectric nanoantennas for light switching and routing,” New J. Phys. 14, 093005 (2012).
    [Crossref]
  21. J. Butet and O. J. F. Martin, “Manipulating the optical bistability in a nonlinear plasmonic nanoantenna array with a reflecting surface,” Plasmonics 10, 203–209 (2015).
    [Crossref]
  22. C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012).
    [Crossref] [PubMed]
  23. C. Argyropoulos, C. Ciracì, and D. R. Smith, “Enhanced optical bistability with film-coupled plasmonic nanocubes,” App. Phys. Lett. 104, 063108 (2014).
    [Crossref]
  24. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).
    [Crossref]
  25. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).
  26. L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78(4), 046609 (2008).
    [Crossref]
  27. D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988).
    [Crossref]
  28. R. L. Chern and X. X. Liu, “Effective parameters and quasi-static resonances for periodic arrays of dielectric spheres,” J. Opt. Soc. Am. B 27(3), 488–497 (2010).
    [Crossref]
  29. K. Kolwas, A. Derkachova, and M. Shopa, “Size characteristics of surface plasmons and their manifestation in scattering properties of metal particles,” J. Quantum Spectrosc. Radiat. 110, 1490–1504 (2009).
    [Crossref]
  30. M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
    [Crossref]
  31. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  32. M. Amin, M. Farhat, and H. Bagci, “A nonlinear plasmonic resonator for three-state all-optical switching,” Opt. Express 22 (6), 6966–6975 (2014).
    [Crossref] [PubMed]
  33. R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31(24), 1434–1437 (1973).
    [Crossref]
  34. 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]

2015 (1)

J. Butet and O. J. F. Martin, “Manipulating the optical bistability in a nonlinear plasmonic nanoantenna array with a reflecting surface,” Plasmonics 10, 203–209 (2015).
[Crossref]

2014 (6)

C. Argyropoulos, C. Ciracì, and D. R. Smith, “Enhanced optical bistability with film-coupled plasmonic nanocubes,” App. Phys. Lett. 104, 063108 (2014).
[Crossref]

M. Amin, M. Farhat, and H. Bagci, “A nonlinear plasmonic resonator for three-state all-optical switching,” Opt. Express 22 (6), 6966–6975 (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]

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (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]

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, 035412 (2014).
[Crossref]

2012 (5)

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

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

R. Noskov, P. Belov, and Y. Kivshar, “Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref] [PubMed]

R. E. Noskov, A. E. Krasnok, and Y. S. Kivshar, “Nonlinear metal-dielectric nanoantennas for light switching and routing,” New J. Phys. 14, 093005 (2012).
[Crossref]

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

2010 (2)

2009 (1)

K. Kolwas, A. Derkachova, and M. Shopa, “Size characteristics of surface plasmons and their manifestation in scattering properties of metal particles,” J. Quantum Spectrosc. Radiat. 110, 1490–1504 (2009).
[Crossref]

2008 (1)

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78(4), 046609 (2008).
[Crossref]

2006 (1)

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
[Crossref]

2004 (2)

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

L. Gao, J. P. Huang, and K. W. Yu, “Effective nonlinear optical properties of composite media of graded spherical particles,” Phys. Rev. B 69(7), 075105 (2004).
[Crossref]

2003 (1)

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

2001 (1)

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

2000 (1)

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal/dielectric composites,” Phys. Report 335(6), 275–371 (2000).
[Crossref]

1998 (1)

M. F. Law, Y. Gu, and K. W. Yu, “Optical nonlinearity enhancment through correlated microstructure,” Phys. Rev. B 58(19), 12536–12539 (1998).
[Crossref]

1996 (1)

R. Neuendorf, M. Quinten, and U. Kreibig, “Optical bistability of small heterogeneous clusters,” J. Chem. Phys. 104(16), 6348–6354 (1996).
[Crossref]

1994 (1)

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

1989 (1)

1988 (1)

D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988).
[Crossref]

1986 (1)

K. M. Leung, “Optical bistability in the scattering and absorption of light from nonlinear microparticles,” Phys. Rev. A 33(4), 2461–2464 (1986).
[Crossref] [PubMed]

1982 (1)

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

1973 (1)

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31(24), 1434–1437 (1973).
[Crossref]

Alu, A.

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

Amin, M.

Argyropoulos, C.

C. Argyropoulos, C. Ciracì, and D. R. Smith, “Enhanced optical bistability with film-coupled plasmonic nanocubes,” App. Phys. Lett. 104, 063108 (2014).
[Crossref]

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

Bagci, H.

Belov, P.

R. Noskov, P. Belov, and Y. Kivshar, “Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref] [PubMed]

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, 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 49(1), 129–134 (1994).
[Crossref]

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]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Brongersma, M. L.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (2014).
[Crossref] [PubMed]

Butet, J.

J. Butet and O. J. F. Martin, “Manipulating the optical bistability in a nonlinear plasmonic nanoantenna array with a reflecting surface,” Plasmonics 10, 203–209 (2015).
[Crossref]

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
[Crossref]

Cai, W. S.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (2014).
[Crossref] [PubMed]

Chen, P. Y.

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

Chern, R. L.

Ciracì, C.

C. Argyropoulos, C. Ciracì, and D. R. Smith, “Enhanced optical bistability with film-coupled plasmonic nanocubes,” App. Phys. Lett. 104, 063108 (2014).
[Crossref]

Cui, Y. H.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (2014).
[Crossref] [PubMed]

D’Aguanno, G.

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

Derkachova, A.

K. Kolwas, A. Derkachova, and M. Shopa, “Size characteristics of surface plasmons and their manifestation in scattering properties of metal particles,” J. Quantum Spectrosc. Radiat. 110, 1490–1504 (2009).
[Crossref]

Farhat, M.

Fung, T. H.

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78(4), 046609 (2008).
[Crossref]

Gao, L.

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78(4), 046609 (2008).
[Crossref]

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

L. Gao, J. P. Huang, and K. W. Yu, “Effective nonlinear optical properties of composite media of graded spherical particles,” Phys. Rev. B 69(7), 075105 (2004).
[Crossref]

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

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

Gu, L. P.

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

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

Gu, Y.

M. F. Law, Y. Gu, and K. W. Yu, “Optical nonlinearity enhancment through correlated microstructure,” Phys. Rev. B 58(19), 12536–12539 (1998).
[Crossref]

Herrmann, J.

Hu, B.

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

Huang, J. P.

L. Gao, J. P. Huang, and K. W. Yu, “Effective nonlinear optical properties of composite media of graded spherical particles,” Phys. Rev. B 69(7), 075105 (2004).
[Crossref]

Huang, Y. Y.

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

Hui, P. M.

D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988).
[Crossref]

Husakou, A.

Jauho, A. P.

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]

Kang, L.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (2014).
[Crossref] [PubMed]

Kauranen, M.

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

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

Kim, K. H.

Kivshar, Y.

R. Noskov, P. Belov, and Y. Kivshar, “Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref] [PubMed]

Kivshar, Y. S.

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, 035412 (2014).
[Crossref]

R. E. Noskov, A. E. Krasnok, and Y. S. Kivshar, “Nonlinear metal-dielectric nanoantennas for light switching and routing,” New J. Phys. 14, 093005 (2012).
[Crossref]

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

Kolwas, K.

K. Kolwas, A. Derkachova, and M. Shopa, “Size characteristics of surface plasmons and their manifestation in scattering properties of metal particles,” J. Quantum Spectrosc. Radiat. 110, 1490–1504 (2009).
[Crossref]

Krasnok, A. E.

R. E. Noskov, A. E. Krasnok, and Y. S. Kivshar, “Nonlinear metal-dielectric nanoantennas for light switching and routing,” New J. Phys. 14, 093005 (2012).
[Crossref]

Kreibig, U.

R. Neuendorf, M. Quinten, and U. Kreibig, “Optical bistability of small heterogeneous clusters,” J. Chem. Phys. 104(16), 6348–6354 (1996).
[Crossref]

Lan, S. F.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (2014).
[Crossref] [PubMed]

Law, M. F.

M. F. Law, Y. Gu, and K. W. Yu, “Optical nonlinearity enhancment through correlated microstructure,” Phys. Rev. B 58(19), 12536–12539 (1998).
[Crossref]

Leung, K. M.

K. M. Leung, “Optical bistability in the scattering and absorption of light from nonlinear microparticles,” Phys. Rev. A 33(4), 2461–2464 (1986).
[Crossref] [PubMed]

Levy, O.

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

Li, Z. Y.

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

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

Liu, X. X.

Luk’yanchuk, B. S.

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
[Crossref]

Martin, O. J. F.

J. Butet and O. J. F. Martin, “Manipulating the optical bistability in a nonlinear plasmonic nanoantenna array with a reflecting surface,” Plasmonics 10, 203–209 (2015).
[Crossref]

Miroshnichenko, A. E.

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, 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]

Mirzaei, A.

Monticone, F.

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

Neuendorf, R.

R. Neuendorf, M. Quinten, and U. Kreibig, “Optical bistability of small heterogeneous clusters,” J. Chem. Phys. 104(16), 6348–6354 (1996).
[Crossref]

Noskov, R.

R. Noskov, P. Belov, and Y. Kivshar, “Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref] [PubMed]

Noskov, R. E.

R. E. Noskov, A. E. Krasnok, and Y. S. Kivshar, “Nonlinear metal-dielectric nanoantennas for light switching and routing,” New J. Phys. 14, 093005 (2012).
[Crossref]

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

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]

Qiu, C. W.

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78(4), 046609 (2008).
[Crossref]

Quinten, M.

R. Neuendorf, M. Quinten, and U. Kreibig, “Optical bistability of small heterogeneous clusters,” J. Chem. Phys. 104(16), 6348–6354 (1996).
[Crossref]

Rodrigues, S. P.

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (2014).
[Crossref] [PubMed]

Ruppin, R.

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31(24), 1434–1437 (1973).
[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. Report 335(6), 275–371 (2000).
[Crossref]

Shadrivov, I. V.

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]

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, 035412 (2014).
[Crossref]

Shalaev, V.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
[Crossref]

Shalaev, V. M.

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal/dielectric composites,” Phys. Report 335(6), 275–371 (2000).
[Crossref]

Shen, Y. R.

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

Shopa, M.

K. Kolwas, A. Derkachova, and M. Shopa, “Size characteristics of surface plasmons and their manifestation in scattering properties of metal particles,” J. Quantum Spectrosc. Radiat. 110, 1490–1504 (2009).
[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, 035412 (2014).
[Crossref]

Smirnova, D. A.

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, 035412 (2014).
[Crossref]

Smith, D. R.

C. Argyropoulos, C. Ciracì, and D. R. Smith, “Enhanced optical bistability with film-coupled plasmonic nanocubes,” App. Phys. Lett. 104, 063108 (2014).
[Crossref]

Stroud, D.

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

D. Stroud and V. E. Wood, “Decoupling approximation for the nonlinear-optical response of composite media,” J. Opt. Soc. Am. B 6(4), 778–786 (1989).
[Crossref]

D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988).
[Crossref]

Tribelsky, M. I.

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
[Crossref]

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]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).
[Crossref]

Wood, V. E.

Yu, K. W.

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78(4), 046609 (2008).
[Crossref]

L. Gao, J. P. Huang, and K. W. Yu, “Effective nonlinear optical properties of composite media of graded spherical particles,” Phys. Rev. B 69(7), 075105 (2004).
[Crossref]

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

M. F. Law, Y. Gu, and K. W. Yu, “Optical nonlinearity enhancment through correlated microstructure,” Phys. Rev. B 58(19), 12536–12539 (1998).
[Crossref]

Zayats, A. V.

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

Zharova, N. A.

App. Phys. Lett. (1)

C. Argyropoulos, C. Ciracì, and D. R. Smith, “Enhanced optical bistability with film-coupled plasmonic nanocubes,” App. Phys. Lett. 104, 063108 (2014).
[Crossref]

J. Chem. Phys. (1)

R. Neuendorf, M. Quinten, and U. Kreibig, “Optical bistability of small heterogeneous clusters,” J. Chem. Phys. 104(16), 6348–6354 (1996).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Quantum Spectrosc. Radiat. (1)

K. Kolwas, A. Derkachova, and M. Shopa, “Size characteristics of surface plasmons and their manifestation in scattering properties of metal particles,” J. Quantum Spectrosc. Radiat. 110, 1490–1504 (2009).
[Crossref]

Nat. Commun. (1)

L. Kang, Y. H. Cui, S. F. Lan, S. P. Rodrigues, M. L. Brongersma, and W. S. Cai, “Electrifying photonic metamaterials for tunable nonlinear optics,” Nat. Commun. 5, 4680 (2014).
[Crossref] [PubMed]

Nature (1)

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

Nature Phonton. (1)

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

New J. Phys. (1)

R. E. Noskov, A. E. Krasnok, and Y. S. Kivshar, “Nonlinear metal-dielectric nanoantennas for light switching and routing,” New J. Phys. 14, 093005 (2012).
[Crossref]

Opt. Express (2)

Phys. Report (1)

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal/dielectric composites,” Phys. Report 335(6), 275–371 (2000).
[Crossref]

Phys. Rev. A (1)

K. M. Leung, “Optical bistability in the scattering and absorption of light from nonlinear microparticles,” Phys. Rev. A 33(4), 2461–2464 (1986).
[Crossref] [PubMed]

Phys. Rev. B (5)

M. F. Law, Y. Gu, and K. W. Yu, “Optical nonlinearity enhancment through correlated microstructure,” Phys. Rev. B 58(19), 12536–12539 (1998).
[Crossref]

L. Gao, J. P. Huang, and K. W. Yu, “Effective nonlinear optical properties of composite media of graded spherical particles,” Phys. Rev. B 69(7), 075105 (2004).
[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, 035412 (2014).
[Crossref]

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

D. Stroud and P. M. Hui, “Nonlinear susceptibilities of granular matter,” Phys. Rev. B 37(15), 8719–8724 (1988).
[Crossref]

Phys. Rev. B. (1)

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]

Phys. Rev. E (3)

L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78(4), 046609 (2008).
[Crossref]

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

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

Phys. Rev. Lett. (4)

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “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, 093901 (2012).
[Crossref] [PubMed]

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
[Crossref]

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31(24), 1434–1437 (1973).
[Crossref]

Plasmonics (1)

J. Butet and O. J. F. Martin, “Manipulating the optical bistability in a nonlinear plasmonic nanoantenna array with a reflecting surface,” Plasmonics 10, 203–209 (2015).
[Crossref]

Sci. Rep. (1)

R. Noskov, P. Belov, and Y. Kivshar, “Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref] [PubMed]

Solid State Commun. (1)

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

Other (4)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
[Crossref]

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999).
[Crossref]

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 The real (a) and the imaginary (b) part of the effective permittivity as a function of the incident wavelength λ for various spherical radii. The results in the dilute limit and the numerical simulations are also shown for comparison.
Fig. 2
Fig. 2 Similar as in Fig. 1, but for the real (a) and the imaginary (b) part of the effective nonlinear susceptibility χeff for the composite system.
Fig. 3
Fig. 3 Distributions of the electric fields inside and outside the nanosphere for (a) a = 1nm and λ = 332.9nm and (b) a = 10nm and λ = 335.4nm.
Fig. 4
Fig. 4 (a)The average local field square 〈|Ec |2〉 as a function of the external applied field square |E 0|2 for ε m =1; (b) 〈|Ec |2〉 versus |E 0|2 for spherical nanoparticles with a=10nm randomly embedded in different host media such as vaccum (ε m = 1), water (ε m = 1.77) and benzene (ε m = 2.25); (c) 〈|Ec |2〉 versus λ for ε m = 2.25.
Fig. 5
Fig. 5 The average local field square 〈|Ec |2〉 as a function of the external applied field square |E 0|2 with different sizes for ε m = 1.

Equations (18)

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

r Φ T M i n = 1 k m 2 n = 1 i n 1 2 n + 1 n ( n + 1 ) ψ n ( k m r ) P n ( 1 ) ( cos θ ) cos ϕ , r Φ T E i n = ε 0 ε m / μ 0 μ m k m 2 n = 1 i n 1 2 n + 1 n ( n + 1 ) ψ n ( k m r ) P n ( 1 ) ( cos θ ) sin ϕ ,
r Φ T M s c = 1 k m 2 n = 1 i n 1 2 n + 1 n ( n + 1 ) Β n T M ζ n ( k m r ) P n ( 1 ) ( cos θ ) cos ϕ , r Φ T E s c = ε 0 ε m / μ 0 μ m k m 2 n = 1 i n 1 2 n + 1 n ( n + 1 ) Β n T E ζ n ( k m r ) P n ( 1 ) ( cos θ ) sin ϕ ,
r Φ T M c = 1 k c 2 n = 1 i n 1 2 n + 1 n ( n + 1 ) Α n T M ψ n ( k c r ) P n ( 1 ) ( cos θ ) cos ϕ , r Φ T E c = ε 0 ε c / μ 0 μ c k c 2 n = 1 i n 1 2 n + 1 n ( n + 1 ) Α n T E ψ n ( k c r ) P n ( 1 ) ( cos θ ) sin ϕ ,
A n T M = ψ n ( k m a ) ζ n ( k m a ) ψ n ( k m a ) ζ n ( k m a ) k m k c ψ n ( k c a ) ζ n ( k m a ) k m ε c / μ c k c ε m / μ m ψ n ( k c a ) ζ n ( k m a ) , A n T E = ψ n ( k m a ) ζ n ( k m a ) ψ n ( k m a ) ζ n ( k m a ) k m k c ψ n ( k c a ) ζ n ( k m a ) k m ε c / μ c k c ε m / μ m ψ n ( k c a ) ζ n ( k m a ) .
E r = 2 ( r Φ T M ) r 2 + ω 2 c 2 ε c μ c r Φ T M , E θ = 1 r 2 ( r Φ T M ) r θ + i ω μ 0 μ c r sin θ ( r Φ T E ) ϕ , E ϕ = 1 r sin θ 2 ( r Φ T M ) r ϕ i ω μ 0 μ c r ( r Φ T E ) θ .
E c r = E 0 cos ϕ k c 2 r 2 n = 1 i n 1 ( 2 n + 1 ) Α n T M ψ n ( k c r ) P n ( 1 ) ( cos θ ) , E c θ = E 0 cos ϕ k c r n = 1 i n 1 2 n + 1 n ( n + 1 ) [ Α n T M ψ n ( k c r ) P n ( 1 ) ( cos θ ) sin θ i A n T E ψ n ( k c r ) P n ( 1 ) ( cos θ ) 1 sin θ ] , E c ϕ = E 0 sin ϕ k c r n = 1 i n 1 2 n + 1 n ( n + 1 ) [ A n T M ψ n ( k c r ) P n ( 1 ) ( cos θ ) 1 sin θ i A n T E ψ n ( k c r ) P n ( 1 ) ( cos θ ) sin θ ] .
D = ε 0 ε ^ c E = ε 0 ( ε c E + χ c | E | 2 ) E ,
ε e f f = D E = f ε c E l i n , c + ( 1 f ) E 0 f E l i n , c + ( 1 f ) E 0 ,
E l i n , c = E x = 1 V c V c ( sin θ cos ϕ E c r + cos θ cos ϕ E c θ sin ϕ E c ϕ ) 3 A 1 T M j 1 ( k c a ) k c a E 0 ,
| E | 2 l i n , c = 1 V c V c ( | E c r | 2 + | E c θ | 2 + | E c ϕ | 2 ) d V 9 | A 1 T M | 2 | j 1 ( k c a ) k c a | 2 | E 0 | 2 .
χ e f f = χ c f | E | 2 E 2 l i n , c | E 0 | 2 E 0 2 ,
| E | 2 E 2 l i n , c = 1 V c V c ( | E c r | 2 + | E c θ | 2 + | E c ϕ | 2 ) ( E c r 2 + E c θ 2 + E c ϕ 2 ) d V | 3 A 1 T M j 1 ( k c a ) k c a | 2 [ 3 A 1 T M j 1 ( k c a ) k c a ] 2 | E 0 | 2 E 0 2 .
E l i n , c = 3 ε c + 2 E 0 and | E | 2 E 2 l i n , c = | 3 ε c + 2 | 2 ( 3 ε c + 2 ) 2 | E 0 | 2 E 0 2 .
ε e f f 1 ε e f f + 2 = f ε c 1 ε c + 2 and χ e f f = χ c f | 3 ε c + 2 | 2 ( 3 ε c + 2 ) 2 .
ε ˜ c = ε c + χ c | E | 2 ε c + χ c | E | 2 n o n , c .
| E | 2 n o n , c = 9 | ψ 1 ( k m a ) ζ 1 ( k m a ) ψ 1 ( k m a ) ζ 1 ( k m a ) ψ 1 ( k ^ c a ) ζ 1 ( k m a ) / 3 ^ c ψ 1 ( k ^ c a ) ζ 1 ( k m a ) | 2 | j 1 ( k ^ c a ) k ^ c a | 2 | E 0 | 2 ,
| E | 2 n o n , c = 9 | 1 ε c + χ c | E | 2 n o n , c + 2 | 2 | E 0 | 2 ,
| E | 2 n o n , c = 1 V c V c ( | E c r ( k ^ c r ) | 2 + | E c θ ( k ^ c r ) | 2 + | E c ϕ ( k ^ c r ) | 2 ) d V .

Metrics