Abstract

We study resonant self-action effects of light in plasmonic γ-Fe2O3 (Au) core (shell) nanoparticles (NPs) in a polymer matrix by the spectroscopic Z-scan technique. Plasmon-assisted enhancement of the local optical field in NPs results in the appearance of saturable absorption, as well as in the amplification of nonlinear refraction by more than an order of magnitude compared with nonresonant conditions.

© 2011 Optical Society of America

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    [CrossRef]
  7. Y. Yang, J. Shi, H. Chen, S. Dai, and Y. Liu, “Enhanced off-resonant optical nonlinearity of Au-CdS core-shell nanoparticles embedded in BaTiO3 thin films,” Chem. Phys. Lett. 370, 1–6 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  24. V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Extraordinary transmission and giant magneto-optical transverse Kerr effect in plasmonic nanostructured films,” J. Opt. Soc. Am. B 26, 1594–1598 (2009).
    [CrossRef]
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    [CrossRef]
  26. I. Ros, P. Schiavuta, V. Bello, G. Mattei, and R. Bozio, “Femtosecond nonlinear absorption in gold nanoshells at surface plasmon resonance,” Phys. Chem. Chem. Phys. 12, 13692–13698(2010).
    [CrossRef] [PubMed]
  27. M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
    [CrossRef]
  28. S. Debrus, J. Lafait, M. May, N. Pincon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
    [CrossRef]
  29. R. Rangel-Rojo, H. Matsuda, H. Kasai, and H. Nakanishi, “Irradiance dependence of the resonant nonlinearities in an organic material,” J. Opt. Soc. Am. B 17, 1376–1382 (2000).
    [CrossRef]
  30. L. De Boni, A. A. Andrade, D. S. Corrêa, D. T. Balogh, S. C. Zilio, L. Misoguti, and C. R. Mendoca, “Nonlinear absorption spectrum in MEH-PPV/chloroform solution: a competition between two-photon and saturated absorption processes,” J. Phys. Chem. B 108, 5221–5224 (2004).
    [CrossRef]
  31. N. Venkatram, R. S. S. Kumar, D. N. Rao, S. K. Medda, S. De, and G. De, “Nonlinear optical absorption and switching properties of gold nanoparticle doped SiO2–TiO2 solgel films,” J. Nanosci. Nanotechnol. 6, 1990–1994 (2006).
    [CrossRef] [PubMed]
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  35. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769(1990).
    [CrossRef]
  36. M. Sheik-Bahae, A. A. Said, and E. W. van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
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2010 (8)

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, 207402 (2010).
[CrossRef] [PubMed]

A. A. Zharov and N. A. Zharova, “Double-resonance plasmon-driven enhancement of nonlinear optical response in a metamaterial with coated nanoparticles,” JETP Lett. 92, 210–213 (2010).
[CrossRef]

G. X. Du, T. Mori, M. Suzuki, Sh. Saito, H. Fukuda, and M. Takahashi, “Evidence of localized surface plasmon enhanced magneto-optical effect in nanodisk array,” Appl. Phys. Lett. 96, 081915 (2010).
[CrossRef]

J. F. Torrado, E. Th. Papaioannou, G. Ctistis, P. Patoka, M. Giersig, G. Armelles, and A. Garcia-Martin, “Plasmon induced modification of the transverse magneto-optical response in Fe antidot arrays,” Phys. Stat. Solidi RRL 4, 271–273 (2010).
[CrossRef]

I. Ros, P. Schiavuta, V. Bello, G. Mattei, and R. Bozio, “Femtosecond nonlinear absorption in gold nanoshells at surface plasmon resonance,” Phys. Chem. Chem. Phys. 12, 13692–13698(2010).
[CrossRef] [PubMed]

L. Wang, K. Yang, C. Clavero, A. J. Nelson, K. J. Carroll, E. E. Carpenter, and R. A. Lukaszew, “Localized surface plasmon resonance enhanced magneto-optical activity in core-shell Fe–Ag nanoparticles,” J. Appl. Phys. 107, 09B303 (2010).
[CrossRef]

A. A. Grunin, A. G. Zhdanov, A. A. Ezhov, E. A. Ganshina, and A. A. Fedyanin, “Surface-plasmon-induced enhancement of magneto-optical Kerr effect in all-nickel subwavelength nanogratings,” Appl. Phys. Lett. 97, 261908 (2010).
[CrossRef]

K. Wang, H. Long, M. Fu, G. Yang, and P. Lu, “Intensity-dependent reversal of nonlinearity sign in a gold nanoparticle array,” Opt. Lett. 35, 1560–1562 (2010).
[CrossRef] [PubMed]

2009 (3)

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Extraordinary transmission and giant magneto-optical transverse Kerr effect in plasmonic nanostructured films,” J. Opt. Soc. Am. B 26, 1594–1598 (2009).
[CrossRef]

I. A. Kolmychek, T. V. Murzina, S. Fourier, J. Wouters, V. K. Valev, T. Verbiest, and O. A. Aktsipetrov, “Second harmonic generation in core (shell) γ-Fe2O3 (Au) nanoparticles,” Solid State Phenom. 152, 508–511 (2009).
[CrossRef]

T. V. Murzina, I. A. Kolmychek, A. A. Nikulin, E. A. Ganshina, and O. A. Aktsipetrov, “Plasmonic and magnetic effects accompanying optical second-harmonic generation in Au/Co/Au nanodisks,” JETP Lett. 90, 504–508 (2009).
[CrossRef]

2008 (4)

J. B. Gonzalez-Diaz, A. Garcia-Martin, J. M. Garcia-Martin, A. Cebollada, and G. Armelles, “Plasmonic Au/Co/Au nanosandwiches with enhanced magneto-optical activity,” Small 4, 202–205 (2008).
[CrossRef] [PubMed]

D. C. Kohlgraf-Owens and P. G. Kik, “Numerical study of surface plasmon enhanced nonlinear absorption and refraction,” Opt. Express 16, 10823–10834 (2008).
[CrossRef] [PubMed]

G. Armelles, J. B. Gonzalez-Diaz, A. Garcia-Martin, Jose M. Garcia-Martin, A. Cebollada, M. U. Gonzalez, S. Acimovic, J. Cesario, R. Quidant, and G. Badenes, “Localized surface plasmon resonance effects on the magneto-optical activity of continuous Au/Co/Au trilayers,” Opt. Express 16, 16104–16112 (2008).
[CrossRef] [PubMed]

Y. Deng, Y. Sun, P. Wang, D. Zhang, H. Ming, and Q. Zhang, “In situ synthesis and nonlinear optical properties of Ag nanocomposite polymer films,” Physica E 40, 911–914 (2008).
[CrossRef]

2007 (3)

M. K. Kodirov, “Nonlinear refraction and nonlinear absorption of silver aggregates in a polymeric matrix,” Opt. Spectrosc. 102, 73–76 (2007).
[CrossRef]

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems,” Phys. Rev. Lett. 98, 077401(2007).
[CrossRef] [PubMed]

A. A. Zharov and V. V. Kurin, “Giant resonant magneto-optic Kerr effect in nanostructured ferromagnetic metamaterials,” J. Appl. Phys. 102, 123514 (2007).
[CrossRef]

2006 (1)

N. Venkatram, R. S. S. Kumar, D. N. Rao, S. K. Medda, S. De, and G. De, “Nonlinear optical absorption and switching properties of gold nanoparticle doped SiO2–TiO2 solgel films,” J. Nanosci. Nanotechnol. 6, 1990–1994 (2006).
[CrossRef] [PubMed]

2005 (3)

R. A. Ganeev, “Nonlinear refraction and nonlinear absorption of various media,” J. Opt. A 7, 717–733 (2005).
[CrossRef]

E. M. Kim, S. S. Elovikov, T. V. Murzina, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95, 227402 (2005).
[CrossRef] [PubMed]

P. Gangopadhyay, S. Gallet, E. Franz, A. Persoons, and T. Verbiest, “Novel superparamagnetic core (shell) nanoparticles for magnetic targeted drug delivery and hyperthermia treatment,” IEEE Trans. Magn. 41, 4194–4196 (2005).
[CrossRef]

2004 (1)

L. De Boni, A. A. Andrade, D. S. Corrêa, D. T. Balogh, S. C. Zilio, L. Misoguti, and C. R. Mendoca, “Nonlinear absorption spectrum in MEH-PPV/chloroform solution: a competition between two-photon and saturated absorption processes,” J. Phys. Chem. B 108, 5221–5224 (2004).
[CrossRef]

2003 (3)

Y. Yang, J. Shi, H. Chen, S. Dai, and Y. Liu, “Enhanced off-resonant optical nonlinearity of Au-CdS core-shell nanoparticles embedded in BaTiO3 thin films,” Chem. Phys. Lett. 370, 1–6 (2003).
[CrossRef]

Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76, 435–439 (2003).
[CrossRef]

M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
[CrossRef]

2000 (3)

S. Debrus, J. Lafait, M. May, N. Pincon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

M. Kyong and M. Lee, “Z-scan studies on the third-order optical nonlinearity of Au nanoparticles embedded in TiO2,” Bull. Korean Chem Soc. 21, 26–28 (2000).

R. Rangel-Rojo, H. Matsuda, H. Kasai, and H. Nakanishi, “Irradiance dependence of the resonant nonlinearities in an organic material,” J. Opt. Soc. Am. B 17, 1376–1382 (2000).
[CrossRef]

1998 (1)

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769(1990).
[CrossRef]

1989 (2)

1981 (2)

A. Wokaun, J. G. Bergman, J. P. Heritage, A. M. Glass, P. F. Liao, and D. H. Olson, “Local fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 849–856 (1981).
[CrossRef]

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local-fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[CrossRef]

Acimovic, S.

Aktsipetrov, O. A.

I. A. Kolmychek, T. V. Murzina, S. Fourier, J. Wouters, V. K. Valev, T. Verbiest, and O. A. Aktsipetrov, “Second harmonic generation in core (shell) γ-Fe2O3 (Au) nanoparticles,” Solid State Phenom. 152, 508–511 (2009).
[CrossRef]

T. V. Murzina, I. A. Kolmychek, A. A. Nikulin, E. A. Ganshina, and O. A. Aktsipetrov, “Plasmonic and magnetic effects accompanying optical second-harmonic generation in Au/Co/Au nanodisks,” JETP Lett. 90, 504–508 (2009).
[CrossRef]

E. M. Kim, S. S. Elovikov, T. V. Murzina, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95, 227402 (2005).
[CrossRef] [PubMed]

Andrade, A. A.

L. De Boni, A. A. Andrade, D. S. Corrêa, D. T. Balogh, S. C. Zilio, L. Misoguti, and C. R. Mendoca, “Nonlinear absorption spectrum in MEH-PPV/chloroform solution: a competition between two-photon and saturated absorption processes,” J. Phys. Chem. B 108, 5221–5224 (2004).
[CrossRef]

Anija, M.

M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
[CrossRef]

Armelles, G.

J. F. Torrado, E. Th. Papaioannou, G. Ctistis, P. Patoka, M. Giersig, G. Armelles, and A. Garcia-Martin, “Plasmon induced modification of the transverse magneto-optical response in Fe antidot arrays,” Phys. Stat. Solidi RRL 4, 271–273 (2010).
[CrossRef]

J. B. Gonzalez-Diaz, A. Garcia-Martin, J. M. Garcia-Martin, A. Cebollada, and G. Armelles, “Plasmonic Au/Co/Au nanosandwiches with enhanced magneto-optical activity,” Small 4, 202–205 (2008).
[CrossRef] [PubMed]

G. Armelles, J. B. Gonzalez-Diaz, A. Garcia-Martin, Jose M. Garcia-Martin, A. Cebollada, M. U. Gonzalez, S. Acimovic, J. Cesario, R. Quidant, and G. Badenes, “Localized surface plasmon resonance effects on the magneto-optical activity of continuous Au/Co/Au trilayers,” Opt. Express 16, 16104–16112 (2008).
[CrossRef] [PubMed]

Badenes, G.

Bader, M. A.

E. M. Kim, S. S. Elovikov, T. V. Murzina, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95, 227402 (2005).
[CrossRef] [PubMed]

Balogh, D. T.

L. De Boni, A. A. Andrade, D. S. Corrêa, D. T. Balogh, S. C. Zilio, L. Misoguti, and C. R. Mendoca, “Nonlinear absorption spectrum in MEH-PPV/chloroform solution: a competition between two-photon and saturated absorption processes,” J. Phys. Chem. B 108, 5221–5224 (2004).
[CrossRef]

Barber, P. W.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local-fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[CrossRef]

Bello, V.

I. Ros, P. Schiavuta, V. Bello, G. Mattei, and R. Bozio, “Femtosecond nonlinear absorption in gold nanoshells at surface plasmon resonance,” Phys. Chem. Chem. Phys. 12, 13692–13698(2010).
[CrossRef] [PubMed]

Belotelov, V. I.

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Extraordinary transmission and giant magneto-optical transverse Kerr effect in plasmonic nanostructured films,” J. Opt. Soc. Am. B 26, 1594–1598 (2009).
[CrossRef]

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems,” Phys. Rev. Lett. 98, 077401(2007).
[CrossRef] [PubMed]

Bergman, J. G.

A. Wokaun, J. G. Bergman, J. P. Heritage, A. M. Glass, P. F. Liao, and D. H. Olson, “Local fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 849–856 (1981).
[CrossRef]

Birnboim, M. H.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Bozio, R.

I. Ros, P. Schiavuta, V. Bello, G. Mattei, and R. Bozio, “Femtosecond nonlinear absorption in gold nanoshells at surface plasmon resonance,” Phys. Chem. Chem. Phys. 12, 13692–13698(2010).
[CrossRef] [PubMed]

Bykov, D. A.

Carpenter, E. E.

L. Wang, K. Yang, C. Clavero, A. J. Nelson, K. J. Carroll, E. E. Carpenter, and R. A. Lukaszew, “Localized surface plasmon resonance enhanced magneto-optical activity in core-shell Fe–Ag nanoparticles,” J. Appl. Phys. 107, 09B303 (2010).
[CrossRef]

Carroll, K. J.

L. Wang, K. Yang, C. Clavero, A. J. Nelson, K. J. Carroll, E. E. Carpenter, and R. A. Lukaszew, “Localized surface plasmon resonance enhanced magneto-optical activity in core-shell Fe–Ag nanoparticles,” J. Appl. Phys. 107, 09B303 (2010).
[CrossRef]

Cebollada, A.

Cesario, J.

Chang, R. K.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local-fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[CrossRef]

Chen, H.

Y. Yang, J. Shi, H. Chen, S. Dai, and Y. Liu, “Enhanced off-resonant optical nonlinearity of Au-CdS core-shell nanoparticles embedded in BaTiO3 thin films,” Chem. Phys. Lett. 370, 1–6 (2003).
[CrossRef]

Clavero, C.

L. Wang, K. Yang, C. Clavero, A. J. Nelson, K. J. Carroll, E. E. Carpenter, and R. A. Lukaszew, “Localized surface plasmon resonance enhanced magneto-optical activity in core-shell Fe–Ag nanoparticles,” J. Appl. Phys. 107, 09B303 (2010).
[CrossRef]

Corrêa, D. S.

L. De Boni, A. A. Andrade, D. S. Corrêa, D. T. Balogh, S. C. Zilio, L. Misoguti, and C. R. Mendoca, “Nonlinear absorption spectrum in MEH-PPV/chloroform solution: a competition between two-photon and saturated absorption processes,” J. Phys. Chem. B 108, 5221–5224 (2004).
[CrossRef]

Ctistis, G.

J. F. Torrado, E. Th. Papaioannou, G. Ctistis, P. Patoka, M. Giersig, G. Armelles, and A. Garcia-Martin, “Plasmon induced modification of the transverse magneto-optical response in Fe antidot arrays,” Phys. Stat. Solidi RRL 4, 271–273 (2010).
[CrossRef]

Dai, S.

Y. Yang, J. Shi, H. Chen, S. Dai, and Y. Liu, “Enhanced off-resonant optical nonlinearity of Au-CdS core-shell nanoparticles embedded in BaTiO3 thin films,” Chem. Phys. Lett. 370, 1–6 (2003).
[CrossRef]

De, G.

N. Venkatram, R. S. S. Kumar, D. N. Rao, S. K. Medda, S. De, and G. De, “Nonlinear optical absorption and switching properties of gold nanoparticle doped SiO2–TiO2 solgel films,” J. Nanosci. Nanotechnol. 6, 1990–1994 (2006).
[CrossRef] [PubMed]

De, S.

N. Venkatram, R. S. S. Kumar, D. N. Rao, S. K. Medda, S. De, and G. De, “Nonlinear optical absorption and switching properties of gold nanoparticle doped SiO2–TiO2 solgel films,” J. Nanosci. Nanotechnol. 6, 1990–1994 (2006).
[CrossRef] [PubMed]

De Boni, L.

L. De Boni, A. A. Andrade, D. S. Corrêa, D. T. Balogh, S. C. Zilio, L. Misoguti, and C. R. Mendoca, “Nonlinear absorption spectrum in MEH-PPV/chloroform solution: a competition between two-photon and saturated absorption processes,” J. Phys. Chem. B 108, 5221–5224 (2004).
[CrossRef]

Debrus, S.

S. Debrus, J. Lafait, M. May, N. Pincon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

Deng, Y.

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Y. Deng, Y. Sun, P. Wang, D. Zhang, H. Ming, and Q. Zhang, “In situ synthesis and nonlinear optical properties of Ag nanocomposite polymer films,” Physica E 40, 911–914 (2008).
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G. X. Du, T. Mori, M. Suzuki, Sh. Saito, H. Fukuda, and M. Takahashi, “Evidence of localized surface plasmon enhanced magneto-optical effect in nanodisk array,” Appl. Phys. Lett. 96, 081915 (2010).
[CrossRef]

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T. V. Murzina, I. A. Kolmychek, A. A. Nikulin, E. A. Ganshina, and O. A. Aktsipetrov, “Plasmonic and magnetic effects accompanying optical second-harmonic generation in Au/Co/Au nanodisks,” JETP Lett. 90, 504–508 (2009).
[CrossRef]

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[CrossRef]

E. M. Kim, S. S. Elovikov, T. V. Murzina, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95, 227402 (2005).
[CrossRef] [PubMed]

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M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
[CrossRef]

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Neeves, A. E.

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L. Wang, K. Yang, C. Clavero, A. J. Nelson, K. J. Carroll, E. E. Carpenter, and R. A. Lukaszew, “Localized surface plasmon resonance enhanced magneto-optical activity in core-shell Fe–Ag nanoparticles,” J. Appl. Phys. 107, 09B303 (2010).
[CrossRef]

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T. V. Murzina, I. A. Kolmychek, A. A. Nikulin, E. A. Ganshina, and O. A. Aktsipetrov, “Plasmonic and magnetic effects accompanying optical second-harmonic generation in Au/Co/Au nanodisks,” JETP Lett. 90, 504–508 (2009).
[CrossRef]

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A. Wokaun, J. G. Bergman, J. P. Heritage, A. M. Glass, P. F. Liao, and D. H. Olson, “Local fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 849–856 (1981).
[CrossRef]

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J. F. Torrado, E. Th. Papaioannou, G. Ctistis, P. Patoka, M. Giersig, G. Armelles, and A. Garcia-Martin, “Plasmon induced modification of the transverse magneto-optical response in Fe antidot arrays,” Phys. Stat. Solidi RRL 4, 271–273 (2010).
[CrossRef]

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J. F. Torrado, E. Th. Papaioannou, G. Ctistis, P. Patoka, M. Giersig, G. Armelles, and A. Garcia-Martin, “Plasmon induced modification of the transverse magneto-optical response in Fe antidot arrays,” Phys. Stat. Solidi RRL 4, 271–273 (2010).
[CrossRef]

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P. Gangopadhyay, S. Gallet, E. Franz, A. Persoons, and T. Verbiest, “Novel superparamagnetic core (shell) nanoparticles for magnetic targeted drug delivery and hyperthermia treatment,” IEEE Trans. Magn. 41, 4194–4196 (2005).
[CrossRef]

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M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
[CrossRef]

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S. Debrus, J. Lafait, M. May, N. Pincon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

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M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
[CrossRef]

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S. Debrus, J. Lafait, M. May, N. Pincon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

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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, 207402 (2010).
[CrossRef] [PubMed]

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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, 207402 (2010).
[CrossRef] [PubMed]

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Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76, 435–439 (2003).
[CrossRef]

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Rangel-Rojo, R.

Rao, D. N.

N. Venkatram, R. S. S. Kumar, D. N. Rao, S. K. Medda, S. De, and G. De, “Nonlinear optical absorption and switching properties of gold nanoparticle doped SiO2–TiO2 solgel films,” J. Nanosci. Nanotechnol. 6, 1990–1994 (2006).
[CrossRef] [PubMed]

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I. Ros, P. Schiavuta, V. Bello, G. Mattei, and R. Bozio, “Femtosecond nonlinear absorption in gold nanoshells at surface plasmon resonance,” Phys. Chem. Chem. Phys. 12, 13692–13698(2010).
[CrossRef] [PubMed]

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M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769(1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Saito, Sh.

G. X. Du, T. Mori, M. Suzuki, Sh. Saito, H. Fukuda, and M. Takahashi, “Evidence of localized surface plasmon enhanced magneto-optical effect in nanodisk array,” Appl. Phys. Lett. 96, 081915 (2010).
[CrossRef]

Schiavuta, P.

I. Ros, P. Schiavuta, V. Bello, G. Mattei, and R. Bozio, “Femtosecond nonlinear absorption in gold nanoshells at surface plasmon resonance,” Phys. Chem. Chem. Phys. 12, 13692–13698(2010).
[CrossRef] [PubMed]

Sella, C.

S. Debrus, J. Lafait, M. May, N. Pincon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

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M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769(1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Shi, J.

Y. Yang, J. Shi, H. Chen, S. Dai, and Y. Liu, “Enhanced off-resonant optical nonlinearity of Au-CdS core-shell nanoparticles embedded in BaTiO3 thin films,” Chem. Phys. Lett. 370, 1–6 (2003).
[CrossRef]

Shi, J. L.

Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76, 435–439 (2003).
[CrossRef]

Singh, N.

M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
[CrossRef]

Sun, Y.

Y. Deng, Y. Sun, P. Wang, D. Zhang, H. Ming, and Q. Zhang, “In situ synthesis and nonlinear optical properties of Ag nanocomposite polymer films,” Physica E 40, 911–914 (2008).
[CrossRef]

Suzuki, M.

G. X. Du, T. Mori, M. Suzuki, Sh. Saito, H. Fukuda, and M. Takahashi, “Evidence of localized surface plasmon enhanced magneto-optical effect in nanodisk array,” Appl. Phys. Lett. 96, 081915 (2010).
[CrossRef]

Takahashi, M.

G. X. Du, T. Mori, M. Suzuki, Sh. Saito, H. Fukuda, and M. Takahashi, “Evidence of localized surface plasmon enhanced magneto-optical effect in nanodisk array,” Appl. Phys. Lett. 96, 081915 (2010).
[CrossRef]

Thomas, J.

M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
[CrossRef]

Tom, R. T.

M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
[CrossRef]

Torrado, J. F.

J. F. Torrado, E. Th. Papaioannou, G. Ctistis, P. Patoka, M. Giersig, G. Armelles, and A. Garcia-Martin, “Plasmon induced modification of the transverse magneto-optical response in Fe antidot arrays,” Phys. Stat. Solidi RRL 4, 271–273 (2010).
[CrossRef]

Valev, V. K.

I. A. Kolmychek, T. V. Murzina, S. Fourier, J. Wouters, V. K. Valev, T. Verbiest, and O. A. Aktsipetrov, “Second harmonic generation in core (shell) γ-Fe2O3 (Au) nanoparticles,” Solid State Phenom. 152, 508–511 (2009).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769(1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Venkatram, N.

N. Venkatram, R. S. S. Kumar, D. N. Rao, S. K. Medda, S. De, and G. De, “Nonlinear optical absorption and switching properties of gold nanoparticle doped SiO2–TiO2 solgel films,” J. Nanosci. Nanotechnol. 6, 1990–1994 (2006).
[CrossRef] [PubMed]

Venturini, J.

S. Debrus, J. Lafait, M. May, N. Pincon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

Verbiest, T.

I. A. Kolmychek, T. V. Murzina, S. Fourier, J. Wouters, V. K. Valev, T. Verbiest, and O. A. Aktsipetrov, “Second harmonic generation in core (shell) γ-Fe2O3 (Au) nanoparticles,” Solid State Phenom. 152, 508–511 (2009).
[CrossRef]

P. Gangopadhyay, S. Gallet, E. Franz, A. Persoons, and T. Verbiest, “Novel superparamagnetic core (shell) nanoparticles for magnetic targeted drug delivery and hyperthermia treatment,” IEEE Trans. Magn. 41, 4194–4196 (2005).
[CrossRef]

von Raben, K. U.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local-fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 649–657 (1981).
[CrossRef]

Wang, K.

Wang, L.

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[CrossRef]

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Y. Deng, Y. Sun, P. Wang, D. Zhang, H. Ming, and Q. Zhang, “In situ synthesis and nonlinear optical properties of Ag nanocomposite polymer films,” Physica E 40, 911–914 (2008).
[CrossRef]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769(1990).
[CrossRef]

Wherrett, B. S.

Wokaun, A.

A. Wokaun, J. G. Bergman, J. P. Heritage, A. M. Glass, P. F. Liao, and D. H. Olson, “Local fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 849–856 (1981).
[CrossRef]

Wouters, J.

I. A. Kolmychek, T. V. Murzina, S. Fourier, J. Wouters, V. K. Valev, T. Verbiest, and O. A. Aktsipetrov, “Second harmonic generation in core (shell) γ-Fe2O3 (Au) nanoparticles,” Solid State Phenom. 152, 508–511 (2009).
[CrossRef]

Yamada, S.

Yang, G.

Yang, K.

L. Wang, K. Yang, C. Clavero, A. J. Nelson, K. J. Carroll, E. E. Carpenter, and R. A. Lukaszew, “Localized surface plasmon resonance enhanced magneto-optical activity in core-shell Fe–Ag nanoparticles,” J. Appl. Phys. 107, 09B303 (2010).
[CrossRef]

Yang, Y.

Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76, 435–439 (2003).
[CrossRef]

Y. Yang, J. Shi, H. Chen, S. Dai, and Y. Liu, “Enhanced off-resonant optical nonlinearity of Au-CdS core-shell nanoparticles embedded in BaTiO3 thin films,” Chem. Phys. Lett. 370, 1–6 (2003).
[CrossRef]

You, G. J.

Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76, 435–439 (2003).
[CrossRef]

Zhang, D.

Y. Deng, Y. Sun, P. Wang, D. Zhang, H. Ming, and Q. Zhang, “In situ synthesis and nonlinear optical properties of Ag nanocomposite polymer films,” Physica E 40, 911–914 (2008).
[CrossRef]

Zhang, Q.

Y. Deng, Y. Sun, P. Wang, D. Zhang, H. Ming, and Q. Zhang, “In situ synthesis and nonlinear optical properties of Ag nanocomposite polymer films,” Physica E 40, 911–914 (2008).
[CrossRef]

Zharov, A. A.

A. A. Zharov and N. A. Zharova, “Double-resonance plasmon-driven enhancement of nonlinear optical response in a metamaterial with coated nanoparticles,” JETP Lett. 92, 210–213 (2010).
[CrossRef]

A. A. Zharov and V. V. Kurin, “Giant resonant magneto-optic Kerr effect in nanostructured ferromagnetic metamaterials,” J. Appl. Phys. 102, 123514 (2007).
[CrossRef]

Zharova, N. A.

A. A. Zharov and N. A. Zharova, “Double-resonance plasmon-driven enhancement of nonlinear optical response in a metamaterial with coated nanoparticles,” JETP Lett. 92, 210–213 (2010).
[CrossRef]

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A. A. Grunin, A. G. Zhdanov, A. A. Ezhov, E. A. Ganshina, and A. A. Fedyanin, “Surface-plasmon-induced enhancement of magneto-optical Kerr effect in all-nickel subwavelength nanogratings,” Appl. Phys. Lett. 97, 261908 (2010).
[CrossRef]

Zhu, R. Y.

Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76, 435–439 (2003).
[CrossRef]

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L. De Boni, A. A. Andrade, D. S. Corrêa, D. T. Balogh, S. C. Zilio, L. Misoguti, and C. R. Mendoca, “Nonlinear absorption spectrum in MEH-PPV/chloroform solution: a competition between two-photon and saturated absorption processes,” J. Phys. Chem. B 108, 5221–5224 (2004).
[CrossRef]

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V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Extraordinary transmission and giant magneto-optical transverse Kerr effect in plasmonic nanostructured films,” J. Opt. Soc. Am. B 26, 1594–1598 (2009).
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V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems,” Phys. Rev. Lett. 98, 077401(2007).
[CrossRef] [PubMed]

Appl. Phys. B (1)

Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76, 435–439 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

G. X. Du, T. Mori, M. Suzuki, Sh. Saito, H. Fukuda, and M. Takahashi, “Evidence of localized surface plasmon enhanced magneto-optical effect in nanodisk array,” Appl. Phys. Lett. 96, 081915 (2010).
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A. A. Grunin, A. G. Zhdanov, A. A. Ezhov, E. A. Ganshina, and A. A. Fedyanin, “Surface-plasmon-induced enhancement of magneto-optical Kerr effect in all-nickel subwavelength nanogratings,” Appl. Phys. Lett. 97, 261908 (2010).
[CrossRef]

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M. Anija, J. Thomas, N. Singh, A. S. Nair, R. T. Tom, T. Pradeep, and R. Philip, “Nonlinear light transmission through oxide-protected Au and Ag nanoparticles: an investigation in the nanosecond domain,” Chem. Phys. Lett. 380, 223–229(2003).
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Y. Yang, J. Shi, H. Chen, S. Dai, and Y. Liu, “Enhanced off-resonant optical nonlinearity of Au-CdS core-shell nanoparticles embedded in BaTiO3 thin films,” Chem. Phys. Lett. 370, 1–6 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769(1990).
[CrossRef]

IEEE Trans. Magn. (1)

P. Gangopadhyay, S. Gallet, E. Franz, A. Persoons, and T. Verbiest, “Novel superparamagnetic core (shell) nanoparticles for magnetic targeted drug delivery and hyperthermia treatment,” IEEE Trans. Magn. 41, 4194–4196 (2005).
[CrossRef]

J. Appl. Phys. (3)

A. A. Zharov and V. V. Kurin, “Giant resonant magneto-optic Kerr effect in nanostructured ferromagnetic metamaterials,” J. Appl. Phys. 102, 123514 (2007).
[CrossRef]

L. Wang, K. Yang, C. Clavero, A. J. Nelson, K. J. Carroll, E. E. Carpenter, and R. A. Lukaszew, “Localized surface plasmon resonance enhanced magneto-optical activity in core-shell Fe–Ag nanoparticles,” J. Appl. Phys. 107, 09B303 (2010).
[CrossRef]

S. Debrus, J. Lafait, M. May, N. Pincon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
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N. Venkatram, R. S. S. Kumar, D. N. Rao, S. K. Medda, S. De, and G. De, “Nonlinear optical absorption and switching properties of gold nanoparticle doped SiO2–TiO2 solgel films,” J. Nanosci. Nanotechnol. 6, 1990–1994 (2006).
[CrossRef] [PubMed]

J. Opt. A (1)

R. A. Ganeev, “Nonlinear refraction and nonlinear absorption of various media,” J. Opt. A 7, 717–733 (2005).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. Chem. B (1)

L. De Boni, A. A. Andrade, D. S. Corrêa, D. T. Balogh, S. C. Zilio, L. Misoguti, and C. R. Mendoca, “Nonlinear absorption spectrum in MEH-PPV/chloroform solution: a competition between two-photon and saturated absorption processes,” J. Phys. Chem. B 108, 5221–5224 (2004).
[CrossRef]

JETP Lett. (2)

A. A. Zharov and N. A. Zharova, “Double-resonance plasmon-driven enhancement of nonlinear optical response in a metamaterial with coated nanoparticles,” JETP Lett. 92, 210–213 (2010).
[CrossRef]

T. V. Murzina, I. A. Kolmychek, A. A. Nikulin, E. A. Ganshina, and O. A. Aktsipetrov, “Plasmonic and magnetic effects accompanying optical second-harmonic generation in Au/Co/Au nanodisks,” JETP Lett. 90, 504–508 (2009).
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Opt. Express (2)

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M. K. Kodirov, “Nonlinear refraction and nonlinear absorption of silver aggregates in a polymeric matrix,” Opt. Spectrosc. 102, 73–76 (2007).
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I. Ros, P. Schiavuta, V. Bello, G. Mattei, and R. Bozio, “Femtosecond nonlinear absorption in gold nanoshells at surface plasmon resonance,” Phys. Chem. Chem. Phys. 12, 13692–13698(2010).
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Phys. Rev. B (2)

A. Wokaun, J. G. Bergman, J. P. Heritage, A. M. Glass, P. F. Liao, and D. H. Olson, “Local fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 849–856 (1981).
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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, 207402 (2010).
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E. M. Kim, S. S. Elovikov, T. V. Murzina, O. A. Aktsipetrov, M. A. Bader, and G. Marowsky, “Surface-enhanced optical third-harmonic generation in Ag island films,” Phys. Rev. Lett. 95, 227402 (2005).
[CrossRef] [PubMed]

V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems,” Phys. Rev. Lett. 98, 077401(2007).
[CrossRef] [PubMed]

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J. F. Torrado, E. Th. Papaioannou, G. Ctistis, P. Patoka, M. Giersig, G. Armelles, and A. Garcia-Martin, “Plasmon induced modification of the transverse magneto-optical response in Fe antidot arrays,” Phys. Stat. Solidi RRL 4, 271–273 (2010).
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Physica E (1)

Y. Deng, Y. Sun, P. Wang, D. Zhang, H. Ming, and Q. Zhang, “In situ synthesis and nonlinear optical properties of Ag nanocomposite polymer films,” Physica E 40, 911–914 (2008).
[CrossRef]

Small (1)

J. B. Gonzalez-Diaz, A. Garcia-Martin, J. M. Garcia-Martin, A. Cebollada, and G. Armelles, “Plasmonic Au/Co/Au nanosandwiches with enhanced magneto-optical activity,” Small 4, 202–205 (2008).
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Solid State Phenom. (1)

I. A. Kolmychek, T. V. Murzina, S. Fourier, J. Wouters, V. K. Valev, T. Verbiest, and O. A. Aktsipetrov, “Second harmonic generation in core (shell) γ-Fe2O3 (Au) nanoparticles,” Solid State Phenom. 152, 508–511 (2009).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Absorption spectrum of PMMA- γ - Fe 2 O 3 (Au) core (shell) NPs (left scale) and the resonant absorption peak deconvoluted from the approximation (right scale). Inset, schematic of a single core (shell) NP.

Fig. 2
Fig. 2

Open-aperture Z-scan results in core (shell) NPs at the wavelength 570 nm and different intensities: 1 8 MW / cm 2 , 2 16 MW / cm 2 , 3 19 MW / cm 2 , 4 25 MW / cm 2 . Inset, open-aperture Z-scan results in gold NPs near the LSP excitation at the intensity of 25 MW / cm 2 .

Fig. 3
Fig. 3

Spectra of the effective nonlinear absorption coefficient, measured at the fundamental intensity of 20 25 MW / cm 2 (filled circles, left scale) and of linear absorption coefficient (solid curve, right scale).

Fig. 4
Fig. 4

T ( z / z 0 ) dependence measured at the fundamental wavelength of 570 nm in the closed-aperture Z-scan experimental scheme (filled circles); dotted line is the result of the approximation of the experimental data by the superposition of the dependencies that correspond to the nonlinear refraction (solid line) and nonlinear absorption (dashed line) processes.

Fig. 5
Fig. 5

Spectra of the effective nonlinear refraction coefficient n 2 eff measured for the fundamental intensity of 20 25 MW / cm 2 .

Equations (7)

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α ( ω ) = α 0 ( ω ) 1 + I / I sat + β 2 ( ω ) I ( ω ) α 0 ( ω ) + [ α 0 ( ω ) I sat + β 2 ( ω ) ] I ( ω ) = α 0 ( ω ) + α 2 ( ω ) I ( ω ) ,
α ( ω ) = α 0 ( ω ) + β 2 ( ω ) I + β 4 ( ω ) I 2 + ,
n ( ω ) = n 0 ( ω ) + n 2 ( ω ) I + n 4 ( ω ) I 2 + ,
δ = ϵ s ϵ a ϵ h ϵ b ϵ s ϵ a + 2 ϵ h ϵ b ,
ϵ a = ϵ c ( 3 - 2 P ) + 2 ϵ s P , ϵ b = ϵ c P + ϵ s ( 3 P ) , P = 1 ( r c r s ) 3 ,
T ( z ) = 1 1 2 2 β ( ω ) I local ( ω ) L eff 1 + ( z / z 0 ) 2 ,
Δ T p v 0.406 ( 1 S ) 0.27 2 π λ n 2 I L eff .

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