Abstract

The spectral map of the nonlinear absorption coefficient of glass-copper nanocomposite in the pump-probe scheme constructed with the use of a simple anharmonic oscillator model reproduced well the spectral map obtained in the experiment. It is shown that spectral features in nonlinear response of glass-metal nanocomposites (GMN) can be engineered by varying the size of nanoparticles. The pronounced dependence of the magnitude of the third-order nonlinearity on the particles size explains the diversity of experimental data related to nonlinear optical response of GMNs in different experiments. Performed modeling proves that silver GMN demonstrate much sharper spectral dependence than copper ones due to strong frequency dependence of local field enhancement factor for silver nanoparticles.

© 2012 OSA

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2008

X. C. Yang, Z. H. Li, W. J. Li, J. X. Xu, Z. W. Dong, and S. X. Qian, “Optical nonlinearity and ultrafast dynamics of ion exchanged silver nanoparticles embedded in soda-lime silicate glass,” Chin. Sci. Bull.53(5), 695–699 (2008).
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Y. Takeda, H. Momida, M. Ohnuma, T. Ohno, and N. Kishimoto, “Wavelength dispersion of nonlinear dielectric function of Cu nanoparticle materials,” Opt. Express16(10), 7471–7480 (2008).
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A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, “Gallium/aluminum nanocomposite material for nonlinear optics and nonlinear plasmonics,” Appl. Phys. Lett.89(3), 031118–031120 (2006).
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[CrossRef]

2005

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[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep.408(3-4), 131–314 (2005).
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B. Karthikeyan, J. Thomas, and R. Philip, “Optical nonlinearity in glass-embedded silver nanoclusters under ultrafast laser excitation,” Chem. Phys. Lett.414(4-6), 346–350 (2005).
[CrossRef]

2003

P. P. Kiran, G. De, and D. N. Rao, “Nonlinear optical properties of copper and silver nanoclusters in SiO2 sol-gel films,” IEEE Proc. – Circuits Dev. and Syst.150(6), 559–562 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2000

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles,” Chem. Phys.251(1-3), 215–226 (2000).
[CrossRef]

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[CrossRef]

1998

1994

1981

1974

U. Kreibig, “Electronic properties of small silver particles: the optical constants and their temperature dependence,” J. Phys. F Met. Phys.4(7), 999–1014 (1974).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

1935

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. I. dielektrizitatskonstanten und leitfahigkeiten der mischk.orper aus isotropen sub-stanzen,” Ann. Phys.416(7), 636–664 (1935).
[CrossRef]

1904

J. C. Maxwell Garnett, “Colours in metal glasses and metal films,” Philos. Trans. R. Soc. London Ser. A203(359-371), 385–420 (1904).
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Almási, G.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B97(3), 679–685 (2009).
[CrossRef]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. Ch. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
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Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bigot, J.-Y.

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys.251(1-3), 181–203 (2000).
[CrossRef]

Boyd, R. W.

Brongersma, M. L.

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science328(5977), 440–441 (2010).
[CrossRef] [PubMed]

J. A. Schuller, E. S. Barnard, W. Cai, Y. Ch. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

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D. A. G. Bruggeman, “Berechnung verschiedener physikalischer konstanten von heterogenen substanzen. I. dielektrizitatskonstanten und leitfahigkeiten der mischk.orper aus isotropen sub-stanzen,” Ann. Phys.416(7), 636–664 (1935).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. Ch. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Daunois, A.

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys.251(1-3), 181–203 (2000).
[CrossRef]

De, G.

P. P. Kiran, G. De, and D. N. Rao, “Nonlinear optical properties of copper and silver nanoclusters in SiO2 sol-gel films,” IEEE Proc. – Circuits Dev. and Syst.150(6), 559–562 (2003).
[CrossRef]

Del Fatti, N.

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles,” Chem. Phys.251(1-3), 215–226 (2000).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Dong, Z. W.

X. C. Yang, Z. H. Li, W. J. Li, J. X. Xu, Z. W. Dong, and S. X. Qian, “Optical nonlinearity and ultrafast dynamics of ion exchanged silver nanoparticles embedded in soda-lime silicate glass,” Chin. Sci. Bull.53(5), 695–699 (2008).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Flytzanis, C.

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles,” Chem. Phys.251(1-3), 215–226 (2000).
[CrossRef]

Fullerton, E. E.

D. Lu, J. Kan, E. E. Fullerton, and Z. Liu, “Tunable surface plasmon polaritons in Ag composite films by adding dielectrics or semiconductors,” Appl. Phys. Lett.98(24), 243114 (2011).
[CrossRef]

Fülöp, J. A.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B97(3), 679–685 (2009).
[CrossRef]

Granqvist, C. G.

Hagan, D. J.

Halonen, M.

Halte, V.

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys.251(1-3), 181–203 (2000).
[CrossRef]

Hamanaka, Y.

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles,” Chem. Phys.251(1-3), 215–226 (2000).
[CrossRef]

Hebling, J.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B97(3), 679–685 (2009).
[CrossRef]

Hunderi, O.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Jun, Y. Ch.

J. A. Schuller, E. S. Barnard, W. Cai, Y. Ch. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Kan, J.

D. Lu, J. Kan, E. E. Fullerton, and Z. Liu, “Tunable surface plasmon polaritons in Ag composite films by adding dielectrics or semiconductors,” Appl. Phys. Lett.98(24), 243114 (2011).
[CrossRef]

Karthikeyan, B.

B. Karthikeyan, J. Thomas, and R. Philip, “Optical nonlinearity in glass-embedded silver nanoclusters under ultrafast laser excitation,” Chem. Phys. Lett.414(4-6), 346–350 (2005).
[CrossRef]

Kiran, P. P.

P. P. Kiran, G. De, and D. N. Rao, “Nonlinear optical properties of copper and silver nanoclusters in SiO2 sol-gel films,” IEEE Proc. – Circuits Dev. and Syst.150(6), 559–562 (2003).
[CrossRef]

Kishimoto, N.

Kooij, E.

H. Wormeester, E. Kooij, and B. Poelsema, “Effective dielectric response of nanostructured layers,” Phys. Status Solidi205(4), 756–763 (2008) (a).
[CrossRef]

Krasavin, A. V.

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, “Gallium/aluminum nanocomposite material for nonlinear optics and nonlinear plasmonics,” Appl. Phys. Lett.89(3), 031118–031120 (2006).
[CrossRef]

Kreibig, U.

U. Kreibig, “Electronic properties of small silver particles: the optical constants and their temperature dependence,” J. Phys. F Met. Phys.4(7), 999–1014 (1974).
[CrossRef]

Li, W. J.

X. C. Yang, Z. H. Li, W. J. Li, J. X. Xu, Z. W. Dong, and S. X. Qian, “Optical nonlinearity and ultrafast dynamics of ion exchanged silver nanoparticles embedded in soda-lime silicate glass,” Chin. Sci. Bull.53(5), 695–699 (2008).
[CrossRef]

Li, Z. H.

X. C. Yang, Z. H. Li, W. J. Li, J. X. Xu, Z. W. Dong, and S. X. Qian, “Optical nonlinearity and ultrafast dynamics of ion exchanged silver nanoparticles embedded in soda-lime silicate glass,” Chin. Sci. Bull.53(5), 695–699 (2008).
[CrossRef]

Liapis, A. C.

Lipovskii, A.

Lipovskii, A. A.

Liu, Z.

D. Lu, J. Kan, E. E. Fullerton, and Z. Liu, “Tunable surface plasmon polaritons in Ag composite films by adding dielectrics or semiconductors,” Appl. Phys. Lett.98(24), 243114 (2011).
[CrossRef]

Lu, D.

D. Lu, J. Kan, E. E. Fullerton, and Z. Liu, “Tunable surface plasmon polaritons in Ag composite films by adding dielectrics or semiconductors,” Appl. Phys. Lett.98(24), 243114 (2011).
[CrossRef]

Lyashenko, D.

Ma, H.

MacDonald, K. F.

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, “Gallium/aluminum nanocomposite material for nonlinear optics and nonlinear plasmonics,” Appl. Phys. Lett.89(3), 031118–031120 (2006).
[CrossRef]

Maier, S. A.

S. A. Maier, “Plasmonics-towards subwavelength optical devices,” Current Nanosci.1(1), 17–22 (2005).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep.408(3-4), 131–314 (2005).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in metal glasses and metal films,” Philos. Trans. R. Soc. London Ser. A203(359-371), 385–420 (1904).
[CrossRef]

Merle, J.-C.

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys.251(1-3), 181–203 (2000).
[CrossRef]

Momida, H.

Nakamura, A.

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles,” Chem. Phys.251(1-3), 215–226 (2000).
[CrossRef]

Nelson, M. A.

Niklasson, G. A.

Novotny, L.

Ohno, T.

Ohnuma, M.

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Pálfalvi, L.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B97(3), 679–685 (2009).
[CrossRef]

Philip, R.

B. Karthikeyan, J. Thomas, and R. Philip, “Optical nonlinearity in glass-embedded silver nanoclusters under ultrafast laser excitation,” Chem. Phys. Lett.414(4-6), 346–350 (2005).
[CrossRef]

Piredda, G.

Plaksin, O. A.

Poelsema, B.

H. Wormeester, E. Kooij, and B. Poelsema, “Effective dielectric response of nanostructured layers,” Phys. Status Solidi205(4), 756–763 (2008) (a).
[CrossRef]

Qian, S. X.

X. C. Yang, Z. H. Li, W. J. Li, J. X. Xu, Z. W. Dong, and S. X. Qian, “Optical nonlinearity and ultrafast dynamics of ion exchanged silver nanoparticles embedded in soda-lime silicate glass,” Chin. Sci. Bull.53(5), 695–699 (2008).
[CrossRef]

Rao, D. N.

P. P. Kiran, G. De, and D. N. Rao, “Nonlinear optical properties of copper and silver nanoclusters in SiO2 sol-gel films,” IEEE Proc. – Circuits Dev. and Syst.150(6), 559–562 (2003).
[CrossRef]

Said, A. A.

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. Ch. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7-8), 20–27 (2006).
[CrossRef]

Schwanecke, A. S.

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, “Gallium/aluminum nanocomposite material for nonlinear optics and nonlinear plasmonics,” Appl. Phys. Lett.89(3), 031118–031120 (2006).
[CrossRef]

Shalaev, V. M.

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science328(5977), 440–441 (2010).
[CrossRef] [PubMed]

Sheik-Bahae, M.

Sheng, P.

Shi, Z.

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep.408(3-4), 131–314 (2005).
[CrossRef]

Svirko, Y. P.

Svirko, Yu.

Takeda, Y.

Thomas, J.

B. Karthikeyan, J. Thomas, and R. Philip, “Optical nonlinearity in glass-embedded silver nanoclusters under ultrafast laser excitation,” Chem. Phys. Lett.414(4-6), 346–350 (2005).
[CrossRef]

Tóth, B. C.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B97(3), 679–685 (2009).
[CrossRef]

Vallee, F.

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles,” Chem. Phys.251(1-3), 215–226 (2000).
[CrossRef]

Van Stryland, E. W.

Wang, J.

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. Ch. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

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H. Wormeester, E. Kooij, and B. Poelsema, “Effective dielectric response of nanostructured layers,” Phys. Status Solidi205(4), 756–763 (2008) (a).
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Figures (5)

Fig. 1
Fig. 1

Imaginary (a) and real (b) components of the permittivity of copper calculated from Eq. (5) at ω0 = 3.46·1015s−1, ωpf = 1.39·1016s−1, ωpb = 3.10·1015s−1, Γf = 1.61·1014s−1, and Γb = 4.68·1014 s−1 (solid lines) and plotted according to the handbook [29] (dash lines).

Fig. 2
Fig. 2

Probe wavelength dependence of the nonlinear optical susceptibility of copper measured [22] (solid lines) and calculated from Eq. (4) for pump wavelengths λ1 = 580nm (upper curves) and λ1 = 620nm (lower curves). Anharmonicity parameter ξ = 4.32·1032nm−2s−2.

Fig. 3
Fig. 3

Calculated (a) and experimental (b) Im( χ GMN (3) ) spectral map [21] for glass copper nanocomposite, anharmonicity parameter ξ = 4.32·1032nm−2s−2.

Fig. 4
Fig. 4

Imaginary part of glass-copper nanocomposite third order susceptibility, Im( χ GMN (3) ) 10 14 (esu) , metal volume fraction f = 10−5, particles size is marked in the figures. The spectral position where changes its sign is shown with dashed line.

Fig. 5
Fig. 5

Calculated spectral maps of real and imaginary part of local field enhancement factor for embedded in glass silver and copper nanoparticles of the same 15 nm radius.

Equations (11)

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α 0 ( ω )= 2ω c Im( ε GMN ( ω ) ).
α( ω 1 , ω 2 )= α 0 ( ω 2 )+ α 2 ( ω 1 , ω 2 )I,
α 2 ( ω 1 , ω 2 )= 48 π 2 Re( ε GMN ) c 2 ω 2 Im{ χ GMN (3) ( ω 2 ; ω 1 , ω 1 , ω 2 ) },
χ GMN (3) ( ω 2 ; ω 1 , ω 1 , ω 2 )=f | L( ω 1 ) | 2 L ( ω 2 ) 2 χ M (3) ( ω 2 ; ω 1 , ω 1 , ω 2 ).
L= 2 ε G + ε GMN 2 ε G + ε M .
ε M = ε ω pf 2 ω 2 +i Γ f ω + ω pb 2 ω 0 2 ω 2 i Γ b ω ,
U= 1 2 m ω 0 2 x 2 + 1 4 mξ x 4 ,
x ¨ + Г b x ˙ + ω 0 2 x+ξ x 3 = e m E(t),
χ Cu (3) ( ω 2 ; ω 1 , ω 1 , ω 2 )= ξ e 2 ω pb 2 4π m 2 1 ( ω 0 2 i ω 2 Г b ω 2 2 ) 2 | ω 0 2 +i ω 1 Г b ω 1 2 | 2 .
Im{ χ GMN (3) }=f | L( ω 1 ) | 2 ( [ Im{ L( ω 2 ) } ] 2 Re{ χ Cu (3) }+ [ Re{ L( ω 2 ) } ] 2 Im{ χ Cu (3) } ),
Γ f ( R )= Γ f + v F /R,

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