Abstract

We present a theoretical study on the nonlocal optical effects on the Goos–Hänchen (GH) shift of reflected light from a composite material of metallic nanoparticles (MNPs). Using different nonlocal effective medium models, it is observed that such effects can be significant for small MNP of sizes down to a few nanometers. For small metallic volume fractions, the composite behaves like dielectric and the nonlocal effects lead to significant different Brewster angles, at which large negative GH shifts take place. For larger volume fractions or shorter wavelengths, the composite behaves more like metals and the nonlocal effects also lead to different Brewster angles but at values close to grazing incidence. These results will have significant implications in the application of different effective medium models for the characterization of these nanometallic composites when the MNPs are down to a few nanometers in size.

© 2013 Optical Society of America

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  1. F. Goos and H. Hänchen, “Ein neuer und fundamentalerVersuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
    [CrossRef]
  2. W. J. Wild and C. L. Giles, “Goos–Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099–2101 (1982).
    [CrossRef]
  3. For the latest reviews, see the recent special issue on “Beam shifts,” J. Opt.15(1), 014001 (2013).
  4. B. Zhao and L. Gao, “Temperature-dependent Goos–Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17, 21433–21441 (2009).
    [CrossRef]
  5. D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tenability,” Appl. Phys. Lett. 97, 041903 (2010).
    [CrossRef]
  6. C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011).
    [CrossRef]
  7. Y. Huang, B. Zhao, and L. Gao, “Goos–Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites,” J. Opt. Soc. Am. A 29, 1436–1444 (2012).
    [CrossRef]
  8. R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B 11, 2871–2876 (1975).
    [CrossRef]
  9. B. B. Dasgupta and R. Fuchs, “Polarizability of a small sphere including nonlocal effect,” Phys. Rev. B 24, 554–561 (1981).
    [CrossRef]
  10. R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
    [CrossRef]
  11. S. P. Apell, A. Ljungbert, and S. Lundqvist, “Nonlocal optical effects at metal surfaces,” Phys. Scr. 30, 367–383 (1984).
    [CrossRef]
  12. S. P. Apell, J. Giraldo, and S. Lundqvist, “Small metal particles: nonlocal optical properties and quantum-sizeeffects,” Phase Transit. 2626, 511–604 (1990).
  13. G. S. Agarwal and R. Inguva, “Effective-medium theory of a heterogeneous medium with individual grains having a nonlocal dielectric function,” Phys. Rev. B 30, 6108–6117 (1984).
    [CrossRef]
  14. R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005).
    [CrossRef]
  15. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
    [CrossRef]
  16. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films, and in metallic solutions,” Philos. Trans. R. Soc. London 205, 237–288 (1906).
    [CrossRef]
  17. D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. 24, 636–664 (1935).
    [CrossRef]
  18. C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
    [CrossRef]
  19. J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
    [CrossRef]
  20. A. Puri and D. N. Pattanayak, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983).
    [CrossRef]
  21. A. Puri and J. L. Birman, “Goos–Hänchen beam shift at total internal reflection with application to spatially dispersive media,” J. Opt. Soc. Am. A 3, 543–549 (1986).
    [CrossRef]
  22. R. Chang, H. P. Chiang, P. T. Leung, and W. S. Tse, “Nonlocal electrodynamic effects in the optical excitation of the surface plasmon resonance,” Opt. Commun. 225, 353–361 (2003).
    [CrossRef]
  23. T. C. Choy, Effective Medium Theory (Clarendon, 1999).
  24. A. Liebsch, Electronic Excitations at Metal Surfaces (Plenum, 1997).
  25. N. D. Mermin, “Lindhard dielectric function in the relaxation time approximation,” Phys. Rev. B 1, 2362–2363 (1970).
    [CrossRef]
  26. G. D. Mahan, Many-Particle Physics (Plenum, 1990), Chapter 5.
  27. J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097403 (2009).
    [CrossRef]
  28. C. David and F. J. G. de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115, 19470–19475 (2011).
    [CrossRef]
  29. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
    [CrossRef]
  30. P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
    [CrossRef]
  31. K. Artmann, “Berechnung der seitenversetzung des totalreflektierten stranles,” Ann. Phys. 2, 87–102 (1948).
    [CrossRef]
  32. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
  33. J. B. Götte, A. Aiello, and J. P. Woerdman, “Loss-induced transition of the Goos–Hänchen effect for metals and dielectrics,” Opt. Express 16, 3961–3969 (2008).
    [CrossRef]
  34. Note that in order to limit the number of figures in our paper, the plots of the dielectric functions are not included but are available upon request.
  35. W. Ekardt, “Size-dependent photoabsorption and photoemission of small metal particles,” Phys. Rev. B 31, 6360–6370 (1985).
    [CrossRef]
  36. L. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: silver versus simple metals,” Phys. Rev. B 4811317 (1993).
    [CrossRef]
  37. J. Tiggesbaumker, L. Koller, K. H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A 48, R1749–R1752 (1993).
    [CrossRef]
  38. S. Palomba, L. Novotny, and R. E. Palmer, “Blue-shifted plasmon resonance of individual size-selected gold nanoparticles,” Opt. Commun. 281, 480–483 (2008).
    [CrossRef]
  39. R. Fuchs, R. G. Barrera, and J. L. Carrillo, “Spectral representations of the electron energy loss in composite media,” Phys. Rev. B 54, 12824–12834 (1996).
    [CrossRef]

2012 (2)

Y. Huang, B. Zhao, and L. Gao, “Goos–Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites,” J. Opt. Soc. Am. A 29, 1436–1444 (2012).
[CrossRef]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

2011 (2)

C. David and F. J. G. de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115, 19470–19475 (2011).
[CrossRef]

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011).
[CrossRef]

2010 (2)

D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tenability,” Appl. Phys. Lett. 97, 041903 (2010).
[CrossRef]

C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

2009 (2)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097403 (2009).
[CrossRef]

B. Zhao and L. Gao, “Temperature-dependent Goos–Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17, 21433–21441 (2009).
[CrossRef]

2008 (2)

S. Palomba, L. Novotny, and R. E. Palmer, “Blue-shifted plasmon resonance of individual size-selected gold nanoparticles,” Opt. Commun. 281, 480–483 (2008).
[CrossRef]

J. B. Götte, A. Aiello, and J. P. Woerdman, “Loss-induced transition of the Goos–Hänchen effect for metals and dielectrics,” Opt. Express 16, 3961–3969 (2008).
[CrossRef]

2005 (1)

R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005).
[CrossRef]

2003 (1)

R. Chang, H. P. Chiang, P. T. Leung, and W. S. Tse, “Nonlocal electrodynamic effects in the optical excitation of the surface plasmon resonance,” Opt. Commun. 225, 353–361 (2003).
[CrossRef]

1996 (1)

R. Fuchs, R. G. Barrera, and J. L. Carrillo, “Spectral representations of the electron energy loss in composite media,” Phys. Rev. B 54, 12824–12834 (1996).
[CrossRef]

1993 (2)

L. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: silver versus simple metals,” Phys. Rev. B 4811317 (1993).
[CrossRef]

J. Tiggesbaumker, L. Koller, K. H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A 48, R1749–R1752 (1993).
[CrossRef]

1990 (1)

S. P. Apell, J. Giraldo, and S. Lundqvist, “Small metal particles: nonlocal optical properties and quantum-sizeeffects,” Phase Transit. 2626, 511–604 (1990).

1987 (1)

R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
[CrossRef]

1986 (1)

1985 (1)

W. Ekardt, “Size-dependent photoabsorption and photoemission of small metal particles,” Phys. Rev. B 31, 6360–6370 (1985).
[CrossRef]

1984 (2)

S. P. Apell, A. Ljungbert, and S. Lundqvist, “Nonlocal optical effects at metal surfaces,” Phys. Scr. 30, 367–383 (1984).
[CrossRef]

G. S. Agarwal and R. Inguva, “Effective-medium theory of a heterogeneous medium with individual grains having a nonlocal dielectric function,” Phys. Rev. B 30, 6108–6117 (1984).
[CrossRef]

1983 (2)

J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
[CrossRef]

A. Puri and D. N. Pattanayak, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983).
[CrossRef]

1982 (2)

P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
[CrossRef]

W. J. Wild and C. L. Giles, “Goos–Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099–2101 (1982).
[CrossRef]

1981 (1)

B. B. Dasgupta and R. Fuchs, “Polarizability of a small sphere including nonlocal effect,” Phys. Rev. B 24, 554–561 (1981).
[CrossRef]

1975 (1)

R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B 11, 2871–2876 (1975).
[CrossRef]

1970 (1)

N. D. Mermin, “Lindhard dielectric function in the relaxation time approximation,” Phys. Rev. B 1, 2362–2363 (1970).
[CrossRef]

1948 (1)

K. Artmann, “Berechnung der seitenversetzung des totalreflektierten stranles,” Ann. Phys. 2, 87–102 (1948).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentalerVersuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

1935 (1)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. 24, 636–664 (1935).
[CrossRef]

1906 (1)

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films, and in metallic solutions,” Philos. Trans. R. Soc. London 205, 237–288 (1906).
[CrossRef]

1904 (1)

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and R. Inguva, “Effective-medium theory of a heterogeneous medium with individual grains having a nonlocal dielectric function,” Phys. Rev. B 30, 6108–6117 (1984).
[CrossRef]

Aiello, A.

Apell, S. P.

S. P. Apell, J. Giraldo, and S. Lundqvist, “Small metal particles: nonlocal optical properties and quantum-sizeeffects,” Phase Transit. 2626, 511–604 (1990).

S. P. Apell, A. Ljungbert, and S. Lundqvist, “Nonlocal optical effects at metal surfaces,” Phys. Scr. 30, 367–383 (1984).
[CrossRef]

Artmann, K.

K. Artmann, “Berechnung der seitenversetzung des totalreflektierten stranles,” Ann. Phys. 2, 87–102 (1948).
[CrossRef]

Barrera, R. G.

R. Fuchs, R. G. Barrera, and J. L. Carrillo, “Spectral representations of the electron energy loss in composite media,” Phys. Rev. B 54, 12824–12834 (1996).
[CrossRef]

Birman, J. L.

A. Puri and J. L. Birman, “Goos–Hänchen beam shift at total internal reflection with application to spatially dispersive media,” J. Opt. Soc. Am. A 3, 543–549 (1986).
[CrossRef]

J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
[CrossRef]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. 24, 636–664 (1935).
[CrossRef]

Carrillo, J. L.

R. Fuchs, R. G. Barrera, and J. L. Carrillo, “Spectral representations of the electron energy loss in composite media,” Phys. Rev. B 54, 12824–12834 (1996).
[CrossRef]

Chang, R.

C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005).
[CrossRef]

R. Chang, H. P. Chiang, P. T. Leung, and W. S. Tse, “Nonlocal electrodynamic effects in the optical excitation of the surface plasmon resonance,” Opt. Commun. 225, 353–361 (2003).
[CrossRef]

Chen, C. W.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011).
[CrossRef]

C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

Chiang, H. P.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011).
[CrossRef]

C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005).
[CrossRef]

R. Chang, H. P. Chiang, P. T. Leung, and W. S. Tse, “Nonlocal electrodynamic effects in the optical excitation of the surface plasmon resonance,” Opt. Commun. 225, 353–361 (2003).
[CrossRef]

Chilkoti, A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Choy, T. C.

T. C. Choy, Effective Medium Theory (Clarendon, 1999).

Chung, H. Y.

C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

Ciracì, C.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Claro, F.

R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
[CrossRef]

Dasgupta, B. B.

B. B. Dasgupta and R. Fuchs, “Polarizability of a small sphere including nonlocal effect,” Phys. Rev. B 24, 554–561 (1981).
[CrossRef]

David, C.

C. David and F. J. G. de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115, 19470–19475 (2011).
[CrossRef]

de Abajo, F. J. G.

C. David and F. J. G. de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115, 19470–19475 (2011).
[CrossRef]

Ekardt, W.

W. Ekardt, “Size-dependent photoabsorption and photoemission of small metal particles,” Phys. Rev. B 31, 6360–6370 (1985).
[CrossRef]

Feibelman, P. J.

P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
[CrossRef]

Fernández-Domínguez, A. I.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Fuchs, R.

R. Fuchs, R. G. Barrera, and J. L. Carrillo, “Spectral representations of the electron energy loss in composite media,” Phys. Rev. B 54, 12824–12834 (1996).
[CrossRef]

R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
[CrossRef]

B. B. Dasgupta and R. Fuchs, “Polarizability of a small sphere including nonlocal effect,” Phys. Rev. B 24, 554–561 (1981).
[CrossRef]

Gao, D.

D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tenability,” Appl. Phys. Lett. 97, 041903 (2010).
[CrossRef]

Gao, L.

Giles, C. L.

W. J. Wild and C. L. Giles, “Goos–Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099–2101 (1982).
[CrossRef]

Giraldo, J.

S. P. Apell, J. Giraldo, and S. Lundqvist, “Small metal particles: nonlocal optical properties and quantum-sizeeffects,” Phase Transit. 2626, 511–604 (1990).

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentalerVersuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

Götte, J. B.

Gray, S. K.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097403 (2009).
[CrossRef]

Gu, Y. W.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentalerVersuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

Hill, R. T.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Huang, Y.

Inguva, R.

G. S. Agarwal and R. Inguva, “Effective-medium theory of a heterogeneous medium with individual grains having a nonlocal dielectric function,” Phys. Rev. B 30, 6108–6117 (1984).
[CrossRef]

Koller, L.

J. Tiggesbaumker, L. Koller, K. H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A 48, R1749–R1752 (1993).
[CrossRef]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Leung, P. T.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011).
[CrossRef]

C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005).
[CrossRef]

R. Chang, H. P. Chiang, P. T. Leung, and W. S. Tse, “Nonlocal electrodynamic effects in the optical excitation of the surface plasmon resonance,” Opt. Commun. 225, 353–361 (2003).
[CrossRef]

Liebsch, A.

J. Tiggesbaumker, L. Koller, K. H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A 48, R1749–R1752 (1993).
[CrossRef]

A. Liebsch, Electronic Excitations at Metal Surfaces (Plenum, 1997).

Liebsch, L.

L. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: silver versus simple metals,” Phys. Rev. B 4811317 (1993).
[CrossRef]

Ljungbert, A.

S. P. Apell, A. Ljungbert, and S. Lundqvist, “Nonlocal optical effects at metal surfaces,” Phys. Scr. 30, 367–383 (1984).
[CrossRef]

Lu, J. Y.

C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

Lundqvist, S.

S. P. Apell, J. Giraldo, and S. Lundqvist, “Small metal particles: nonlocal optical properties and quantum-sizeeffects,” Phase Transit. 2626, 511–604 (1990).

S. P. Apell, A. Ljungbert, and S. Lundqvist, “Nonlocal optical effects at metal surfaces,” Phys. Scr. 30, 367–383 (1984).
[CrossRef]

Mahan, G. D.

G. D. Mahan, Many-Particle Physics (Plenum, 1990), Chapter 5.

Maier, S. A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films, and in metallic solutions,” Philos. Trans. R. Soc. London 205, 237–288 (1906).
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S. Palomba, L. Novotny, and R. E. Palmer, “Blue-shifted plasmon resonance of individual size-selected gold nanoparticles,” Opt. Commun. 281, 480–483 (2008).
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[CrossRef]

Pendry, J. B.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
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A. Puri and J. L. Birman, “Goos–Hänchen beam shift at total internal reflection with application to spatially dispersive media,” J. Opt. Soc. Am. A 3, 543–549 (1986).
[CrossRef]

J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
[CrossRef]

A. Puri and D. N. Pattanayak, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983).
[CrossRef]

Ruppin, R.

R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B 11, 2871–2876 (1975).
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Sanchez, E. J.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011).
[CrossRef]

Schatz, G. C.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097403 (2009).
[CrossRef]

Smith, D. R.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

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J. Tiggesbaumker, L. Koller, K. H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A 48, R1749–R1752 (1993).
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C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005).
[CrossRef]

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R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005).
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[CrossRef]

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C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
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Appl. Phys. A (1)

C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010).
[CrossRef]

Appl. Phys. B (1)

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011).
[CrossRef]

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D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tenability,” Appl. Phys. Lett. 97, 041903 (2010).
[CrossRef]

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

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C. David and F. J. G. de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115, 19470–19475 (2011).
[CrossRef]

Opt. Commun. (2)

R. Chang, H. P. Chiang, P. T. Leung, and W. S. Tse, “Nonlocal electrodynamic effects in the optical excitation of the surface plasmon resonance,” Opt. Commun. 225, 353–361 (2003).
[CrossRef]

S. Palomba, L. Novotny, and R. E. Palmer, “Blue-shifted plasmon resonance of individual size-selected gold nanoparticles,” Opt. Commun. 281, 480–483 (2008).
[CrossRef]

Opt. Express (2)

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J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904).
[CrossRef]

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films, and in metallic solutions,” Philos. Trans. R. Soc. London 205, 237–288 (1906).
[CrossRef]

Phys. Rev. A (2)

W. J. Wild and C. L. Giles, “Goos–Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099–2101 (1982).
[CrossRef]

J. Tiggesbaumker, L. Koller, K. H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A 48, R1749–R1752 (1993).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

N. D. Mermin, “Lindhard dielectric function in the relaxation time approximation,” Phys. Rev. B 1, 2362–2363 (1970).
[CrossRef]

R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B 11, 2871–2876 (1975).
[CrossRef]

B. B. Dasgupta and R. Fuchs, “Polarizability of a small sphere including nonlocal effect,” Phys. Rev. B 24, 554–561 (1981).
[CrossRef]

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J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
[CrossRef]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097403 (2009).
[CrossRef]

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S. P. Apell, A. Ljungbert, and S. Lundqvist, “Nonlocal optical effects at metal surfaces,” Phys. Scr. 30, 367–383 (1984).
[CrossRef]

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Science (1)

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Solid State Commun. (1)

R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005).
[CrossRef]

Other (6)

T. C. Choy, Effective Medium Theory (Clarendon, 1999).

A. Liebsch, Electronic Excitations at Metal Surfaces (Plenum, 1997).

For the latest reviews, see the recent special issue on “Beam shifts,” J. Opt.15(1), 014001 (2013).

G. D. Mahan, Many-Particle Physics (Plenum, 1990), Chapter 5.

Note that in order to limit the number of figures in our paper, the plots of the dielectric functions are not included but are available upon request.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

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Figures (7)

Fig. 1.
Fig. 1.

Geometric configuration of the problem.

Fig. 2.
Fig. 2.

Nonlocal effects on the GH shifts from MNPs of different sizes for both of (a) MG and (b) B models. Solid lines are for MNPs of 5 nm in radius while dashed lines are for 10 nm MNPs. The dashed-dotted and dotted lines are results from local (Drude) model for the 5 and 10 nm MNPs, respectively. The incident wavelength is fixed at 1.55 μm and the volume fraction at 0.1. Only Model 1 is applied in this calculation.

Fig. 3.
Fig. 3.

Nonlocal effects for the MG model according to Model 1 (see text) over a broad range of MNP volume fractions at a wavelength of (a) 1.15 μm and (b) 0.632 μm. Solid lines are for nonlocal results and dotted lines are for local ones. The MNP size is fixed at 5 nm.

Fig. 4.
Fig. 4.

Similar to Fig. 3, but for results from Model 2 (see text) at a wavelength of (a) 1.15 μm and (b) 0.632 μm. The dr parameter is chosen as dr=0.12nm (solid line), dr=0 (i.e., local result, dashed line), and dr=0.12nm (dotted line), respectively, with the imaginary part of dr set at zero.

Fig. 5.
Fig. 5.

Similar to Fig. 3, but for the B model.

Fig. 6.
Fig. 6.

Similar to Fig. 4, but for the B model.

Fig. 7.
Fig. 7.

Study of the effect due to the imaginary part of the parameter dr. This ranges from 0.05 to +0.05 with the real part fixed at 0.12 nm. Volume fraction is fixed at 0.1.

Equations (11)

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ε¯MGεiε¯MG+2εi=fiεjεiεj+2εi,
(ε¯Bεi)fi2ε¯B+εi=(εjε¯B)fj2ε¯B+εj,
ε1(ω)=εrωP2ω(ω+iγ),
ξ(ω)=[2π(2+1)a0j2(ka)ε(k,ω)dk]1.
ε1=ξ1(ω)=[6πa0j12(ka)ε(k,ω)dk]1[3aF(a)]1,
ε1(ω)=ξ1(ω)=[3aF(a)+K1+εLK]1,
ε(k,ω)=εrωP2ω2+iωγβ2k2,
α=a3(ε1ε2)(1dr/a)ε1+2ε2+2(ε1ε2)dr/a,
ζε2ζ+2ε2=(ε1ε2)(1dr/a)ε1+2ε2+2(ε1ε2)dr/aA,
ζ=(1+2A1A)ε2.
D=1kdϕdθ,

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