Abstract

We study the behavior of plasmon resonances of metal nanospheres embedded in an absorbing medium. First-principles far-field computations based on the general Lorenz–Mie theory show that increasing absorption in the host medium broadens and suppresses plasmon resonances in the extinction and effective scattering efficiency factors and suppresses resonance features in the phase function. These effects of absorption are analogous to those on the morphology-dependent resonances of dielectric particles with large size parameters.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  5. M. Quinten and J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13(2), 89–96 (1996).
    [Crossref]
  6. A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6(2), 365–369 (1999).
    [Crossref]
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    [Crossref]
  8. W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4-6), 709–714 (2001).
    [Crossref]
  9. P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, and S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41(15), 2740–2759 (2002).
    [Crossref]
  10. G. Videen and W. Sun, “Yet another look at light scattering from particles in absorbing media,” Appl. Opt. 42(33), 6724–6727 (2003).
    [Crossref]
  11. W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83(3-4), 483–492 (2004).
    [Crossref]
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  21. B. Aernouts, R. Watté, R. van Beers, F. Delport, M. Merchiers, J. de Block, J. Lammertyn, and W. Saeys, “Flexible tool for simulating the bulk optical properties of polydisperse spherical particles in an absorbing host: experimental validation,” Opt. Express 22(17), 20223–20238 (2014).
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  22. M. I. Mishchenko, G. Videen, and P. Yang, “Extinction by a homogeneous spherical particle in an absorbing medium,” Opt. Lett. 42(23), 4873–4876 (2017).
    [Crossref]
  23. M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
    [Crossref]
  24. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
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  26. M. Quinten, Optical Properties of Nanoparticle Systems (Wiley-VCH, 2011).
  27. M. I. Mishchenko and P. Yang, “Far-field Lorenz–Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
    [Crossref]
  28. M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz–Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
    [Crossref]
  29. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
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    [Crossref]
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    [Crossref]
  32. N. V. Smith, “Optical constants of sodium and potassium from 0.5 to 4.0 eV by split-beam ellipsometry,” Phys. Rev. 183(3), 634–644 (1969).
    [Crossref]
  33. R. L. Peck, A. G. Brolo, and R. Gordon, “Absorption leads to narrower plasmonic resonances,” J. Opt. Soc. Am. B 36(8), F117–F122 (2019).
    [Crossref]
  34. C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
    [Crossref]
  35. M. I. Mishchenko and M. A. Yurkin, “Co- and counter-propagating wave effects in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer (2020).

2019 (1)

2018 (3)

M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
[Crossref]

M. I. Mishchenko and P. Yang, “Far-field Lorenz–Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz–Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

2017 (1)

2014 (1)

2007 (4)

2006 (3)

2004 (1)

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83(3-4), 483–492 (2004).
[Crossref]

2003 (1)

2002 (1)

2001 (2)

W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18(6), 1275–1278 (2001).
[Crossref]

W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4-6), 709–714 (2001).
[Crossref]

1999 (1)

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6(2), 365–369 (1999).
[Crossref]

1996 (1)

M. Quinten and J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13(2), 89–96 (1996).
[Crossref]

1995 (1)

1993 (1)

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3(3), 147–156 (1993).
[Crossref]

1979 (2)

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

1977 (1)

1974 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1969 (1)

N. V. Smith, “Optical constants of sodium and potassium from 0.5 to 4.0 eV by split-beam ellipsometry,” Phys. Rev. 183(3), 634–644 (1969).
[Crossref]

Aernouts, B.

Baillis, D.

Baum, B. A.

Berg, M. J.

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” Prog. Electromagn. Res. Symp. Proc. Taipei, pp. 717–721 (2013).

Biscans, B.

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” Prog. Electromagn. Res. Symp. Proc. Taipei, pp. 717–721 (2013).

Bohren, C. F.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Brolo, A. G.

Bruscaglioni, P.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3(3), 147–156 (1993).
[Crossref]

Calvo-Perez, O.

Ceolato, R.

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” Prog. Electromagn. Res. Symp. Proc. Taipei, pp. 717–721 (2013).

Christensen, N. J.

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz–Mie theory,” ACM Trans. Graph. 26(3), 60 (2007).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Chylek, P.

W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18(6), 1275–1278 (2001).
[Crossref]

W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4-6), 709–714 (2001).
[Crossref]

Chýlek, P.

de Block, J.

Delport, F.

Dlugach, J. M.

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz–Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
[Crossref]

Dombrovsky, L. A.

L. A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach (Begell House, 2010).

Durant, S.

Frisvad, J. R.

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz–Mie theory,” ACM Trans. Graph. 26(3), 60 (2007).
[Crossref]

Fu, Q.

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100(1-3), 137–142 (2006).
[Crossref]

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83(3-4), 483–492 (2004).
[Crossref]

Gao, B.-C.

Gilra, D. P.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

Gordon, R.

Gratz, M.

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6(2), 365–369 (1999).
[Crossref]

Greffet, J.-J.

Hu, Y. X.

Huang, H.-L.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Ismaelli, A.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3(3), 147–156 (1993).
[Crossref]

Jensen, H. W.

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz–Mie theory,” ACM Trans. Graph. 26(3), 60 (2007).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kreibig, U.

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6(2), 365–369 (1999).
[Crossref]

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

Lammertyn, J.

Lebedev, A. N.

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6(2), 365–369 (1999).
[Crossref]

Lock, J. A.

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz–Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

Loeb, N. G.

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83(3-4), 483–492 (2004).
[Crossref]

Merchiers, M.

Mishchenko, M. I.

M. I. Mishchenko and P. Yang, “Far-field Lorenz–Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz–Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

M. I. Mishchenko, G. Videen, and P. Yang, “Extinction by a homogeneous spherical particle in an absorbing medium,” Opt. Lett. 42(23), 4873–4876 (2017).
[Crossref]

M. I. Mishchenko, “Electromagnetic scattering by a fixed finite object embedded in an absorbing medium,” Opt. Express 15(20), 13188–13202 (2007).
[Crossref]

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, and S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41(15), 2740–2759 (2002).
[Crossref]

M. I. Mishchenko and M. A. Yurkin, “Co- and counter-propagating wave effects in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer (2020).

Mundy, W. C.

Park, S. K.

Peck, R. L.

Pilon, L.

Platnick, S. E.

Quinten, M.

M. Quinten and J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13(2), 89–96 (1996).
[Crossref]

M. Quinten, Optical Properties of Nanoparticle Systems (Wiley-VCH, 2011).

Rakic, A. D.

Randrianalisoa, J.

Riviere, N.

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” Prog. Electromagn. Res. Symp. Proc. Taipei, pp. 717–721 (2013).

Rostalski, J.

M. Quinten and J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13(2), 89–96 (1996).
[Crossref]

Roux, J. A.

Saeys, W.

Smith, A. M.

Smith, N. V.

N. V. Smith, “Optical constants of sodium and potassium from 0.5 to 4.0 eV by split-beam ellipsometry,” Phys. Rev. 183(3), 634–644 (1969).
[Crossref]

Stenzel, O.

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6(2), 365–369 (1999).
[Crossref]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Sudiarta, W.

W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18(6), 1275–1278 (2001).
[Crossref]

W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4-6), 709–714 (2001).
[Crossref]

Sun, W.

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100(1-3), 137–142 (2006).
[Crossref]

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83(3-4), 483–492 (2004).
[Crossref]

G. Videen and W. Sun, “Yet another look at light scattering from particles in absorbing media,” Appl. Opt. 42(33), 6724–6727 (2003).
[Crossref]

Tsay, S.-C.

van Beers, R.

Videen, G.

Vollmer, M.

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

Vukadinovic, N.

Watté, R.

Winker, D. M.

Wiscombe, W. J.

Yang, P.

Yin, J.

Yurkin, M. A.

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz–Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

M. I. Mishchenko and M. A. Yurkin, “Co- and counter-propagating wave effects in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer (2020).

Zaccanti, G.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3(3), 147–156 (1993).
[Crossref]

ACM Trans. Graph. (1)

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz–Mie theory,” ACM Trans. Graph. 26(3), 60 (2007).
[Crossref]

Appl. Opt. (3)

Eur. Phys. J. D (1)

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6(2), 365–369 (1999).
[Crossref]

J. Colloid Interface Sci. (2)

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Am. B (1)

J. Quant. Spectrosc. Radiat. Transfer (6)

M. I. Mishchenko and P. Yang, “Far-field Lorenz–Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz–Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4-6), 709–714 (2001).
[Crossref]

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83(3-4), 483–492 (2004).
[Crossref]

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100(1-3), 137–142 (2006).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Part. Part. Syst. Charact. (1)

M. Quinten and J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13(2), 89–96 (1996).
[Crossref]

Phys. Rev. (1)

N. V. Smith, “Optical constants of sodium and potassium from 0.5 to 4.0 eV by split-beam ellipsometry,” Phys. Rev. 183(3), 634–644 (1969).
[Crossref]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Waves Random Media (1)

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3(3), 147–156 (1993).
[Crossref]

Other (7)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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

M. Quinten, Optical Properties of Nanoparticle Systems (Wiley-VCH, 2011).

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Figures (5)

Fig. 1.
Fig. 1. The real (left-hand panel) and imaginary (right-hand panel) parts of the spectral refractive indices of the four metals used in this study.

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Fig. 2.
Fig. 2. Spectral extinction efficiency factors of 10-nm spherical particles made of noble and Drude metals.

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Fig. 3.
Fig. 3. Spectral scattering efficiency factors of 10-nm spherical particles made of noble and Drude metals.

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Fig. 4.
Fig. 4. Spectral extinction and effective scattering efficiency factors of the 10-nm spherical Na particle.

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Fig. 5.
Fig. 5. Spectral dependence of the phase function of the 10-nm spherical Al particle. The refractive indices of the host medium are ${m_1} = 1.33$ (left-hand panel) and ${m_1} = 1.33 + \textrm{i}0.3$ (right-hand panel).

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Equations (7)

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m 1 = m 1 ′ + i m 1 ′ ′
m 2 = m 2 ′ + i m 2 ′ ′ ,
F ( Θ ) = C sca eff 4 π F ~ ( Θ ) ,
C sca eff = 2 π ∫   0 π d Θ  sin Θ F 11 ( Θ )
1 2 ∫   0 π d Θ  sin Θ F ~ 11 ( Θ ) = 1 ,
Q ext = C ext π R 2
Q sca eff = C sca eff π R 2