Abstract

Metal nanoshells, which consist of nanometer-scale dielectric cores surrounded by thin metallic shells, have been designed and studied for their linear optical responses. The plasmon resonance of metal nanoshells displays geometric tunability controlled by the ratio of shell thickness either to the core radius or to the total radius of the particle. Using Mie theory the surface plasmon resonance (SPR) of metallic nanoshells (Au, Ag, Cu) is studied for different geometries and physical environments. Considering a final radius of about 20nm, the SPR peak position can be tuned from 510nm (2.43eV)to660nm (1.88eV) for Au, from 360nm (3.44eV)to560nm (2.21eV) for Ag, and from 553nm (2.24eV)to655nm (1.89eV) for Cu, just by varying the ratio tRShell and the environments inside and outside. With the decrease of the tRShell ratio the SPR peak position gets redshifted exponentially and the shift is higher for a higher refractive index surroundings. The plasmon linewidth strongly depends on the surface scattering process and its FWHM increases with the reduction of shell thickness.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  2. R. D. Averitt, S. L. Westcott, and N. J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Soc. Am. B 16, 1824-1832 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  9. Y. Sun and Y. Xia, “Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes,” Anal. Chem. 74, 5297-5305 (2002).
    [CrossRef] [PubMed]
  10. J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257-259 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
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  16. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. A. Curry, G. Nusz, A. Chilkoti, and A. Wax, “Substrate effect on refractive index dependence of plasmon resonance for individual silver nanoparticles observed using darkfield microspectroscopy,” Opt. Express 13, 2668-2677 (2005).
    [CrossRef] [PubMed]
  25. H. Wang, F. Tam, N. K. Grady, and N. J. Halas, “Cu nanoshells: effects of interband transitions on the nanoparticle plasmon resonance,” J. Phys. Chem. B 109, 18218-18222 (2005).
    [CrossRef]

2006

A. M. Schwartzberg, T. Y. Olson, Ch. E. Talley, and J. Z. Zhang, “Synthesis, characterization, and tunable optical properties of hollow gold nanospheres,” J. Phys. Chem. B 110, 19935-19944 (2006).
[CrossRef] [PubMed]

2005

C. Noguez, “Optical properties of isolated and supported metal nanoparticles,” Opt. Mater. 27, 1204-1211 (2005).
[CrossRef]

A. Curry, G. Nusz, A. Chilkoti, and A. Wax, “Substrate effect on refractive index dependence of plasmon resonance for individual silver nanoparticles observed using darkfield microspectroscopy,” Opt. Express 13, 2668-2677 (2005).
[CrossRef] [PubMed]

H. Wang, F. Tam, N. K. Grady, and N. J. Halas, “Cu nanoshells: effects of interband transitions on the nanoparticle plasmon resonance,” J. Phys. Chem. B 109, 18218-18222 (2005).
[CrossRef]

2003

E. Pordan and P. Nordlander, “Structural tunability of the plasmon resonances in metallic nanoshells,” Nano Lett. 3, 543-547 (2003).
[CrossRef]

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257-259 (2003).
[CrossRef]

E. Prodan, P. Nordlander, and N. J. Halas, “Effects of dielectric screening on the optical properties of metallic nanoshells,” Chem. Phys. Lett. 368, 94-101 (2003).
[CrossRef]

2002

E. Prodan, A. Lee, and P. Nordlander, “The effect of a dielectric core and embedding medium on the polarizability of metallic nanoshells,” Chem. Phys. Lett. 360, 325-332 (2002).
[CrossRef]

Y. Sun and Y. Xia, “Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes,” Anal. Chem. 74, 5297-5305 (2002).
[CrossRef] [PubMed]

2001

G. D. Hale, J. B. Jackson, O. E. Shmakova, T. R. Lee, and N. J. Halas, “Enhancing the active lifetime of luminescent semiconducting polymers via doping with metal nanoshells,” Appl. Phys. Lett. 78, 1502-1504 (2001).
[CrossRef]

S. Sershen, S. L. Westcott, J. L. West, and N. J. Halas, “An opto-mechanical nanoshell-polymer composite,” Appl. Phys. B 73, 379-381 (2001).
[CrossRef]

2000

S. Sershen, S. L. Westcott, N. J. Halas, and J. L. West, “Temperature-sensitive polymer-nanoshell composites for photothermally modulated drug delivery,” J. Biomed. Mater. Res. 51, 293-298 (2000).
[CrossRef] [PubMed]

1999

R. D. Averitt, S. L. Westcott, and N. J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Soc. Am. B 16, 1824-1832 (1999).
[CrossRef]

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

1996

T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. El-Sayed, “Shape-controlled synthesis of colloidal platinum nanoparticles,” Science 272, 1924-1926 (1996).
[CrossRef] [PubMed]

1985

1981

1972

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

1951

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242-1246 (1951).
[CrossRef]

1908

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaller metallösungen,” Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Ackerman, T. P.

Aden, A. L.

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242-1246 (1951).
[CrossRef]

Ahmadi, T. S.

T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. El-Sayed, “Shape-controlled synthesis of colloidal platinum nanoparticles,” Science 272, 1924-1926 (1996).
[CrossRef] [PubMed]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, 1979).

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt-Saunders, 1976).

Averitt, R. D.

Bohren, C. F.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Chilkoti, A.

Christy, R. W.

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

Curry, A.

El-Sayed, M. A.

T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. El-Sayed, “Shape-controlled synthesis of colloidal platinum nanoparticles,” Science 272, 1924-1926 (1996).
[CrossRef] [PubMed]

Flytzanis, C.

Grady, N. K.

H. Wang, F. Tam, N. K. Grady, and N. J. Halas, “Cu nanoshells: effects of interband transitions on the nanoparticle plasmon resonance,” J. Phys. Chem. B 109, 18218-18222 (2005).
[CrossRef]

Green, T. C.

T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. El-Sayed, “Shape-controlled synthesis of colloidal platinum nanoparticles,” Science 272, 1924-1926 (1996).
[CrossRef] [PubMed]

Halas, N. J.

H. Wang, F. Tam, N. K. Grady, and N. J. Halas, “Cu nanoshells: effects of interband transitions on the nanoparticle plasmon resonance,” J. Phys. Chem. B 109, 18218-18222 (2005).
[CrossRef]

E. Prodan, P. Nordlander, and N. J. Halas, “Effects of dielectric screening on the optical properties of metallic nanoshells,” Chem. Phys. Lett. 368, 94-101 (2003).
[CrossRef]

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257-259 (2003).
[CrossRef]

S. Sershen, S. L. Westcott, J. L. West, and N. J. Halas, “An opto-mechanical nanoshell-polymer composite,” Appl. Phys. B 73, 379-381 (2001).
[CrossRef]

G. D. Hale, J. B. Jackson, O. E. Shmakova, T. R. Lee, and N. J. Halas, “Enhancing the active lifetime of luminescent semiconducting polymers via doping with metal nanoshells,” Appl. Phys. Lett. 78, 1502-1504 (2001).
[CrossRef]

S. Sershen, S. L. Westcott, N. J. Halas, and J. L. West, “Temperature-sensitive polymer-nanoshell composites for photothermally modulated drug delivery,” J. Biomed. Mater. Res. 51, 293-298 (2000).
[CrossRef] [PubMed]

R. D. Averitt, S. L. Westcott, and N. J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Soc. Am. B 16, 1824-1832 (1999).
[CrossRef]

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Hale, G. D.

G. D. Hale, J. B. Jackson, O. E. Shmakova, T. R. Lee, and N. J. Halas, “Enhancing the active lifetime of luminescent semiconducting polymers via doping with metal nanoshells,” Appl. Phys. Lett. 78, 1502-1504 (2001).
[CrossRef]

Henglein, A.

T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. El-Sayed, “Shape-controlled synthesis of colloidal platinum nanoparticles,” Science 272, 1924-1926 (1996).
[CrossRef] [PubMed]

Hirsch, L. R.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257-259 (2003).
[CrossRef]

Huffman, D. R.

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

Jackson, J. B.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257-259 (2003).
[CrossRef]

G. D. Hale, J. B. Jackson, O. E. Shmakova, T. R. Lee, and N. J. Halas, “Enhancing the active lifetime of luminescent semiconducting polymers via doping with metal nanoshells,” Appl. Phys. Lett. 78, 1502-1504 (2001).
[CrossRef]

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Johnson, P. B.

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

Kerker, M.

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242-1246 (1951).
[CrossRef]

Lee, A.

E. Prodan, A. Lee, and P. Nordlander, “The effect of a dielectric core and embedding medium on the polarizability of metallic nanoshells,” Chem. Phys. Lett. 360, 325-332 (2002).
[CrossRef]

Lee, T. R.

G. D. Hale, J. B. Jackson, O. E. Shmakova, T. R. Lee, and N. J. Halas, “Enhancing the active lifetime of luminescent semiconducting polymers via doping with metal nanoshells,” Appl. Phys. Lett. 78, 1502-1504 (2001).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt-Saunders, 1976).

Mie, G.

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaller metallösungen,” Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Noguez, C.

C. Noguez, “Optical properties of isolated and supported metal nanoparticles,” Opt. Mater. 27, 1204-1211 (2005).
[CrossRef]

Nordlander, P.

E. Pordan and P. Nordlander, “Structural tunability of the plasmon resonances in metallic nanoshells,” Nano Lett. 3, 543-547 (2003).
[CrossRef]

E. Prodan, P. Nordlander, and N. J. Halas, “Effects of dielectric screening on the optical properties of metallic nanoshells,” Chem. Phys. Lett. 368, 94-101 (2003).
[CrossRef]

E. Prodan, A. Lee, and P. Nordlander, “The effect of a dielectric core and embedding medium on the polarizability of metallic nanoshells,” Chem. Phys. Lett. 360, 325-332 (2002).
[CrossRef]

Nusz, G.

Oldenburg, S. J.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Olson, T. Y.

A. M. Schwartzberg, T. Y. Olson, Ch. E. Talley, and J. Z. Zhang, “Synthesis, characterization, and tunable optical properties of hollow gold nanospheres,” J. Phys. Chem. B 110, 19935-19944 (2006).
[CrossRef] [PubMed]

Pordan, E.

E. Pordan and P. Nordlander, “Structural tunability of the plasmon resonances in metallic nanoshells,” Nano Lett. 3, 543-547 (2003).
[CrossRef]

Prodan, E.

E. Prodan, P. Nordlander, and N. J. Halas, “Effects of dielectric screening on the optical properties of metallic nanoshells,” Chem. Phys. Lett. 368, 94-101 (2003).
[CrossRef]

E. Prodan, A. Lee, and P. Nordlander, “The effect of a dielectric core and embedding medium on the polarizability of metallic nanoshells,” Chem. Phys. Lett. 360, 325-332 (2002).
[CrossRef]

Ricard, D.

Roussignol, P.

Schwartzberg, A. M.

A. M. Schwartzberg, T. Y. Olson, Ch. E. Talley, and J. Z. Zhang, “Synthesis, characterization, and tunable optical properties of hollow gold nanospheres,” J. Phys. Chem. B 110, 19935-19944 (2006).
[CrossRef] [PubMed]

Sershen, S.

S. Sershen, S. L. Westcott, J. L. West, and N. J. Halas, “An opto-mechanical nanoshell-polymer composite,” Appl. Phys. B 73, 379-381 (2001).
[CrossRef]

S. Sershen, S. L. Westcott, N. J. Halas, and J. L. West, “Temperature-sensitive polymer-nanoshell composites for photothermally modulated drug delivery,” J. Biomed. Mater. Res. 51, 293-298 (2000).
[CrossRef] [PubMed]

Shmakova, O. E.

G. D. Hale, J. B. Jackson, O. E. Shmakova, T. R. Lee, and N. J. Halas, “Enhancing the active lifetime of luminescent semiconducting polymers via doping with metal nanoshells,” Appl. Phys. Lett. 78, 1502-1504 (2001).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Sun, Y.

Y. Sun and Y. Xia, “Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes,” Anal. Chem. 74, 5297-5305 (2002).
[CrossRef] [PubMed]

Talley, Ch. E.

A. M. Schwartzberg, T. Y. Olson, Ch. E. Talley, and J. Z. Zhang, “Synthesis, characterization, and tunable optical properties of hollow gold nanospheres,” J. Phys. Chem. B 110, 19935-19944 (2006).
[CrossRef] [PubMed]

Tam, F.

H. Wang, F. Tam, N. K. Grady, and N. J. Halas, “Cu nanoshells: effects of interband transitions on the nanoparticle plasmon resonance,” J. Phys. Chem. B 109, 18218-18222 (2005).
[CrossRef]

Toon, O. B.

Wang, H.

H. Wang, F. Tam, N. K. Grady, and N. J. Halas, “Cu nanoshells: effects of interband transitions on the nanoparticle plasmon resonance,” J. Phys. Chem. B 109, 18218-18222 (2005).
[CrossRef]

Wang, Z. L.

T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. El-Sayed, “Shape-controlled synthesis of colloidal platinum nanoparticles,” Science 272, 1924-1926 (1996).
[CrossRef] [PubMed]

Wax, A.

West, J. L.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257-259 (2003).
[CrossRef]

S. Sershen, S. L. Westcott, J. L. West, and N. J. Halas, “An opto-mechanical nanoshell-polymer composite,” Appl. Phys. B 73, 379-381 (2001).
[CrossRef]

S. Sershen, S. L. Westcott, N. J. Halas, and J. L. West, “Temperature-sensitive polymer-nanoshell composites for photothermally modulated drug delivery,” J. Biomed. Mater. Res. 51, 293-298 (2000).
[CrossRef] [PubMed]

Westcott, S. L.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257-259 (2003).
[CrossRef]

S. Sershen, S. L. Westcott, J. L. West, and N. J. Halas, “An opto-mechanical nanoshell-polymer composite,” Appl. Phys. B 73, 379-381 (2001).
[CrossRef]

S. Sershen, S. L. Westcott, N. J. Halas, and J. L. West, “Temperature-sensitive polymer-nanoshell composites for photothermally modulated drug delivery,” J. Biomed. Mater. Res. 51, 293-298 (2000).
[CrossRef] [PubMed]

R. D. Averitt, S. L. Westcott, and N. J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Soc. Am. B 16, 1824-1832 (1999).
[CrossRef]

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Xia, Y.

Y. Sun and Y. Xia, “Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes,” Anal. Chem. 74, 5297-5305 (2002).
[CrossRef] [PubMed]

Zhang, J. Z.

A. M. Schwartzberg, T. Y. Olson, Ch. E. Talley, and J. Z. Zhang, “Synthesis, characterization, and tunable optical properties of hollow gold nanospheres,” J. Phys. Chem. B 110, 19935-19944 (2006).
[CrossRef] [PubMed]

Anal. Chem.

Y. Sun and Y. Xia, “Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes,” Anal. Chem. 74, 5297-5305 (2002).
[CrossRef] [PubMed]

Ann. Phys.

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaller metallösungen,” Ann. Phys. 25, 377-445 (1908).
[CrossRef]

Appl. Opt.

Appl. Phys. B

S. Sershen, S. L. Westcott, J. L. West, and N. J. Halas, “An opto-mechanical nanoshell-polymer composite,” Appl. Phys. B 73, 379-381 (2001).
[CrossRef]

Appl. Phys. Lett.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, “Controlling the surface enhanced Raman effect via the nanoshell geometry,” Appl. Phys. Lett. 82, 257-259 (2003).
[CrossRef]

G. D. Hale, J. B. Jackson, O. E. Shmakova, T. R. Lee, and N. J. Halas, “Enhancing the active lifetime of luminescent semiconducting polymers via doping with metal nanoshells,” Appl. Phys. Lett. 78, 1502-1504 (2001).
[CrossRef]

Chem. Phys. Lett.

E. Prodan, A. Lee, and P. Nordlander, “The effect of a dielectric core and embedding medium on the polarizability of metallic nanoshells,” Chem. Phys. Lett. 360, 325-332 (2002).
[CrossRef]

E. Prodan, P. Nordlander, and N. J. Halas, “Effects of dielectric screening on the optical properties of metallic nanoshells,” Chem. Phys. Lett. 368, 94-101 (2003).
[CrossRef]

J. Appl. Phys.

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242-1246 (1951).
[CrossRef]

J. Biomed. Mater. Res.

S. Sershen, S. L. Westcott, N. J. Halas, and J. L. West, “Temperature-sensitive polymer-nanoshell composites for photothermally modulated drug delivery,” J. Biomed. Mater. Res. 51, 293-298 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

J. Phys. Chem. B

H. Wang, F. Tam, N. K. Grady, and N. J. Halas, “Cu nanoshells: effects of interband transitions on the nanoparticle plasmon resonance,” J. Phys. Chem. B 109, 18218-18222 (2005).
[CrossRef]

A. M. Schwartzberg, T. Y. Olson, Ch. E. Talley, and J. Z. Zhang, “Synthesis, characterization, and tunable optical properties of hollow gold nanospheres,” J. Phys. Chem. B 110, 19935-19944 (2006).
[CrossRef] [PubMed]

Nano Lett.

E. Pordan and P. Nordlander, “Structural tunability of the plasmon resonances in metallic nanoshells,” Nano Lett. 3, 543-547 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mater.

C. Noguez, “Optical properties of isolated and supported metal nanoparticles,” Opt. Mater. 27, 1204-1211 (2005).
[CrossRef]

Phys. Rev. B

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

Science

T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. El-Sayed, “Shape-controlled synthesis of colloidal platinum nanoparticles,” Science 272, 1924-1926 (1996).
[CrossRef] [PubMed]

Other

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt-Saunders, 1976).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

G. Arfken, Mathematical Methods for Physicists (Academic, 1979).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the metal nanoshell geometries used for calculating linear optical properties.

Fig. 2
Fig. 2

Simulated extinction spectra for Ag nanoshells (a) in vacuum, with constant thickness ( 5 nm ) and varying R Core ; (b) in vacuum, with constant R Core ( 10 nm ) and varying thickness; (c) in vacuum, with constant R Shell ( 20 nm ) and varying R Core ; (d) in water, with constant thickness ( 5 nm ) and varying R Core ; (e) in water, with constant R Core ( 10 nm ) and varying thickness; (f) in water, with constant R Shell ( 20 nm ) and varying R Core ; (g) in silica, with constant thickness ( 5 nm ) and varying R Core ; (h) in silica, with constant R Core ( 10 nm ) and varying thickness; (i) in silica, with constant R Shell ( 20 nm ) and varying R Core .

Fig. 3
Fig. 3

Simulated extinction spectra for Au nanoshells (a) in vacuum, with constant thickness ( 5 nm ) and varying R Core ; (b) in vacuum, with constant R Core ( 10 nm ) and varying thickness; (c) in vacuum, with constant R Shell ( 20 nm ) and varying R Core ; (d) in water, with constant thickness ( 5 nm ) and varying R Core ; (e) in water, with constant R Core ( 10 nm ) and varying thickness; (f) in water, with constant R Shell ( 20 nm ) and varying R Core ; (g) in silica, with constant thickness ( 5 nm ) and varying R Core ; (h) in silica, with constant R Core ( 10 nm ) and varying thickness, (i) in silica, with constant R Shell ( 20 nm ) and varying R Core .

Fig. 4
Fig. 4

Simulated extinction spectra for Cu nanoshells (a) in vacuum, with constant thickness ( 5 nm ) and varying R Core ; (b) in vacuum, with constant R Core ( 10 nm ) and varying thickness; (c) in vacuum, with constant R Shell ( 20 nm ) and varying R Core ; (d) in water, with constant thickness ( 5 nm ) and varying R Core ; (e) in water, with constant R Core ( 10 nm ) and varying thickness; (f) in water, with constant R Shell ( 20 nm ) and varying R Core ; (g) in silica, with constant thickness ( 5 nm ) and varying R Core ; (h) in silica, with constant R Core ( 10 nm ) and varying thickness; (i) in silica, with constant R Shell ( 20 nm ) and varying R Core .

Fig. 5
Fig. 5

Summary of the SPR peak position (continuous curves) and intensity (dashed curves) behaviors for the Ag, Au, and Cu nanoshells (in rows) keeping the t, R Core , and R Shell (in columns) fixed.

Fig. 6
Fig. 6

Bulk refractive index (experimental) of Ag (squares), Au (circles), and Cu (triangles) in the region of interest (from [23]).

Equations (17)

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x = k R = 2 π n R λ ,
m = n p n ,
σ ext = 2 π k 2 l = 1 ( 2 l + 1 ) Re { a l + b l } ,
σ sca = 2 π k 2 l = 1 ( 2 l + 1 ) ( a l 2 + b l 2 ) ,
σ abs = σ ext σ sca .
a l = m ψ l ( m x ) ψ l ( x ) ψ l ( m x ) ψ l ( x ) m ψ l ( m x ) ξ l ( x ) ψ l ( m x ) ξ l ( x ) ,
b l = ψ l ( m x ) ψ l ( x ) m ψ l ( m x ) ψ l ( x ) ψ l ( m x ) ξ l ( x ) m ψ l ( m x ) ξ l ( x ) .
ψ l ( z ) = z j l ( z ) , ξ l ( z ) = z h l ( z ) ,
a l = ψ l ( y ) [ ψ l ( m 2 y ) A l χ l ( m 2 y ) ] ψ l ( y ) [ ψ l ( m 2 y ) A l χ l ( m 2 y ) ] ξ l ( y ) [ ψ l ( m 2 y ) A l χ l ( m 2 y ) ] ξ l ( y ) [ ψ l ( m 2 y ) A l χ l ( m 2 y ) ] ,
b l = m 2 ψ l ( y ) [ ψ l ( m 2 y ) B l χ l ( m 2 y ) ] ψ l ( y ) [ ψ l ( m 2 y ) B l χ l ( m 2 y ) ] m 2 ξ l ( y ) [ ψ l ( m 2 y ) B l χ l ( m 2 y ) ] ξ l ( y ) [ ψ l ( m 2 y ) B l χ l ( m 2 y ) ] ,
A l = m 2 ψ l ( m 2 x ) ψ l ( m 1 x ) m 1 ψ l ( m 2 x ) ψ l ( m 1 x ) m 2 χ l ( m 2 x ) ψ l ( m 1 x ) m 1 χ l ( m 2 x ) ψ l ( m 1 x ) ,
B l = m 2 ψ l ( m 1 x ) ψ l ( m 2 x ) m 1 ψ l ( m 2 x ) ψ l ( m 1 x ) m 2 χ l ( m 2 x ) ψ l ( m 1 x ) m 1 ψ l ( m 1 x ) χ l ( m 2 x ) ,
x = k R c , y = k R s h .
ε exp ( ω ) = ε inter ( ω ) + ε intra ( ω ) .
ε intra ( ω ) = 1 ω p 2 ω 2 + i ω Γ ,
Γ = Γ bulk + Γ R = v F λ e + v F R .
ε ( ω , R ) = ε inter ( ω ) + ε intra NP ( ω , R ) = ε exp ( ω ) ε intra ( ω ) + ε intra NP ( ω , R ) = ε exp ( ω ) + ω p 2 ω 2 + i ω Γ bulk ω p 2 ω 2 + i ω ( Γ bulk + v F R ) .

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