Abstract

We present a theoretical study of the dispersion relation of surface-plasmon resonances of mesoscopic metal–dielectric–metal microspheres. By analyzing the solutions to Maxwell’s equations, we obtain a simple geometric condition for which the system exhibits a band of surface-plasmon modes whose resonant frequencies are weakly dependent on the multipole number. Using a modified Mie calculation, we find that a large number of modes belonging to this flat-dispersion band can be excited simultaneously by a plane wave, thus enhancing the absorption cross section. We demonstrate that the enhanced absorption peak of the sphere is geometrically tunable over the entire visible range.

© 2006 Optical Society of America

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  1. K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
    [CrossRef] [PubMed]
  2. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, Phys. Rev. Lett. 94, 017402 (2005).
    [CrossRef] [PubMed]
  3. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
    [CrossRef] [PubMed]
  4. J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, Appl. Phys. Lett. 82, 257 (2003).
    [CrossRef]
  5. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
    [CrossRef] [PubMed]
  6. R. Ruppin, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, 1982), pp. 345-398.
  7. H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, Appl. Phys. Lett. 84, 4421 (2004).
    [CrossRef]
  8. P. Gadenne, F. Brouers, V. M. Shalaev, and A. K. Sarychev, J. Opt. Soc. Am. B 15, 68 (1998).
    [CrossRef]
  9. K. P. Velikov, G. E. Zegers, and A. van Blaaderen, Langmuir 19, 1384 (2003).
    [CrossRef]
  10. O. B. Toon and T. P. Ackerman, Appl. Opt. 20, 3657 (1981).
    [CrossRef] [PubMed]
  11. T. Kaiser and G. Schweiger, Comput. Phys. 7, 682 (1993).
    [CrossRef]
  12. W. Yang, Appl. Opt. 42, 1710 (2003).
    [CrossRef] [PubMed]
  13. H. Du, Appl. Opt. 43, 1951 (2004).
    [CrossRef] [PubMed]
  14. V. E. Cachorro and L. L. Salcedo, J. Electromagn. Waves Appl. 5, 913 (1991).
    [CrossRef]
  15. E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

2005

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

2004

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, Appl. Phys. Lett. 84, 4421 (2004).
[CrossRef]

H. Du, Appl. Opt. 43, 1951 (2004).
[CrossRef] [PubMed]

2003

W. Yang, Appl. Opt. 42, 1710 (2003).
[CrossRef] [PubMed]

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

K. P. Velikov, G. E. Zegers, and A. van Blaaderen, Langmuir 19, 1384 (2003).
[CrossRef]

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, Appl. Phys. Lett. 82, 257 (2003).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

1998

1993

T. Kaiser and G. Schweiger, Comput. Phys. 7, 682 (1993).
[CrossRef]

1991

V. E. Cachorro and L. L. Salcedo, J. Electromagn. Waves Appl. 5, 913 (1991).
[CrossRef]

1981

Ackerman, T. P.

Bergman, D. J.

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

Boardman, A. D.

R. Ruppin, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, 1982), pp. 345-398.

Brongersma, M. L.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, Appl. Phys. Lett. 84, 4421 (2004).
[CrossRef]

Brouers, F.

Cachorro, V. E.

V. E. Cachorro and L. L. Salcedo, J. Electromagn. Waves Appl. 5, 913 (1991).
[CrossRef]

Du, H.

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Fan, S.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, Appl. Phys. Lett. 84, 4421 (2004).
[CrossRef]

Fromm, D. P.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Gadenne, P.

Halas, N. J.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, Appl. Phys. Lett. 82, 257 (2003).
[CrossRef]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Hirsch, L. R.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, Appl. Phys. Lett. 82, 257 (2003).
[CrossRef]

Jackson, J. B.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, Appl. Phys. Lett. 82, 257 (2003).
[CrossRef]

Kaiser, T.

T. Kaiser and G. Schweiger, Comput. Phys. 7, 682 (1993).
[CrossRef]

Kino, G. S.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Li, K.

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Moerner, W. E.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Nordlander, P.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

Ruppin, R.

R. Ruppin, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, 1982), pp. 345-398.

Salcedo, L. L.

V. E. Cachorro and L. L. Salcedo, J. Electromagn. Waves Appl. 5, 913 (1991).
[CrossRef]

Sarychev, A. K.

Schuck, P. J.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Schweiger, G.

T. Kaiser and G. Schweiger, Comput. Phys. 7, 682 (1993).
[CrossRef]

Shalaev, V. M.

Shin, H.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, Appl. Phys. Lett. 84, 4421 (2004).
[CrossRef]

Stockman, M. I.

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

Sundaramurthy, A.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Toon, O. B.

van Blaaderen, A.

K. P. Velikov, G. E. Zegers, and A. van Blaaderen, Langmuir 19, 1384 (2003).
[CrossRef]

Velikov, K. P.

K. P. Velikov, G. E. Zegers, and A. van Blaaderen, Langmuir 19, 1384 (2003).
[CrossRef]

West, J. L.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, Appl. Phys. Lett. 82, 257 (2003).
[CrossRef]

Westcott, S. L.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, Appl. Phys. Lett. 82, 257 (2003).
[CrossRef]

Yang, W.

Yanik, M. F.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, Appl. Phys. Lett. 84, 4421 (2004).
[CrossRef]

Zegers, G. E.

K. P. Velikov, G. E. Zegers, and A. van Blaaderen, Langmuir 19, 1384 (2003).
[CrossRef]

Zia, R.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, Appl. Phys. Lett. 84, 4421 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. B. Jackson, S. L. Westcott, L. R. Hirsch, J. L. West, and N. J. Halas, Appl. Phys. Lett. 82, 257 (2003).
[CrossRef]

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, Appl. Phys. Lett. 84, 4421 (2004).
[CrossRef]

Comput. Phys.

T. Kaiser and G. Schweiger, Comput. Phys. 7, 682 (1993).
[CrossRef]

J. Electromagn. Waves Appl.

V. E. Cachorro and L. L. Salcedo, J. Electromagn. Waves Appl. 5, 913 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Langmuir

K. P. Velikov, G. E. Zegers, and A. van Blaaderen, Langmuir 19, 1384 (2003).
[CrossRef]

Phys. Rev. Lett.

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Science

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003).
[CrossRef] [PubMed]

Other

R. Ruppin, in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, 1982), pp. 345-398.

E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (3)

Fig. 1
Fig. 1

(Color online) (a) Dispersion relations of TM (squares) and TE (crosses) modes of the MDM sphere. Near the plasmon frequency ω s p (solid line), there is a flat band of TM modes that are weakly dependent on multipole number. (b) Dispersion relation of the same structure without a metal core. The insets show schematic cross sections of the systems.

Fig. 2
Fig. 2

(a) Optimized absorption cross-section spectrum of a MDM sphere with R = 500 nm . (b) Mode decomposition of the spectrum from l = 1 (bottom) to l = 15 (top). (c) Absorption spectrum of a metal sphere of radius R + L + T . (d) Absorption spectrum of a sphere with a dielectric core of radius R + L and a metal shell of thickness T.

Fig. 3
Fig. 3

(Color online) Absorption spectra of a silver titania MDM sphere with R = 500 nm and various dielectric shell thicknesses L. The value of T is chosen to maximize the peak height.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

0 = { η h l ( k d S ) h l ( k m S ) [ k d S h l ( k d S ) ] [ k m S h l ( k m S ) ] } { η j l ( k d R ) j l ( k m R ) [ k d R j l ( k d R ) ] [ k m R j l ( k m R ) ] } { η j l ( k d S ) h l ( k m S ) [ k d S j l ( k d S ) ] [ k m S h l ( k m S ) ] } × { η h l ( k d R ) j l ( k m R ) [ k d R h l ( k d R ) ] [ k m R j l ( k m R ) ] } ,
ϵ m ( ω l ) + ϵ d = 0 ,
( 2 n 1 ) π = 2 k d L ,
L = L λ sp 4 ϵ d ,

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