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 (2)

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 (2)

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 (5)

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

W. Yang, Appl. Opt. 42, 1710 (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 (1)

1993 (1)

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

1991 (1)

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

1981 (1)

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.

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]

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. (3)

Appl. Phys. Lett. (2)

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

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

Comput. Phys. (1)

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

J. Electromagn. Waves Appl. (1)

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

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

Langmuir (1)

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

Phys. Rev. Lett. (2)

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 (2)

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 (2)

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)

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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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