Abstract

We used the particle swarm optimization algorithm, an evolutionary computational technique, to design metal nanoparticle arrays that produce broadband plasmonic field enhancement over the entire visible spectral range. The resulting structures turn out to be aperiodic and feature dense Fourier spectra with many closely packed particle clusters. We conclude that broadband field-enhancement effects in nanoplasmonics can be achieved by engineering aperiodic arrays with a large number of spatial frequencies that provide the necessary interplay between long-range diffractive interactions at multiple length scales and near-field quasi-static coupling within small nanoparticle clusters.

© 2010 Optical Society of America

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  1. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
    [CrossRef]
  2. J. S. Biteen, D. Pacifici, N. S. Lewis, and H. A. Atwater, Nano Lett. 5, 1768 (2005).
    [CrossRef] [PubMed]
  3. K. R. Catchpole and A. Polman, Opt. Express 16, 21793 (2008).
    [CrossRef] [PubMed]
  4. S. Boriskina and L. Dal Negro, Opt. Express 16, 12511 (2008).
    [CrossRef] [PubMed]
  5. E. Macia, Rep. Prog. Phys. 69, 397 (2006).
    [CrossRef]
  6. L. Dal Negro, N. N. Feng, and A. Gopinath, J. Opt. A 10, 064013 (2008).
    [CrossRef]
  7. A. Gopinath, S. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, Nano Lett. 8, 2423 (2008).
    [CrossRef] [PubMed]
  8. A. Gopinath, S. Boriskina, B. Reinhard, and L. Dal Negro, Opt. Express 17, 3741 (2009).
    [CrossRef] [PubMed]
  9. C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, Phys. Rev. B 79, 085404 (2009).
    [CrossRef]
  10. A. Gopinath, S. Boriskina, R. Premasiri, L. Ziegler, B. Reinhard, and L. Dal Negro, Nano Lett. 9, 11 (2009).
    [CrossRef]
  11. C. Forestiere, G. F. Walsh, G. Miano, and L. Dal Negro, Opt. Express 17, 24288 (2009).
    [CrossRef]
  12. J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence (Morgan Kaufmann, 2001).
  13. M. Donelli, R. Azaro, F. G. B. De Natale, and A. Massa, IEEE Trans. Antennas Propag. 54, 888 (2006).
    [CrossRef]
  14. M. Shokooh-Saremi and R. Magnusson, Opt. Lett. 32, 894 (2007).
    [CrossRef] [PubMed]
  15. J. H. Holland, Genetic Algorithms (Addison-Wesley, 1989).
  16. J. Kennedy and R. C. Eberhart in Proceedings of IEEE Conference on Systems, Man, and Cybernetics (IEEE, 1997), Vol. 5, pp. 4104-4108.
  17. B. Thors, H. Steyskal, and H. Holter, IEEE Trans. Antennas Propag. 53, 3280 (2005).
    [CrossRef]
  18. C. Forestiere, G. Miano, S. Boriskina, and L. Dal Negro, Opt. Express 17, 9648 (2009).
    [CrossRef] [PubMed]
  19. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  20. M. I. Stockman, S. V. Faleev, and D. J. Bergman, Phys. Rev. Lett. 87, 167401 (2001).
    [CrossRef] [PubMed]
  21. J. B. Khurgin and G. Sun, Appl. Phys. Lett. 94, 221111 (2009).
    [CrossRef]
  22. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

2009 (6)

A. Gopinath, S. Boriskina, B. Reinhard, and L. Dal Negro, Opt. Express 17, 3741 (2009).
[CrossRef] [PubMed]

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, Phys. Rev. B 79, 085404 (2009).
[CrossRef]

A. Gopinath, S. Boriskina, R. Premasiri, L. Ziegler, B. Reinhard, and L. Dal Negro, Nano Lett. 9, 11 (2009).
[CrossRef]

C. Forestiere, G. F. Walsh, G. Miano, and L. Dal Negro, Opt. Express 17, 24288 (2009).
[CrossRef]

C. Forestiere, G. Miano, S. Boriskina, and L. Dal Negro, Opt. Express 17, 9648 (2009).
[CrossRef] [PubMed]

J. B. Khurgin and G. Sun, Appl. Phys. Lett. 94, 221111 (2009).
[CrossRef]

2008 (4)

L. Dal Negro, N. N. Feng, and A. Gopinath, J. Opt. A 10, 064013 (2008).
[CrossRef]

A. Gopinath, S. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, Nano Lett. 8, 2423 (2008).
[CrossRef] [PubMed]

K. R. Catchpole and A. Polman, Opt. Express 16, 21793 (2008).
[CrossRef] [PubMed]

S. Boriskina and L. Dal Negro, Opt. Express 16, 12511 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (2)

E. Macia, Rep. Prog. Phys. 69, 397 (2006).
[CrossRef]

M. Donelli, R. Azaro, F. G. B. De Natale, and A. Massa, IEEE Trans. Antennas Propag. 54, 888 (2006).
[CrossRef]

2005 (2)

J. S. Biteen, D. Pacifici, N. S. Lewis, and H. A. Atwater, Nano Lett. 5, 1768 (2005).
[CrossRef] [PubMed]

B. Thors, H. Steyskal, and H. Holter, IEEE Trans. Antennas Propag. 53, 3280 (2005).
[CrossRef]

2001 (1)

M. I. Stockman, S. V. Faleev, and D. J. Bergman, Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

1997 (1)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Atwater, H. A.

J. S. Biteen, D. Pacifici, N. S. Lewis, and H. A. Atwater, Nano Lett. 5, 1768 (2005).
[CrossRef] [PubMed]

Azaro, R.

M. Donelli, R. Azaro, F. G. B. De Natale, and A. Massa, IEEE Trans. Antennas Propag. 54, 888 (2006).
[CrossRef]

Bergman, D. J.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

Biteen, J. S.

J. S. Biteen, D. Pacifici, N. S. Lewis, and H. A. Atwater, Nano Lett. 5, 1768 (2005).
[CrossRef] [PubMed]

Boriskina, S.

Catchpole, K. R.

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Dal Negro, L.

C. Forestiere, G. Miano, S. Boriskina, and L. Dal Negro, Opt. Express 17, 9648 (2009).
[CrossRef] [PubMed]

A. Gopinath, S. Boriskina, B. Reinhard, and L. Dal Negro, Opt. Express 17, 3741 (2009).
[CrossRef] [PubMed]

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, Phys. Rev. B 79, 085404 (2009).
[CrossRef]

A. Gopinath, S. Boriskina, R. Premasiri, L. Ziegler, B. Reinhard, and L. Dal Negro, Nano Lett. 9, 11 (2009).
[CrossRef]

C. Forestiere, G. F. Walsh, G. Miano, and L. Dal Negro, Opt. Express 17, 24288 (2009).
[CrossRef]

A. Gopinath, S. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, Nano Lett. 8, 2423 (2008).
[CrossRef] [PubMed]

L. Dal Negro, N. N. Feng, and A. Gopinath, J. Opt. A 10, 064013 (2008).
[CrossRef]

S. Boriskina and L. Dal Negro, Opt. Express 16, 12511 (2008).
[CrossRef] [PubMed]

Dasari, R. R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

De Natale, F. G. B.

M. Donelli, R. Azaro, F. G. B. De Natale, and A. Massa, IEEE Trans. Antennas Propag. 54, 888 (2006).
[CrossRef]

Donelli, M.

M. Donelli, R. Azaro, F. G. B. De Natale, and A. Massa, IEEE Trans. Antennas Propag. 54, 888 (2006).
[CrossRef]

Eberhart, R. C.

J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence (Morgan Kaufmann, 2001).

J. Kennedy and R. C. Eberhart in Proceedings of IEEE Conference on Systems, Man, and Cybernetics (IEEE, 1997), Vol. 5, pp. 4104-4108.

Faleev, S. V.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

Feld, M. S.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Feng, N. N.

L. Dal Negro, N. N. Feng, and A. Gopinath, J. Opt. A 10, 064013 (2008).
[CrossRef]

A. Gopinath, S. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, Nano Lett. 8, 2423 (2008).
[CrossRef] [PubMed]

Forestiere, C.

Gopinath, A.

A. Gopinath, S. Boriskina, B. Reinhard, and L. Dal Negro, Opt. Express 17, 3741 (2009).
[CrossRef] [PubMed]

A. Gopinath, S. Boriskina, R. Premasiri, L. Ziegler, B. Reinhard, and L. Dal Negro, Nano Lett. 9, 11 (2009).
[CrossRef]

L. Dal Negro, N. N. Feng, and A. Gopinath, J. Opt. A 10, 064013 (2008).
[CrossRef]

A. Gopinath, S. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, Nano Lett. 8, 2423 (2008).
[CrossRef] [PubMed]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

Holland, J. H.

J. H. Holland, Genetic Algorithms (Addison-Wesley, 1989).

Holter, H.

B. Thors, H. Steyskal, and H. Holter, IEEE Trans. Antennas Propag. 53, 3280 (2005).
[CrossRef]

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kennedy, J.

J. Kennedy and R. C. Eberhart in Proceedings of IEEE Conference on Systems, Man, and Cybernetics (IEEE, 1997), Vol. 5, pp. 4104-4108.

J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence (Morgan Kaufmann, 2001).

Khurgin, J. B.

J. B. Khurgin and G. Sun, Appl. Phys. Lett. 94, 221111 (2009).
[CrossRef]

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Lewis, N. S.

J. S. Biteen, D. Pacifici, N. S. Lewis, and H. A. Atwater, Nano Lett. 5, 1768 (2005).
[CrossRef] [PubMed]

Macia, E.

E. Macia, Rep. Prog. Phys. 69, 397 (2006).
[CrossRef]

Magnusson, R.

Massa, A.

M. Donelli, R. Azaro, F. G. B. De Natale, and A. Massa, IEEE Trans. Antennas Propag. 54, 888 (2006).
[CrossRef]

Miano, G.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

Pacifici, D.

J. S. Biteen, D. Pacifici, N. S. Lewis, and H. A. Atwater, Nano Lett. 5, 1768 (2005).
[CrossRef] [PubMed]

Perelman, L. T.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Polman, A.

Premasiri, R.

A. Gopinath, S. Boriskina, R. Premasiri, L. Ziegler, B. Reinhard, and L. Dal Negro, Nano Lett. 9, 11 (2009).
[CrossRef]

Reinhard, B.

A. Gopinath, S. Boriskina, R. Premasiri, L. Ziegler, B. Reinhard, and L. Dal Negro, Nano Lett. 9, 11 (2009).
[CrossRef]

A. Gopinath, S. Boriskina, B. Reinhard, and L. Dal Negro, Opt. Express 17, 3741 (2009).
[CrossRef] [PubMed]

Reinhard, B. M.

A. Gopinath, S. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, Nano Lett. 8, 2423 (2008).
[CrossRef] [PubMed]

Rubinacci, G.

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, Phys. Rev. B 79, 085404 (2009).
[CrossRef]

Shi, Y.

J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence (Morgan Kaufmann, 2001).

Shokooh-Saremi, M.

Steyskal, H.

B. Thors, H. Steyskal, and H. Holter, IEEE Trans. Antennas Propag. 53, 3280 (2005).
[CrossRef]

Stockman, M. I.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

Sun, G.

J. B. Khurgin and G. Sun, Appl. Phys. Lett. 94, 221111 (2009).
[CrossRef]

Thors, B.

B. Thors, H. Steyskal, and H. Holter, IEEE Trans. Antennas Propag. 53, 3280 (2005).
[CrossRef]

Walsh, G. F.

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Ziegler, L.

A. Gopinath, S. Boriskina, R. Premasiri, L. Ziegler, B. Reinhard, and L. Dal Negro, Nano Lett. 9, 11 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

J. B. Khurgin and G. Sun, Appl. Phys. Lett. 94, 221111 (2009).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

M. Donelli, R. Azaro, F. G. B. De Natale, and A. Massa, IEEE Trans. Antennas Propag. 54, 888 (2006).
[CrossRef]

B. Thors, H. Steyskal, and H. Holter, IEEE Trans. Antennas Propag. 53, 3280 (2005).
[CrossRef]

J. Opt. A (1)

L. Dal Negro, N. N. Feng, and A. Gopinath, J. Opt. A 10, 064013 (2008).
[CrossRef]

Nano Lett. (3)

A. Gopinath, S. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, Nano Lett. 8, 2423 (2008).
[CrossRef] [PubMed]

J. S. Biteen, D. Pacifici, N. S. Lewis, and H. A. Atwater, Nano Lett. 5, 1768 (2005).
[CrossRef] [PubMed]

A. Gopinath, S. Boriskina, R. Premasiri, L. Ziegler, B. Reinhard, and L. Dal Negro, Nano Lett. 9, 11 (2009).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, Phys. Rev. B 79, 085404 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

M. I. Stockman, S. V. Faleev, and D. J. Bergman, Phys. Rev. Lett. 87, 167401 (2001).
[CrossRef] [PubMed]

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Rep. Prog. Phys. (1)

E. Macia, Rep. Prog. Phys. 69, 397 (2006).
[CrossRef]

Other (4)

J. H. Holland, Genetic Algorithms (Addison-Wesley, 1989).

J. Kennedy and R. C. Eberhart in Proceedings of IEEE Conference on Systems, Man, and Cybernetics (IEEE, 1997), Vol. 5, pp. 4104-4108.

J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence (Morgan Kaufmann, 2001).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

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Figures (2)

Fig. 1
Fig. 1

Geometry of (a) the optimized silver nanoparticle array and (b) its Fourier transform magnitude (log scale). In (b) a = 125 nm is the minimum center to center distance, and the Fourier transform magnitude has been normalized to its maximum value. The central peak and the cross in the middle of the Fourier space result from the square symmetry of the finite-size array.

Fig. 2
Fig. 2

(a) Maximum field-enhancement spectrum of the optimized array (triangles) of silver nanoparticles, illuminated, at normal incidence, by a circularly polarized plane wave of unitary intensity, compared with the performances of periodic array (circles), in which all allowed positions are filled by a particle, and with the single particle (squares). (b) Cumulative distribution function of field enhancement (CDFE) (logarithmic scale) versus wavelength (x axis) and field enhancement (y axis).

Equations (4)

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

v k , m w = β v k 1 , m w + C 1 ( θ k , m w θ k , m pb ) ρ 1 + C 2 ( θ k , m w θ k , m gb ) ρ 2 ,
θ k , m w = { 1 if θ k , m w < 1 1 + exp ( v k , m w ) 0 otherwise } ,
v k , m w = { V max if v k , m w , > V max V max if v k , m w < V max v k , m w otherwise } .
FF = M = 1 50 FE MAX ( λ M ) .

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