Abstract

In this paper, we investigate the plasmonic near-field localization and the far-field scattering properties of non-periodic arrays of Ag nanoparticles generated by prime number sequences in two spatial dimensions. In particular, we demonstrate that the engineering of plasmonic arrays with large spectral flatness and particle density is necessary to achieve a high density of electromagnetic hot spots over a broader frequency range and a larger area compared to strongly coupled periodic and quasi-periodic structures. Finally, we study the far-field scattering properties of prime number arrays illuminated by plane waves and we discuss their angular scattering properties. The study of prime number arrays of metal nanoparticles provides a novel strategy to achieve broadband enhancement and localization of plasmonic fields for the engineering of nanoscale nano-antenna arrays and active plasmonic structures.

© 2009 OSA

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  1. L. Dal Negro, N. N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
    [CrossRef]
  2. A. Gopinath, S. V. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
    [CrossRef]
  3. R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544 (2008).
    [CrossRef]
  4. A. Gopinath, S. V. Boriskina, B. M. Reinhard, and L. Dal Negro, “Deterministic Aperiodic Arrays of Metal nanoparticles for surface-enhanced Raman scattering (SERS),” Opt. Express 17(5), 3741–3753 (2009).
    [CrossRef]
  5. S. G. Williams, Symbolic dynamics and its applications, (American Mathematical Society, 2004).
  6. P. Prusinkiewicz, and A. Lindenmayer, The algorithmic beauty of plants, (Springer Verlag, 1990).
  7. J. Mishra, and S. N. Mishra, L-System Fractals, (Elsevier, 2007).
  8. M. R. Schroeder, Number theory in science and communication, (Springer Verlag, 1985).
  9. G. H. Hardy, and E. M. Wright, An introduction to the theory of numbers, (Oxford University Press, 2008).
  10. S. J. Miller, and R. Takloo-Bighash, An Invitation to Modern Number Theory, (Princeton University Press, 2006).
  11. M. Queffelec, “Substitution dynamical systems-spectral analysis,” (Springer, 1987).
  12. E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
    [CrossRef]
  13. M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
    [CrossRef]
  14. L. Dal Negro and N. N. Feng, “Spectral gaps and mode localization in Fibonacci chains of metal nanoparticles,” Opt. Express 15(22), 14396 (2007).
    [CrossRef]
  15. C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B Condens. Matter 79(8), 85404 (2009).
    [CrossRef]
  16. L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B Condens. Matter 66(9), 094204 (2002).
    [CrossRef]
  17. A. Gopinath, N. Lawrence, S. Boriskina, L. Dal Negro, “Enhancement of the 1.54μm Erbium emission in aperiodic plasmonic arrays” in preparation.
  18. C. Forestiere, G. Miano, S. V. Boriskina, and L. Dal Negro, “The role of nanoparticle shapes and deterministic aperiodicity for the design of nanoplasmonic arrays,” Opt. Express 17(12), 9648–9661 (2009).
    [CrossRef]
  19. C. Janot, Quasicrystals: A Primer, (Oxford University Press, 1997).
  20. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B Condens. Matter 6(12), 4370–4379 (1972).
    [CrossRef]
  21. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
    [CrossRef]
  22. M. R. Schroeder, “A simple function and its Fourier transform,” Math. Intelligencer 4(3), 158–161 (1982).
    [CrossRef]
  23. M. L. Stein, S. M. Ulam, and M. B. Wells, “A visual display of some properties of the distribution of primes,” Am. Math. Mon. 71(5), 516 (1964).
    [CrossRef]
  24. J. D. Johnston, “Transform Coding of Audio Signals Using Perceptual Noise Criteria,” IEEE J. Sel. Areas Comm. 6(2), 314 (1988).
    [CrossRef]
  25. L. Novotny, and B. Hecht, Principles of Nano-Optics, (Cambridge University Press, 2006).
  26. C. Forestiere, A. Gopinath, G. Miano, L. Dal Negro, S. Boriskina, “Structural resonances in finite-size periodic plasmonic arrays,” in preparation.
  27. A. Alù and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantennas,” Phys. Rev. B Condens. Matter 78(19), 195111 (2008).
    [CrossRef]
  28. L. Novotny, “Effective Wavelength Scaling for Optical Antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
    [CrossRef]
  29. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple scattering of light by particles: radiative transfer and coherent backscattering, (Cambridge University Press, 2006).
  30. J. D. Jackson, Classical Electrodynamics, (Wiley, 1998).

2009 (3)

2008 (4)

A. Alù and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantennas,” Phys. Rev. B Condens. Matter 78(19), 195111 (2008).
[CrossRef]

R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544 (2008).
[CrossRef]

L. Dal Negro, N. N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

A. Gopinath, S. V. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef]

2007 (3)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef]

L. Novotny, “Effective Wavelength Scaling for Optical Antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
[CrossRef]

L. Dal Negro and N. N. Feng, “Spectral gaps and mode localization in Fibonacci chains of metal nanoparticles,” Opt. Express 15(22), 14396 (2007).
[CrossRef]

2006 (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
[CrossRef]

2002 (1)

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B Condens. Matter 66(9), 094204 (2002).
[CrossRef]

1992 (1)

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
[CrossRef]

1988 (1)

J. D. Johnston, “Transform Coding of Audio Signals Using Perceptual Noise Criteria,” IEEE J. Sel. Areas Comm. 6(2), 314 (1988).
[CrossRef]

1982 (1)

M. R. Schroeder, “A simple function and its Fourier transform,” Math. Intelligencer 4(3), 158–161 (1982).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B Condens. Matter 6(12), 4370–4379 (1972).
[CrossRef]

1964 (1)

M. L. Stein, S. M. Ulam, and M. B. Wells, “A visual display of some properties of the distribution of primes,” Am. Math. Mon. 71(5), 516 (1964).
[CrossRef]

Agrawal, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantennas,” Phys. Rev. B Condens. Matter 78(19), 195111 (2008).
[CrossRef]

Boriskina, S. V.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B Condens. Matter 6(12), 4370–4379 (1972).
[CrossRef]

Dal Negro, L.

C. Forestiere, G. Miano, S. V. Boriskina, and L. Dal Negro, “The role of nanoparticle shapes and deterministic aperiodicity for the design of nanoplasmonic arrays,” Opt. Express 17(12), 9648–9661 (2009).
[CrossRef]

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B Condens. Matter 79(8), 85404 (2009).
[CrossRef]

A. Gopinath, S. V. Boriskina, B. M. Reinhard, and L. Dal Negro, “Deterministic Aperiodic Arrays of Metal nanoparticles for surface-enhanced Raman scattering (SERS),” Opt. Express 17(5), 3741–3753 (2009).
[CrossRef]

A. Gopinath, S. V. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef]

R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544 (2008).
[CrossRef]

L. Dal Negro, N. N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

L. Dal Negro and N. N. Feng, “Spectral gaps and mode localization in Fibonacci chains of metal nanoparticles,” Opt. Express 15(22), 14396 (2007).
[CrossRef]

Dallapiccola, R.

Dulea, M.

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
[CrossRef]

Engheta, N.

A. Alù and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantennas,” Phys. Rev. B Condens. Matter 78(19), 195111 (2008).
[CrossRef]

Feng, N. N.

A. Gopinath, S. V. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef]

L. Dal Negro, N. N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

L. Dal Negro and N. N. Feng, “Spectral gaps and mode localization in Fibonacci chains of metal nanoparticles,” Opt. Express 15(22), 14396 (2007).
[CrossRef]

Forestiere, C.

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B Condens. Matter 79(8), 85404 (2009).
[CrossRef]

C. Forestiere, G. Miano, S. V. Boriskina, and L. Dal Negro, “The role of nanoparticle shapes and deterministic aperiodicity for the design of nanoplasmonic arrays,” Opt. Express 17(12), 9648–9661 (2009).
[CrossRef]

Gopinath, A.

A. Gopinath, S. V. Boriskina, B. M. Reinhard, and L. Dal Negro, “Deterministic Aperiodic Arrays of Metal nanoparticles for surface-enhanced Raman scattering (SERS),” Opt. Express 17(5), 3741–3753 (2009).
[CrossRef]

A. Gopinath, S. V. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef]

R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544 (2008).
[CrossRef]

L. Dal Negro, N. N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Johansson, M.

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B Condens. Matter 6(12), 4370–4379 (1972).
[CrossRef]

Johnston, J. D.

J. D. Johnston, “Transform Coding of Audio Signals Using Perceptual Noise Criteria,” IEEE J. Sel. Areas Comm. 6(2), 314 (1988).
[CrossRef]

Kroon, L.

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B Condens. Matter 66(9), 094204 (2002).
[CrossRef]

Lennholm, E.

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B Condens. Matter 66(9), 094204 (2002).
[CrossRef]

Maciá, E.

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
[CrossRef]

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef]

Miano, G.

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B Condens. Matter 79(8), 85404 (2009).
[CrossRef]

C. Forestiere, G. Miano, S. V. Boriskina, and L. Dal Negro, “The role of nanoparticle shapes and deterministic aperiodicity for the design of nanoplasmonic arrays,” Opt. Express 17(12), 9648–9661 (2009).
[CrossRef]

Nahata, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef]

Novotny, L.

L. Novotny, “Effective Wavelength Scaling for Optical Antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
[CrossRef]

Reinhard, B. M.

A. Gopinath, S. V. Boriskina, B. M. Reinhard, and L. Dal Negro, “Deterministic Aperiodic Arrays of Metal nanoparticles for surface-enhanced Raman scattering (SERS),” Opt. Express 17(5), 3741–3753 (2009).
[CrossRef]

A. Gopinath, S. V. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef]

Riklund, R.

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B Condens. Matter 66(9), 094204 (2002).
[CrossRef]

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
[CrossRef]

Rubinacci, G.

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B Condens. Matter 79(8), 85404 (2009).
[CrossRef]

Schroeder, M. R.

M. R. Schroeder, “A simple function and its Fourier transform,” Math. Intelligencer 4(3), 158–161 (1982).
[CrossRef]

Stein, M. L.

M. L. Stein, S. M. Ulam, and M. B. Wells, “A visual display of some properties of the distribution of primes,” Am. Math. Mon. 71(5), 516 (1964).
[CrossRef]

Stellacci, F.

Ulam, S. M.

M. L. Stein, S. M. Ulam, and M. B. Wells, “A visual display of some properties of the distribution of primes,” Am. Math. Mon. 71(5), 516 (1964).
[CrossRef]

Vardeny, Z. V.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef]

Wells, M. B.

M. L. Stein, S. M. Ulam, and M. B. Wells, “A visual display of some properties of the distribution of primes,” Am. Math. Mon. 71(5), 516 (1964).
[CrossRef]

Am. Math. Mon. (1)

M. L. Stein, S. M. Ulam, and M. B. Wells, “A visual display of some properties of the distribution of primes,” Am. Math. Mon. 71(5), 516 (1964).
[CrossRef]

IEEE J. Sel. Areas Comm. (1)

J. D. Johnston, “Transform Coding of Audio Signals Using Perceptual Noise Criteria,” IEEE J. Sel. Areas Comm. 6(2), 314 (1988).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

L. Dal Negro, N. N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A, Pure Appl. Opt. 10(6), 064013 (2008).
[CrossRef]

Math. Intelligencer (1)

M. R. Schroeder, “A simple function and its Fourier transform,” Math. Intelligencer 4(3), 158–161 (1982).
[CrossRef]

Nano Lett. (1)

A. Gopinath, S. V. Boriskina, N. N. Feng, B. M. Reinhard, and L. Dal Negro, “Photonic-plasmonic scattering resonances in deterministic aperiodic structures,” Nano Lett. 8(8), 2423–2431 (2008).
[CrossRef]

Nature (1)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef]

Opt. Express (4)

Phys. Rev. B Condens. Matter (5)

A. Alù and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantennas,” Phys. Rev. B Condens. Matter 78(19), 195111 (2008).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B Condens. Matter 6(12), 4370–4379 (1972).
[CrossRef]

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
[CrossRef]

C. Forestiere, G. Miano, G. Rubinacci, and L. Dal Negro, “Role of aperiodic order in the spectral, localization, and scaling properties of plasmon modes for the design of nanoparticle arrays,” Phys. Rev. B Condens. Matter 79(8), 85404 (2009).
[CrossRef]

L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B Condens. Matter 66(9), 094204 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

L. Novotny, “Effective Wavelength Scaling for Optical Antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
[CrossRef]

Rep. Prog. Phys. (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69(2), 397–441 (2006).
[CrossRef]

Other (13)

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

C. Forestiere, A. Gopinath, G. Miano, L. Dal Negro, S. Boriskina, “Structural resonances in finite-size periodic plasmonic arrays,” in preparation.

A. Gopinath, N. Lawrence, S. Boriskina, L. Dal Negro, “Enhancement of the 1.54μm Erbium emission in aperiodic plasmonic arrays” in preparation.

C. Janot, Quasicrystals: A Primer, (Oxford University Press, 1997).

S. G. Williams, Symbolic dynamics and its applications, (American Mathematical Society, 2004).

P. Prusinkiewicz, and A. Lindenmayer, The algorithmic beauty of plants, (Springer Verlag, 1990).

J. Mishra, and S. N. Mishra, L-System Fractals, (Elsevier, 2007).

M. R. Schroeder, Number theory in science and communication, (Springer Verlag, 1985).

G. H. Hardy, and E. M. Wright, An introduction to the theory of numbers, (Oxford University Press, 2008).

S. J. Miller, and R. Takloo-Bighash, An Invitation to Modern Number Theory, (Princeton University Press, 2006).

M. Queffelec, “Substitution dynamical systems-spectral analysis,” (Springer, 1987).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple scattering of light by particles: radiative transfer and coherent backscattering, (Cambridge University Press, 2006).

J. D. Jackson, Classical Electrodynamics, (Wiley, 1998).

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