Abstract

Bound and leaky modes with complex wavenumber in chains (linear arrays) of plasmonic nanospheres are characterized for both longitudinal and transverse polarization states (with respect to the array axis). The proposed method allows for the description of each mode evolution when varying frequency. As a consequence, full characterization of the guided modes with complex wavenumber is provided in terms of propagation direction, guidance or radiance, proper or improper, and physical or nonphysical conditions. Each nanosphere is modeled according to the single dipole approximation, and the metal permittivity is described by the Drude model. Modal wavenumbers are obtained by computing the complex zeroes of the homogeneous equation characterizing the field in the one dimensional periodic array. The required periodic Green’s function is analytically continued into the complex wavenumber space by using the Ewald method. Furthermore, a parametric analysis of the mode wavenumbers is performed with respect to the geometrical parameters of the array.

© 2011 OSA

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  1. P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
    [CrossRef]
  2. S. Steshenko, F. Capolino, S. A. Tretyakov, and C. R. Simovski, “Super-Resolution and Near-Field Enhancement with Layers of Resonant Arrays of Nanoparticles,” in Applications of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 4.1.
  3. C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Sub-wavelength resolution in linear arrays of plasmonic particles,” J. Appl. Phys. 101(12), 123102 (2007).
    [CrossRef]
  4. C. Simovski, S. Tretyakov, and A. Viitanen, “Subwavelength imaging in a superlens of plasmon nanospheres,” Tech. Phys. Lett. 33(3), 264–266 (2007).
    [CrossRef]
  5. S. Steshenko, F. Capolino, P. Alitalo, and S. A. Tretyakov, “Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(1), 016607 (2011).
    [CrossRef] [PubMed]
  6. A. F. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9(12), 4228–4233 (2009).
    [CrossRef] [PubMed]
  7. X. Liu and A. Alu, “Subwavelength leaky-wave optical nanoantennas: directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82(14), 144305 (2010).
    [CrossRef]
  8. J. Beermann, S. M. Novikov, K. Leosson, and S. I. Bozhevolnyi, “Surface enhanced Raman imaging: periodic arrays and individual metal nanoparticles,” Opt. Express 17(15), 12698–12705 (2009).
    [CrossRef] [PubMed]
  9. F. Liu, Z. Cao, C. Tang, L. Chen, and Z. Wang, “Ultrathin diamond-like carbon film coated silver nanoparticles-based substrates for surface-enhanced Raman spectroscopy,” ACS Nano 4(5), 2643–2648 (2010).
    [CrossRef] [PubMed]
  10. I. Firkowska, S. Giannona, J. A. Rojas-Chapana, K. Luecke, O. Brustle, and M. Giersig, “Biocompatible Nanomaterials and Nanodevices Promising for Biomedical Applications ” in Nanomaterials for Application in Medicine and Biology, M. Giersig, and G. B. Khomutov, eds. (Springer, Berlin, 2008), p. I.1.
  11. A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124(35), 10596–10604 (2002).
    [CrossRef] [PubMed]
  12. I. E. Sendroiu and R. M. Corn, “Nanoparticle diffraction gratings for DNA detection on photopatterned glass substrates,” Biointerphases 3(3), FD23–FD29 (2008).
    [CrossRef] [PubMed]
  13. A. L. Fructos, S. Campione, F. Capolino, and F. Mesa, “Characterization of complex plasmonic modes in two-dimensional periodic arrays of metal nanospheres,” J. Opt. Soc. Am. B 28(6), 1446–1458 (2011).
    [CrossRef]
  14. S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
    [CrossRef]
  15. S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69(12), 125418 (2004).
    [CrossRef]
  16. R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41(10), 578–580 (2005).
    [CrossRef]
  17. R. A. Shore and A. D. Yaghjian, ““Traveling electromagnetic waves on linear periodic arrays of lossless penetrable spheres,” IEICE Trans. Commun. E88B(6), 2346–2352 (2005).
    [CrossRef]
  18. D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31(1), 98–100 (2006).
    [CrossRef] [PubMed]
  19. A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
    [CrossRef]
  20. A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74(20), 205436 (2006).
    [CrossRef]
  21. R. A. Shore and A. D. Yaghjian, “Complex Waves on 1D, 2D, and 3D Periodic Arrays of Lossy and Lossless Magnetodielectric Spheres,” AFRL-RY-HS-TR-2010–0019, (Air Force Research Laboratory, Hanscom, MA 2010).
  22. K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express 15(26), 17482–17493 (2007).
    [CrossRef] [PubMed]
  23. T. Yang and K. B. Crozier, “Dispersion and extinction of surface plasmons in an array of gold nanoparticle chains: influence of the air/glass interface,” Opt. Express 16(12), 8570–8580 (2008).
    [CrossRef] [PubMed]
  24. A. Alù and N. Engheta, “Effect of small random disorders and imperfections on the performance of arrays of plasmonic nanoparticles,” N. J. Phys. 12(1), 013015 (2010).
    [CrossRef]
  25. S. Campione and F. Capolino, “Linear and Planar Periodic Arrays of Metallic Nanospheres: Fabrication, Optical Properties and Applications,” in Selected Topics in Metamaterials and Photonic Crystals, A. Andreone, A. Cusano, A. Cutolo, and V. Galdi, eds. (World Scientific Publishing, 2011), pp. 141–194.
  26. M. Conforti and M. Guasoni, “Dispersive properties of linear chains of lossy metal nanoparticles,” J. Opt. Soc. Am. B 27(8), 1576–1582 (2010).
    [CrossRef]
  27. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  28. S. Steshenko and F. Capolino, “Single Dipole Approximation for Modeling Collections of Nanoscatterers,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 8.1.
  29. D. E. Muller, “A Method for Solving Algebraic Equations Using an Automatic Computer,” Math. Tables Other Aids Comput. 10(56), 208–215 (1956).
    [CrossRef]
  30. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes: the art of scientific computing (Cambridge University Press, 2007).
  31. “IMSL Fortran Numerical Library,” (Visual Numerics Corporate Headquarters, 2500 Wilcrest Drive, Suite 200, Houston, TX), www.vni.com .
  32. F. Capolino, D. R. Wilton, and W. A. Johnson, “Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223(1), 250–261 (2007).
    [CrossRef]
  33. V. R. Komanduri, F. Capolino, D. R. Jackson, and D. R. Wilton, “Computation of the one-dimensional free-space periodic green's function for leaky waves using the ewald method,” in Proc. URSI Gen. Ass.(Chicago, IL, 2008).
  34. F. T. Celepcikay, D. R. Wilton, D. R. Jackson, and F. Capolino, “Choosing splitting parameters and summation limits in the numerical evaluation of 1-D and 2-D periodic Green's functions using the Ewald method,” Radio Sci. 43(6), RS6S01 (2008).
    [CrossRef]
  35. J. D. Jackson, Classical Electrodynamics (Wiley, 1998).
  36. V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
    [CrossRef]
  37. D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11(11), 2851–2861 (1994).
    [CrossRef]
  38. R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182(4–6), 273–279 (2000).
    [CrossRef]
  39. W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B Condens. Matter 39(14), 9852–9858 (1989).
    [CrossRef] [PubMed]
  40. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).
  41. F. Capolino, D. R. Jackson, and D. R. Wilton, “Field Representations in Periodic Artificial Materials Excited by a Source,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 12.1.
  42. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, 1994).
  43. P. Baccarelli, S. Paulotto, and C. Di Nallo, “Full-wave analysis of bound and leaky modes propagating along 2D periodic printed structures with arbitrary metallisation in the unit cell,” IET Proc. Microwaves, Antennas Propag. 1(1), 217–225 (2007).
    [CrossRef]
  44. F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antenn. Propag. 55(6), 1644–1655 (2007).
    [CrossRef]
  45. F. Capolino, D. R. Jackson, and D. R. Wilton, “Fundamental properties of the field at the interface between air and a periodic artificial material excited by a line source,” IEEE Trans. Antenn. Propag. 53(1), 91–99 (2005).
    [CrossRef]
  46. A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14(4), 1557–1567 (2006).
    [CrossRef] [PubMed]
  47. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
    [CrossRef]
  48. A. A. Oliner and D. R. Jackson, “Leaky-wave antennas,” in Antenna Engineering Handbook, J. Volakis, ed. (McGraw Hill, 2007), p. 11.1.
  49. F. Capolino, D. R. Jackson, and D. R. Wilton, “Mode excitation from sources in two-dimensional EBG waveguides using the array scanning method,” IEEE Microw. Wirel. Compon. Lett. 15(2), 49–51 (2005).
    [CrossRef]
  50. P. J. B. Clarricoats and K. R. Slinn, “Complex modes of propagation in dielectric-loaded circular waveguide,” Electron. Lett. 1(5), 145–146 (1965).
    [CrossRef]
  51. J. D. Rhodes, “General constraints on propagation characteristics of electromagnetic waves in uniform inhomogeneous waveguides,” in Proc. Inst. Electr. Eng. 118, 849–856 (1971).
  52. T. F. Jablonski, “Complex modes in open lossless dielectric waveguides,” J. Opt. Soc. Am. A 11(4), 1272–1282 (1994).
    [CrossRef]
  53. T. Rozzi, L. Pierantoni, and M. Farina, “General constraints on the propagation of complex waves in closed lossless isotropic waveguides,” IEEE Trans. Microw. Theory Tech. 46(5), 512–516 (1998).
    [CrossRef]
  54. R. Islam and G. V. Eleftheriades, “On the Independence of the Excitation of Complex Modes in Isotropic Structures,” IEEE Trans. Antenn. Propag. 58(5), 1567–1578 (2010).
    [CrossRef]
  55. J. R. James, “Leaky waves on a dielectric rod,” Electron. Lett. 5(11), 252–254 (1969).
    [CrossRef]

2011 (2)

S. Steshenko, F. Capolino, P. Alitalo, and S. A. Tretyakov, “Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(1), 016607 (2011).
[CrossRef] [PubMed]

A. L. Fructos, S. Campione, F. Capolino, and F. Mesa, “Characterization of complex plasmonic modes in two-dimensional periodic arrays of metal nanospheres,” J. Opt. Soc. Am. B 28(6), 1446–1458 (2011).
[CrossRef]

2010 (5)

X. Liu and A. Alu, “Subwavelength leaky-wave optical nanoantennas: directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82(14), 144305 (2010).
[CrossRef]

F. Liu, Z. Cao, C. Tang, L. Chen, and Z. Wang, “Ultrathin diamond-like carbon film coated silver nanoparticles-based substrates for surface-enhanced Raman spectroscopy,” ACS Nano 4(5), 2643–2648 (2010).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Effect of small random disorders and imperfections on the performance of arrays of plasmonic nanoparticles,” N. J. Phys. 12(1), 013015 (2010).
[CrossRef]

M. Conforti and M. Guasoni, “Dispersive properties of linear chains of lossy metal nanoparticles,” J. Opt. Soc. Am. B 27(8), 1576–1582 (2010).
[CrossRef]

R. Islam and G. V. Eleftheriades, “On the Independence of the Excitation of Complex Modes in Isotropic Structures,” IEEE Trans. Antenn. Propag. 58(5), 1567–1578 (2010).
[CrossRef]

2009 (2)

2008 (3)

I. E. Sendroiu and R. M. Corn, “Nanoparticle diffraction gratings for DNA detection on photopatterned glass substrates,” Biointerphases 3(3), FD23–FD29 (2008).
[CrossRef] [PubMed]

T. Yang and K. B. Crozier, “Dispersion and extinction of surface plasmons in an array of gold nanoparticle chains: influence of the air/glass interface,” Opt. Express 16(12), 8570–8580 (2008).
[CrossRef] [PubMed]

F. T. Celepcikay, D. R. Wilton, D. R. Jackson, and F. Capolino, “Choosing splitting parameters and summation limits in the numerical evaluation of 1-D and 2-D periodic Green's functions using the Ewald method,” Radio Sci. 43(6), RS6S01 (2008).
[CrossRef]

2007 (6)

F. Capolino, D. R. Wilton, and W. A. Johnson, “Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223(1), 250–261 (2007).
[CrossRef]

K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express 15(26), 17482–17493 (2007).
[CrossRef] [PubMed]

P. Baccarelli, S. Paulotto, and C. Di Nallo, “Full-wave analysis of bound and leaky modes propagating along 2D periodic printed structures with arbitrary metallisation in the unit cell,” IET Proc. Microwaves, Antennas Propag. 1(1), 217–225 (2007).
[CrossRef]

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antenn. Propag. 55(6), 1644–1655 (2007).
[CrossRef]

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Sub-wavelength resolution in linear arrays of plasmonic particles,” J. Appl. Phys. 101(12), 123102 (2007).
[CrossRef]

C. Simovski, S. Tretyakov, and A. Viitanen, “Subwavelength imaging in a superlens of plasmon nanospheres,” Tech. Phys. Lett. 33(3), 264–266 (2007).
[CrossRef]

2006 (5)

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[CrossRef]

D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31(1), 98–100 (2006).
[CrossRef] [PubMed]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
[CrossRef]

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74(20), 205436 (2006).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14(4), 1557–1567 (2006).
[CrossRef] [PubMed]

2005 (4)

F. Capolino, D. R. Jackson, and D. R. Wilton, “Mode excitation from sources in two-dimensional EBG waveguides using the array scanning method,” IEEE Microw. Wirel. Compon. Lett. 15(2), 49–51 (2005).
[CrossRef]

F. Capolino, D. R. Jackson, and D. R. Wilton, “Fundamental properties of the field at the interface between air and a periodic artificial material excited by a line source,” IEEE Trans. Antenn. Propag. 53(1), 91–99 (2005).
[CrossRef]

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41(10), 578–580 (2005).
[CrossRef]

R. A. Shore and A. D. Yaghjian, ““Traveling electromagnetic waves on linear periodic arrays of lossless penetrable spheres,” IEICE Trans. Commun. E88B(6), 2346–2352 (2005).
[CrossRef]

2004 (2)

S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69(12), 125418 (2004).
[CrossRef]

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
[CrossRef]

2003 (1)

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
[CrossRef]

2002 (1)

A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124(35), 10596–10604 (2002).
[CrossRef] [PubMed]

2000 (2)

R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182(4–6), 273–279 (2000).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

1998 (1)

T. Rozzi, L. Pierantoni, and M. Farina, “General constraints on the propagation of complex waves in closed lossless isotropic waveguides,” IEEE Trans. Microw. Theory Tech. 46(5), 512–516 (1998).
[CrossRef]

1994 (2)

1989 (1)

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B Condens. Matter 39(14), 9852–9858 (1989).
[CrossRef] [PubMed]

1969 (1)

J. R. James, “Leaky waves on a dielectric rod,” Electron. Lett. 5(11), 252–254 (1969).
[CrossRef]

1965 (1)

P. J. B. Clarricoats and K. R. Slinn, “Complex modes of propagation in dielectric-loaded circular waveguide,” Electron. Lett. 1(5), 145–146 (1965).
[CrossRef]

1956 (1)

D. E. Muller, “A Method for Solving Algebraic Equations Using an Automatic Computer,” Math. Tables Other Aids Comput. 10(56), 208–215 (1956).
[CrossRef]

Alitalo, P.

S. Steshenko, F. Capolino, P. Alitalo, and S. A. Tretyakov, “Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(1), 016607 (2011).
[CrossRef] [PubMed]

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[CrossRef]

Alu, A.

X. Liu and A. Alu, “Subwavelength leaky-wave optical nanoantennas: directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82(14), 144305 (2010).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, “Effect of small random disorders and imperfections on the performance of arrays of plasmonic nanoparticles,” N. J. Phys. 12(1), 013015 (2010).
[CrossRef]

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74(20), 205436 (2006).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14(4), 1557–1567 (2006).
[CrossRef] [PubMed]

Atwater, H. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
[CrossRef]

Baccarelli, P.

P. Baccarelli, S. Paulotto, and C. Di Nallo, “Full-wave analysis of bound and leaky modes propagating along 2D periodic printed structures with arbitrary metallisation in the unit cell,” IET Proc. Microwaves, Antennas Propag. 1(1), 217–225 (2007).
[CrossRef]

Beermann, J.

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Bozhevolnyi, S. I.

Campione, S.

Cao, Z.

F. Liu, Z. Cao, C. Tang, L. Chen, and Z. Wang, “Ultrathin diamond-like carbon film coated silver nanoparticles-based substrates for surface-enhanced Raman spectroscopy,” ACS Nano 4(5), 2643–2648 (2010).
[CrossRef] [PubMed]

Capolino, F.

A. L. Fructos, S. Campione, F. Capolino, and F. Mesa, “Characterization of complex plasmonic modes in two-dimensional periodic arrays of metal nanospheres,” J. Opt. Soc. Am. B 28(6), 1446–1458 (2011).
[CrossRef]

S. Steshenko, F. Capolino, P. Alitalo, and S. A. Tretyakov, “Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(1), 016607 (2011).
[CrossRef] [PubMed]

F. T. Celepcikay, D. R. Wilton, D. R. Jackson, and F. Capolino, “Choosing splitting parameters and summation limits in the numerical evaluation of 1-D and 2-D periodic Green's functions using the Ewald method,” Radio Sci. 43(6), RS6S01 (2008).
[CrossRef]

F. Capolino, D. R. Wilton, and W. A. Johnson, “Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223(1), 250–261 (2007).
[CrossRef]

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antenn. Propag. 55(6), 1644–1655 (2007).
[CrossRef]

F. Capolino, D. R. Jackson, and D. R. Wilton, “Mode excitation from sources in two-dimensional EBG waveguides using the array scanning method,” IEEE Microw. Wirel. Compon. Lett. 15(2), 49–51 (2005).
[CrossRef]

F. Capolino, D. R. Jackson, and D. R. Wilton, “Fundamental properties of the field at the interface between air and a periodic artificial material excited by a line source,” IEEE Trans. Antenn. Propag. 53(1), 91–99 (2005).
[CrossRef]

Celepcikay, F. T.

F. T. Celepcikay, D. R. Wilton, D. R. Jackson, and F. Capolino, “Choosing splitting parameters and summation limits in the numerical evaluation of 1-D and 2-D periodic Green's functions using the Ewald method,” Radio Sci. 43(6), RS6S01 (2008).
[CrossRef]

Chen, L.

F. Liu, Z. Cao, C. Tang, L. Chen, and Z. Wang, “Ultrathin diamond-like carbon film coated silver nanoparticles-based substrates for surface-enhanced Raman spectroscopy,” ACS Nano 4(5), 2643–2648 (2010).
[CrossRef] [PubMed]

Citrin, D. S.

Clarricoats, P. J. B.

P. J. B. Clarricoats and K. R. Slinn, “Complex modes of propagation in dielectric-loaded circular waveguide,” Electron. Lett. 1(5), 145–146 (1965).
[CrossRef]

Conforti, M.

Corn, R. M.

I. E. Sendroiu and R. M. Corn, “Nanoparticle diffraction gratings for DNA detection on photopatterned glass substrates,” Biointerphases 3(3), FD23–FD29 (2008).
[CrossRef] [PubMed]

Crozier, K. B.

Di Nallo, C.

P. Baccarelli, S. Paulotto, and C. Di Nallo, “Full-wave analysis of bound and leaky modes propagating along 2D periodic printed structures with arbitrary metallisation in the unit cell,” IET Proc. Microwaves, Antennas Propag. 1(1), 217–225 (2007).
[CrossRef]

Doyle, W. T.

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B Condens. Matter 39(14), 9852–9858 (1989).
[CrossRef] [PubMed]

Eleftheriades, G. V.

R. Islam and G. V. Eleftheriades, “On the Independence of the Excitation of Complex Modes in Isotropic Structures,” IEEE Trans. Antenn. Propag. 58(5), 1567–1578 (2010).
[CrossRef]

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Engheta, N.

A. Alù and N. Engheta, “Effect of small random disorders and imperfections on the performance of arrays of plasmonic nanoparticles,” N. J. Phys. 12(1), 013015 (2010).
[CrossRef]

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74(20), 205436 (2006).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14(4), 1557–1567 (2006).
[CrossRef] [PubMed]

Farina, M.

T. Rozzi, L. Pierantoni, and M. Farina, “General constraints on the propagation of complex waves in closed lossless isotropic waveguides,” IEEE Trans. Microw. Theory Tech. 46(5), 512–516 (1998).
[CrossRef]

Felsen, L. B.

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antenn. Propag. 55(6), 1644–1655 (2007).
[CrossRef]

Fructos, A. L.

Gerasimov, V. S.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
[CrossRef]

Guasoni, M.

Haes, A. J.

A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124(35), 10596–10604 (2002).
[CrossRef] [PubMed]

Ho, K. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Isaev, I. L.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
[CrossRef]

Islam, R.

R. Islam and G. V. Eleftheriades, “On the Independence of the Excitation of Complex Modes in Isotropic Structures,” IEEE Trans. Antenn. Propag. 58(5), 1567–1578 (2010).
[CrossRef]

Jablonski, T. F.

Jackson, D. R.

F. T. Celepcikay, D. R. Wilton, D. R. Jackson, and F. Capolino, “Choosing splitting parameters and summation limits in the numerical evaluation of 1-D and 2-D periodic Green's functions using the Ewald method,” Radio Sci. 43(6), RS6S01 (2008).
[CrossRef]

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antenn. Propag. 55(6), 1644–1655 (2007).
[CrossRef]

F. Capolino, D. R. Jackson, and D. R. Wilton, “Mode excitation from sources in two-dimensional EBG waveguides using the array scanning method,” IEEE Microw. Wirel. Compon. Lett. 15(2), 49–51 (2005).
[CrossRef]

F. Capolino, D. R. Jackson, and D. R. Wilton, “Fundamental properties of the field at the interface between air and a periodic artificial material excited by a line source,” IEEE Trans. Antenn. Propag. 53(1), 91–99 (2005).
[CrossRef]

James, J. R.

J. R. James, “Leaky waves on a dielectric rod,” Electron. Lett. 5(11), 252–254 (1969).
[CrossRef]

Johnson, W. A.

F. Capolino, D. R. Wilton, and W. A. Johnson, “Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223(1), 250–261 (2007).
[CrossRef]

Karpov, S. V.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9(12), 4228–4233 (2009).
[CrossRef] [PubMed]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
[CrossRef]

Leosson, K.

Liu, F.

F. Liu, Z. Cao, C. Tang, L. Chen, and Z. Wang, “Ultrathin diamond-like carbon film coated silver nanoparticles-based substrates for surface-enhanced Raman spectroscopy,” ACS Nano 4(5), 2643–2648 (2010).
[CrossRef] [PubMed]

Liu, X.

X. Liu and A. Alu, “Subwavelength leaky-wave optical nanoantennas: directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82(14), 144305 (2010).
[CrossRef]

Mackowski, D. W.

Maier, S. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
[CrossRef]

Markel, V. A.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
[CrossRef]

Mesa, F.

Muller, D. E.

D. E. Muller, “A Method for Solving Algebraic Equations Using an Automatic Computer,” Math. Tables Other Aids Comput. 10(56), 208–215 (1956).
[CrossRef]

Novikov, S. M.

Obuschenko, A. V.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
[CrossRef]

Park, S. Y.

S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69(12), 125418 (2004).
[CrossRef]

Paulotto, S.

P. Baccarelli, S. Paulotto, and C. Di Nallo, “Full-wave analysis of bound and leaky modes propagating along 2D periodic printed structures with arbitrary metallisation in the unit cell,” IET Proc. Microwaves, Antennas Propag. 1(1), 217–225 (2007).
[CrossRef]

Pierantoni, L.

T. Rozzi, L. Pierantoni, and M. Farina, “General constraints on the propagation of complex waves in closed lossless isotropic waveguides,” IEEE Trans. Microw. Theory Tech. 46(5), 512–516 (1998).
[CrossRef]

Polman, A.

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
[CrossRef]

Pustovit, V. N.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
[CrossRef]

Rozzi, T.

T. Rozzi, L. Pierantoni, and M. Farina, “General constraints on the propagation of complex waves in closed lossless isotropic waveguides,” IEEE Trans. Microw. Theory Tech. 46(5), 512–516 (1998).
[CrossRef]

Ruppin, R.

R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182(4–6), 273–279 (2000).
[CrossRef]

Salandrino, A.

Sendroiu, I. E.

I. E. Sendroiu and R. M. Corn, “Nanoparticle diffraction gratings for DNA detection on photopatterned glass substrates,” Biointerphases 3(3), FD23–FD29 (2008).
[CrossRef] [PubMed]

Shore, R. A.

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41(10), 578–580 (2005).
[CrossRef]

R. A. Shore and A. D. Yaghjian, ““Traveling electromagnetic waves on linear periodic arrays of lossless penetrable spheres,” IEICE Trans. Commun. E88B(6), 2346–2352 (2005).
[CrossRef]

Sigalas, M. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Simovski, C.

C. Simovski, S. Tretyakov, and A. Viitanen, “Subwavelength imaging in a superlens of plasmon nanospheres,” Tech. Phys. Lett. 33(3), 264–266 (2007).
[CrossRef]

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[CrossRef]

Simovski, C. R.

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Sub-wavelength resolution in linear arrays of plasmonic particles,” J. Appl. Phys. 101(12), 123102 (2007).
[CrossRef]

Simsek, E.

Slinn, K. R.

P. J. B. Clarricoats and K. R. Slinn, “Complex modes of propagation in dielectric-loaded circular waveguide,” Electron. Lett. 1(5), 145–146 (1965).
[CrossRef]

Soukoulis, C. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Steshenko, S.

S. Steshenko, F. Capolino, P. Alitalo, and S. A. Tretyakov, “Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(1), 016607 (2011).
[CrossRef] [PubMed]

Stroud, D.

S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69(12), 125418 (2004).
[CrossRef]

Tang, C.

F. Liu, Z. Cao, C. Tang, L. Chen, and Z. Wang, “Ultrathin diamond-like carbon film coated silver nanoparticles-based substrates for surface-enhanced Raman spectroscopy,” ACS Nano 4(5), 2643–2648 (2010).
[CrossRef] [PubMed]

Togan, E.

Tretyakov, S.

C. Simovski, S. Tretyakov, and A. Viitanen, “Subwavelength imaging in a superlens of plasmon nanospheres,” Tech. Phys. Lett. 33(3), 264–266 (2007).
[CrossRef]

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[CrossRef]

Tretyakov, S. A.

S. Steshenko, F. Capolino, P. Alitalo, and S. A. Tretyakov, “Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(1), 016607 (2011).
[CrossRef] [PubMed]

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Sub-wavelength resolution in linear arrays of plasmonic particles,” J. Appl. Phys. 101(12), 123102 (2007).
[CrossRef]

Van Duyne, R. P.

A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124(35), 10596–10604 (2002).
[CrossRef] [PubMed]

Viitanen, A.

C. Simovski, S. Tretyakov, and A. Viitanen, “Subwavelength imaging in a superlens of plasmon nanospheres,” Tech. Phys. Lett. 33(3), 264–266 (2007).
[CrossRef]

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[CrossRef]

Viitanen, A. J.

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Sub-wavelength resolution in linear arrays of plasmonic particles,” J. Appl. Phys. 101(12), 123102 (2007).
[CrossRef]

Wang, Z.

F. Liu, Z. Cao, C. Tang, L. Chen, and Z. Wang, “Ultrathin diamond-like carbon film coated silver nanoparticles-based substrates for surface-enhanced Raman spectroscopy,” ACS Nano 4(5), 2643–2648 (2010).
[CrossRef] [PubMed]

Wilton, D. R.

F. T. Celepcikay, D. R. Wilton, D. R. Jackson, and F. Capolino, “Choosing splitting parameters and summation limits in the numerical evaluation of 1-D and 2-D periodic Green's functions using the Ewald method,” Radio Sci. 43(6), RS6S01 (2008).
[CrossRef]

F. Capolino, D. R. Wilton, and W. A. Johnson, “Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223(1), 250–261 (2007).
[CrossRef]

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antenn. Propag. 55(6), 1644–1655 (2007).
[CrossRef]

F. Capolino, D. R. Jackson, and D. R. Wilton, “Mode excitation from sources in two-dimensional EBG waveguides using the array scanning method,” IEEE Microw. Wirel. Compon. Lett. 15(2), 49–51 (2005).
[CrossRef]

F. Capolino, D. R. Jackson, and D. R. Wilton, “Fundamental properties of the field at the interface between air and a periodic artificial material excited by a line source,” IEEE Trans. Antenn. Propag. 53(1), 91–99 (2005).
[CrossRef]

Yaghjian, A. D.

R. A. Shore and A. D. Yaghjian, ““Traveling electromagnetic waves on linear periodic arrays of lossless penetrable spheres,” IEICE Trans. Commun. E88B(6), 2346–2352 (2005).
[CrossRef]

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41(10), 578–580 (2005).
[CrossRef]

Yang, T.

ACS Nano (1)

F. Liu, Z. Cao, C. Tang, L. Chen, and Z. Wang, “Ultrathin diamond-like carbon film coated silver nanoparticles-based substrates for surface-enhanced Raman spectroscopy,” ACS Nano 4(5), 2643–2648 (2010).
[CrossRef] [PubMed]

Biointerphases (1)

I. E. Sendroiu and R. M. Corn, “Nanoparticle diffraction gratings for DNA detection on photopatterned glass substrates,” Biointerphases 3(3), FD23–FD29 (2008).
[CrossRef] [PubMed]

Electron. Lett. (3)

R. A. Shore and A. D. Yaghjian, “Travelling electromagnetic waves on linear periodic arrays of lossless spheres,” Electron. Lett. 41(10), 578–580 (2005).
[CrossRef]

P. J. B. Clarricoats and K. R. Slinn, “Complex modes of propagation in dielectric-loaded circular waveguide,” Electron. Lett. 1(5), 145–146 (1965).
[CrossRef]

J. R. James, “Leaky waves on a dielectric rod,” Electron. Lett. 5(11), 252–254 (1969).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

F. Capolino, D. R. Jackson, and D. R. Wilton, “Mode excitation from sources in two-dimensional EBG waveguides using the array scanning method,” IEEE Microw. Wirel. Compon. Lett. 15(2), 49–51 (2005).
[CrossRef]

IEEE Trans. Antenn. Propag. (3)

R. Islam and G. V. Eleftheriades, “On the Independence of the Excitation of Complex Modes in Isotropic Structures,” IEEE Trans. Antenn. Propag. 58(5), 1567–1578 (2010).
[CrossRef]

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antenn. Propag. 55(6), 1644–1655 (2007).
[CrossRef]

F. Capolino, D. R. Jackson, and D. R. Wilton, “Fundamental properties of the field at the interface between air and a periodic artificial material excited by a line source,” IEEE Trans. Antenn. Propag. 53(1), 91–99 (2005).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

T. Rozzi, L. Pierantoni, and M. Farina, “General constraints on the propagation of complex waves in closed lossless isotropic waveguides,” IEEE Trans. Microw. Theory Tech. 46(5), 512–516 (1998).
[CrossRef]

IEICE Trans. Commun. (1)

R. A. Shore and A. D. Yaghjian, ““Traveling electromagnetic waves on linear periodic arrays of lossless penetrable spheres,” IEICE Trans. Commun. E88B(6), 2346–2352 (2005).
[CrossRef]

IET Proc. Microwaves, Antennas Propag. (1)

P. Baccarelli, S. Paulotto, and C. Di Nallo, “Full-wave analysis of bound and leaky modes propagating along 2D periodic printed structures with arbitrary metallisation in the unit cell,” IET Proc. Microwaves, Antennas Propag. 1(1), 217–225 (2007).
[CrossRef]

J. Am. Chem. Soc. (1)

A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124(35), 10596–10604 (2002).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, “Sub-wavelength resolution in linear arrays of plasmonic particles,” J. Appl. Phys. 101(12), 123102 (2007).
[CrossRef]

J. Comput. Phys. (1)

F. Capolino, D. R. Wilton, and W. A. Johnson, “Efficient computation of the 3D Green's function for the Helmholtz operator for a linear array of point sources using the Ewald method,” J. Comput. Phys. 223(1), 250–261 (2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Math. Tables Other Aids Comput. (1)

D. E. Muller, “A Method for Solving Algebraic Equations Using an Automatic Computer,” Math. Tables Other Aids Comput. 10(56), 208–215 (1956).
[CrossRef]

N. J. Phys. (1)

A. Alù and N. Engheta, “Effect of small random disorders and imperfections on the performance of arrays of plasmonic nanoparticles,” N. J. Phys. 12(1), 013015 (2010).
[CrossRef]

Nano Lett. (1)

A. F. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9(12), 4228–4233 (2009).
[CrossRef] [PubMed]

Opt. Commun. (1)

R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. 182(4–6), 273–279 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (8)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70(5), 054202 (2004).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
[CrossRef]

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74(20), 205436 (2006).
[CrossRef]

X. Liu and A. Alu, “Subwavelength leaky-wave optical nanoantennas: directive radiation from linear arrays of plasmonic nanoparticles,” Phys. Rev. B 82(14), 144305 (2010).
[CrossRef]

P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74(23), 235425 (2006).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
[CrossRef]

S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69(12), 125418 (2004).
[CrossRef]

Phys. Rev. B Condens. Matter (1)

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B Condens. Matter 39(14), 9852–9858 (1989).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

S. Steshenko, F. Capolino, P. Alitalo, and S. A. Tretyakov, “Effective model and investigation of the near-field enhancement and subwavelength imaging properties of multilayer arrays of plasmonic nanospheres,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(1), 016607 (2011).
[CrossRef] [PubMed]

Radio Sci. (1)

F. T. Celepcikay, D. R. Wilton, D. R. Jackson, and F. Capolino, “Choosing splitting parameters and summation limits in the numerical evaluation of 1-D and 2-D periodic Green's functions using the Ewald method,” Radio Sci. 43(6), RS6S01 (2008).
[CrossRef]

Tech. Phys. Lett. (1)

C. Simovski, S. Tretyakov, and A. Viitanen, “Subwavelength imaging in a superlens of plasmon nanospheres,” Tech. Phys. Lett. 33(3), 264–266 (2007).
[CrossRef]

Other (15)

S. Steshenko, F. Capolino, S. A. Tretyakov, and C. R. Simovski, “Super-Resolution and Near-Field Enhancement with Layers of Resonant Arrays of Nanoparticles,” in Applications of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 4.1.

I. Firkowska, S. Giannona, J. A. Rojas-Chapana, K. Luecke, O. Brustle, and M. Giersig, “Biocompatible Nanomaterials and Nanodevices Promising for Biomedical Applications ” in Nanomaterials for Application in Medicine and Biology, M. Giersig, and G. B. Khomutov, eds. (Springer, Berlin, 2008), p. I.1.

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

S. Steshenko and F. Capolino, “Single Dipole Approximation for Modeling Collections of Nanoscatterers,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 8.1.

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

R. A. Shore and A. D. Yaghjian, “Complex Waves on 1D, 2D, and 3D Periodic Arrays of Lossy and Lossless Magnetodielectric Spheres,” AFRL-RY-HS-TR-2010–0019, (Air Force Research Laboratory, Hanscom, MA 2010).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).

F. Capolino, D. R. Jackson, and D. R. Wilton, “Field Representations in Periodic Artificial Materials Excited by a Source,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 12.1.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, 1994).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes: the art of scientific computing (Cambridge University Press, 2007).

“IMSL Fortran Numerical Library,” (Visual Numerics Corporate Headquarters, 2500 Wilcrest Drive, Suite 200, Houston, TX), www.vni.com .

V. R. Komanduri, F. Capolino, D. R. Jackson, and D. R. Wilton, “Computation of the one-dimensional free-space periodic green's function for leaky waves using the ewald method,” in Proc. URSI Gen. Ass.(Chicago, IL, 2008).

A. A. Oliner and D. R. Jackson, “Leaky-wave antennas,” in Antenna Engineering Handbook, J. Volakis, ed. (McGraw Hill, 2007), p. 11.1.

J. D. Rhodes, “General constraints on propagation characteristics of electromagnetic waves in uniform inhomogeneous waveguides,” in Proc. Inst. Electr. Eng. 118, 849–856 (1971).

S. Campione and F. Capolino, “Linear and Planar Periodic Arrays of Metallic Nanospheres: Fabrication, Optical Properties and Applications,” in Selected Topics in Metamaterials and Photonic Crystals, A. Andreone, A. Cusano, A. Cutolo, and V. Galdi, eds. (World Scientific Publishing, 2011), pp. 141–194.

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Figures (9)

Fig. 1
Fig. 1

Linear chain of plasmonic nanospheres embedded in a homogeneous medium with permittivity ε h . The radius of each nanosphere is r, and the array spatial period is d.

Fig. 2
Fig. 2

Illustration of a physical complex wave for an observer along the positive z axis, according to its classification provided in Table 1. (A) and (B) represent forward and backward bound waves. (C) and (D) represent forward and backward leaky waves.

Fig. 3
Fig. 3

Dispersion diagram for T-pol. (a) Real part and (b) imaginary part of the wavenumber of the fundamental FW k z = β z + i α z .

Fig. 4
Fig. 4

Modal wavenumbers in the complex relative k z plane for T-pol, normalized with respect to (a) the spatial period d, and (b) the host wavenumber k = k 0 ε h (here ε h = 1 ). Note that in (b), crossing “1” in the abscissa means crossing the light line. The shown curves are parametric curves of frequency, and the arrows indicate direction of increasing frequency.

Fig. 5
Fig. 5

As in Fig. 3, for L-pol.

Fig. 6
Fig. 6

As in Fig. 4, for L-pol. Inset in (b) shows the modal wavenumbers zero crossing.

Fig. 7
Fig. 7

Dependence of the ‘Proper 1’ bound mode (solid line) and ‘Improper 1’ leaky mode (dashed line) for T-pol in Fig. 3 with respect to the geometrical parameters of the linear array. The analyzed array is the same as in Sec. 3. In (a) d = 75 nm and r varies from 15 nm to 35 nm. In (b) r = 25 nm and d varies from 55 nm to 100 nm.

Fig. 8
Fig. 8

Parameter analysis as in Fig. 7, but for the ‘Improper 1’ leaky mode for L-pol in Fig. 5.

Fig. 9
Fig. 9

Complex k z wavenumber plane (assuming k < π / d ). The field produced by a dipole source is represented by the integration path along the real axis. For an observer along the positive z axis, the path can be deformed in the upper half space. The poles encountered represent waves (each mode is represented by an infinite set of residues). The SDPs around the branch points at k z = k z b , p = k 2 π p / d represent the “space wave” or continuous spectrum terms [41,44,45,49]. Physical modes (only the harmonic in the fundamental BZ, i.e., p = 0, is indicated) are those relative to poles captured in the three indicated regions (R1, R2 and R3). In each region, it is indicated the type of physical pole that can be captured (physical wave harmonic). PB = proper bound, PL = proper leaky, and IL = improper leaky wave.

Tables (1)

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Table 1 Classification of Physical Modes with Complex Wavenumbers, Based on the Wavenumber of the Mode-Harmonic in the Fundamental BZ

Equations (22)

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p n = α ee E n loc ,
α ee = 6 π ε 0 ε h i k 3 m ψ 1 ( m k r ) ψ 1 ( k r ) ψ 1 ( k r ) ψ 1 ( m k r ) m ψ 1 ( m k r ) ξ 1 ( k r ) ξ 1 ( k r ) ψ 1 ( m k r ) ,
E 0 loc ( k z ) = E inc ( k z ) + G _ ( k z ) p 0 ,
G _ ( k z ) = n = ( n 0 ) G _ n e i n k z d ,
G _ n = e i k | n | d 4 π ε 0 ε h [ ( k 2 | n | d + i k ( | n | d ) 2 1 ( | n | d ) 3 ) I _ ( k 2 | n | d + 3 i k ( | n | d ) 2 3 ( | n | d ) 3 ) z ^ z ^ ] ,
A _ ( k z ) p 0 = α ee E inc ( k z ) ,            A _ ( k z ) = I _ α ee G _ ( k z ) .
E mode ( r , k z ) = p = e i k z , p z e p mode ( x , y , k z ) ,
E ( r , r 0 ) = d 2 π - e i k z z e 0 ( x , y , r 0 , k z )     d k z ,
E ( r , r 0 ) = n E n mode ( r , r 0 , k z n ) + E t o t sp ( r , r 0 ) .
G _ ( k z ) = G _ spectral ( k z ) + G _ spatial ( k z ) ,
G _ spectral ( k z ) = 1 ε h ε 0 [ k 2 G spectral ( k z ) I _ + H _ spectral ( k z ) ] ,
G _ spatial ( k z ) = 1 ε h ε 0 [ k 2 G spatial ( k z ) I _ + H _ spatial ( k z ) ] .
G spectral ( k z ) = 1 4 π d p = E 1 G ( k ρ , p 2 4 E 2 )   ,
G spatial ( k z ) = 1 8 π n = ( n 0 ) e i k z n d r n f ( r n ) + f ( 0 ) 2 i k 8 π ,
f ( r n ) = e i k r n erfc ( β ) + e i k r n erfc ( β + ) ,        β ± = r n E ± i k 2 E ,
H _ spectral ( k z ) = 1 4 π d p = F _ spectral, p ( k z ) ,
H _ spatial ( k z ) = 1 8 π n = ( n 0 ) e i k z n d F _ spatial, n ( k z ) + 1 8 π f ( 0 ) + 2 i k 3 3 I _ ,
F _ spectral, p ( k z ) = [ 2 E 2 E 2 G ( k ρ , p 2 4 E 2 ) ( I _ z ^ z ^ ) E 1 G ( k ρ , p 2 4 E 2 ) k z , p 2 z ^ z ^ ] ,
F _ spatial, n ( k z ) = ( f ( r n ) r n 2 f ( r n ) r n 3 ) I _ + ( f ( r n ) r n 3 f ( r n ) r n 2 + 3 f ( r n ) r n 3 ) z ^ z ^ ,
H 0 (1) ( k ρ , p ρ ) 2 π k ρ , p ρ e i ( k ρ , p ρ π 4 ) e i k ρ , p ρ k ρ , p ρ       ( π < arg  k ρ , p < 2 π ) ,
{ π < arg ( ξ e m π i ) < 0 ,     m = 1         Improper 0 < arg ( ξ e m π i ) < π ,       m = 0          Proper    π < arg ( ξ e m π i ) < 2 π ,     m = + 1         Improper .
H 0 (1) ( k ρ , p ρ ) = H 0 (1) ( ξ ρ ) 2 m J 0 ( ξ ρ ) e i Re ( ξ ) ρ e Im ( ξ ) ρ ξ ρ ( 1 m ) m e i Re ( ξ ) ρ e Im ( ξ ) ρ ξ ρ ,

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