Abstract

In this contribution, we propose a computational tool for the synthesis of metallic nanowires with optimized optical properties, e.g. maximal scattering cross-section at a given wavelength. For this, we employ a rigorous numerical method, based on the solution of surface integral equations, along with a heuristic optimization technique that belongs to the population-based set known as Evolutionary Algorithms. Also, we make use of a general representation scheme to model, in a more realistic manner, the arbitrary geometry of the nanowires. The performance of this approach is evaluated through some examples involving various wavelengths, materials, and optimization strategies. The results of our numerical experiments show that this hybrid technique is a suitable and versatile tool straightforwardly extensible for the design of different configurations of interest in Plasmonics.

© 2012 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  35. O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Optical scattering resonances of single and coupled dimer plasmonic nanoantennas,” Opt. Express 15, 17736–17746 (2007).
    [CrossRef] [PubMed]
  36. C. I. Valencia, E. R. Méndez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by two-dimensional particles,” J. Opt. Soc. Am. B 20, 2150–2161 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  39. H. G. Beyer, The Theory of Evolution Strategies (Springer-Verlag, 2001).
  40. J. Gielis, “A generic geometric transformation that unifies a wide range of natural and abstract shapes,” Am. J. Bot. 90, 333–338 (2003).
    [CrossRef] [PubMed]
  41. T. Wriedt, “Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superel-lipsoids and realistically shaped particles,” Part. Part. Syst. Charact 4, 256–268 (2002).
    [CrossRef]
  42. J. G. Digalakis and K. G. Margaritis, “An experimental study of benchmarking functions for genetic algorithms,” Intern. J. Computer Math. 77, 481–506 (2002).
    [CrossRef]
  43. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
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  45. R. Poli, J. Kennedy, and T. Blackwell, “Particle Swarm Optimisation: an overview,” Swarm Intell. 1, 33–57 (2007).
    [CrossRef]
  46. N. Berkovitch, P. Ginzburg, and M. Orenstein, “Concave plasmonic particles: broad-band geometrical tunability in the near-infrared,” Nano Lett 10, 1405–1408 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]

2012

R. Rodríguez-Oliveros and J. A. Sánchez-Gil, “Gold nanostars as thermoplasmonic nanoparticles for optical heating,” Opt. Express 20, 621–626 (2012).
[CrossRef] [PubMed]

C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012)
[CrossRef] [PubMed]

F. López-Tejeira, R. Paniagua-Domínguez, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Fano-like interference of plasmon resonances at a single rod-shaped nanoantenna,” New J. Phys. 14, 023035 (2012).
[CrossRef]

2011

J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11, 1280–1283 (2011).
[CrossRef] [PubMed]

R. Rodríguez-Oliveros and J. A. Sánchez-Gil, “Localized surface-plasmon resonances on single and coupled nanoparticles through surface integral equations for flexible surface,” Opt. Express 19, 12208–12219 (2011).
[CrossRef] [PubMed]

S. Kessentini, D. Barchiesi, T. Grosges, and M. Lamy de la Chapelle, “Selective and collaborative optimization methods for plasmonics: a comparison,” PIERS Online 7, 291–295 (2011).

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P. M. Adam, and R. Rodríguez-Oliveros, “Metal nanostars: stochastic optimization of resonant scattering properties,” Superlattice Microst. 49, 288–293 (2011).
[CrossRef]

M. J. Mendes, I. Tobías, A. Martí, and A. Luque, “Light concentration in the near-field of dielectric spheroidal particles with mesoscopic sizes,” Opt. Express 19, 2847–2858 (2011).
[CrossRef]

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nanoparticles,” Nano Lett. 11, 2329–2333 (2011).
[CrossRef] [PubMed]

J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011).
[CrossRef] [PubMed]

E. A. Coronado, E. R. Encina, and F. D. Stefani, “Optical properties of metallic nanoparticles: manipulating light, heat and forces at the nanoscale,” Nanoscale 3, 4042–4059 (2011).
[CrossRef] [PubMed]

C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jackel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11, 402–407 (2011).
[CrossRef] [PubMed]

2010

S. Barbosa, A. Agrawal, L. Rodríguez-Lorenzo, I. Pastoriza-Santos, R. A. Alvarez-Puebla, A. Kornowski, H. Weller, and L. M. Liz-Marzán, “Tuning size and sensing properties in colloidal gold nanostars,” Langmuir 26, 14943–14950 (2010).
[CrossRef] [PubMed]

L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, F. J. García de Abajo, and L. M. Liz-Marzán, “Surface-enhanced Raman scattering using star-shaped gold colloidal nanoparticles,” J. Phys. Chem. C 114, 7336–7340 (2010).
[CrossRef]

S. K. Dondapati, T. K. Sau, C. Hrelescu, T. A. Klar, F. D. Stefani, and J. Feldmann, “Label-free biosensing based on single gold nanostars as plasmonic transducers,” ACS Nano 4, 6318–6322 (2010).
[CrossRef] [PubMed]

V. Giannini, A. Fernandez-Dominguez, Y. Sonnefraud, T. Roschuk, R. Fernandez-García, and S. A. Maier, “Controlling light localization and light-matter interactions with nanoplasmonics,” Small 6, 2498–2507 (2010).
[CrossRef] [PubMed]

U. Guler and R. Turan, “Effect of particle properties and light polarization on the plasmonic resonances in metallic nanoparticles,” Opt. Express 18, 17322–17338 (2010).
[CrossRef] [PubMed]

V. Giannini, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Surface plasmon resonances of metallic nanostars/nanoflowers for surface-enhanced Raman scattering,” Plasmonics 5, 99–104 (2010).
[CrossRef]

C. Forestiere, M. Donelli, G. F. Walsh, E. Zeni, G. Miano, and L. Dal Negro, “Particle-swarm optimization of broadband nanoplasmonic arrays,” Opt. Lett. 35, 133–135 (2010).
[CrossRef] [PubMed]

N. Berkovitch, P. Ginzburg, and M. Orenstein, “Concave plasmonic particles: broad-band geometrical tunability in the near-infrared,” Nano Lett 10, 1405–1408 (2010).
[CrossRef] [PubMed]

2009

2008

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. García de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).
[CrossRef]

C. G. Khoury and T. Vo-Dinh, “Gold nanostars for surface-enhanced raman scattering: synthesis, characterization and optimization,” J. Phys. Chem. C 112, 18849–18859 (2008).

P. Senthil Kumar, I. Pastoriza-Santos, B. Rodríguez-González, F. Javier García de Abajo, and L. M. Liz-Marzán, “High-yield synthesis and optical response of gold nanostars,” Nanotechnology 19, 015606 (2008).
[CrossRef] [PubMed]

D. Macías and A. Vial, “Optimal design of plasmonic nanostructures for plasmon-interference assisted lithography,” Appl. Phys. B 93, 159–163 (2008).
[CrossRef]

T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
[CrossRef] [PubMed]

I. Grigorenko, S. Haas, A. Balatsky, and A. F. J. Levi, “Optimal control of electromagnetic field using metallic nanoclusters,” New J. Phys. 10, 043017 (2008).
[CrossRef]

2007

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
[CrossRef] [PubMed]

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Optical scattering resonances of single and coupled dimer plasmonic nanoantennas,” Opt. Express 15, 17736–17746 (2007).
[CrossRef] [PubMed]

V. Giannini and J. A. Sánchez-Gil, “Calculations of light scattering from isolated and interacting metallic nanowires of arbitrary cross section by means of Green’s theorem surface integral equations in parametric form,” J. Opt. Soc. Am. A 24, 2822–2830 (2007).
[CrossRef]

C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111, 3806–3819 (2007).
[CrossRef]

R. Poli, J. Kennedy, and T. Blackwell, “Particle Swarm Optimisation: an overview,” Swarm Intell. 1, 33–57 (2007).
[CrossRef]

2006

D. Macías, G. Olague, and E. R. Méndez, “Inverse scattering with far-field intensity data: random surfaces that belong to a well-defined statistical class,” Wave Random Complex 16, 545–560 (2006).
[CrossRef]

2004

2003

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220, 137–141 (2003).
[CrossRef]

C. I. Valencia, E. R. Méndez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by two-dimensional particles,” J. Opt. Soc. Am. B 20, 2150–2161 (2003).
[CrossRef]

J. Gielis, “A generic geometric transformation that unifies a wide range of natural and abstract shapes,” Am. J. Bot. 90, 333–338 (2003).
[CrossRef] [PubMed]

2002

T. Wriedt, “Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superel-lipsoids and realistically shaped particles,” Part. Part. Syst. Charact 4, 256–268 (2002).
[CrossRef]

J. G. Digalakis and K. G. Margaritis, “An experimental study of benchmarking functions for genetic algorithms,” Intern. J. Computer Math. 77, 481–506 (2002).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1954

U. Hohenester and J. Krenn, “Surface plasmon resonances of single and coupled metallic nanoparticles: A boundary integral method approach,” Phys. Rev. B 72, 195429 (2005).

1952

M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” J. Res. Nat. Bur. Stand. 49, 409–436 (1952).

Adam, P. M.

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P. M. Adam, and R. Rodríguez-Oliveros, “Metal nanostars: stochastic optimization of resonant scattering properties,” Superlattice Microst. 49, 288–293 (2011).
[CrossRef]

Agrawal, A.

S. Barbosa, A. Agrawal, L. Rodríguez-Lorenzo, I. Pastoriza-Santos, R. A. Alvarez-Puebla, A. Kornowski, H. Weller, and L. M. Liz-Marzán, “Tuning size and sensing properties in colloidal gold nanostars,” Langmuir 26, 14943–14950 (2010).
[CrossRef] [PubMed]

Alvarez-Puebla, R. A.

S. Barbosa, A. Agrawal, L. Rodríguez-Lorenzo, I. Pastoriza-Santos, R. A. Alvarez-Puebla, A. Kornowski, H. Weller, and L. M. Liz-Marzán, “Tuning size and sensing properties in colloidal gold nanostars,” Langmuir 26, 14943–14950 (2010).
[CrossRef] [PubMed]

Álvarez-Puebla, R. A.

L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, F. J. García de Abajo, and L. M. Liz-Marzán, “Surface-enhanced Raman scattering using star-shaped gold colloidal nanoparticles,” J. Phys. Chem. C 114, 7336–7340 (2010).
[CrossRef]

Aussenegg, F. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220, 137–141 (2003).
[CrossRef]

Bachelot, R.

Balatsky, A.

I. Grigorenko, S. Haas, A. Balatsky, and A. F. J. Levi, “Optimal control of electromagnetic field using metallic nanoclusters,” New J. Phys. 10, 043017 (2008).
[CrossRef]

Barbosa, S.

S. Barbosa, A. Agrawal, L. Rodríguez-Lorenzo, I. Pastoriza-Santos, R. A. Alvarez-Puebla, A. Kornowski, H. Weller, and L. M. Liz-Marzán, “Tuning size and sensing properties in colloidal gold nanostars,” Langmuir 26, 14943–14950 (2010).
[CrossRef] [PubMed]

Barchiesi, D.

Baudrion, A. L.

Berkovitch, N.

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nanoparticles,” Nano Lett. 11, 2329–2333 (2011).
[CrossRef] [PubMed]

N. Berkovitch, P. Ginzburg, and M. Orenstein, “Concave plasmonic particles: broad-band geometrical tunability in the near-infrared,” Nano Lett 10, 1405–1408 (2010).
[CrossRef] [PubMed]

Beyer, H. G.

H. G. Beyer, The Theory of Evolution Strategies (Springer-Verlag, 2001).

Blackwell, T.

R. Poli, J. Kennedy, and T. Blackwell, “Particle Swarm Optimisation: an overview,” Swarm Intell. 1, 33–57 (2007).
[CrossRef]

Capretti, A.

C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012)
[CrossRef] [PubMed]

Carbó-Argibay, E.

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. García de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).
[CrossRef]

Charra, F.

C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jackel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11, 402–407 (2011).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Coronado, E. A.

E. A. Coronado, E. R. Encina, and F. D. Stefani, “Optical properties of metallic nanoparticles: manipulating light, heat and forces at the nanoscale,” Nanoscale 3, 4042–4059 (2011).
[CrossRef] [PubMed]

Dal Negro, L.

C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012)
[CrossRef] [PubMed]

C. Forestiere, M. Donelli, G. F. Walsh, E. Zeni, G. Miano, and L. Dal Negro, “Particle-swarm optimization of broadband nanoplasmonic arrays,” Opt. Lett. 35, 133–135 (2010).
[CrossRef] [PubMed]

Digalakis, J. G.

J. G. Digalakis and K. G. Margaritis, “An experimental study of benchmarking functions for genetic algorithms,” Intern. J. Computer Math. 77, 481–506 (2002).
[CrossRef]

Ding, W.

Dondapati, S. K.

S. K. Dondapati, T. K. Sau, C. Hrelescu, T. A. Klar, F. D. Stefani, and J. Feldmann, “Label-free biosensing based on single gold nanostars as plasmonic transducers,” ACS Nano 4, 6318–6322 (2010).
[CrossRef] [PubMed]

Donelli, M.

Douillard, L.

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[CrossRef]

V. Giannini, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Surface plasmon resonances of metallic nanostars/nanoflowers for surface-enhanced Raman scattering,” Plasmonics 5, 99–104 (2010).
[CrossRef]

V. Giannini and J. A. Sánchez-Gil, “Calculations of light scattering from isolated and interacting metallic nanowires of arbitrary cross section by means of Green’s theorem surface integral equations in parametric form,” J. Opt. Soc. Am. A 24, 2822–2830 (2007).
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[CrossRef] [PubMed]

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Optical scattering resonances of single and coupled dimer plasmonic nanoantennas,” Opt. Express 15, 17736–17746 (2007).
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C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jackel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11, 402–407 (2011).
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P. Senthil Kumar, I. Pastoriza-Santos, B. Rodríguez-González, F. Javier García de Abajo, and L. M. Liz-Marzán, “High-yield synthesis and optical response of gold nanostars,” Nanotechnology 19, 015606 (2008).
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P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nanoparticles,” Nano Lett. 11, 2329–2333 (2011).
[CrossRef] [PubMed]

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V. Giannini, A. Fernandez-Dominguez, Y. Sonnefraud, T. Roschuk, R. Fernandez-García, and S. A. Maier, “Controlling light localization and light-matter interactions with nanoplasmonics,” Small 6, 2498–2507 (2010).
[CrossRef] [PubMed]

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E. A. Coronado, E. R. Encina, and F. D. Stefani, “Optical properties of metallic nanoparticles: manipulating light, heat and forces at the nanoscale,” Nanoscale 3, 4042–4059 (2011).
[CrossRef] [PubMed]

S. K. Dondapati, T. K. Sau, C. Hrelescu, T. A. Klar, F. D. Stefani, and J. Feldmann, “Label-free biosensing based on single gold nanostars as plasmonic transducers,” ACS Nano 4, 6318–6322 (2010).
[CrossRef] [PubMed]

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M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” J. Res. Nat. Bur. Stand. 49, 409–436 (1952).

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C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012)
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A. Tassadit, D. Macías, J. A. Sánchez-Gil, P. M. Adam, and R. Rodríguez-Oliveros, “Metal nanostars: stochastic optimization of resonant scattering properties,” Superlattice Microst. 49, 288–293 (2011).
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D. Macías and A. Vial, “Optimal design of plasmonic nanostructures for plasmon-interference assisted lithography,” Appl. Phys. B 93, 159–163 (2008).
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Wehrens, R.

R. Wehrens and M. B. Lutgarde, “Classical and nonclassical optimization methods,” in Encyclopedia of Analytical Chemistry, R. A. Meyers, ed. (Wiley, 2000), pp. 9678–9689.

Weller, H.

S. Barbosa, A. Agrawal, L. Rodríguez-Lorenzo, I. Pastoriza-Santos, R. A. Alvarez-Puebla, A. Kornowski, H. Weller, and L. M. Liz-Marzán, “Tuning size and sensing properties in colloidal gold nanostars,” Langmuir 26, 14943–14950 (2010).
[CrossRef] [PubMed]

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T. Wriedt, “Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superel-lipsoids and realistically shaped particles,” Part. Part. Syst. Charact 4, 256–268 (2002).
[CrossRef]

Zeni, E.

Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

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J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11, 1280–1283 (2011).
[CrossRef] [PubMed]

ACS Nano

S. K. Dondapati, T. K. Sau, C. Hrelescu, T. A. Klar, F. D. Stefani, and J. Feldmann, “Label-free biosensing based on single gold nanostars as plasmonic transducers,” ACS Nano 4, 6318–6322 (2010).
[CrossRef] [PubMed]

Adv. Mater.

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. García de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).
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[CrossRef]

Appl. Phys. Lett.

C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, and J. Feldmann, “Single gold nanostars enhance Raman scattering,” Appl. Phys. Lett. 94, 153113 (2009).
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[CrossRef]

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J. Opt. Soc. Am. B

J. Phys. Chem. B

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

J. Phys. Chem. C

C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111, 3806–3819 (2007).
[CrossRef]

L. Rodríguez-Lorenzo, R. A. Álvarez-Puebla, F. J. García de Abajo, and L. M. Liz-Marzán, “Surface-enhanced Raman scattering using star-shaped gold colloidal nanoparticles,” J. Phys. Chem. C 114, 7336–7340 (2010).
[CrossRef]

C. G. Khoury and T. Vo-Dinh, “Gold nanostars for surface-enhanced raman scattering: synthesis, characterization and optimization,” J. Phys. Chem. C 112, 18849–18859 (2008).

J. Res. Nat. Bur. Stand.

M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” J. Res. Nat. Bur. Stand. 49, 409–436 (1952).

Langmuir

S. Barbosa, A. Agrawal, L. Rodríguez-Lorenzo, I. Pastoriza-Santos, R. A. Alvarez-Puebla, A. Kornowski, H. Weller, and L. M. Liz-Marzán, “Tuning size and sensing properties in colloidal gold nanostars,” Langmuir 26, 14943–14950 (2010).
[CrossRef] [PubMed]

Nano Lett

N. Berkovitch, P. Ginzburg, and M. Orenstein, “Concave plasmonic particles: broad-band geometrical tunability in the near-infrared,” Nano Lett 10, 1405–1408 (2010).
[CrossRef] [PubMed]

Nano Lett.

J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11, 1280–1283 (2011).
[CrossRef] [PubMed]

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7, 2871–2875 (2007).
[CrossRef] [PubMed]

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nanoparticles,” Nano Lett. 11, 2329–2333 (2011).
[CrossRef] [PubMed]

C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jackel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11, 402–407 (2011).
[CrossRef] [PubMed]

C. Forestiere, A. J. Pasquale, A. Capretti, G. Miano, A. Tamburrino, S. Y. Lee, B. M. Reinhard, and L. Dal Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012)
[CrossRef] [PubMed]

Nanoscale

E. A. Coronado, E. R. Encina, and F. D. Stefani, “Optical properties of metallic nanoparticles: manipulating light, heat and forces at the nanoscale,” Nanoscale 3, 4042–4059 (2011).
[CrossRef] [PubMed]

Nanotechnology

P. Senthil Kumar, I. Pastoriza-Santos, B. Rodríguez-González, F. Javier García de Abajo, and L. M. Liz-Marzán, “High-yield synthesis and optical response of gold nanostars,” Nanotechnology 19, 015606 (2008).
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Opt. Express

Opt. Lett.

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T. Wriedt, “Using the T-Matrix method for light scattering computations by non-axisymmetric particles: superel-lipsoids and realistically shaped particles,” Part. Part. Syst. Charact 4, 256–268 (2002).
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Plasmonics

V. Giannini, R. Rodríguez-Oliveros, and J. A. Sánchez-Gil, “Surface plasmon resonances of metallic nanostars/nanoflowers for surface-enhanced Raman scattering,” Plasmonics 5, 99–104 (2010).
[CrossRef]

Small

V. Giannini, A. Fernandez-Dominguez, Y. Sonnefraud, T. Roschuk, R. Fernandez-García, and S. A. Maier, “Controlling light localization and light-matter interactions with nanoplasmonics,” Small 6, 2498–2507 (2010).
[CrossRef] [PubMed]

Superlattice Microst.

A. Tassadit, D. Macías, J. A. Sánchez-Gil, P. M. Adam, and R. Rodríguez-Oliveros, “Metal nanostars: stochastic optimization of resonant scattering properties,” Superlattice Microst. 49, 288–293 (2011).
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[CrossRef]

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Supplementary Material (1)

» Media 1: MOV (570 KB)     

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Figures (14)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Geometries generated with Eq. (9). In all these cases we have assumed rint = 1.

Fig. 3
Fig. 3

Proof-of-concept test to illustrate of the convergence behavior of an evolution strategy. The contour lines correspond to the benchmark function given by Eq. (11) ( Media 1).

Fig. 4
Fig. 4

Convergence behavior of the (μ/ρ, λ) − ES, the (μ/ρ + λ) − ES and the PSO algorithms employed in this work.

Fig. 5
Fig. 5

(a)Geometries and (b) Optimized Spectra obtained with the (μ/ρ, λ) − ES, the (μ/ρ +λ) − ES and the PSO algorithms. The solid black line shows the spectral position of the optimum.

Fig. 6
Fig. 6

Logarithmic near-field intensity maps associated to the geometry obtained with the (μ/ρ +λ) − ES corresponding to (a) the wavelength of resonance (λ = 532 nm) and (b) out of it (λ = 700) nm. The field intensity inside the nanostars is set to 1 for the sake of clarity.

Fig. 7
Fig. 7

(a)Resulting star-like geometries obtained after optimization, (b) SCS related to the geometries optimized with the (μ/ρ + λ) − ES considering different wavelengths. As in Fig. 6, the solid black vertical lines indicate the spectral position of the optimum.

Fig. 8
Fig. 8

Convergence behavior associated to the (μ/ρ + λ) − ES for a nanostar of gold. The wavelengths considered for the optimization are λ = 532 nm and λ = 633 nm. The nanostructure was illuminated with a p-polarized plane wave at normal incidence

Fig. 9
Fig. 9

(a) Geometries and (b) Optimized Spectra obtained with the (μ/ρ +λ) − ES. The black vertical lines represent the wavelengths considered from the optimization process.

Fig. 10
Fig. 10

SCS surface for : (a) λ = 532 nm and Ag, (b) λ = 532 nm and Au, (c) λ = 633 nm and Ag, (d) λ = 633 nm and Au. In all these cases the star-like geometry was illuminated with a p-polarized plane wave at normal incidence.

Fig. 11
Fig. 11

(a)Geometries and (b) Optimized Spectra obtained with the (μ/ρ +λ) − ES for silver star-like geometries with five and six tips. As in previously, the solid black vertical line indicates the spectral position of the maximum.

Fig. 12
Fig. 12

Near-field intensity maps associated to the geometries shown in Fig. 11

Fig. 13
Fig. 13

(a) Configuration of the dimer geometry to be optimized: the gap width is fixed at W = 20 nm. (b) NF (at the gap center) spectra (solid curve) corresponding to the dimer nanoantenna (L = 99 nm and h = 15 nm) optimized with the (μ/ρ + λ) − ES for maximum near-field intensity at the gap center at λ = 800 nm (normal incidence). The SCS is also shown (dashed curve) for comparison. Inset: Convergence behavior of the algorithm.

Fig. 14
Fig. 14

NF at the gap center (solid curves) and SCS (dashed curves) spectra of two dimer nanoantennas optimized with the (μ/ρ +λ) − ES for maximum near-field intensity at the gap center at λ = 510 nm (normal incidence). The results shown correspond to two realizations of the algorithm: L = 99.7 nm and h = 15 nm (red curve), and L = 120 nm and h = 40 nm (blue curve).

Equations (11)

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Ψ ( r , t ) = ( 0 , ψ ( r ) , 0 ) exp { i ω t } ,
R p ( θ | ω ) = i 2 α I ( q ) d s exp { i q sc r } × [ ( i q sc n ^ ) φ ( r | ω ) χ ( r | ω ) ] ,
C p ( ω ) = 0 2 π | R p ( θ | ω ) | 2 | ψ p ( ω ) inc | 2 d θ .
× H ( r ) = i ω c ε I E ( r )
E 1 ( p ) ( r | ω ) = E 1 ( p ) ( r | ω ) inc ω 4 c d S { φ ( r | ω ) × [ x 3 x 3 | r r | 2 ( n ( r r ) ) H 2 ( 1 ) ( n I ω c | r r | ) 1 n I ω c | r r | H 1 ( 1 ) ( n I ω c | r r | ) ] χ ( r | ω ) x 3 x 3 n I ω c | r r | H 1 ( 1 ) ( n I ω c | r r | ) } ,
E 2 ( p ) ( r | ω ) = 0 ,
E 3 ( p ) ( r | ω ) = E 3 ( p ) ( r | ω ) inc ω 4 c d S { φ ( r | ω ) × [ x 1 x 1 | r r | 2 ( n ( r r ) ) H 2 ( 1 ) ( n I ω c | r r | ) d x 3 d x 1 n I ω c | r r | H 1 ( 1 ) ( n I ω c | r r | ) ] + χ ( r | ω ) x 1 x 1 n I ω c | r r | H 1 ( 1 ) ( n I ω c | r r | ) } ,
C p ( ω | p ) = 0 2 π | R p ( θ , ω | p ) | 2 | ψ p ( ω ) inc | 2 d θ ,
x 1 = r ( θ ) cos ( θ ) and x 3 = r ( θ ) sin ( θ ) ,
r ( θ ) = r int [ | cos ( m θ 4 ) a | n 2 + | sin ( m θ 4 ) b | n 3 ] 1 n 1 .
f ( x i ) = i = 1 2 x i 2 for 5.12 x i 5.12

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