374
L. D. Negro et al.
53. L. Dal Negro, N.-N. Feng, Spectral gaps and mode localization in Fibonacci chains of metal
nanoparticles. Opt. Express 15(22), 14396–14403 (2007)
54. C. Forestiere, G. Miano, G. Rubinacci, 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 79(8), 085404 (2009)
55. M.L. Brongersma, J.W. Hartman, H.A. Atwater, Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit. Phys. Rev. B 62, 356–359 (2000)
56. C. Janot, Quasicrystals: a primer (Oxford University Press, Oxford, 1997)
57. N.G. De Bruijn, Algebraic theory of Penrose’s non-periodic tilings of the plane. Kon. Nederl.
Akad. Wetensch. Proc. Ser. A 43, 84 (1981)
58. C. Radin, The pinwheel tilings of the plane. Ann. Math. 139(3), 661–702 (1994)
59. S.Y. Lee, C. Forestiere, A.J. Pasquale, J. Trevino, G. Walsh, P. Galli, M. Romagnoli, L.
Dal Negro, Plasmon-enhanced structural coloration of metal films with isotropic pinwheel
nanoparticle arrays. Opt. Express 19(24), 23818–23830 (2011)
60. L. Danzer, Three-dimensional analogs of the planar Penrose tilings and quasicrystals. Discrete
Math. 76(1), 1–7 (1989)
61. P. Prusinkiewicz, A. Lindenmayer, The Algorithmic Beauty of Plants (Springer-Verlag, New
York, 1990)
62. P. Ball, Shapes. Nature’s Patterns (Oxford University Press, New York, 2009)
63. R.V. Jean, Phyllotaxis (Cambridge University Press, Cambridge, 1995)
64. D.A.W. Thompson, On Growth and Form (Dover, New York, 1992)
65. J. Trevino, S.F. Liew, H. Noh, H. Cao, L. Dal Negro, Geometrical structure, multifractal spectra
and localized optical modes of aperiodic Vogel spirals. Opt. Express 20(3), 3015–3033 (2012)
66. N. Lawrence, J. Trevino, L. Dal Negro, Aperiodic arrays of active nanopillars for radiation
engineering. J. Appl. Phys. 111(11), 113101–113109 (2012)
67. J. Trevino, C. Forestiere, G. Di Martino, S. Yerci, F. Priolo, L. Dal Negro, Plasmonic-photonic
arrays with aperiodic spiral order for ultra-thin film solar cells. Opt. Express 20(S3), A418–
A430 (2012)
68. A. Capretti, G.F. Walsh, S. Minissale, J. Trevino, C. Forestiere, G. Miano, L. Dal Negro,
Multipolar second harmonic generation from planar arrays of Au nanoparticles. Opt. Express
20(14), 15797–15806 (2012)
69. J. Trevino, H. Cao, L. Dal Negro, Circularly symmetric light scattering from nanoplasmonic
spirals. Nano Lett. 11, 2008 (2011)
70. U. Fano, The theory of anomalous diffraction gratings and of quasi-stationary waves on
metallic surfaces (Sommerfeld’s waves). JOSA 31, 213–222 (1941)
71. E.F. Pecora, N. Lawrence, P. Gregg, J. Trevino, P. Artoni, A. Irrera, F. Priolo, L. Dal Negro,
Nanopatterning of silicon nanowires for enhancing visible photoluminescence. Nanoscale
4(9), 2863–2866 (2012)
72. S.F. Liew, H. Noh, J. Trevino, L.D. Negro, H. Cao, Localized photonic band edge modes and
orbital angular momenta of light in a golden-angle spiral. Opt. Express 19(24), 23631–23642
(2011)
73. L. Dal Negro, N. Lawrence, J. Trevino, Analytical light scattering and orbital angular mementum spectra of arbitrary Vogel spirals. Opt. Express 20(16), 18209–18223 (2012)
74. M. Naylor, Golden,
√
2, and ϕ flowers: a spiral story. Math. Mag. 75(3), 163–172 (2002)
75. G.J. Mitchison, Phyllotaxis and the Fibonacci series. Science 196(4287), 270–275 (1977)
76. S. Chavez-Cerda, M. Padgett, I. Allison, G.H.C. New, J.C. Gutierrez-Vega, A.T. O’Neil, I.
MacVicar, J. Courtial, Holographic generation and orbital angular momentum of high-order
Mathieu beams. J. Opt. B Quantum Semiclass. Opt. 4, S52–S57 (2002)
77. N. Lawrence, J. Trevino, L. Dal Negro, Control of optical orbital angular momentum by Vogel
spiral arrays of metallic nanoparticles. Opt. Lett. 37, 5076 (2012)
78. C.S. Calude, Randomness and Complexity: From Leibniz to Chaitin (World Scientific, Singapore, 2007)
79. J.G. Chaitin, Exploring Randomness (Springer, London, 2001)
L. D. Negro et al.
53. L. Dal Negro, N.-N. Feng, Spectral gaps and mode localization in Fibonacci chains of metal
nanoparticles. Opt. Express 15(22), 14396–14403 (2007)
54. C. Forestiere, G. Miano, G. Rubinacci, 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 79(8), 085404 (2009)
55. M.L. Brongersma, J.W. Hartman, H.A. Atwater, Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit. Phys. Rev. B 62, 356–359 (2000)
56. C. Janot, Quasicrystals: a primer (Oxford University Press, Oxford, 1997)
57. N.G. De Bruijn, Algebraic theory of Penrose’s non-periodic tilings of the plane. Kon. Nederl.
Akad. Wetensch. Proc. Ser. A 43, 84 (1981)
58. C. Radin, The pinwheel tilings of the plane. Ann. Math. 139(3), 661–702 (1994)
59. S.Y. Lee, C. Forestiere, A.J. Pasquale, J. Trevino, G. Walsh, P. Galli, M. Romagnoli, L.
Dal Negro, Plasmon-enhanced structural coloration of metal films with isotropic pinwheel
nanoparticle arrays. Opt. Express 19(24), 23818–23830 (2011)
60. L. Danzer, Three-dimensional analogs of the planar Penrose tilings and quasicrystals. Discrete
Math. 76(1), 1–7 (1989)
61. P. Prusinkiewicz, A. Lindenmayer, The Algorithmic Beauty of Plants (Springer-Verlag, New
York, 1990)
62. P. Ball, Shapes. Nature’s Patterns (Oxford University Press, New York, 2009)
63. R.V. Jean, Phyllotaxis (Cambridge University Press, Cambridge, 1995)
64. D.A.W. Thompson, On Growth and Form (Dover, New York, 1992)
65. J. Trevino, S.F. Liew, H. Noh, H. Cao, L. Dal Negro, Geometrical structure, multifractal spectra
and localized optical modes of aperiodic Vogel spirals. Opt. Express 20(3), 3015–3033 (2012)
66. N. Lawrence, J. Trevino, L. Dal Negro, Aperiodic arrays of active nanopillars for radiation
engineering. J. Appl. Phys. 111(11), 113101–113109 (2012)
67. J. Trevino, C. Forestiere, G. Di Martino, S. Yerci, F. Priolo, L. Dal Negro, Plasmonic-photonic
arrays with aperiodic spiral order for ultra-thin film solar cells. Opt. Express 20(S3), A418–
A430 (2012)
68. A. Capretti, G.F. Walsh, S. Minissale, J. Trevino, C. Forestiere, G. Miano, L. Dal Negro,
Multipolar second harmonic generation from planar arrays of Au nanoparticles. Opt. Express
20(14), 15797–15806 (2012)
69. J. Trevino, H. Cao, L. Dal Negro, Circularly symmetric light scattering from nanoplasmonic
spirals. Nano Lett. 11, 2008 (2011)
70. U. Fano, The theory of anomalous diffraction gratings and of quasi-stationary waves on
metallic surfaces (Sommerfeld’s waves). JOSA 31, 213–222 (1941)
71. E.F. Pecora, N. Lawrence, P. Gregg, J. Trevino, P. Artoni, A. Irrera, F. Priolo, L. Dal Negro,
Nanopatterning of silicon nanowires for enhancing visible photoluminescence. Nanoscale
4(9), 2863–2866 (2012)
72. S.F. Liew, H. Noh, J. Trevino, L.D. Negro, H. Cao, Localized photonic band edge modes and
orbital angular momenta of light in a golden-angle spiral. Opt. Express 19(24), 23631–23642
(2011)
73. L. Dal Negro, N. Lawrence, J. Trevino, Analytical light scattering and orbital angular mementum spectra of arbitrary Vogel spirals. Opt. Express 20(16), 18209–18223 (2012)
74. M. Naylor, Golden,
√
2, and ϕ flowers: a spiral story. Math. Mag. 75(3), 163–172 (2002)
75. G.J. Mitchison, Phyllotaxis and the Fibonacci series. Science 196(4287), 270–275 (1977)
76. S. Chavez-Cerda, M. Padgett, I. Allison, G.H.C. New, J.C. Gutierrez-Vega, A.T. O’Neil, I.
MacVicar, J. Courtial, Holographic generation and orbital angular momentum of high-order
Mathieu beams. J. Opt. B Quantum Semiclass. Opt. 4, S52–S57 (2002)
77. N. Lawrence, J. Trevino, L. Dal Negro, Control of optical orbital angular momentum by Vogel
spiral arrays of metallic nanoparticles. Opt. Lett. 37, 5076 (2012)
78. C.S. Calude, Randomness and Complexity: From Leibniz to Chaitin (World Scientific, Singapore, 2007)
79. J.G. Chaitin, Exploring Randomness (Springer, London, 2001)