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L. D. Negro et al.
9.1 Introduction
Engineering aperiodic order in arrays of metallic nanostructures offers a great and
largely unexplored potential for tailoring electromagnetic interactions and enhancing the near field intensity and the optical cross sections (i.e, scattering, absorption,
nonlinear processes) of plasmonic media and metamaterials. Fascinating new scenarios emerge when combining aperiodic geometries with resonant nanoparticles
supporting surface oscillations of conduction electrons localized on the nanoscale,
known as Localized Surface Plasmons (LSPs).
Analogously to the coupling of atomic and molecular orbitals in solid state and
quantum chemistry, the LSPs resonances of individual nanoparticles resonantly couple by near-field (i.e., quasi-static) interactions enhancing the intensity of incident
electromagnetic fields over nanoscale spatial regions referred to as “electromagnetic
hot-spots”. Additionally, arrays of nanoparticles separated by distances comparable
or larger than the wavelength of light interact by radiative electromagnetic interactions (i.e., diffractive coupling and multiple scattering), giving rise to collective
photonic modes largely tunable by the aperiodic array geometry.
Recently, roughened metal surfaces and random media have demonstrated
dramatic enhancement of the linear and non-linear optical properties of semiconductor quantum dots and single molecules [1–3]. However, the technological appeal
of disordered systems remains very limited. Random structures, while in fact providing a convenient path to electromagnetic field localization and enhancement, lack
simple design rules for deterministic optimization. These difficulties have limited
the ability to conceive, manipulate, and engineer optical resonances and scattering
phenomena in deterministic nanoparticle systems that lack spatial periodicity.
In this chapter, we will review our research activities on the design, nanofabrication, and engineering applications of multi-scale nanoparticle arrays with a degree of
structural complexity that interpolates in a tunable fashion between disordered random systems and regular periodic structures. We refer to this general class of artificial metal-dielectric materials as Deterministic Aperiodic Nano Structures (DANS).
In contrast to disordered random systems, DANS are generated by deterministic
algorithms rooted in computational geometry and crystallography [4–6], symbolic
dynamics [7–9], number theory [10–12], and can be fabricated using conventional
nano-lithographic or imprint techniques. Moreover, they are amenable to predictive theories. Importantly, the Fourier diffraction spectra of DANS can be tailored
from purely discrete ones, such as for periodic and quasiperiodic crystals, to diffuse
spectra as for amorphous and random systems. Moreover, DANS can support mixed
diffraction spectra, and can additionally encode non-crystallographic point symmetries of arbitrary order (i.e., up to infinity-fold rotational symmetry) as well as more
abstract mathematical symmetries [13]. However, differently from well-investigated
fractal structures, DANS do not always exhibit scale-invariance symmetry (i.e., self-
L. D. Negro et al.
9.1 Introduction
Engineering aperiodic order in arrays of metallic nanostructures offers a great and
largely unexplored potential for tailoring electromagnetic interactions and enhancing the near field intensity and the optical cross sections (i.e, scattering, absorption,
nonlinear processes) of plasmonic media and metamaterials. Fascinating new scenarios emerge when combining aperiodic geometries with resonant nanoparticles
supporting surface oscillations of conduction electrons localized on the nanoscale,
known as Localized Surface Plasmons (LSPs).
Analogously to the coupling of atomic and molecular orbitals in solid state and
quantum chemistry, the LSPs resonances of individual nanoparticles resonantly couple by near-field (i.e., quasi-static) interactions enhancing the intensity of incident
electromagnetic fields over nanoscale spatial regions referred to as “electromagnetic
hot-spots”. Additionally, arrays of nanoparticles separated by distances comparable
or larger than the wavelength of light interact by radiative electromagnetic interactions (i.e., diffractive coupling and multiple scattering), giving rise to collective
photonic modes largely tunable by the aperiodic array geometry.
Recently, roughened metal surfaces and random media have demonstrated
dramatic enhancement of the linear and non-linear optical properties of semiconductor quantum dots and single molecules [1–3]. However, the technological appeal
of disordered systems remains very limited. Random structures, while in fact providing a convenient path to electromagnetic field localization and enhancement, lack
simple design rules for deterministic optimization. These difficulties have limited
the ability to conceive, manipulate, and engineer optical resonances and scattering
phenomena in deterministic nanoparticle systems that lack spatial periodicity.
In this chapter, we will review our research activities on the design, nanofabrication, and engineering applications of multi-scale nanoparticle arrays with a degree of
structural complexity that interpolates in a tunable fashion between disordered random systems and regular periodic structures. We refer to this general class of artificial metal-dielectric materials as Deterministic Aperiodic Nano Structures (DANS).
In contrast to disordered random systems, DANS are generated by deterministic
algorithms rooted in computational geometry and crystallography [4–6], symbolic
dynamics [7–9], number theory [10–12], and can be fabricated using conventional
nano-lithographic or imprint techniques. Moreover, they are amenable to predictive theories. Importantly, the Fourier diffraction spectra of DANS can be tailored
from purely discrete ones, such as for periodic and quasiperiodic crystals, to diffuse
spectra as for amorphous and random systems. Moreover, DANS can support mixed
diffraction spectra, and can additionally encode non-crystallographic point symmetries of arbitrary order (i.e., up to infinity-fold rotational symmetry) as well as more
abstract mathematical symmetries [13]. However, differently from well-investigated
fractal structures, DANS do not always exhibit scale-invariance symmetry (i.e., self-