Light in Deterministically Generated Aperiodic Optical Materials
The control of light-matter interaction in deterministic complex media without translational invariance offers the ultimate potential for the creation and manipulation of light states. Unlike periodically arranged photonic crystals (or photonic bandgaps), deterministic non-periodic structures show unique light localization and transport properties related to the multi-fractal character of their energy spectra. We refer to this fascinating class of photonic materials as Deterministic Non-Periodic Structures (DNPS). DNPS are defined by simple mathematical rules which generate a non-periodic modulation of their optical constants encoding a fascinating complexity, described by fractal Fourier spectra (Figure 1). DNPS share distinctive physical properties with both periodic media, i.e. the formation of large energy gaps, and disordered random media, i.e. the presence of localized states with large electric field enhancement effects. However, unlike random media, DNPS are deterministically generated according to simple mathematical prescriptions based on symbolic dynamics. It has been demonstrated that DNPS can sustain strongly localized modes, known as critical states,with high field enhancement, which are the analogue of Anderson-localized solutions in perfectly random potentials (random media). In particular, it has been shown that aperiodic dielectrics give rise to highly fragmented, self-similar transmission spectra with multi-fractal geometry, multi-fractal wavefunctions, critical light localization and anomalous light transport properties.
These phenomena clearly demonstrate that the transport of excitations, including wave and electron transport, in aperiodic environments is dramatically modified with respect to periodic or random media. It can be expected that the unique manifestations of aperiodic order will have a major impact for the design of a variety of novel photonic devices based on anomalous light diffusion (sub-diffusion) and wave localization effects.
Figure 1: (a) Absolute value of the Fourier coefficients of (a) periodic nanoparticle array (b) quasiperiodic Fibonacci array (c) deterministic aperiodic Thue-Morse array (singular continuous Fourier spectrum) (d) deterministic aperiodic Rudin-Shapiro array ( absolutely continuous Fourier spectrum).
However, until now the study of DNPS has been mainly confined to the theoretical analysis of quasi-periodic dielectric systems and perturbed periodic (chirped) systems, mostly in one spatial dimension.
On the other extreme, an extensive literature exists on field localization and enhancement random metal-dielectric resonant structures. In particular, it has been shown that the interplay between the resonant excitation of surface plasmons and near-field coupling on a random network (with a statistical fractal support) can lead to giant field enhancement effects, or hot electromagnetic spots (≈ 106 intensity enhancement) with sub-wavelength localization.
However, the combination of deterministic non-periodic structures with localized resonances in plasmonic nanostructured arrays has yet to be addressed, despite its fundamental interest and large potential for the controlled fabrication of deterministic nanophotonics devices based on giant enhancement and sub-wavelength field localization.
Our research activities explore for the first time the use of metal/dielectric 2D structures based on aperiodic order for the engineering of electromagnetic hot spots on predictable locations on chip-size devices. Our approach is based on the excitation of collective plasmon (SP) resonances in non-periodic, deterministic chips which we fabricate by electron-beam lithography (Figure. 2).
The arrays are generated by 2D generalizations of simple mathematical rules, such as Fibonacci, Thue-Morse or Rudin-Shapiro sequences (see Figure 4). Results of three-dimensional (3D) FDTD and FEM numerical calculations indicate that electromagnetic hot-spots (~50nm localization length) can be excited at optical frequencies over small area (1x1 µm2) in deterministic aperiodic arrays metal nanoparticles (Figure 2, top).
Our full-vector analysis have shown that by combining surface plasmon polariton (SPP) near-field coupling with aperiodic patterns of metal nanoparticles we can induce strong SPP localization and large field enhancement effects on planar chips.
The use of non-periodic, deterministic 2D metal nano-particle planar arrays represents a convenient approach to manipulate enhanced local fields induced at predictable locations on chip-scale devices. This possibility is central to the main goal of our project, which consists in the engineering of a chemical/imaging system based on plasmon-enhanced SERS detection.
Figure 2: (top) FDTD calculated intensity enhancement for RS lattices with 50nm minimum spacing (Au, 30 nm above particle plane). (bottom) Rudin-Shapiro lattice fabricated with e-beam lithography. Inset shows expanded view.
