Biomedical Engineering Reference
In-Depth Information
sensing,lightemission,andphotondispersionmanagement[13,16],
the study of deterministic aperiodic optical structures is a highly
interdisciplinary research field, conceptually rooted in discrete
geometry(i.e.,tilingtheory,pointpatternstheory,andmathematical
crystallography [25-27]), dynamical systems theory (i.e., specifi-
cally, discrete dynamical systems and automatic sequences) [28-
30], and number theory [31-33]. As a result, the optics of aperiodic
media has the potential to generate many exciting and cross-
disciplinary opportunities that only recently began to be actively
pursued [24].
Understanding the optical response of aperiodic deterministic
systems offers an almost unexplored potential for the manipulation
of the complex diffractive phenomena of interest to singular optics
applications, such as the generation of structured light beams with
compound optical vortices.
The scope of this chapter is to provide a background and to dis-
cussthemanipulationofOAMlightstatesusingplasmonicdetermin-
istic aperiodic nano structures (DANS) with Vogel spiral geometry
[16, 34]. DANS are optical structures in which the refractive index
variesoverlengthscalescomparableorsmallerthanthewavelength
of light. They include dielectric and metallic structures, metallo-
dielectric plasmonic nanostructures, and metamaterials. DANS can
be conveniently fabricated using conventional nanolithographic
techniques while displaying transport and localization properties
akin to random systems. Most importantly, the Fourier space of
DANS can be simply designed to range from a pure-point discrete
spectrum, such as for periodic and quasi-periodic crystals, to a
diffused spectrum with short-range correlations, as for disordered
amorphous systems. In addition, the aperiodic reciprocal space of
DANS results in distinctively complex diffraction patterns encoding
non-crystallographic point symmetries of arbitrary order, as well as
more abstract mathematical symmetries [13].
As we will specifically discuss in the rest of this topic chapter,
DANS with isotropic Fourier space can be designed in the absence
of Bragg peaks based on the concept of aperiodic Vogel spiral
geometry [35]. Vogel spiral arrays of metallic nanoparticles define
a novel engineering approach, based on the geometric control of
polarization-insensitive planar diffraction phenomena, to enhance
