Nature-inspired optimization of quasicrystalline arrays and all-dielectric optical filters and metamaterials.

摘要

Quasicrystalline solids were first observed in nature in 1980s. Their lattice geometry is devoid of translational symmetry; however it possesses long-range order as well as certain orders of rotational symmetry forbidden by translational symmetry. Mathematically, such lattices are related to aperiodic tilings. Since their discovery there has been great interest in utilizing aperiodic geometries for a wide variety of electromagnetic (EM) and optical applications. The first thrust of this dissertation addresses applications of quasicrystalline geometries for wideband antenna arrays and plasmonic nano-spherical arrays. The first application considered is the design of suitable antenna arrays for micro-UAV (unmanned aerial vehicle) swarms based on perturbation of certain types of aperiodic tilings. Due to safety reasons and to avoid possible collision between micro-UAVs it is desirable to keep the minimum separation distance between the elements several wavelengths. As a result typical periodic planar arrays are not suitable, since for periodic arrays increasing the minimum element spacing beyond one wavelength will lead to the appearance of grating lobes in the radiation pattern. It will be shown that using this method antenna arrays with very wide bandwidths and low sidelobe levels can be designed. It will also be shown that in conjunction with a phase compensation method these arrays show a large degree of versatility to positional noise. Next aperiodic aggregates of gold nano-spheres are studied. Since traditional unit cell approaches cannot be used for aperiodic geometries, we start be developing new analytical tools for aperiodic arrays. A modified version of generalized Mie theory (GMT) is developed which defines scattering coefficients for aperiodic spherical arrays. Next two specific properties of quasicrystalline gold nano-spherical arrays are considered. The optical response of these arrays can be explained in terms of the grating response of the array (photonic resonance) and the plasmonic response of the spheres (plasmonic resonance). In particular the couplings between the photonic and plasmonic modes are studied. In periodic arrays this coupling leads to the formation of a so called photonic-plasmonic hybrid mode. The formation of hybrid modes is studied in quasicrystalline arrays. Quasicrystalline structures in essence possess several periodicities which in some cases can lead to the formation of multiple hybrid modes with wider bandwidths. It is also demonstrated that the performance of these arrays can be further enhanced by employing a perturbation method. The second property considered is local field enhancements in quasicrystalline arrays of gold nanospheres. It will be shown that despite a considerably smaller filling factor quasicrystalline arrays generate larger local field enhancements which can be even further enhanced by optimally placing perturbing spheres within the prototiles that comprise the aperiodic arrays.;The second thrust of research in this dissertation focuses on designing all-dielectric filters and metamaterial coatings for the optical range. In higher frequencies metals tend to have a high loss and thus they are not suitable for many applications. Hence dielectrics are used for applications in optical frequencies. In particular we focus on designing two types of structures. First a near-perfect optical mirror is designed. The design is based on optimizing a subwavelength periodic dielectric grating to obtain appropriate effective parameters that will satisfy the desired perfect mirror condition. Second, a broadband anti-reflective all-dielectric grating with wide field of view is designed. The second design is based on a new computationally efficient genetic algorithm (GA) optimization method which shapes the sidewalls of the grating based on optimizing the roots of polynomial functions.