A plate-array metamaterial in cylindrical geometries
File(s)
Author(s)
Putley, Henry James
Type
Thesis
Abstract
A metamaterial composed of closely-spaced, thin metallic plates, sandwiched between layers of dielectric, is modelled for the purposes of engendering hierarchical photonic crystals along one- and two-axes. The plate-array is considered infinite in its depth but is made to occupy a circular cross-section, so as to define a plate-array metamaterial cylinder, or metacylinder. By homogenizing the plate-array in the limit of small inter-plate spacing, we arrive to an effective medium description for the plate-array that describes the motion of waves within the dielectric channels. This model is encapsulated by an effective one-dimensional wave equation in the interior and a pair of continuity equations at the cylindrical surface. The solutions exterior to the metacylinder are provided in terms of expansions in Bessel functions, a treatment referred to as the dynamic multipole method. By writing the interior solutions as sums over regular waves, we arrive to the scattering matrix for an arbitrary arrangement of metacylinders, before considering macroscopic structures of an underlying periodic order. This semi-analytic formalism lends itself to numerical simulations, with which we investigate phenomena such as: the quasi-modes of metacylinder ring resonators, the reflection and transmission of plane-waves by a metacylinder diffraction grating, Rayleigh-Bloch modes of a tunable dispersion, and the effective properties of a 2D plate-array metasurface. We also outline concepts from 2D topological photonics for the purposes of realising the valley-Hall insulator phase in a honeycomb photonic crystal. The overlapping of a non-trivial band gap for both transverse electric and transverse magnetic polarizations corresponds to a complete photonic band gap engendered by the spatial symmetry breaking of the direct lattice. In turn, the honeycomb lattice is shown to host edge modes when two media, of opposite boundary condition but identical symmetry-breaking perturbation, are joined to form an interface.
Version
Open Access
Date Issued
2023-12-22
Date Awarded
01/05/2024
License URL
Advisor
Craster, Richard
Sponsor
QinetiQ (Firm)
Grant Number
EP/L016230/1
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)