Perturbation Theory in the Design of Degenerate Rectangular Dielectric Resonators

Abstract

Abstract-The design of resonators with degenerate magnetic and electric modes usually requires the ability to perturb one or both types of modes in order to induce alignment of magnetic and electric properties. In this paper perturbation theory is used to identify different types of inclusions that can be used to realize fundamentalmode degeneracy in a rectangular dielectric resonator and thus, can ultimately be used in the design of negative-index metamaterials. For reasons associated with fabrication in the infrared-frequency regime, rectangular resonator designs are of particular interest.

Extreme coupling: A route towards local magnetic metamaterials

“…Of the suggested ways to design a metasurface, using local artificial magnetism is not the only one. Optically dense arrays of solid transparent particles operating at a magnetic Mie resonance may also possess local magnetic response [29][30][31][32][33]. These metasurfaces, as a rule, are targeted to the infrared range, though in accordance with Ref.…”

“…At the example of meta-atoms with an artificial magnetic response we will show that the multipole analysis is an appropriate tool to identify the desired metaatoms, which might eventually be used to build up local metamaterials [29][30][31][32][33]. For the sake of simplicity we will term these meta-atoms local meta-atoms in what follows.…”

Dipole Approximation to Predict the Resonances of Dimers Composed of Dielectric Resonators for Directional Emission

“…Thus, we propose the development of a fully retarded, dipole approximation model to estimate the effective polarizabilities of a dimer made of dielectric resonators starting from the polarizabilities of the two resonators composing the dimer. We analyze the situation of full cubes as well as split cubes, which have been shown to exhibit overlapping electric and magnetic resonances (Campione et al, ; Warne et al, , ). Comparisons with full‐wave simulations confirm the validity of the proposed model, which can be used to predict the electric and magnetic resonances of a dimer under parallel or orthogonal (to the dimer axis) excitation.…”

Full-wave simulation of a three-dimensional metamaterial prism

“…The aim of this article is to utilize a unit cell containing an electric and magnetic complement and degenerate pair of resonators to form a three‐dimensional (3D), n = −1 refractive index prism. The unit cell for the prism is based on metallic resonators as opposed to dielectric ones as considered in . Thus, for the purposes of accentuating the negative‐index response and thereby obtaining easy‐to‐interpret visualization results, the microwave‐frequency range is the operating band of interest.…”

“…The 3D prism presented in this article is designed using an approach combining isolated‐particle simulations and subcell modeling techniques . Although the isolated‐resonator (single unit cell) simulations provides a simple and efficient means of extracting the resonator electric and magnetic moments and identifying a candidate resonator (or combination of resonators) that yields the desired resonant response, the subcell modeling approach is a follow‐on design step introduced to simplify the unit‐cell mesh geometry and ultimately allow for a larger collection of unit cells to be simulated.…”