Abstract
This paper studies constructing advanced effective materials using arrays of circular radially-anisotropic (RA) cylinders. Homogenization of such cylinders is considered in an electrodynamic case based on Mie scattering theory. The homogenization procedure consists of two steps. First, we present an effectively isotropic model for individual cylinders, and second, we discuss the modeling of a lattice of RA cylinders. Radial anisotropy brings us extra parameters, which makes it possible to adjust the desired effective response for a fixed frequency. The analysis still remains simple enough, enabling a derivation of analytical design equations. The considered applications include generating artificial magnetism using all-dielectric cylinders, which is currently a very sought-after phenomenon in optical frequencies. We also study how negative refraction is achieved using magnetodielectric RA cylinders.
Highlights
Much theoretical and experimental work has been done in research on advanced artificial electromagnetic metamaterials in recent years [1]
We theoretically studied constructing an effective medium using an array of RA cylinders under TEz excitation
We derived approximative analytical models for material parameters ε0eff and μ0eff as functions of five design parameters, namely radial and tangential permittivities and the axial permeability of the individual cylinders, ερ, εφ and μz, respectively, area fraction p of the cylinders in the lattice and the fixed cylinder size parameter x = k0 ρc, which depends on the frequency and the cylinder radius
Summary
Much theoretical and experimental work has been done in research on advanced artificial electromagnetic metamaterials in recent years [1]. If the number or alternating sectors/layers is large enough and the intrinsic details of the cylinder are very small with respect to the wavelength, the cylinder shows different responses in radial and tangential directions Such structures could be modeled radially anisotropically with material parameters of dyadic form, ε and μ, whose components are constants in cylindrical coordinates. The objective of this paper is to show that these effective parameter values can be tailored for a certain frequency by tuning the occurrence of the electric and magnetic Mie resonances of the individual RA cylinders by appropriately choosing the components of the intrinsic dyadics ε and μ. The possible applications that we consider include creating and tuning an artificial magnetic response using all-dielectric cylinders, which would prove very useful in the visible range, where natural magnetism is negligible Another intriguing objective is double-negative (DNG) materials. RA or εc , μc ε, μ (a) Homogenization of individual cylinders unit cell εc ρc μc (external) homogenization εeff μeff d≪λ (b) Homogenization of a lattice of cylinders
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