All-dielectric metamaterials: simulation of nanorod and arrays
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1223-EE06-08
All-dielectric metamaterials: simulation of nanorod and arrays Elena Poklonskaya1, Yuriy Poplavko2, Gunnar Suchaneck1 and Gerald Gerlach1 1
TU Dresden, Solid State Electronics Lab, 01062 Dresden, Germany National Technical University of Ukraine – KPI, Microelectronics Department, 03056 Kiev, Ukraine 2
ABSTRACT In this work, scattered electric and magnetic fields of all-dielectric metamaterials were derived using a commercial RF finite-element partial differential equations solver. We present the implementation of rod-type composites consisting of a mixture of two components: the first one, which is called guest, is made of Ba1-xSrxTiO3 (0 ≤ x ≤ 1) and the second one, the host, made of SiO2. Analysis includes both the scattering effect, well described by the MIE theory, and dielectric inhomogeneous structure properties, determined using the MAXWELL-GARNETT approximation. INTRODUCTION Metamaterials are a new class of ordered composites that exhibit exceptional properties not readily exist in nature. These properties arise from qualitatively new response functions that are: (1) not observed in the constituent materials and (2) result from the inclusion of artificially fabricated, extrinsic, low-dimensional inhomogeneities [1]. However, the concept of artificial materials was already introduced at the end of the 1940´s in microwave engineering. W.E. KOCK developed the first metamaterials called artificial dielectrics in the late 1940s with metal-lens antenna and metallic delay lenses [2, 3]. Artificial dielectrics were made by distributing small polarizable particles in a uniform background material reproducing oscillating dipoles similar to the atoms of a dielectric [4] on a macroscopic scale. They are composed of arrays of metal or dielectric inclusions of high permittivity in a continuous material of relatively low permittivity [5]. Applications of artificial dielectrics such as microwave lenses usually require a material of a low dispersion. Because the propagation speed of wave energy (the group velocity) is different from the phase velocity [6]: dv vg = v − λ , (1) dλ where vg = ∂ω/∂k is the group velocity, k the wave vector, ω(k) the wave's angular frequency, v the phase velocity and λ the wavelength, a large dispersion of ω(k) is required to support backward wave propagation (negative refractive index) [7]. This is obtained when the particles resonate at or near the desired operating frequency. Therefore, the special properties of metamaterials rely on strong electromagnetic resonances restricting their application to a narrow spectral range. Long cylinders of a high permittivity dielectric material in a low permittivity environment serve as a waveguide for electromagnetic waves at a certain frequency [8]. The interface of a cylinder with infinite permittivity represents infinite impedance for a wave coming
from the high permittivity material inside to the low permittivity environment resulting in open circuit boundary conditions (OCB) at the interface [9]: n × H = 0,
n⋅E = 0
(2)
with n the
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