  Polaritonic materials, owing to a strong phonon-polariton resonance in the
THz and far-infrared parts of the electromagnetic spectrum, offer both
high-index dielectric and metallic response in this regime. This complex
response makes them suitable candidates for the design of metamaterial-related
phenomena and applications. Here we show that one type of
polaritonic-material-based structures that are particularly suitable for the
achievement of a wide range of metamaterial properties are systems of
polaritonic rods. To study the interplay between the material and the
structural resonances in such systems we employ as model systems rods of LiF
and SiC and we calculate first the scattering properties of a single rod,
identifying and discussing the behavior of the different resonances for
different rod diameters. To analyze the response of ensembles of polaritonic
rods we employ an effective medium approach based on the Coherent Potential
Approximation (CPA), which is shown to be superior to the simple
Maxwell-Garnett approximation for polaritonic and high-index dielectric
metamaterials. Calculating and analyzing the CPA effective parameters, we found
that our systems exhibit a large variety of interesting metamaterial
properties, including hyperbolic dispersion, epsilon-near-zero and negative
refractive index response. This rich response, achievable in almost any system
of polaritonic rods, is highly engineerable by properly selecting the radius
and the filling ratio of the rods, making polaritonic rod systems an ideal
platform for demonstration of multifunctional metamaterials.
