Acoustic metamaterials: numerical analysis of negative refraction

1
Acoustic metamaterials numerical analysis of
negative refraction

• Cristina Pachiu(1), J. L. Izbicki(2)
• National Institute for RD in Microtechnologies,
  Erou Iancu Nicolae 126A, Bucharest 077190,
  Romania
• Laboratoire dAcoustique Ultrasonore et
  dElectronique LAUE UMR 6068 CNRS, Université du
  Havre, France

Metamaterials are artificial materials micro or
nanoscale designed to elicit unusual and very
useful properties at the macroscale. The interest
in acoustical metamaterials stems from scientific
successes reported in the creation of photonic
crystals with band-gaps, negative refractive
index and cloaking phenomena.
Figure 1. Acoustic cloaking in 2010 it was
developed a first two-dimensional acoustic cloak
that makes objects in the center invisible to
sonar and other ultrasound waves(1).
Figure 2. Cloaking shell -alternating layers of
two isotropic metamaterials, 1 and 2, identical
design with 2D phononic crystals.
Phononic crystals are composite materials made of
a periodic arrangement of several elastic
materials their dispersion curves present
absolute forbidden bands, e.g., frequency domains
where the propagation of elastic wave is
prohibited whatever the direction of propagation
of the incident wave.
A numerical analysis of negative refraction
process is reported using a phononic crystal with
an elastic solid matrix. The phononic crystal
considered in this study is made of a periodic
arrangement of holes in aluminum where the
elastic properties are given in (2). Negative
refraction of elastic waves has been also studied
with the help of the FEM method, using the MatLab
code. The dispersion curve exhibits one or
several branches with a negative slope, i.e., the
frequency is decreasing with increasing wave
vector modulus. Negative refraction can occur if
only one branch with a negative slope exists in a
frequency range this region is marked by the gray
rectangles.
Figure 3. 2D PhnCs solid circular rods embedded
in a background solid material with square
lattice.
PhnCs f45
PhnCs f50
PhnCs f 60
Figure 4. Dispersion curves for three different
filling factors in the phononic crystal.
The research presented in this paper is supported
by the Sectoral Operational Programme Human
Resources Development POSDRU/89/1.5/S/63700...

1. http//www.news.illinois.edu
2. APPLIED PHYSICS LETTERS 96, 101905, 2010