Acoustic metamaterials: numerical analysis of negative

Acoustic metamaterials: numerical analysis of
negative refraction
Cristina Pachiu(1), J. L. Izbicki(2)
(1) National Institute for R&D in Microtechnologies, Erou Iancu Nicolae 126A, Bucharest 077190, Romania
(2) Laboratoire d’Acoustique Ultrasonore et d’Electronique 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
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
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
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
Figure 3. 2D PhnCs: solid circular rods
embedded in a background solid
material with square lattice.
f= 60 %
Figure 4. Dispersion curves for three different filling factors in the phononic
The research presented in this paper is supported by the Sectoral Operational Programme Human Resources Development
(2) APPLIED PHYSICS LETTERS 96, 101905, 2010
A 10-a editie a
Seminarului National de nanostiinta si nanotehnologie
18 mai 2011
Biblioteca Academiei Romane