# Acoustic metamaterials

Providing a simple definition of what is a metamaterial is a rather difficult task.
An attempt is to say that this field combines all the design strategies that are employed to manipulate the waves in an unconventional manner.
The design of these artificial materials typically involves subwavelength scatterer (resonant or not), which will dramatically affect the response of the all system.

By using Helmholtz resonators, a quasi-perfect absorption at low frequencies (240 Hz) has been achieved with a deep subwavelength cell.
A similar design is also able to efficiently slow down the acoustic wave propagation.

The Parity-Time (PT) symmetry has been first introduced in quantum mechanics before being extended to all wave physics including optics, electromagnetism and acoustics.
On a first approach, a PT-symmetric system is a system where loss and gain compensate each others. Using PT-symmetry, many counter-intuitive wave phenomena can be demonstrated, like unidirectional invisibility and unconventional scattering.
We have predicted, for instance, supersonic group velocities in PT-symmetric phononic crystals.

# Acoustic waves in granular media

Granular media, due to their micro-inhomogeneous character, are not well described by the standard continuum theory of elasticity.
By contrast to classical continua where the sizes of the vibrating particles are assumed to be negligible compared to the distance between the particles, the sizes of the particles in a granular assembly are comparable to the distance between neighbors.
In addition, considering the sliding, torsion and rolling resistances at the level of the contacts between the particles, a consistent description of the elasticity of a granular medium needs to take into account the rotational degrees of freedom of each individual particle.
The generalization of the classical elasticity theory accounting for the rotational degrees of freedom of point bodies is known as the Cosserat or micropolar theory and has been first introduced by the Cosserat brothers in 1909.

In this topic, the properties of rotational-related modes of propagation are analyzed theoretically, numerically and experimentally.
Thus, the propagation of a coupled rotational-translational mode has been experimentally observed,
representing the first experimental evidence of the effects of the rotational degrees of freedom one century after the work of the Cosserat brothers.

# Nonlinearity, nonreciprocity

Breaking reciprocity for acoustic wave is of major interest from the physic point of view but also for its ultrasonic applications.
The reciprocity can be broken using a space-time modulation of the medium, applying an external bias to the system or combining nonlinearity with spatial asymmetry.

Because of gravity, the static stresses in a granular crystal is inhomogeneous. Because of this inhomogeneity, the attenuation of acoustic wave and the nonlinear behavior of the contact between the beads vary with depth.
As a result, the nonlinear generation of frequencies is asymmetric.

Also, when a static electric field is applied on a piezoelectric semiconductor, the drift of the electrons modify the exchange of energy between the electrons and the acoustic wave via the electron-phonon coupling.
When the drift velocity of the electrons is higher than the acoustic velocity, the acoustic wave will experience gain. This effect is inherently non-reciprocal because of the unique drift direction of the electrons.
An acoustic isolator can be designed, which is broadband in frequency and leave the waveform quasi-intact in the passing direction.