2D numerical simulation of acoustic wave phase conjugation in active medium

The effect of parametric wave phase conjugation (WPC) applied to ultrasound acoustic waves in magnetostrictive solids has been addressed numerically by S. Ben Khelil et al. (see J. Acoust. Soc. of America, vol.109, no.l, p.75-81, 2001) using a 1D unsteady formulation. We now apply the numerical method presented by P. Voinovich et al. (see Proc. XXX Summer School "Advanced Problems in Mechanics", p.625-9, 2002; Shock Waves Journal, vol.13, no.3, p.221-30, 2003) to the analysis of probable 2D effects by a practical implementation of WPC. The model describes universally elastic solids and liquids. A source term is included in the model similar to that of Ben Khelil et al. to describe coupling between deformation formation of magnetostrictive material and an external periodic magnetic field. Supplementary to the 1D simulations, the present model involves longitudinal/transverse mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed. The processes under study include propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance and formation of time-reversed waves, their radiation into liquid and focusing.