Numerical simulation of phase conjugation of the second harmonic in a sound beam propagating through an immersed elastic solid with rough surfaces

A numerical investigation is performed to explore the possibility of using wave phase conjugation to correct for phase aberrations in a nonlinear sound beam that propagates through an immersed elastic layer with rough surfaces. The numerical method is based on an angular spectrum approach using the Westervelt equation. It accounts for both longitudinal and transverse elastic wave interactions inside the solid, and second harmonic generation in the fluid and solid. The method includes the full effects of diffraction and is not limited by the parabolic approximation. Surface roughness at the liquid-solid interfaces is modeled by phase screens that have a step, sinusoidal or randomly distributed pattern. The properties and dimensions of the fluid and the elastic layer are such that the wave field is progressive. Of interest is the conjugation of the second harmonic pressure field generated nonlinearly in a focused sound beam, and the ability of the conjugated beam to correct for the phase aberrations and refocus. The effects of the longitudinal and transverse wave interactions in the solid, the nonlinearity of the solid, and the size and shape of the phase screens are examined in the study. Phase conjugation is shown to reduce distortion of the second harmonic introduced by the rough surfaces and improve its refocusing, even in cases where the incoming wave is rendered completely incoherent by the phase aberrations. The goal of this research is to provide a model to verify and predict future experiments performed at the Institute of Electronics, Microelectronics, and Nanomagnetics in Lille, France, and at the Wave Research Center in Moscow.