Multipole expansion for nonlinear acoustic scattering at the difference-frequency.

Abstract

In this work, the scattering at the difference-frequency (DF) of two finite-amplitude plane waves by a rigid sphere in a fluid is studied. The DF-scattering is present in some acoustic imaging methods such as vibro-acoustography. This has motivated us to perform this study. We obtain for the first time the multipole expansion for the DF-scattered pressure in the farfield. Theory is based on the successive approximation and the Green’s function methods. From the multipole expansion, we derive some quantities such as scattering cross-section and the total DF-scattered power. Furthermore, we show that the DF-scattered pressure increases with the observation distance r like r ln r, while it varies almost linearly with the difference-frequency. Despite the amplification, we demonstrate that the DF-scattered pressure does not grow indefinitely because of absorption in the fluid. The theory is applied to the scattering in the Rayleigh limit (scatterer much smaller than the incident wavelengths). Only monopole and dipole moments are relevant in this limit. In conclusion, we believe that this theory can help to understand better the nonlinear scattering in acoustics.