Difference-frequency generation in nonlinear scattering of acoustic waves by a rigid sphere

In this paper, the partial-wave expansion method is applied to describe the difference-frequency pressure generated in a nonlinear scattering of two acoustic waves with an arbitrary wavefront by means of a rigid sphere. Particularly, the difference-frequency generation is analyzed in the nonlinear scattering with a spherical scatterer involving two intersecting plane waves in the following configurations: collinear, crossing at right angles, and counter-propagating. For the sake of simplicity, the plane waves are assumed to be spatially located in a spherical region which diameter is smaller than the difference-frequency wavelength. Such arrangements can be experimentally accomplished in vibro-acoustography and nonlinear acoustic tomography techniques. It turns out to be that when the sphere radius is of the order of the primary wavelengths, and the downshift ratio (i.e. the ratio between the fundamental frequency and the difference-frequency) is larger than five, difference-frequency generation is mostly due to a nonlinear interaction between the primary scattered waves. The exception to this is the collinear scattering for which the nonlinear interaction of the primary incident waves is also relevant. In addition, the difference-frequency scattered pressure in all scattering configurations decays as r-1lnrr-1lnr and 1/r1/r, where r is the radial distance from the scatterer to the observation point.

► The generation of difference-frequency scattered waves in nonlinear acoustic scattering is analyzed.
► The partial-wave expansion method is used to obtain the farfield difference-frequency pressure.
► The method is used on the scattering of two intersecting plane waves by a rigid sphere.
► The difference-frequency pressure is mostly caused by the interaction of the incident primary waves as well as the scattered primary waves.