Theoretical analysis of the difference – frequency generation in nonlinear Rayleigh seattering of acoustic beams

Abstract

In this work, the difference-frequency (DF) generation in the scattering of two acoustic waves by a sphere in the Rayleigh limit is theoretically analyzed. A multipole series is derived for the DF scattered pressure at the farfield by applying the method of successive approximation and the Green’s function technique to the Westervelt’s nonlinear wave equation. In the Rayleigh limit, this series has only the monopole, dipole, and quadrupole moments. These moments depend on the nonlinear interaction of the primary incident and scattered waves. Theoretical results are obtained for the case of two intersecting plane waves localized within a spherical spatial region. The radius of the interaction region is assumed to be much smaller than the distance from the scatterer to observation point (radial distance). A similar configuration is found in vibro-acoustography imaging system. The directive patterns of the DF scattered field are illustrated for plane waves intersecting at 0º; 45º; 90º; and 180º. The center- and differece-frequencies of the waves are 1:5MHz and 50 kHz, respectively, while the spherical scatterer radius is 0:125mm. These frequencies are typically used in vibro-acoustography. The behavior of the DF scattered pressure is also analyzed for two colinear plane waves with varying radial distance from the scatterer, center- and the difference-frequency. Results indicate that the interaction of the primary scattered waves is the main process behind difference-frequency generation for most parameter combinations chosen here. Based on this conclusion, we will also discuss the DF generation process in vibro-acoustography.