A cascaded second-order approach to computing third-order scattering of noncollinear acoustic beams

A theoretical development of the third-order nonlinear scattering of sound from two noncollinear ultrasonic beams produced by baffled piston sources is presented. The third-order intermodulation (IM3) frequency components are derived by exploiting cascaded second-order nonlinear effects where the quadratic nonlinear interaction of second-order frequency components with first-order (primary) frequency components is considered. It is shown that cascaded second-order interactions generate intermodulation frequency components that are equivalent to those generated by cubic nonlinear effects. Comparison of measured and modeled amplitude sweeps demonstrate the three-to-one gain in decibels of the amplitudes of the third-order intermodulation frequency components to that of the primary frequency components. Measurements are also presented for the farfield interaction of distantly spaced sources, which results in a highly focused ultrasonic parametric array. Also considered are the nearfield interaction of closely spaced sources, which results in scattering, with good agreement to the theory.