Second-order cumulative field of a finite acoustic beam

Analysis and numerical computation have been performed for second-order cumulative field of a finite acoustic beam, by decomposing finite acoustic beam into a set of plane waves and using second-order perturbation technique. The study indicates that there is no second-order nonlinearity for the cross-interaction of two different plane wave components, and that the sum of second-order cumulative wave caused by the self-interaction of each plane wave component constitutes ultimate second-order cumulative field of the finite acoustic beam. Moreover, the analytical expression of second-order cumulative field has been presented, which has clearly physical meaning.