Ultrasonic nonlinear fields generated from transmitters with varied aperture angles

The transmitter aperture dependence of the ultrasonic nonlinear field was investigated by using Westervelt equation, Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and spheroidal beam equation (SBE) models. 1.0-MHz focusing spherical transducers with varied half aperture angles from 10° to 40° was employed as the transmitter, the curvatures of which were fixed as 8 cm. The results show that: (1) KZK equation could simulate the acoustic distribution well for half aperture angle less than 20°; (2) the divergence between KZK equation and Westervelt equation is in proportion to the half aperture angle and surface pressure amplitude; (3) although the focus pressure was different for KZK and Westervelt equation, the shape of focal region of KZK equation was almost the same of Westervelt equation; and (4) the SBE model could simulate the acoustic distribution for a large aperture angle range.