The nonlinearity has significant effect on the ultrasonic therapy using phased arrays.A numerical approach is developed to calculate the nonlinear sound field generated from a phased array based on the Gaussian superposition technique.The parameters of the phased array elements are first estimated from the focal parameters using the inverse matrix algorithm;Then the elements are expressed as a set of Gaussian functions;Finally,the nonlinear sound field can be calculated using the Gaussian superposition technique.In the numerical simulation,a 64×1 phased array is used as the transmitter.In the linear case,the difference between the results of the Gaussian superposition technique and the Fresnel integral is less than 0.5%,which verifies the feasibility of the approach.In the nonlinear case,the nonlinear fields of single-focus modes and double-focus modes are calculated.The results reveal that the nonlinear effects can improve the focusing performance,and the nonlinear effects are related with the source pressures and the excitation frequencies.
