The nonlinearity has significant effect on the ultrasonic therapy using phased ar- rays. 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.
