中文摘要：

通过频域有限差分方法求解KZK方程,对Gauss型超声换能器的基波和高次谐波声场进行计算,研究了各次谐波的分布规律,发现高次谐波声场在径向同样服从Gauss函数的分布规律,并且对于任意的n,第n次谐波的波束宽度和n~（1/2）成反比,这表明谐波阶次越高,声场特性越好。后半部分对上述结论给出了理论证明。本研究验证了相关的实验结果,从而实现了对非线性Gauss型超声场在实验、数值计算、理论证明三个方面的完整描述。

英文摘要：

The KZK equation was solved by employing a frequency domain finite difference method to compute and simulate the fundamental and higher-order harmonic fields of a Gaussian ultrasonic transducer, The distribution of every harmonic component was investigated, The investigation indicates that the higher-order harmonic fields have similar Gaussian radial distribution as the fundamental field, and for an arbitrary n, the beam-width of the nth-harmonic is inversely-proportional to √n. This implies the property of the field becomes better and better with the increase of harmonic order. A theoretical proof was given. The investigation verifies relevant experimental result and realizes a full description to nonlinear Gaussian ultrasonic field .