Second-harmonic generation of the Bessel sound beam of several lobes

By the Gaussian expansion approach we investigate fundamental- and second-harmonic generation in practical Bessel beams of several lobes. The analysis is based on the integral solutions of the Khokhlov-Zabolotskaya-Kuznetsov equation under the quasilinear approximation. The influence of the medium attenuation on beam profile is considered. Numerical results show that the absorption parameter has a significant effect on the beam profile of the second harmonic. Under certain circumstances, the second harmonic of a practical Bessel beam with several lobes still has the main properties of an ideal Bessel beam of infinite aperture when it propagates within its depth of field.