Bessel-Gauss ultrasonic beam and its second harmonic generation

We have studied theoretically the propagation features of the fundamental component and the second harmonic generation in the Bessel-Gauss beam, with the emphasis on the second harmonic case. The analysis is based on the linearized and quasilinear solutions of the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear wave equation. The analytical and approximate expressions for the fundamental and the second harmonic components are derived. The results show that the Bessel-Gauss fundamental beam is radially distributed as a Bessel-Gauss function, and interestingly the second harmonic beam, like the fundamental, is still a Bessel-Gauss function distribution in the radial direction. Another main property is that for the Bessel-Gauss ultrasonic field, the beamwidth of the second harmonic is exactly equal to in times that of the fundamental. Some potential applications of this beam in the acoustic nonlinearity parameter B/A imaging or measurement are suggested.