Nonlinear propagation of Bessel-Gauss ultrasonic beams

We investigate theoretically the properties of the fundamental and second h armonic components of the Bessel beam with a finite aperture, the Bessel-Ga uss beam, whose transverse profile is given by the product of Bessel and Ga ussian functions. The analysis is based on the linearized and quasilinear s olutions of the Khokhlov-Zabolotskaya-Kuznetsov nonlinear wave equation. Th e analytical and approximate expressions are derived for the fundamental an d the second harmonic generation in this beam. It is thereby demonstrated t hat under certain circumstances, the second harmonic in the Bessel-Gauss be am is nearly radially nondiffracting, and that the beamwidth is approximate ly one-half of that of the fundamental. This result is an extension to the previous work on the nonlinearity of the Bessel beam, where the infinite ex tent of the beam has been assumed. (C) 1999 American Institute of Physics. [S0021-8979(99)09215-4].