We investigate the second-harmonic generation of the $n\mathrm{th}$-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an $n\mathrm{th}$-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam of the order $2n,$ and that the axial pressure amplitude is proportional to the square root of propagation distance. A variety of applications in many fields of nonlinear acoustics and nonlinear optics is expected.

• Received 3 May 1999

DOI:https://doi.org/10.1103/PhysRevE.61.2038