Second-harmonic generation of the nth-order Bessel beam

We investigate the second-harmonic generation of the nth-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 nth-order Bessel beam, the seco nd-harmonic beam is nearly diffraction-free in the radial direction and beh aves as a Bessel beam of the order 2n, and that the axial pressure amplitud e is proportional to the square root of propagation distance. A variety of applications in many fields of nonlinear acoustics and nonlinear optics is expected.