Study on the property of the second harmonic in the nearfield of a Bessel ultrasonic field based on the Fourier-Bessel series

A new method based on the Fourier-Bessel series is applied in KZK equation to calculate the second harmonic component of a zero-order Bessel ultrasonic field in viscous medium. An analytical solution of a series form is obtained and a new conclusion is drawn. Assuming the source sound pressure to be J(0) (alpha(0) r), the second harmonic sound pressure has a radial distribution of J(0)(2) (alpha(0) r) function profile in the near field. This conclusion explains the experimental results reported in literature appropriately and indicates that the second harmonic field has different radial distributions in the near and far field, thus solves the problem of radial distribution of the second harmonic in the nearfield of Bessel ultrasonic field. Moreover, the conclusion implies that the second harmonic field has similar limited diffraction property as the fundamental. A numerical computation and simulation example is given subsequently.