The second harmonic component in the Bessel beam

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Abstract
The analysis is based on the Khokhlov–Zabolotskaya–Kuznetsov wave equation. Analytical and approximate solutions are derived for the second harmonic component in the Bessel nondiffracting beam. The theoretical results indicate that the second harmonic beam is nearly nondiffracting in the radial direction and the pressure amplitude is proportional to the square root of propagation distance in the quasilinear approximation, and that the beamwidth of the second harmonic is just 1/2 times that of the fundamental component in the Bessel field, not as 1/√2 times in the fields radiated by other sources.

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