Abstract
We investigate theoretically the properties of the fundamental and second harmonic components of the Bessel beam with a finite aperture, the Bessel–Gauss beam, whose transverse profile is given by the product of Bessel and Gaussian functions. The analysis is based on the linearized and quasilinear solutions of the Khokhlov–Zabolotskaya–Kuznetsov nonlinear wave equation. The analytical and approximate expressions are derived for the fundamental and the second harmonic generation in this beam. It is thereby demonstrated that under certain circumstances, the second harmonic in the Bessel–Gauss beam is nearly radially nondiffracting, and that the beamwidth is approximately 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 extent of the beam has been assumed.
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