Nonlinear Bessel beams

Acoustic radiation force on a sphere in a progressive and standing zero-order quasi-Bessel-Gauss beam.

We present a further analysis for the second-harmonic generation of Bessel beams in lossy media. The emphasis is put on the effect of absorption to the radial pattern of the second-harmonic beam. It is shown that within the absorption length of the second harmonic, the Bessel second-harmonic beam approaches limited diffraction in the radial direction and behaves as in the case of lossless media.

https://iopscience.iop.org/article/10.1088/0256-307X/19/5/325/pdf

Second-Harmonic Generation of Bessel Beams in Lossy Media

Second-harmonic generation of practical Bessel beams

This paper presents an analytical result concerning second-harmonic generation of a general limited diffraction beam in nonlinear media. The result is based on quasilinear solutions of the Khokhlov?Zabolotskaya?Kuznetsov nonlinear wave equation. It is shown that second-harmonic generation by the nonlinear interaction of two arbitrary Bessel beams gives a nearly radially limited diffraction beam. For an arbitrary limited diffraction beam from the linear superposition of basis mode Bessel beams, results also indicate that the second-harmonic beam remains an almost radially or transversely limited diffraction beam.

Second-harmonic generation of limited diffraction beams

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.

Desheng Ding

Papers

Nonlinear propagation of Bessel–Gauss ultrasonic beams