Low sidelobe limited diffraction beams in the nonlinear regime

In linear propagation, sidelobe levels of Bessel limited diffraction beams are only about 8 dB down relative to the mainlobe. In the nonlinear regime, these beams will have a region near the source where the side-lobe level of the second harmonic is 16 dB down, but this region has usually been considered to be so small that it is of little practical interest. In this paper it is shown that when there are only 1 to 3 sidelobes in a finite aperture Bessel beam, the second harmonic field will have low sidelobes for distances up to half of the depth of field. This result is backed up by simulations. In a medium with absorption, previous theory has shown that the sidelobes of the Bessel beam will also be reduced but only for absorption that was too high to be of practical use. Simulations presented here show that for breast tissue, which only has about 10% of the absorption of previous criteria, one will still get sidelobes which are comparable to that of a rectangular aperture even when the sidelobes would be high in a non-absorbing medium.