Simulating the diffraction pattern in the focal plane of a lens-axicon system

Laser beam concentration into a narrow ring with a lens and axicon is considered, as there are applications in working surfaces, cutting wafers and slices, and in welding or soldering tubes to heat-exchanger plates. A model is constructed and a working formula is derived for the diffraction pattern in the focal plane of such a system when the axicon is illuminated by a plane wave. For large h/, where h is axicon height and is wavelength, a formula is obtained that passes asymptotically into the approximate Belanger and Rioux ones.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 36–41, December, 1987.