Transformation of a Laguerre-Gaussian LG(l,0) Beam by the Combination of Axicon and Fork-Shaped Grating

摘要

We present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian LG(l,0) laser beam (possessing topological charge l) by a combination of a fork-shaped grating (FG) with integer topological charge (TC) p and an axicon attached with its base to the FG. The beam enters with its waist in the plane of this composed optical element, and passes with its axis through the center of the axicon and the FG (i.e. the origin of the fork-shaped splitting). The diffracted wave field amplitude and intensity distributions are calculated and analyzed in the back focal plane of a convergent lens. The diffracted beam is derived as a sum of a zeroth diffraction order propagating along the optical axis, and deviated higher diffraction orders. While the zeroth diffraction order carries the same TC as that of the incident beam, the beam in the mth diffraction order has TC which is an algebraic sum of l and the product mp. The influence of the axicon on the radial intensity distributions is also analyzed.