Amplitude-modulated log-polar coordinate mapping for generating top-hat line-shaped beams with steep edges and a high aspect ratio

Abstract

We present a method, based on conformal mapping, to generate top-hat line-shaped beams. The familiar Cartesian to log-polar coordinate transformation and additional amplitude modulation are combined to trans-form an input beam with a circular symmetry into a straight line with a uniform intensity distribution. We implement an experiment by using a spatial light modulator and computer-generated holograms as optical elements for unwrapping and phase correction. An optical system consisting of a cylindrical lens and an interferometer with two dove prisms is additionally employed to improve the quality and aspect ratio of the top hat profile. Numerical simulations and experimental results are presented to evaluate the proposed technique quantitatively. The obtained results demonstrate that the amplitude-modulated log-polar transformation not only effectively converts any input beams with a circular symmetry but also can produce a top-hat line-shaped focus with steep edges and a high aspect ratio.