Numerical Beamforming and Parametric Descriptions of Laguerre-Gaussian Vortex Beams

Abstract

Vortex beams are beams with a helical wavefront that have found applications in optical or acoustic tweezers to manipulate microscopic particles. Vortex beam imposes torque or force to particles, allowing them to trap the object within the beam's field and induce motion or displacement in a non-contact manner. One type of such beam is a Laguerre-Gaussian beam, where the solution of a Gaussian wave equation is modified by the Laguerre polynomial term that determines the pattern and helical characteristic of the beam. In this paper, a numerical method based on the mathematical expression of the Laguerre-Gaussian beam is implemented to describe how the parameters change the physical behavior of the beam. This work has shown that a straightforward numerical method is capable of producing this kind of beam. Therefore, this approach can be used for generating vortex beams for physical emissions, complex numerical simulations, or demonstrations for teaching purposes.