Direct generation of vortex beam by changing the laser cavity mirror

Vortex beams have been applied in multiple engineering and scientific applications due to their distinctive orbit angular momentum and vortex phase characteristics. Traditional methods suffer from complicated setup for the generation of vortex beams not only costly but also non-scalable. In this study, we propose a novel approach for the direct generation of vortex beams and coaxial muti-vortex beams through the use of laser resonator mirror. We have designed a diffractive output mirror of the laser resonator using Gerchberg-Saxton (GS) algorithm inspired by the mode matching theory and optical diffraction principles. Through the analysis of the pumping power in a four-level laser configuration, we have established correlations between ring-shaped pumping light and target vortex beam characteristics, thereby providing essential design guidelines for vortex beam generation within resonators.