Modified Gerchberg–Saxton algorithm to generate vector beams

Abstract

This study focuses on improving a modified Gerchberg-Saxton (GS) algorithm to generate vector beams under strong focusing conditions. The main goal is to solve the instability problems that happen when the beam waist is very small, where standard methods usually fail. To achieve this, we introduced a regularization strategy using separate relaxation parameters for amplitude and phase to independently smooth the iterative process. After testing some combinations, our results show that by adjusting these parameters, either the intensity or the polarization distribution can be better reconstructed. Therefore, fidelity parameters for both magnitudes are defined to monitor their evolution during the iterative process for each combination and to evaluate the optimal trade-off.