Modified Gerchberg–Saxton algorithm to generate vector beams

Abstract

This study explores the generation of vector beams using a modified Gerchberg-Saxton (GS) algorithm in the context of computer-generated holography (CGH). The objective is to reconstruct two orthogonal electric field components with predefined intensity profiles and relative phase distribution between components. The methodology involves applying the GS algorithm independently to each component while imposing their relative phase, allowing the global phase to evolve freely. The vector beams generated are Laguerre-Gaussian beams with varying topological charges, and the holograms are computed for three different cases. The results show successful convergence in the central regions of the beams despite the presence of speckle-like noise. The polarization pattern follows the expected behavior, which means that the relative phase is well reconstructed. Metrics such as similarity and phase error confirm the algorithm’s convergence. These results check the viability of the method to be experimentally implemented, as they are computed according to the laboratory conditions