Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

TL;DR

This paper analyzes how misalignments affect the structure of vortex beams diffracted by holograms, providing analytical models and exploring implications for optical vortex generation and measurements.

Contribution

It introduces analytical representations for diffracted vortex beams considering misalignments, advancing understanding of beam structure evolution under practical conditions.

Findings

Misalignments cause significant changes in intensity and phase distributions.

Analytical models based on superpositions of Kummer and hypergeometric-Gaussian beams.

Insights for optimizing optical vortex generation and measurement techniques.

Abstract

Spatial characteristics of diffracted beams produced by a "fork" hologram from an incident circular Laguerre-Gaussian beam whose axis differ from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the "proper" topological charge m of the incident vortex beam and the topological charge l of the singularity "imparted" by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical-vortex beam generation and optical measurements are discussed.