Transformation of Optical Vortex Beams by Holograms with Embedded Phase Singularity

TL;DR

This paper theoretically investigates how holograms with embedded phase singularities transform optical vortex beams, revealing the complex amplitude structures, ripple effects, and conditions for optimal vortex generation and healing.

Contribution

It introduces models for the diffracted beam's complex amplitude and analyzes the influence of divergent spherical waves on the beam structure, advancing understanding of vortex beam transformation.

Findings

Diffracted beams can be described by Kummer or hypergeometric-Gaussian models.

Ripple structures are caused by divergent spherical waves from hologram discontinuities.

Optimal conditions exist for healing the input beam's singularity, enhancing energy concentration.

Abstract

Spatial characteristics of diffracted beams produced by the "fork" holograms from incident circular Lauerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most cases its structure is formed under the influence of the divergent spherical wave originating from the discontinuity in the beam spatial profile or its derivatives caused by the hologram's groove bifurcation. Presence of this wave is manifested by the ripple structure in the near-field diffracted beam profiles and in the power-law amplitude decay at the beam periphery. Conditions when the divergent wave is not excited are discussed. The diffracted beam carries a screw wavefront dislocation (optical vortex) whose order equals to algebraic sum of the incident beam azimuthal index and the topological charge of the singularity imparted by the hologram. The input beam singularity can be healed when the above sum is zero. In such cases the diffracted beam can provide better energy concentration in the central intensity peak than the Gaussian beam whose initial distribution coincides with the Gaussian envelope of the incident beam. Applications are possible for generation of optical-vortex beams with prescribed properties and for analyzing the optical-vortex beams in problems of information processing.