# Field component modulation of vortex beams in uniaxial crystals driven by angular and topological charge dependencies

## TL;DR

This paper studies how vortex beams change as they travel through a crystal, revealing how their structure depends on beam properties and crystal orientation.

## Contribution

A full vectorial numerical model is used to map the joint effects of propagation angle and topological charge on field components in uniaxial crystals.

## Key findings

- Longitudinal field components show M-dependent oscillations peaking at orthogonal incidence.
- Transverse field components reach maximum amplitude at parallel propagation.
- Anisotropy reduces longitudinal phase winding to (M-1).

## Abstract

We investigate the propagation of linearly polarized vortex–Gaussian beams carrying topological charge M through a rutile uniaxial crystal at arbitrary angles relative to the optical axis. Using a full vectorial numerical model, we provide a systematic mapping of how both the propagation angle \documentclass[12pt]{minimal}
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\begin{document}$$\theta$$\end{document} and the topological charge jointly govern the evolution of the transverse and longitudinal electric–field components. The results reveal a pronounced and angle-dependent modulation of all field components, accompanied by a strong and predictable amplification with increasing M. In particular, the longitudinal component exhibits an M-dependent oscillatory behavior that peaks near orthogonal incidence, while the generated transverse component reaches its maximum close to parallel propagation. The phase distributions show a clear topological imprint, including a reduction of the longitudinal-field phase winding to \documentclass[12pt]{minimal}
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\begin{document}$$(M-1)$$\end{document} due to anisotropy-driven coupling. These observations shed light on the coupled roles of anisotropy, propagation angle, and vortex charge in shaping the vectorial structure of light inside uniaxial crystals. The results hold relevance for applications in optical manipulation, vector-beam generation, and quantum and classical information processing.