Generalized spiral transformation for high-resolution sorting of vortex modes

TL;DR

This paper introduces a versatile generalized spiral transformation scheme that enhances high-resolution vortex mode sorting by leveraging different spiral types, notably demonstrating superior performance of the Archimedean spiral in optical applications.

Contribution

The paper presents a novel generalized spiral transformation scheme that improves vortex mode sorting resolution and performance, especially using the Archimedean spiral.

Findings

Archimedean spiral mapping outperforms logarithmic spiral in mode sorting

The scheme is adaptable to various spiral types and applications

Potential for broad use in optical transformations and related fields

Abstract

We propose a generalized spiral transformation scheme that is versatile to incorporate various types of spirals such as the Archimedean spiral and the Fermat spiral. Taking advantage of the equidistant feature, we choose the Archimedean spiral mapping and demonstrate its application in high-resolution orbital angular momentum mode sorting. Given a fixed minimum spiral width, the Archimedean spiral mapping shows superior performance over the logarithmic spiral mapping. This generalized transformation scheme may also find various applications in optical transformation and can be easily extended to other fields related to conformal mapping.