Geometric representation of higher-order optical modes

TL;DR

This paper introduces an octant geometric representation for higher-order optical modes, including Laguerre-Gaussian and Hermite-Gaussian modes, facilitating intuitive manipulation and extension of topological concepts to high-dimensional optical systems.

Contribution

It presents a novel octant-based geometric framework that captures high-dimensional optical modes and enables advanced manipulation and topological analysis.

Findings

The octant representation includes standard Poincaré spheres as subspaces.

It allows intuitive manipulation of classical modes and optical qudits.

Provides a framework for extending Berry phases and topological invariants.

Abstract

An octant representation of higher-order optical modes that includes Laguerre-Gaussian and Hermite-Gaussian modes is presented. The octant picture captures the high-dimensional nature of three-state optical systems and beyond, with standard Poincar\'e spheres for orbital angular momentum forming subspaces of the entire state space. This representation enables intuitive manipulation of both classical modes and optical qudits and provides a framework for extending Berry phases and topological invariants to high dimensions.