Generalized Orbital Angular Momentum Symmetry in Parametric Amplification

TL;DR

This paper explores the symmetry properties of down-converted beams in optical parametric amplification with structured light, revealing a multi-sphere Poincaré structure for higher-order modes and potential for parallel beam control.

Contribution

It extends the understanding of Poincaré sphere symmetry from first-order to higher-order modes, introducing a multi-sphere structure linked to orbital angular momentum.

Findings

Symmetry extends to higher-order modes as multiple Poincaré spheres.

Each sphere corresponds to a specific orbital angular momentum value.

Symmetry is independently reproduced in each subspace, enabling parallel control.

Abstract

We investigate interesting symmetry properties verified by the down-converted beams produced in optical parametric amplification with structured light. We show that the Poincar\'e sphere symmetry, previously demonstrated for first-order spatial modes, translates to a multiple Poincar\'e sphere structure for higher orders. Each one of these multiple spheres is associated with a two-dimensional subspace defined by a different value of the orbital angular momentum. Therefore, the symmetry verified by first order modes is reproduced independently in each subspace. This effect can be useful for parallel control of independently correlated beams.