Optical Quasi-symmetry Groups for Meron Lattices

TL;DR

This paper introduces the concept of quasi-symmetry groups in optics, enabled by spin-orbit interactions, which allow the formation of meron lattices and topological textures even when sources lack nominal symmetry.

Contribution

It presents the first theoretical framework for quasi-symmetry in optics, demonstrating how strong spin-orbit interactions enable topological light structures beyond traditional symmetry constraints.

Findings

Quasi-symmetry groups protect meron lattice formation.

Robust polarization zones with identical topological textures.

Effective mirror operators derived for C3 polarized dipoles.

Abstract

We introduce quasi-symmetry groups in optics emerging from the commutation between mirror operation and the spin-orbit interaction (SOI) of light. Contrary to the principle of symmetry inheritance in free-space optics, where the symmetry of any structured field is strictly constrained by that of its source, we show that strong SOI enables quasi-symmetry-protected formation of meron lattices even when the underlying optical sources violate the nominal rotational symmetry. By analyzing the Hermiticity of the electric-dipole radiation amplitude in a circular polarization basis, we derive an effective mirror operator acting only on a subset of C3 polarized dipole emitters, forming a quasi-symmetry group that commutes with SOI. This quasi-symmetry guarantees exact C3 merons and gives rise to a robust polarization zone within which continuously varying input polarizations generate identical topological textures. Our work establishes quasi-symmetry as a new fundamental principle in optical physics and opens pathways to engineered topological structures of light beyond conventional symmetry constraints.