Symmetry-protected non-Abelian geometric phases in optical waveguides with nonorthogonal modes

TL;DR

This paper explores how non-Abelian geometric phases can be generated and protected in optical waveguides with nonorthogonal modes, extending coupled-mode theory and analyzing stability in complex waveguide arrangements.

Contribution

It introduces a framework for non-Abelian phases in nonorthogonal waveguides and studies their robustness against higher-order effects and mode nonorthogonality.

Findings

Dark states enable nontrivial U(2) mixing through adiabatic control.

Symmetry of dark states protects geometric evolution despite mode nonorthogonality.

Higher-order coupling effects influence the stability of U(3) phases.

Abstract

The generation of non-Abelian geometric phases from a system of evanescently coupled waveguides is extended towards the framework of nonorthogonal coupled-mode theory. Here, we study an experimentally feasible tripod arrangement of waveguides that contain dark states from which a nontrivial U(2)-mixing can be obtained by means of an adiabatic parameter variation. We investigate the influence of higher-order contributions beyond nearest-neighbour coupling as well as self-coupling on the stability of a U(3)-phase generated from an optical tetrapod setup. Our results indicate that, despite the mode nonorthogonality, the symmetry of dark states protects the geometric evolution of light from distortion.