Origins and conservation of topological polarization defects in resonant photonic-crystal diffraction

TL;DR

This paper introduces a generalized topological charge concept to describe polarization defects in resonant photonic crystal diffraction, revealing their origins from mode degeneracies and their conservation governed by lattice geometry.

Contribution

It provides a unified framework for defining and analyzing polarization defects and their topological charges in photonic crystal slabs, including their origins and conservation laws.

Findings

Polarization defects originate from mode degeneracies caused by lattice coupling.

Total topological charge in a diffraction order is conserved across the Brillouin zone.

Topological charge conservation depends solely on lattice geometry.

Abstract

We present a continuative definition of topological charge to depict the polarization defects on any resonant diffraction orders in photonic crystal slab regardless they are radiative or evanescent. By using such a generalized definition, we investigate the origins and conservation of integer polarization defects across the whole Brollouin zone. We found that these polarization defects eventually originate from the mode degeneracy that is induced by lattice coupling as a consequence of momentum space folding, or inter-band coupling that can be either Hermitian or Non-hermitian. By counting all types of polarization defects, the total topological charge numbers in a given diffraction order is a conserved quantity across the whole Brillouin zone that is determined by lattice geometry only.