Exceptional Cones in 4D Parameter Space

TL;DR

This paper explores topological physics in four-dimensional non-Hermitian synthetic parameter space using PT-symmetric photonic crystals, revealing exceptional hypersurfaces and points with potential applications in optical sensing.

Contribution

It introduces the realization of a 3D exceptional hypersurface in 4D parameter space and demonstrates the existence of exceptional degenerate points with unique properties.

Findings

Discovery of a 3D exceptional hypersurface in 4D space

Identification of exceptional degenerate points with Dirac cone behavior

Narrow reflection plateau near EDPs indicating high sensitivity

Abstract

The notion of synthetic dimensions has expanded the realm of topological physics to four dimensional (4D) space lately. In this work, non-Hermiticity is used as a synthetic parameter in PT-symmetric photonic crystals to study the topological physics in 4D non-Hermitian synthetic parameter space. We realize a 3D exceptional hypersurface (EHS) in such 4D parameter space, and the degeneracy points emerge due to the symmetry of synthetic parameters. We further demonstrate the existence of exceptional degenerate points (EDPs) on the EHS that originates from the chirality of exceptional points (EPs), and the exceptional surface near EDPs behaves like a Dirac cone. We further show that a very narrow reflection plateau can be found near these EDPs, and their sensitivity towards the PT-symmetry breaking environmental perturbation can make these degeneracy points useful in optical sensing and many other nonlinear and quantum optical applications.