Universal Topology of Exceptional Points in Nonlinear Non-Hermitian Systems

TL;DR

This paper reveals a universal topology in nonlinear systems supporting second-order exceptional points, enhancing understanding and guiding future experimental and technological developments in nonlinear non-Hermitian physics.

Contribution

It introduces a universal topology for nonlinear second-order exceptional points, extending linear EP concepts and providing a framework for classification and optimization.

Findings

Universal topology in nonlinear parameter space for 2nd order EPs

Emergence of EPs as coalescence of 4 nonlinear eigenvectors

Guidance for experimental discovery and technological applications

Abstract

Exceptional points (EPs) are non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to unusual physical effects across scientific disciplines. The concept of EPs has recently been extended to nonlinear physical systems. We theoretically demonstrate a universal topology in the nonlinear parameter space for a large class of physical systems that support 2nd order EPs in the linear regime. Knowledge of this topology (called elliptic umbilic singularity in bifurcation theory) deepens our understanding of 2nd order linear EPs, which here emerge as coalescence of 4 nonlinear eigenvectors. This helps guide future experimental discovery of nonlinear EPs and their classification, establish rigorous bounds of sensitivity enhancement of EPs in nonlinear systems, and helps envision and optimize technological applications of nonlinear EPs. Our theoretical approach is general and can be extended to nonlinear perturbations of 3rd and higher-order EPs.