Physics & Astronomy Faculty Publications

Document Type

Article

Publication Date

3-31-2026

Abstract

Photonic systems with exceptional points, where eigenvalues and corresponding eigenstates coalesce, have attracted interest due to their topological features and enhanced sensitivity to external perturbations. Non-Hermitian mode-coupling matrices provide a tractable analytic framework to model gain, loss, and chirality across optical, electronic, and mechanical platforms without the complexity of full open-system dynamics. Exceptional points define their spectral topology, and enable applications in mode control, amplification, and sensing. Yet N -mode couplers, the minimal setting for N th-order exceptional points, are often studied in specific designs that overlook their algebraic structure. We introduce a general sl(N , C) framework for arbitrary N -mode couplers in classical and quantum regimes, and develop it explicitly for N = 3. This case admits algebraic diagonalization, where a propagation-dependent gauge aligns local and dynamical spectra and reveals the geometric phase connecting adiabatic and exact propagation. An exact Wei–Norman propagator captures the full dynamics and makes crossing exceptional points explicit. Our framework enables classification of coupler families. We study the family spanning PT -symmetric and non-Hermitian cyclic couplers, where two exceptional points of order three lie within a continuum of exceptional points of order two, ruling out pure encircling. As an application, we study these exceptional points for a lossy three-leg beam splitter and reveal its propagation dynamics as a function of initial states, such as Fock and NOON states. Our approach provides a systematic route to analyze non-Hermitian mode couplers and guide design in classical and quantum platforms.

Comments

© 2026 Chinese Laser Press

Publication Title

Photonics Research

DOI

10.1364/PRJ.583226

Download

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.