State matrix representations for the unified treatment of non-Hermitian photonic multilayer systems
Phys. Rev. B 114, 204307 – Published 15 October, 2026
DOI: https://doi.org/10.1103/wd5r-11gs
Abstract
This work addresses a frequently overlooked aspect of one-dimensional non-Hermitian multilayered systems: the distinction between modal and operational non-Hermitian responses. While the scattering matrix is commonly used to identify special operational regimes in non-Hermitian systems, the full-state transfer matrix provides a more comprehensive view of both internal and external system dynamics. Here, we systematically explore the behavior of the full-state transfer matrix in non-Hermitian multilayers and we moreover examine how the special case of parity-time (PT) symmetry shapes modal phase response and influences transmission and reflection properties. We establish a complete mathematical framework and further elucidate, through a series of representative examples, the differences between scattering/wave transfer-matrix and full-state transfer matrix eigenvalue spectra and PT-phase criteria, uncovering patterns that inform both design and theoretical understanding. Our results demonstrate the full-state transfer matrix as a versatile tool for analyzing non-Hermitian multilayers, with potential applications in linear optics, impedance characterization, and tunable photonic systems.
