Non-Hermitian nanophotonic and plasmonic waveguides

Non-Hermitian Hamiltonians arising from parity-time (PT)-symmetric potentials have been extensively explored in optical systems, owing to their ability to generate asymmetric and even nonreciprocal light propagation. In this paper, we investigate such PT potentials in plasmonic systems, demonstrating asymmetric optical propagation in deeply subwavelength waveguides. In particular, we investigate a five layer plasmonic waveguide composed of metallic layers separated by dielectric media containing either loss or gain in equal quantities. Through an analytic solution of Maxwell's equations, we identify the four lowest order modes of the waveguide, including two positive index modes and two negative index modes, and investigate their evolution with increasing but balanced gain and loss, kappa. Both the exact analytic approach and an approximate one based on Rayleigh-Schrodinger perturbation theory demonstrate eigenvalue merging and state coalescence with increasing kappa, unlike the familiar energy-level splitting observed in conventional coupled systems. The state coalescence always occurs between modes of opposite parity. Also, by changing the coupling between the waveguide layers, state coalescence can occur between modes with opposite refractive indices, resulting in the merging of a positive index mode with a negative index mode at the exceptional point. We use dispersion diagrams and field profiles to illustrate the asymmetric plasmon propagation properties with increasing kappa. We also show that at the system's exceptional point, the modal power varies quadratically along the waveguide. This study represents a spectral analysis of deeply subwavelength PT-symmetric plasmonic and multimodal photonic waveguides and provides a foundation for designing asymmetric and unidirectional nanophotonic devices.