Revisit the Poynting vector in PT-symmetric coupled waveguides

We show that the time-averaged Poynting vector of S--> = E--> x H-->*/2 in parity-time (PT) symmetric coupled waveguides is always positive and cannot explain the stopped light at exceptional points (EPs). In order to solve this paradox, we must accept the fact that the fields E--> and H--> and the Poynting vector in non-Hermitian systems are in general complex. Based on the original definition of the instantaneous Poynting vector S--> = E--> x H-->, a formula on the group velocity is proposed, which agrees perfectly well with that calculated directly from the dispersion curves. It explains not only the stopped light at EPs, but also the fast-light effect near it. This investigation bridges a gap between the classic electrodynamics and the non-Hermitian physics, and highlights the novelty of non-Hermitian optics. (c) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Automated summary

This study shows that the time-averaged Poynting vector in parity-time (PT) symmetric coupled waveguides is always positive and cannot explain the phenomenon of stopped light at exceptional points (EPs). By considering the fields and Poynting vector in non-Hermitian systems as complex, a formula for the group velocity is proposed, which accurately explains the stopped light and fast-light effect at EPs. This research bridges the gap between classical electrodynamics and non-Hermitian physics, emphasizing the novelty of non-Hermitian optics.