Revisit the Poynting vector in P T-symmetric coupled waveguides

We show that the time-averaged Poynting vector of S→=E→×H→^∗/2 in parity-time (P T) 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→×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.