Dwell time and group delays in complex media

We analyze the dwell time and group delays of electromagnetic waves during transmission and tunneling through complex media, which are non-Hermitian and dispersive. We show that the dwell time, group delays of reflection and transmission, and Dicke times are no longer equal, even though the structure remains mirror symmetric. An additional contribution from the dissipative response of the complex media - termed the energy loss time - must be taken into account. Numerical simulations and analysis reveal several interesting effects. For example, a high local energy density does not necessarily imply a high local loss time, and the local field inside a dissipative medium may extract energy from the environment rather than lose it. The theory is also applicable to gain media and parity-time (PT) symmetric structures and performs well in both the superluminal (fast light) and subluminal (slow light) regimes. This study addresses a significant gap in the understanding of field transmission and tunneling through non-Hermitian dispersive media and contributes to advancements in PT-symmetric optics.