Transition from slow and frozen to superluminal and backward light through loss or gain in dispersion-engineered waveguides

We describe the generic effects of loss or gain on pulse propagation in photonic-crystal and plasmonic waveguides that support "frozen" or "in-band" slow light at dispersion inflection points in the absence of loss (or gain). Using an analytical perturbation theory, we find that propagating and evanescent modes hybridize when loss exceeds a certain threshold, resulting in a reduced attenuation rate and switching from slow to superluminal velocity. Numerical simulations for photonic-crystal waveguides reveal the dynamic nature of this transition with forward-backward pulse velocity oscillations for loss above the threshold. Importantly, we show that the light intensity is enhanced close to the input end of the waveguide even under strong material losses, indicating the potential for slow-light enhancement of optical effects, even in such lossy waveguides.