Evanescent gain for slow and stopped light in negative refractive index heterostructures

We theoretically and numerically analyze a five-layer ``trapped rainbow'' waveguide made of a passive negative refractive index (NRI) core layer and gain strips in the cladding. Analytic transfer-matrix calculations and full-wave time-domain simulations are deployed to calculate, both in the frequency and in the time domain, the losses or gain experienced by complex-wave-vector and complex-frequency modes. We find excellent agreement between five distinct sets of results, showing that the use of evanescent pumping (gain) can compensate the losses in the NRI slow- and stopped-light regimes.