  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-wavevector and
complex-frequency modes. We find an excellent agreement between five distinct
sets of results, all showing that the use of evanescent pumping (gain) can
compensate the losses in the NRI slow-light regime.
