  We derive and validate a set of coupled Bloch wave equations for analyzing
the reflection and transmission properties of active semiconductor photonic
crystal waveguides. In such devices, slow-light propagation can be used to
enhance the material gain per unit length, enabling, for example, the
realization of short optical amplifiers compatible with photonic integration.
The coupled wave analysis is compared to numerical approaches based on the
Fourier modal method and a frequency domain finite element technique. The
presence of material gain leads to the build-up of a backscattered field, which
is interpreted as distributed feedback effects or reflection at passive-active
interfaces, depending on the approach taken. For very large material gain
values, the band structure of the waveguide is perturbed, and deviations from
the simple coupled Bloch wave model are found.
