Response function for gain and refractive index dynamics in active semiconductor waveguides

Based on semiclassical density matrix equations, we derive a simple analytical expression for the pump-probe response function of an active semiconductor optical waveguide. The results are in good agreement with published pump-probe measurements of gain and refractive index dynamics in laser amplifiers. In particular, an experimentally observed delay in carrier heating is explained, and spectral effects not previously considered are shown to be significant under typical experimental conditions.