A moving refractive index front can induce an indirect transition between states before or after the front. A linear Schrödinger equation can be used to describe the transition of a slowly varying signal envelope at the front. In waveguides with weak dispersion usually spatial evolution of the pulse temporal profile is tracked. However, we show that for waveguides with strong dispersion it is beneficial to track temporal evolution of the pulse spatial profile. Simulation examples close to the band edge of a photonic crystal waveguide are presented. We also compare the numerical results with the theoretical predictions from the phase continuity criterion.
