Figure 5:

Top row: intensity of a Gaussian pulse traveling in a backwards direction in a stationary grating as time advances from left to right (the x axis has the same scale in all graphs). The grating is set in motion at t = 0: in the second row with $\delta =-0.002$ , c _g  < c ₁, and in the third row with $\delta =+0.002$ , c _g  > c ₁. In each case the pulse excites nearly parallel Bloch eigenstates which rapidly de-phase giving rise to inflation of the pulse. For $\delta =-0.002$ the Bloch waves have real wave vectors and gradually separate. For $\delta =+0.002$ the wave vectors are complex: they stay put and grow exponentially in amplitude.