  We describe a general mechanism of controllable energy exchange between waves
propagating in a dynamic artificial crystal. We show that if a spatial
periodicity is temporarily imposed on the transmission properties of a
wave-carrying medium whilst a wave is inside, this wave is coupled to a
secondary counter-propagating wave and energy oscillates between the two. The
oscillation frequency is determined by the width of the spectral band gap
created by the periodicity and the frequency difference between the coupled
waves. The effect is demonstrated with spin waves in a dynamic magnonic
crystal.
