  We study the dynamics of a waveguide made of coupled resonators with a
sinusoidal modulation of the resonance frequencies. We present a modulation
scheme that achieves complete dynamic localization and is experimentally
suitable for optical cavities. Furthermore, we highlight the importance of the
way the modulation is turned on and off. One striking consequence is that,
while a state returns to its starting amplitude at the end of every cycle, it
can also be fully time-reversed if the modulation is turned off mid-cycle.
Finally, we show that localization is always achieved when the modulation
envelope is adiabatic with respect to the oscillation frequency. The results
are experimentally feasible using existing integrated photonic technologies,
and are relevant to applications like tunable delay lines, dispersion
compensation, and imaging.
