Bloch oscillation and unidirectional translation of frequency in a dynamically modulated ring resonator

The ability to control the spectrum of light is of fundamental significance in many applications of light. We consider a dynamically modulated ring resonator that supports a set of resonant modes equally spaced in their resonant frequencies, and is modulated at a frequency that is slightly detuned from the modal frequency spacing. We find that such a system can be mapped into a tight-binding model of photons under a constant effective force, and, as a result, the system exhibits Bloch oscillation along the frequency axis. The sign of the detuning is mapped to the sign of the effective force and hence controls the direction of the Bloch oscillation. We also show that a periodic switching of the detuning can lead to unidirectional transport of light along the frequency axis. Our work points to a new capability for manipulating the frequencies of light using dynamic microcavity structures.

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