| Summary: | We provide an analytic solution to the coupled-mode equations describing the steady-state of a
single periodically modulated optical resonator driven by a monochromatic input. The phenomenology of
this system was qualitatively understood only in the adiabatic limit, i.e., for low
modulation speed. However, both in and out of this regime, we find highly non-trivial
effects for specific parameters of the modulation. For example, we show complete
suppression of the transmission even with zero detuning between the input and the static
resonator
frequency. We also demonstrate the possibility for complete, lossless frequency conversion of the
input into the sideband frequencies, as well as for optimizing the transmitted
signal towards a
given target temporal waveform. The analytic results are validated by first-principle
simulations.
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