# Exact solution to the steady-state dynamics of a periodically-modulated resonator

## TL;DR

This paper presents an exact analytical solution for the steady-state behavior of a periodically-modulated optical resonator, revealing complex phenomena beyond the adiabatic limit, including transmission suppression and lossless frequency conversion.

## Contribution

It provides the first exact solution to the coupled-mode equations for a modulated resonator, uncovering non-trivial effects at various modulation speeds.

## Key findings

- Complete transmission suppression at zero detuning.
- Lossless frequency conversion into side-band frequencies.
- Optimization of transmitted signals for target waveforms.

## Abstract

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 side-band frequencies, as well as for optimizing the transmitted signal towards a given target temporal waveform. The analytic results are validated by first-principle simulations.