Complete inelastic transparency of time-modulated resonant photonic circuits

Photonic circuits modulated in time can convert the input light frequency $\omega_0$ shifting it by multiples of the modulation frequency $\omega_p$ and, in certain cases, amplify the total input light power. Of special interest are photonic circuits employing microwave capacitors, which instantaneously modulate photonic waveguides with frequency $\omega_p \ll \omega_0$. While the amplification of light is negligible in such circuits, ideally, frequency conversion can be completed with the conservation of the light amplitude. Therefore, similar to the elastically transparent photonic structures (i.e., structures conserving both the light amplitude and frequency), we can say that a photonic circuit parametrically modulated in time exhibits complete inelastic transparency if a wave enters the structure with frequency $\omega_0$ and exits it with a different frequency and the same amplitude. Here, we develop an approach that allows us to introduce and investigate a broad class of time-modulated photonic circuits exhibiting complete inelastic transparency. Light enters these circuits with a resonant frequency $\omega_0$, cascades between their $N$ eigenstates separated by the modulation frequency $\omega_p$, and exits with frequency $\omega_0 + (N-1)\omega_p$ and the output amplitude close to the input amplitude. As examples, we consider circuits of ring microresonators and SNAP microresonators.