High-order spectral filtering based on photonic synthetic dimensions.

Photonic synthetic dimensions offer a novel approach to generating additional dimensions in photonic systems by harnessing non-spatial degrees of freedom. This technique has demonstrated significant potential for the development of advanced all-optical devices. Here, we present a design and experimental demonstration of tunable high-order filters based on driving photon propagation in synthetic orbital angular momentum and polarization dimensions in a single cavity. We provide rigorous proof for the equality between the coupled ring resonator arrays and the synthetic lattice in a resonant cavity. We illustrate the dispersion relation of the constructed cavity and show that the synthetic dimension-based filter has an electric-controlled tunable center frequency and passband bandwidth. Our all-optical filter design would inspire the invention of functional optical devices using photonic synthetic lattices.