Cascaded optical resonator-based programmable photonic integrated circuits.

Programmable photonic integrated circuits have mainly been developed based on the single wavelength channel operation of fundamental building blocks consisting of Mach-Zehnder interferometers (MZIs) with tunable phase shifters. We propose and study optical circuit models consisting of cascaded optical resonators that enable the independent operation of multiple wavelength channels in a more compact footprint than the conventional MZIs. By adopting experimental values reported for silicon micro-ring resonators, the fidelities of different types of 2×2 unitary transformations and higher-dimensional unitary transformations are examined by employing the Reck algorithm and the Clements algorithm.