Graph Representations for Programmable Photonic Circuits

We propose graph representations for reconfigurable photonic mesh circuits. Waveguide mesh circuits are abstracted into a graph to highlight the connectivity and topology. We model the optical ports as graph nodes. Performance metrics for each connection are incorporated into the edge attributes in categories such as propagation loss, crosstalk penalty, power consumption, phase accumulation, and so on. We use three types of graph representations for tunable couplers to model the flow of light and create a circuit graph representation to an example hexagonal mesh. The representation should respect the physics of waveguide circuits (e.g. directional flow of light). Of the three types, the directed graph with eight artificial nodes performs best for solving light distributions with feedback paths. This graph representation is demonstrated in four distribution cases: a single pair input-output, multi-pair inputs and outputs without collisions, a single input to multiple outputs (distribution), and multiple distributions without collisions. The programming tolerance against malfunctioning tunable elements is also demonstrated. With this circuit representation, we can reduce all these distribution cases to different graph problems and leverage a wealth of existing algorithms developed in graph theory to program the photonic mesh. Thus we provide a systematical strategy to design and program complex reconfigurable photonic circuits, especially in photonic meshes with feedback paths.