Length-Matching Routing for Programmable Photonic Circuits Using Best-First Strategy

In the realm of programmable photonic integrated circuits (PICs), precise wire length control is crucial for the performance of on-chip programmable components such as optical ring resonators, Mach-Zehnder interferometers, and optical true time-delay lines. Unlike conventional routing algorithms that prioritize shortest-path solutions, these photonic components require exact-length routing to maintain the desired optical properties. To address these challenges, this paper presents different length-matching routing strategies to find exact-length paths while balancing search space and runtime efficiently. We propose a novel admissible heuristic estimator and a pruning method, designed to enhance the accuracy and efficiency of the search process. The algorithms are derived from the Best-First search with modified evaluation functions. For two-pin length-matching routing, we formally prove that the proposed algorithms are complete under monotonic heuristics. For multi-pin length-matching challenges, we introduce a pin-ordering mechanism based on detour margins to reduce the likelihood of prematurely blocking feasible routes. Through evaluations on various length-matching benchmarks, we analyze runtime and heuristic performance, demonstrating the effectiveness of the proposed approaches across different layout scenarios.