True-time delay and mode-matching in Archimedean spiral silicon photonic waveguides

We report a comprehensive analysis and design optimization of true-time delay (TTD) photonic waveguides using compact Archimedean spiral geometries, with a focus on low-loss silicon nitride (Si₃N₄) and silicon-on-insulator (SOI) platforms. Using a combination of finite element and finite-difference time-domain simulations at 1550 nm, we evaluated the propagation characteristics, mode-matching behavior, and bending losses of various waveguide designs. Our results demonstrate that Si₃N₄ rectangular waveguides exhibit superior performance for long optical paths, achieving minimal radiation and scattering losses, whereas SOI is more suitable for compact integration. We further investigated curvature-engineered bends (Euler, Bézier, and circular) and identified Quartic Bézier bends as optimal for tight-radius, low-loss guiding. By minimizing crosstalk through tailored waveguide gaps and carefully engineered S-bend transitions, we present a scalable low-loss TTD architecture. These findings offer critical insights for integrating ultralow-loss, material-efficient delay lines into photonic circuits for applications in signal processing, LiDAR, phased array antennas, and neuromorphic computing.