Engineering the Frozen Mode Near a Stationary Inflection Point in Coupled Single-Mode Waveguides with Lateral Gratings

We introduce a systematic approach to designing slow-light photonic integrated circuits supporting a frozen mode associated with a third-order exceptional point of degeneracy (EPD), known as a stationary inflection point (SIP). The proposed approach employs three-way coupled waveguides incorporating lateral gratings and operating at telecommunication wavelengths. We investigate two distinct waveguide configurations and demonstrate the formation of SIPs through full-wave eigenmode simulations. We also analyze the sensitivity of the dispersion characteristics to geometric perturbations and realistic fabrication constraints. A periodic waveguide with integrated tapered terminations is fabricated and experimentally characterized, revealing spectral features that are qualitatively consistent with numerical predictions. Simulations of finite-length structures further demonstrate substantial group-delay enhancement near the SIP frequency. These results establish a practical approach to realizing frozen-mode waveguides and integrating SIP-based slow-light functionalities into silicon photonic circuits.