Dispersion Engineering With Photonic Inverse Design

Dispersion engineering, such as the design of slow light waveguide systems, is an effective tool for a wide range of photonic applications, but presents a difficult optical design challenge. Most applications require a slow light waveguide design that mitigates group velocity dispersion, and efficient coupling solutions over the slow light operating bandwidth. In this work, we optimize the slow light dispersion relation of a photonic crystal waveguide with three dimensional (3D) inverse design methods. In addition, we design mode couplers for the photonic crystal waveguide. The optimized waveguide supports a slow light mode with a group index of <inline-formula><tex-math notation="LaTeX">$\mathbf {n_g = 25}$</tex-math></inline-formula> and a normalized bandwidth group index product of <inline-formula><tex-math notation="LaTeX">$\mathbf {0.38}$</tex-math></inline-formula>. A compact mode coupler to a strip waveguide is designed with an average efficiency of 92.7% within the slow light operating bandwidth. Lastly, we design a fully etched grating which couples directly to the slow light mode with a 32.5% average efficiency.