Robust topology optimization of photonic crystal waveguides with tailored dispersion properties

A robust topology optimization method is formulated to tailor dispersion properties of photonic crystal waveguides, with consideration of manufacturing uncertainties. Slightly dilated and eroded realizations are considered as well as the real structure, and by worst-case optimization, we also ensure a satisfactory performance in the case of an under- or overetching scenario in the manufacturing process. Two photonic crystal waveguides facilitating slow light with group indexes of ng=25 and ng=100 and bandwidths of Δω/ω=2.3% and 0.3%, respectively, are obtained through the proposed robust design procedure. In addition, a novel waveguide design with two different constant group index waveguide regions is demonstrated. The numerical examples illustrate the efficiency of the robust optimization formulation and indicate that the topology optimization procedure can provide a useful tool for designing waveguides that are robust to manufacturing uncertainties such as under or overetching.