Robust multi-objective optimization of 2x2 multimode interference coupler using expected improvement

In this paper, we present a novel approach to find the robust optimum of integrated photonic devices affected by implementation error. We apply robust optimization on a cheap surrogate model of an expensive integrated photonic device simulation. Robust optimization is the process of finding the best design point, in the presence of uncertainties, by minimizing the maximum realizable value of the objective with respect to the uncertainty set. The interpolation across the sampled values is performed by Kriging, a surrogate modelling technique with a statistical basis, which provides an estimate of the error in the interpolation. Using this error estimate, Kriging provides a metric, known as expected improvement, which indicates where a new sample should be added in order to reach the nominal optimum efficiently. In this work, we combine expected improvement with robust optimization in order to exhibit how a robust optimum on an integrated photonic device can be found. This method is illustrated by robustly minimizing two objectives, excess loss and imbalance, of a 2x2 multimode interference coupler in the presence of uncertainties arising from variations in the fabricated design geometry. We also demonstrate how different weighting factors affect the multi-objective optimization problem. Keywords: Robust optimization, Design-for-Manufacturing, surrogate modelling, expected improvement, multimode interference coupler, fabrication uncertainty