Robust optimization of 2x2 multimode interference couplers with fabrication uncertainties

In this paper, we propose a novel design-for-manufacture strategy for integrated photonics which speci cally addresses the commonly encountered scenario in which probability distributions of the manufacturing variations are not available, however their bounds are known. The best design point for the device, in the presence of these uncertainties, can be found by applying robust optimization. This is performed by minimizing the maximum realizable value of the objective with respect to the uncertainty set so that an optimum is found whose performance is relatively immune to fabrication variations. Instead of applying robust optimization directly on a computationally expensive simulation model of the integrated photonic device, we construct a cheap surrogate model by uniformly sampling the simulated device at di erent values of the design variables and interpolating the resulting objective using a Kriging metamodel. By applying robust optimization on the constructed surrogate, the global robust optimum can be found at low computational cost. As an illustration of the method's general applicability, we apply the robust optimization approach on a 2x2 multimode interference (MMI) coupler. We robustly minimize the imbalance in the presence of uncertainties arising from variations in the fabricated design geometry. For this example device, we also study the in uence of the number of sample points on the quality of the metamodel and on the robust optimization process. Keywords: Robust optimization, Design-for-Manufacture, Integrated photonics, Multimode interference (MMI) coupler, Surrogate modeling, Metamodel, Implementation error, fabrication uncertainty