Martin Hammerschmidt

Philipp-Immanuel Schneider, Martin Hammerschmidt, Lin Zschiedrich et al.

Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to different local minimization algorithms for this numerical optimization problem. Bayesian optimization uses Gaussian-process regression to find promising parameter values. We examine how pre-computed simulation results can be used to train the Gaussian process and to accelerate the optimization.

Philipp-Immanuel Schneider, Xavier Garcia Santiago, Victor Soltwisch et al.

Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays nano-fabrication technologies for which a rational design is no longer feasible. Also, numerical resources are available to enable the computational photonic material design and to identify structures that meet predefined optical properties for specific applications. However, the optimization objective function is in general non-convex and its computation remains resource demanding such that the right choice for the optimization method is crucial to obtain excellent results. Here, we benchmark five global optimization methods for three typical nano-optical optimization problems: \removed{downhill simplex optimization, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, particle swarm optimization, differential evolution, and Bayesian optimization} \added{particle swarm optimization, differential evolution, and Bayesian optimization as well as multi-start versions of downhill simplex optimization and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm}. In the shown examples from the field of shape optimization and parameter reconstruction, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods.