Guaranteed global optimization of thin-film optical systems

Abstract

A parallel deterministic global optimization algorithm for thin-film multilayer optical coatings is developed. This algorithm enables locating a global solution to an optimization problem in this class to within a user-specified tolerance. More specifically, the algorithm is a parallel branch-and-bound method with applicable bounds on the merit function computed using Taylor models. This study is the first one, to the best of our knowledge, to attempt guaranteed global optimization of this important class of problems, thereby providing an overview and an assessment of the current state of such techniques in this domain. As a proof of concept on a small scale, the method is illustrated numerically and experimentally in the context of antireflection coatings for silicon solar cells—we design and fabricate a three-layer dielectric stack on silicon that exhibits an average reflectance of (2.53 ± 0.10)%, weighted over a broad range of incident angles and the solar spectrum. The practicality of our approach is assessed by comparing its computational cost relative to traditional stochastic global optimization techniques which provide no guarantees on their solutions. While our method is observed to be significantly more computationally expensive, we demonstrate via our proof of concept that it is already feasible to optimize sufficiently simple practical problems at a reasonable cost, given the current accessibility of cloud computing resources. Ongoing advances in distributed computing are likely to bring more design problems within the reach of deterministic global optimization methods, yielding rigorous guaranteed solutions in the presence of practical manufacturing constraints.