Uncertainty Study of Periodic-Grating Wideband Filters With Sparse Polynomial-Chaos Expansions

The performance of periodic-grating resonant structures, which find various applications as optical devices, is highly dependent on their geometric features. This Letter investigates the response of such wideband configurations, when a non-trivial number of random geometric variables are considered. To avoid computationally expensive solutions, we develop sparse Polynomial-Chaos (PC) approximations for the quantity of interest, using a limited number of basis functions. Initially, the size of the PC series is reduced by excluding terms that describe highly complex interactions. Then, the most significant terms are computed via the Orthogonal-Matching-Pursuit algorithm, in the context of compressed sensing. The latter necessitates only a few deterministic model evaluations, and produces sparse, yet accurate, PC formulae. Numerical results for a broadband grating filter verify the proposed two-step approach, and display the structure's performance variability under uncertainty conditions.