Uncertainty quantification of grating filters via a Polynomial-Chaos method with a variance-adaptive design domain

In this work, we describe an algorithm based on Polynomial-Chaos (PC) expansions for the study of uncertainty quantification problems involving grating filters. The proposed method adaptively builds anisotropic PC models for the quantities of interest, considering varying polynomial orders. In addition, optimal experimental designs are constructed that exploit the local variance of the samples, further increasing the reliability of the computations. The method is applied to the uncertainty quantification of a typical resonant grating filter, where the efficiency of the proposed approach over standard techniques is demonstrated.