Uncertainty quantification for an optical grating coupler with an adjoint-based Leja adaptive collocation method

Abstract

This paper addresses uncertainties arising in the nano-scale fabrication of optical devices. The stochastic collocation method is used to propagate uncertainties in material and geometry to the scattering parameters of the system. A dimension-adaptive scheme based on Leja nodes is employed to reduce the computational complexity. By combining the Leja adaptive algorithm with an adjoint-based error indicator, an even smaller complexity is obtained. The scheme's efficiency is demonstrated by numerical results for an optical grating coupler. For this model problem, the adaptive strategy allows to compute statistical moments, probabilities and global sensitivity indices, taking into account a moderately high number of uncertain input parameters. In particular, it is found that geometric sensitivities outweigh sensitivities with respect to material parameters for the considered setting.