Multiscale Approach and The Convergence for the time-dependent Maxwell-Schr\"{o}dinger System in Heterogeneous Nanostructures

This paper discusses the multiscale approach and the convergence of the time-dependent Maxwell-Schr\"{o}dinger system with rapidly oscillating discontinuous coefficients arising from the modeling of a heterogeneous nanostructure with a periodic microstructure. The homogenization method and the multiscale asymptotic method for the nonlinear coupled equations are presented. The efficient numerical algorithms based on the above methods are proposed. Numerical simulations are then carried out to validate the method presented in this paper.