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

TL;DR

This paper develops a multiscale homogenization approach for the time-dependent Maxwell-Schrödinger system in heterogeneous nanostructures, providing convergence analysis, efficient algorithms, and numerical validation for systems with rapidly oscillating coefficients.

Contribution

It introduces a novel multiscale homogenization method and numerical algorithms for coupled Maxwell-Schrödinger equations in nanostructures with periodic microstructures.

Findings

Validated the homogenization method through numerical simulations.

Demonstrated convergence of the multiscale approach.

Provided efficient algorithms for complex nanostructure modeling.

Abstract

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.