Modeling and FDTD discretization of stochastic Maxwell's equations with Drude dispersion

We develop the stochastic Maxwell's equations with Drude model under both additive and multiplicative noises. The additive noises characterize the random fluctuations in the electric current and magnetic current densities in Maxwell's equations, while the multiplicative noise describes the external fluctuation of electric field in the Drude dispersion equation of motion. For the stochastic models with Drude dispersion, we derive the averaged global energy law considering both types of noises. The CN-FDTD and Yee-FDTD discretization schemes are developed for solving the stochastic system over staggered grids. We establish the discrete averaged global energy laws for the CN-FDTD and Yee-FDTD schemes. Numerical experiments show the discrete averaged global energy evolutions and the convergence rates of the schemes for the stochastic Maxwell's equations with Drude model. We numerically simulate and analyze the stochastic electromagnetic propagation within Drude materials under various sinusoidal sources, initial wave conditions and additive and multiplicative noises.