This dissertation study three different approaches for stochastic electromagnetic fields based on the time domain Maxwell\u27s equations and Drude\u27s model: stochastic Galerkin method, stochastic collocation method, and Monte Carlo class methods. For each method, we study its regularity, stability, and convergence rates. Numerical experiments have been presented to verify our theoretical results. For stochastic collocation method, we also simulate the backward wave propagation in metamaterial phenomenon. It turns out that the stochastic Galerkin method admits the best accuracy property but hugest computational workload as the resultant PDEs system is usually coupled. The Monte Carlo class methods are easy to implement and do parallel computing but the accuracy is relatively low. The stochastic collocation method inherits the advantages of both of these two methods
