Accurate modeling and simulation of electromagnetic wave propagation in dispersive dielectrics such as water, human tissue, has a variety of applications. For example in medical imaging, elecromagnetic waves are used for non-invasive interrogation of human tissue to detect anomalies. In non-destructive evaluation of materials electromagnetic interrogation is used to detect defects in these materials.
We present the construction and analysis of two novel operator splitting methods for Maxwell's equations in dispersive media of Debye type which are used to model electromagnetic wave propagation in polar materials like water and human tissue. We construct sequential and symmetrized operator splitting schemes which are first order, and second order, respectively accurate in time. Both schemes are second order accurate in space. We prove that the operator splitting methods are unconditionally stable via energy techniques. The accuracy and stability properties of the schemes are compared to established methods for the numerical simulation of electromagnetic wave propagation such as the Yee scheme and the Crank-Nicolson method. Finally, we will present results of numerical simulations that confirm our theoretical analysis.