An analytical study of the discrete perfectly matched layer for the time-domain Maxwell equations in cylindrical coordinates

We present an analysis of the perfectly matched layer in cylindrical coordinates discretized with a staggered second-order accurate finite difference time domain method. For fixed discretization parameters, layer width, and a quadratic loss function, we find the numerical reflection produced by the discrete layer is accurately predicted by the infinite resolution reflection coefficient for σ_max∈[0,σ_max^c], where σ_max is the maximum value of the absorption parameter in the layer. We also find that the finite resolution reflection coefficient achieves its minimum value at a σ^m_max>σ_max^c. Numerical experiments validate the analysis.