Complex coordinate stretching as a generalized absorbing boundary condition

By complex coordinate stretching and a change of variables, it is shown simply that PML is reflectionless for all frequencies and all angles. Also, Maxwell's equations for PML media reduce to ordinary Maxwell's equations with complex coordinate systems. Many closed-form solutions for Maxwell's equations map to corresponding closed-form solutions in complex coordinate systems. Numerical simulations with the closed-form solutions show that metallic boxes lined with PML media are highly absorptive. These closed-form solutions lend a better understanding to the absorptive properties of PML media. For instance, they explain why a PML medium is absorptive when a dielectric or metallic interface extends to the edge to a simulation region where PML media reside. More importantly, the complex coordinate stretching method can be generalized to non-Cartesian coordinate systems, providing absorbing boundary conditions in these coordinate systems.