Ideal absorption condition for FDTD method in isotropic lossy dispersive media

Abstract

The behaviour of the electromagnetic field in isotropic lossy media is described with the PML split field forms in a modified set of Maxwell's equations in stretched coordinates. The general expressions for propagation constants, impedance, reflection and transmission coefficients with original constitutive parameters in isotropic lossy media and stretched complex coefficients are derived. We call these general expressions the PMLS characteristics. Based on the PMLS, a set of equivalent constitutive parameters are provided to replace the original constitutive parameters in Cartesian coordinates. The equivalent constitutive parameters can be chosen as special values that are suitable for the calculation by FDTD method or other electromagnetic modelling methods. We prove that the difference between the fields calculated in the original constitutive parameters and in the equivalent constitutive parameters is a complex constant. This field equivalent aspect is called constitutive equivalent principle. For any values of the original constitutive parameters in isotropic lossy media, a set of stretched complex coefficients can be specified to provide equivalent constitutive parameters in which an absorption boundary condition is established for FDTD method. We call the absorption boundary condition the Ideal Absorption Condition (IAC). We prove that the Perfectly Matched Layers (PML) is a special case of the IAC when the electric conductivity and magnetic conductivity in the original constitutive parameters equal zero. For the verification of the IAC, the input admittance for a dipole antenna in a homogeneous lossy material calculated by FDTD method with IAC was compared by a Three-Term Exponential Product analytical solution.