Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy medium

A two time-derivative Lorentz material (2TDLM) is introduced to define polarization and magnetization fields that lead to an absorbing layer that can be matched to a lossy dielectric medium. The 2TDLM is a generalization of the successful uniaxial polarization and magnetization time-derivative Lorentz material (TDLM) which has been introduced as an absorbing boundary condition for simulation regions dealing with lossless materials. Expressions are derived to describe the propagation of an arbitrary plane wave in this 2TDLM Maxwellian absorbing material. They are used to study the scattering from a semi-infinite 2TDLM half-space of an arbitrary plane wave incident upon it from a lossy isotropic dielectric medium. Matching conditions are derived which produce reflectionless transmission through such an interface for any angle of incidence and frequency. Numerical tests are given which demonstrate the effectiveness of the resulting 2TDLM absorbing layer.