Maxwellian material-based absorbing boundary conditions for lossy media in3-D

A two time-derivative Lorentz material (2TDLM), which has been shown previo usly to be the correct Maxwellian medium choice to match an absorbing layer to a lossy region, is extended here to a complete absorbing boundary condi tion (ABC) for three-dimensional (3-D) finite-difference time-domain (FDTD) simulators. The implementation of the lossy 2TDLM (L2TDLM) ABC is presente d. It is shown that in contrast to the one-dimensional (1-D) and two-dimens ional (2-D) versions, the full 3-D ABC requires a three time-derivative Lor entz material in the edge and corner regions to achieve a rigorous matching of the resulting Maxwellian absorbing layer to the lossy medium. The 3-D A BC implementation thus requires the introduction of an auxiliary field to h andle the edge and corner regions to achieve a state-space form of the upda te equations in the ABC layers, Fully 3-D examples including pulsed dipole radiation and pulsed Gaussian beam propagation in lossless and lossy materi als as well as pulse propagation along a microstrip over lossless and lossy materials are included to illustrate the effectiveness of the L2TDLM ABC.