The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using engineered artificial materials

A Maxwellian material interpretation of the Berenger (see J. Computat. Phys., vol.114, p.185-200, 1994) perfectly matched layer (PML) is developed using polarization and magnetization fields. The PML material is found to be a passive lossy electric and magnetic medium with particular conductivity and Debye dispersion characteristics. Although it is recognized that the PML medium is physically unrealizable, this polarization and magnetization field interpretation reveals the necessary characteristics of a perfect electromagnetic absorber. A Maxwellian material that has perfect absorption properties and may be physically realizable is derived with these concepts. This Maxwellian absorber is based upon a time-derivative Lorentz material (TD-LM) model for the dispersive and absorptive electric and magnetic properties of a material. This TD-LM model represents a straightforward generalization of the standard Lorentz material model to include the time derivatives of the fields as driving mechanisms for the polarization and magnetization fields. The numerical implementation of the perfect absorber is given and the resulting reflection coefficients from a perfect electric conductor-backed slab of this material are characterized. It is shown for broad bandwidth pulsed fields that this Maxwellian TD-LM slab, like the non-Maxwellian PML, has absorption characteristics in the 70-110-dB range for large angles of incidence. Strategies are discussed for engineering this dispersive electric and magnetic TD-LM absorber artificially with a substrate that has an array of pairs of appropriately designed small coil-loaded dipole radiating elements embedded in it.