On the Limitations of the Time-Domain Impedance Boundary Condition

Limitations of the time-domain Leontovich impedance boundary condition are discussed for a canonical problem consisting of a planar interface with a conducting half-space. The exact analytical solution obtained using an extension of the Cagniard-DeHoop technique is presented and compared with the approximate one found via the impedance boundary concept. Ranges of applicability of the latter are introduced and numerically tested on illustrative examples. A proper understanding of these limitations may prove to be crucial in the emerging field of time-domain integral equation formulations in planar stratified media.