Pulse propagation in a Debye medium with static conductivity

Many physical materials that we wish to interrogate with electromagnetic signals are conductive. Thus, we need to understand the propagation dynamics of electromagnetic pulses through dispersive, conductive materials. Closed-form solutions are preferable to numerical solutions in that they provide an explicit expression for the dependence of the propagated field on the physical parameters. Here, we study the propagation of an ultrawideband electromagnetic pulse through a semiconductor with complex dielectric permittivity given by a Debye model with static levels of conductivity. Although the Debye model with static conductivity provides a fairly rudimentary approximation to the electromagnetic response of conductive materials such as rock, soil, and biological tissue, it is a more complex and complete model than those used in previous analytic and numerical research. For example, Wait, Song and Chen, and Dvorak assumed both the dielectric permittivity and the electric conductivity to be constant for their analytic studies of electromagnetic pulse propagation, as did Luebbers, et al. in their numerical work. In addition, King and Wu used a non-causal approximation of the complex dielectric permittivity that is valid only for very low frequency pulses.