Dependence of the precursors on the medium parameters in passive Lorentzian medium

The appearance of precursor fields in a causally dispersive dielectric is due to the interrelated effects of phase dispersion and frequency dependent attenuation of the medium. Until now, rigorous studies of these transient fields have been performed showing the evolution of the precursors and their unique penetrating features that can be used in imaging and material identification. To be able to use the precursors for material identification we need to know the dependance of the precursors on medium parameters. The purpose of this paper is to study the dependance of the Sommerfeld and Brillouin precursors in passive Lorentzian media on the medium parameters. The finite difference time domain and joint time frequency analysis are used as numerical techniques for this purpose. This combination illuminates the temporal and spectral dependence of the precursors to the medium parameters. It also provides a complete and accurate time and frequency evolution of the total field inside the dispersive medium. This combination is a robust tool which can be used to analyze any dispersive media.