Propagation of the electromagnetic fields in dispersive media has been extensively studied since the beginning of the century. The earliest introductory research effort into the problem of dispersive wave propagation was conducted by Hamilton in 1839 when the concept of group velocity seems to have been first introduced. The energy propagation velocity and its relation to the phase and group velocities is an important result of these studies. The wave propagation mechanisms in a linear dispersive medium have been investigated analytically and validated empirically. With the Lorentz model well established as a causal model of dielectric response Sommerfeld considered the propagation of a unit-step-function modulated scalar-wave signal in a single resonance Lorentz model medium. This lead to the derivation of the Sommerfeld precursor, or forerunner which is the transient part of response. Brillouin furthered Sommerfeld’s research with more rigorous analysis and found a second set of forerunners, called Brillouin precursor. The fundamental study of Sommerfeld and Brillouin forms the basis of all further research in this field. The most interesting result is that there is alway a transient response which has no similarity to the main signal. The transient response is totally determined by the medium parameters. Wave propagation in dispersive media have been studied by approximate analytical methods which are not valid in some region. In this thesis the finite difference time domain method as a numerical technique is utilized to investigate the transient response and the effects of medium parameters of Lorentz model on wave propagation. The instantaneous frequency is derived by Wigner-Ville method. precursors exhibit some interesting features. The main feature is low propagation loss in comparison with the main signal. Therefore, precursors can be used to penetrate in Debye type media such as water, wet soil for telecommunication or detection purposes. Precursors could be used in microwave heating applicatio as the source which increases the performance because these waveforms attenuate nonexponentially. Therefore, these signals could penetrate more than other signals and warm up the medium uniformly. In this thesis, a comparison between this particular pulse and a general excitation, modulated rectangular pulse, will be presented. Finite difference time domain simulations under a specific algorithm for calculation of temperature distribution pattern of microwave heating are employed to evaluate the performance of precursor based excitation and to compare it with modulated rectangular pulse. Based on the simulated results the temperature distribution due to the propagation of the double Brillouin pulse spreads further inside the medium compared to other signals such as sinusoidal modulated rectangular pulse.
