Time and Frequency Evolution of the Precursors in Dispersive Media and their Applications

Until now, few rigorous studies of the precursors in structures exhibiting superluminal group velocities have been performed. One dimensional photonic crystals(1DPC) and active Lorentzian media are among the ones which are able to exhibit superluminal propagation. In the first part of the thesis we have studied the evolution of the precursors in active Lorentzian media and 1DPC. The problem of the propagation of the precursors in active Lorentzian media is addressed, by employing the steepest descent method to provide a detailed description of the propagation of the pulse inside the dispersive medium in the time domain. The problem of the time and frequency evolution of the precursors in 1DPC is studied, using the finite-difference time-domain (FDTD) techniques in conjunction with joint time-frequency analysis (JTFA). Our study clearly shows that the precursor fields associated with superluminal pulse propagation travel at subluminal speeds. It is also shown that FDTD analysis and JTFA can be combined to study the dynamic evolution of the transient and steady state pulse propagation in dispersive media. The second part of the thesis concentrates on the applications of the precursors. An interesting property of the precursors is their lower than exponential attenuation rate inside a lossy dielectric, such as water. This property of the precursors has made them an interesting candidate for applications such as ground penetrating radar and underwater communication. It was recently pointed out that a pulse which is generated inside of water and assumes the shape of the Brillouin precursor would be optimally suited for long range propagation in water (described by the single-pole Debye model). Here, we have considered the optimal pulse propagation problem, accounting for the interaction of the pulse with the air/water interface at oblique incidence. In addition, we argue that pulse excitations which are rough approximation of the Brillouin precursor will eventually evolve into the Brillouin precursor itself shortly after they enter water. Therefore, the excitation of a long-propagating pulse is not sensitive to its shape. Finally, we studied the performance of the optimized pulse in terms of the energy of the scattered field from an object inside water. Based on the simulation results the optimized pulse scattered field has higher energy compared to pulses with the same energy and different temporal distribution. The FDTD technique is employed in all the simulations.Ph