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Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.

In a causally dispersive medium the signal arrival appears in the dynamical field evolution as an increase in the field amplitude from that of the precursor fields to that of the steady-state signal. The interrelated effects of phase dispersion and frequency dependent attenuation and/or amplification alter the pulse in such a fundamental way that results in the appearance of precursor fields. Although superluminal group velocities have been found in various dispersive media, the pulse "front" and associated precursors will never travel faster than c , and hence these are the vehicles through which relativistic causality is preserved. While many rigorous studies of wave propagation and associated abnormal group velocities in passive Lorentzian media have been performed, the corresponding problem in active media has remained theoretically unexplored. This problem is addressed in the present paper, by employing the steepest descent method for the determination of the response of an active Lorentzian medium to a step modulated pulse. The steepest descent method provides a detailed description of the propagation of the pulse inside the dispersive medium in the time domain. Moreover, the evolution of the saddle points illuminates the relation between the medium parameters and the temporal evolution of the propagating pulse within the medium. Hence, useful physical insights are obtained and the interesting differences between the passive and active case are deduced.

Superluminal group velocities, defined as group velocities exceeding the speed of light in vacuum, c, have been theoretically predicted and experimentally observed in various types of dispersive media, such as passive and active Lorentzian media, one-dimensional photonic crystals, and undersized waveguides. Though superluminal group velocities have been found in these media, it has been suggested that the pulse "front" and associated transient field oscillations, known as the precursors or forerunners, will never travel faster than c, and hence relativistic causality is always preserved. Until now, few rigorous studies of these transient fields in structures exhibiting superluminal group velocities have been performed. In this paper, we present the dynamic evolution of these earliest field oscillations in one-dimensional photonic crystals (1DPC), using 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, and thus, the arrival of these precursor fields must be associated with the arrival of "genuine information." Our study demonstrates the expected result that abnormal group velocities do not contradict Einstein causality. This work also shows 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 behavior of two structures composed of split ring resonators (SRRs) and strip wires (SWs) is examined through full wave simulations. It is shown that both structures exhibit a transmission peak in the region where the real parts of the electric permittivity and magnetic permeability are presumed to be negative, a property which is usually assumed to imply a negative index of refraction. However, an analysis of the dispersion characteristics and insertion phase of the two structures shows that the first structure, in which the SRRs and SWs are printed on opposite sides of a dielectric substrate, is a left-handed medium in the passband, whereas the second structure, in which SRRs and SWs are printed on the same side, is a right-handed medium in the passband. Hence the transmission magnitude alone does not provide sufficient evidence of a negative index of refraction. To determine the sign of the index correctly, the insertion phase for propagation through several lengths of the structure or calculations of dispersion diagrams are necessary. The impact of the unit cell size on the "handedness" of the structure is also examined.

The dynamics of wave propagation in media with negative index of refraction is analyzed through analytical calculations, simulations, and experiments. Using a free space setup, the transmission characteristics of two split ring resonator and strip wire left-handed media (LHM), designed for operation at K -band frequencies (18-26 GHz), are measured. The first LHM, which is 3 unit cells long in the propagation direction, exhibits a maximum negative group delay of -0.9 ns . The second LHM (4 unit cells long) exhibits a maximum negative group delay of -1.2 ns . For both LHM the bandwidth of the negative group delay (and hence the negative group velocity) region was approximately 250 MHz.