Wave propagation in dispersive media and one-dimensional photonic crystals

Motivated by the recent experiments of the superluminal group velocity in the anomalous dispersive medium, the propagation of light pulses through dispersive media is investigated by solving Maxwell's equations without any approximation. It is found that the coherence of light plays an important role for the superluminal propagation. It is also shown that it is the anomalous dispersion, the real part of the susceptibility (not the amplification, the imaginary part of the susceptibility) that plays the essential role in the superluminal propagation. A general proof based on the Kramers-Kronig relations is presented to show that: in a linear normal or anomalous dispersive medium, any discontinuity in an electromagnetic pulse always propagates at the average phase velocity, the light speed in vacuum. The nature of the discontinuity is preserved during the propagation. Therefore the information carried by the discontinuity cannot be transmitted superluminally. The subject of how to control the propagation of a pulse through a slab system, which is doped with two-level or three-level atoms, is also theoretically investigated. The doped atoms can be passive or active. By adjusting the thickness or background dielectric constant of the slab, the reflected pulse can be controlled from superluminal to subluminal or from subluminal to superluminal.; Photonic band gap materials are expected to play an important role in the development of new optical devices. Since any incident light is not fully coherent in practice, we investigated the propagation of coherent and partially coherent light pulses through a one-dimensional photonic crystal (1DPC) and discussed the effect of the coherence of the pulses on the propagation properties inside the 1DPC. The evolution of a light pulse inside the 1DPC is affected by the coherence of the pulse.; Negative refractive index materials become an interesting subject since such materials was verified in experiments recently. The Hartman effect inside the 1DPC composed of negative index materials (NIMs) is considered and the negative Hartman effect is found inside the 1DPC of NIMs. The origin of the negative Hartman effect is due to the negative refractive index of the materials. At the same time, the wave propagation inside the 1DPC composed of single-negative (permittivity- or permeability-negative) materials is also investigated. Such 1DPCs composed of single-negative materials may act as equivalent left-handed materials below the critical frequency only for the case of normal incidence. Above this critical frequency, the 1DPCs become the equivalent right-handed materials. For the inclined incidence, such 1DPCs cannot be completely equivalent to the left-handed materials. Furthermore, a new type of omnidirectional gaps is found in the 1DPCs composed of single-negative materials. Such omnidirectional gaps are resulted from the interaction of evanescent waves. The spectral position of a defect mode intentionally introduced in such omnidirectional gaps is nearly invariant with the scaling and is very weak dependent on the incident angles.