Modeling pulse propagation in loss compensated materials that exhibit the negative refractive index property

Rapid development in nanofabrication has led to the design of new materials with very unusual properties. The exhibition of negative and zero indices of refraction are among the most striking properties of these materials, which have become the focus of intensive research worldwide. The potential for applications that is possible due to the new light manipulation capabilities of these materials has been the driving force behind this research. Most of the research in this field has primarily been experimental while the theoretical studies have mainly been limited to computer modeling, which in itself is a challenging problem. This research requires considerable computational resources and the development of new computer algorithms.;The origin of the unusual properties in these materials comes from the combination of dielectric host materials with metallic nanosructures. These materials are often referred to as nanocomposite metamaterials. The plasmonic resonance in properly engineered metallic nanostructures gives rise to the resonant interaction of the incident electromagnetic field with metamaterials in such a way as to stimulate a magnetic permeability and an electric permittivity with negative real parts. The resonant nature of this phenomenon leads to considerable losses in metamaterials, which has made the study of loss compensation one of the key subjects in this field.;The two techniques of loss compensation in metamaterials are considered in this dissertation. One of these techniques consists of doping the host material with active atoms. In the second technique, loss compensation is achieved by embedding these active atomic inclusions directly into the nanostructures. This dissertation presents the derivation of the systems of governing equations and studies the coherent pulse amplification for both cases.