The goal of this thesis is to formulate and numerically solve an accurate theoretical full-wave model that describes the wave propagation characteristics in different optical structures containing Double Negative (DNG) materials. To study the resonant characteristics of Split Ring Resonators for the development of negative index materials and to investigate the proposed method (multi dispersive materials) for a broad band negative index material. Several time-frequency techniques (Fourier Transform method, Z-Transform method and Auxilary Differential Equation method) to represent material properties will be investigated and evaluated. It is also the objective of this thesis to diversify the applicability of DNG materials in novel optical structures and devices. A rigorous numerical simulation of the model is another objective. Numerical tools will be used to investigate the effects of the key parameters in the problem. The resulting tools and analysis are expected to have applications in many fields, such as: 1. Investigation of the time-domain effects in novel DNG structures. 2. Improvement of the existing structures to maximize device efficiency