Metamaterials constitute a relatively new field which is very promising because it exhibits properties that may not be readily found in nature. One of promising lines of research is the study of novel characteristics of the prop- agation of electromagnetic (EM) waves in gradient refractive index (GRIN) lenses. In this Thesis, three geometrical optics methods as well as a wave numerical method have been developed for the investigation of EM waves propagation through media with certain refractive indices. Furthermore, we study the propagation of EM waves through specific geometrical configura- tions as well as through complex random networks of GRIN lenses, such as Luneburg (LL) and Luneburg Hole (LH) lenses. We show that waveguides, which are formed by LLs, offer the capability of better controlling the prop- agation characteristics of EM waves.
In addition, we show that branched flows and extreme events can arise in such complex photonic systems. In addition to GRIN lenses networks, we use the discrete nonlinear Schr ̈o- dinger equation to investigate the propagation of an EM wavepacket through certain configurations of optical fiber lattices and investigate the effects of randomness and nonlinearity in the diffusion exponent.
Finally, we study surface plasmon polaritons (SPPs). We investigate how the presence of active (gain) dielectrics change the dispersion relation and enhance the propagation length of SPPs. We finally show that the use of an active dielectric with gain, which compensates for metal absorption losses, enhances substantially the plasmon propagation.