In this chapter, we focus on metamaterials composed primarily of dielectric materials that are engineered on the nanometer scale so as to have emergent optical properties not otherwise present. Œe increased localization of the optical želd as a result of these engineered materials is responsible for phenomena such as form-birefringence, structural dispersion, and enhanced optical nonlinear interactions. Equivalently, characteristics such as the local polarizability of the metamaterial and the dispersion may be controlled by geometry, properties of constituent materials, and their composition. Œe introduction of periodicity in metamaterials results in a modižcation in the dispersion relation that can be used to create an artižcial bandgap [1-3]. Œe manipulation and modiž- cation of this periodicity allows the bandgap to shi¹ and parts of the bandgap to be accessed by propagating modes. Photonic crystal (PhC) waveguides rely on this concept: a line of defects is introduced into the otherwise periodic structure so as to guide light. Œe conžnement of light within the PhC lattice is also used to realize devices such as super collimators [16,73], super prisms [8], super lenses [9], omnidirectional žlters, [10] and lasers [11] through proper design and optimization of Bloch modes.