| Periodic dielectric or metallic structures can be designed to possess very unusual electromagnetic properties. In particular, if the period of the structure is similar to or smaller than the wavelength of the electromagnetic wave of interest, the structure can be regarded as an artificial electromagnetic medium with homogeneous, effective material properties. By choosing the type of lattice and by tailoring the unit cell structure, desired electromagnetic properties can be achieved.;A self-collimating photonic crystal is designed to possess a spatial dispersion characteristic that enables nearly diffraction-less propagation of a finite-size beam in the absence of any waveguide. Metallic metamaterials are introduced, and it is shown that simple effective medium descriptions provide an accurate picture especially in the low-frequency regime. It is possible to enhance the refractive index of a dielectric material with inclusion of properly designed metallic elements, which results in a high-index metamaterial. Moreover, with multiple, interweaving metallic networks, it is demonstrated that a metamaterial system can support much more modes, even in the low-frequency regime, than a typical dielectric medium and that its properties can be well explained with a non-Maxwellian effective medium theory.;In this dissertation, three dimensional dielectric photonic crystals and metallic metamaterials with novel electromagnetic properties are introduced. Their properties are theoretically investigated with spatial symmetry considerations as well as effective medium theories. A new type of effective medium theory is developed to address the rich physics inherent in the new class of metamaterials proposed in the dissertation. The predictions of the theories are verified with numerical simulations based on frequency-domain and time-domain methods. |
