Wave interference is an interesting and important quantum phenomenon found in various physical systems. In photonic crystals, the systems are composed of periodic dielectric structures, where the propagation of vector electromagnetic wave is modulated by the periodic dielectric distribution, giving rise to the frequency spectrum called photonic band structure” with band gaps. Such systems offer a lot of potential applications such as waveguides, modulators, resonant cavities and etc. The 1st part of the thesis focuses on the development of an efficient method for the calculation of the photonic band structure, a mean field type of theory. This theory is applied to 2D and 3D photonic crystals. Wave interference also occurs in impure metals. In these systems, electron waves are scattering by randomly localized impurities. The interference here occurs in a self-intersecting loop of electron trajectory, between the time-reversal pair of clockwise and counterclockwise paths, leading to the interesting quantum phenomenon called weak localization. This phenomenon is characterized by a time scale called the dephasing time, which typically diverges at 0K. The recent experiments in weak localization, however, have reported a puzzling, contradicting observation, namely, the saturation of dephasing time at low temperatures. The other part of the thesis deals with the weak localization phenomenon in a system with non-uniform distribution of disorder, in connection of the dephasing issue.

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