Photonic crystals (PCs) are devices with the ability to confine electromagnetic (EM) waves due to their EM bandgap. The three-dimensional woodpile PC studied in this dissertation is appealing because unlike its two-dimensional counter parts, it is able to confine and guide EM waves in all three dimensions. This dissertation examines the fundamental properties of resonant cavities and use of cavities and waveguides (WGs) to create channel-drop filters in the woodpile PC.Resonant cavities are a major building block of photonic integrated circuits devices. Therefore it is important to understand how to control the properties of their resonant modes, such as quality factor (Q), resonant frequency, magnitude, and mode shape. This dissertation examines the effects of incident EM wave polarization, cavity size, cavity permittivity, cavity confinement, material loss, and lattice disorder on the properties of the resonant mode.Channel-drop filters are devices that can be used to transfer EM energy of a specific frequency from one WG to another. Channel-drop filters could be used to optically add or remove a specific carrier frequency from a fiber optic cable transporting many carrier frequencies. Channel-drop filters made from a PC are able to perform this task completely optically. This would speed up the optical network since conversion of the optical signal to an electronic signal is not required. In this dissertation six channel-drop filter configurations are examined. These structures are made both in a single stacking layer and separated by many layers. Five of the structures demonstrated good energy transfer from the input (bus) WG to the output (drop) WG. The ability to control the frequency and Q of the transferred EM mode is achieved by varying the cavity size and confinement.
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