The objective of this dissertation work is to examine light localization in semiconductors provided by a complete photonic bandgap via three-dimensional (3D) woodpile photonic crystals. A 3D photonic crystal is a periodic nanostructure that demonstrates omni-directional Bragg reflection. These materials are anticipated to become a powerful tool for engineering light propagation and localization within subwavelength scales due to their complete photonic bandgap and the distinctive dispersion relation.;The approach of realizing microcavities in this dissertation is to combine multi-directional etching fabrication methods with mode gap design. Modulation of unit cell size along a line-defect 3D waveguide could bring a guiding mode into the mode gap region of the waveguide and form a microcavity with a resonance inside the complete photonic bandgap. The designed microcavities could be fabricated by multi-directional etching methods because they can structurally be decomposed into two sets of connected and straight dielectric rods.;Ultra-high-quality factor microcavities and sub-wavelength-scale waveguides are designed without introduction of local disorders. Monopole, dipole, and quadrupole resonant modes are demonstrated with a small modal volume. The smallest modal volumes obtained are 0.36 cubic half-wavelengths for a resonance field in vacuum, and 2.88 cubic half-wavelengths for a resonance field in a dielectric. Direct metal contacts with the microcavities do not significantly deteriorate the quality factors because the resonant fields are located inside the microcavities. Single-mode woodpile waveguides are also designed in both lateral and vertical propagation directions.;The multi-directional etching method is a simple approach to the fabrication of woodpile photonic crystals and designed optical components with a variety of crystal orientations and surfaces, including (110), (001), (100), and (010) planes. An arbitrary surface plane (mn0) is obtained with this method, where m and n are integers. Moreover, it can also produce large area woodpile photonic crystals with high precision in silicon and GaAs materials.;These optical components in woodpile photonic crystals would be building blocks of high-density, low-loss 3D integrated optics, cavity quantum electrodynamics (QED), nonlinear optics, and enable the realization of current-injection optical devices.
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