The topic of this dissertation is photonic crystal nanocavities for semiconductor cavity quantum electrodynamics. For the purposes of this study, these nanocavities may be one dimensional (1D) or two dimensional (2D) in design. The 2D devices are active and contain embedded InAs quantum dots (QDs), whereas the 1D devices are passive and contain no active emitters. The 2D photonic crystal nanocavities are fabricated in a slab of GaAs with a single layer of InAs QDs embedded in the slab. When a cavity mode substantially overlaps the QD ensemble, the dots affect the linewidths of the observed modes, leading to broadening of the linewidth at low excitation powers due to absorption and narrowing of the linewidths at high excitation powers due to gain when the QD ensemble absorption is saturated. We observe lasing from a few QDs in such a nanocavity. A technique is discussed with allows us to tune the resonance wavelength of a nanocavity by condensation of an inert gas onto the sample, which is held at cryogenic temperatures. The structural quality at the interfaces of epitaxially grown semiconductor heterostructures is investigated, and a growth instability is discovered which leads to roughness on the bottom of the GaAs slabs. Adjustment of MBE growth parameters leads to the elimination of this roughness, and the result is higher nanocavity quality factors. A number of methods for optimizing the fabrication of nanocavities is presented, which lead to higher quality factors. It is shown that some fundamental limiting factor, not yet fully understood, is preventing high quality factors at wavelengths shorter than 950 nm. Silicon 1D devices without active emitters are investigated by means of a tapered microfiber loop, and high quality factors are observed. This measurement technique is compared to a cross-polarized resonant scattering method. The quality factors observed in the silicon nanocavities are higher than those observed in GaAs, consistent with our observation that quality factors are in general higher at longer wavelengths.

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