Optical resonators for laser frequency stabilization and tests of Lorentz invariance

[Truncated abstract] This thesis is comprised of two parts: The first part details the implementation of two room temperature sapphire Fabry-Perot cavities as an optical frequency reference. The second part presents the first optical odd-parity test of Lorentz invariance, using an asymmetric optical resonator. We draw from the developments in the rst part of the thesis to maximize the performance of the odd-parity test of Lorentz invariance. While sapphire presents material properties superior to the ULE and fused silica commonly used in Fabry-Perot resonators, the non-zero coe cient of thermal expansion of sapphire necessitates a high degree of temperature control. The optical cavities are housed in separate vacuum chambers with multi-stage temperature control reaching nanoKelvin stability over a second. To frequency lock the 1064 nm laser to the stable Fabry-Perot cavities we use the Pound-Drever-Hall technique and employ Acousto-Optic Modulators (AOM) for fast frequency control...