A New Etalon Geometry: The Spiral Phase Plate Etalon.

This dissertation reports on theory, simulations, and experiments that extend the conventional Fabry-Perot etalon to a new geometry, namely the spiral phase plate etalon. In the development of the theory, the spiral phase plate etalon is treated in the thin plate approximation and thick plate approximation. The thin plate approximation elucidates properties of the device such as the presence of a coherent superposition of orbital angular momentum modes with different winding numbers in the device, and an intensity pattern that varies as a function of angle. The thick plate approximation captures additional angular interference phenomena in the high finesse limit of the device not seen in the thin plate approximation. These are distinguishing features of the spiral phase plate etalon compared to the conventional Fabry-Perot etalon, which is treated for the first time in this dissertation. In the experiment, optical transmission through the spiral phase plate etalon is probed with a laser beam, and observed to have an intensity variation as a function of angle. The angular intensity pattern is observed to rotate when the laser frequency is varied. These properties of the spiral phase plate etalon are measured and experimentally quantified for the first time. The experimental data is compared to theory, and simulations of the optical intensity profiles in which the dominant source of noise is shot noise. In each case, the statistical uncertainty of the parameters used to describe the spiral phase plate etalon are determined, for which the phase sensitivity of the angular intensity pattern to rotation is deduced. The simulations are also used to understand systematic errors in the data. In addition, the optimal parameters to design a spiral phase plate etalon for best position and frequency resolution (sensitivity) of the optical angular intensity pattern to rotation is obtained. This device is expected to have wide ranging applications, including the possibility to serve as a unique tool in optical frequency metrology, as well as in the study of atomic and molecular physics, quantum optics and quantum information science.PhDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/96000/1/yisrum_2.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96000/2/yisrum_1.pd