xviii, 213 p. / A print copy of this title is available through the UO Libraries under the call number: SCIENCE QC476.5 .F67 2006 / We investigate models describing two classes of microresonators: those having the
shape of a dome, and those having an oval (deformed circle or sphere) shape. We
examine the effects of dielectric interfaces in these structures. For the dome cavity, we derive efficient numerical methods for finding exact electromagnetic
resonances. In the dome consisting of a concave conductor and a planar,
dielectric Bragg mirror, we discover a phenomenon which we call paraxial mode mixing
(PMM) or classical spin-orbit coupling. PMM is the sensitive selection of the true
electromagnetic modes. The true modes are generally mixtures of pairs of vectorial
Laguerre-Gauss modes. While each member of an LG pair possesses definite orbital
angular momentum and spin (polarization), the mixed modes do not, and exhibit rich, non-uniform polarization patterns. The mixing is governed by an orthogonal transformation
specified by the mixing angle (MA). The differences in reflection phases of a Bragg mirror at electric s and p polarization can be characterized in the paraxial
regime by a wavelength-dependent quantity εs - εp. The MA is primarily determined
by this quantity and varies with an apparent arctangent dependence, concomitant
with an anticrossing of the maximally mixed modes. The MA is zero order in quantities
that are small in the paraxial limit, suggesting an effective two-state degenerate
perturbation theory. No known effective Hamiltonian and/or electromagnetic perturbation
theory exists for this singular, vectorial, mixed boundary problem. We develop
a preliminary formulation which partially reproduces the quantitative mixing behavior.
Observation of PMM will require both small cavities and highly reflective mirrors.
Uses include optical tweezers and classical and quantum information. For oval dielectric resonators, we develop reduced models for describing whispering
gallery modes by utilizing sequential tunneling, the Goos-H¨anchen (GH) effect, and
the generalized Born-Oppenheimer (adiabatic) approximation (BOA). While the GH
effect is found to be incompatible with sequential tunneling, the BOA method is found
to be a useful connection between ray optics and the exact wave solution. The GH effect is also shown to nicely explain a new class of stable V-shaped dome
cavity modes. / Adviser: Dr. Jens Noeckel.
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/3778 |
| Date | 03 1900 |
| Creators | Foster, David H. |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Format | 416237 bytes, 2265 bytes, 11481036 bytes, text/plain, text/plain, application/pdf |
| Relation | University of Oregon theses, Dept. of Physics, 2006, Doctor of Philosophy |
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