Fabry-Perot and Whispering Gallery Modes In Realistic Resonator Models
Foster, David H.
MetadataShow full item record
Foster, David H.
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.