David H. Foster

Directional tunneling escape from nearly spherical optical resonators.

We report the surprising observation of directional tunneling escape from nearly spherical fused-silica optical resonators, in which most of the phase space is filled with nonchaotic regular trajectories. Experimental and theoretical studies of the dependence of the far-field emission pattern on both the degree of deformation and the excitation condition show that nonperturbative phase-space structures in the internal ray dynamics profoundly affect tunneling leakage of the whispering-gallery modes.

Bragg-induced orbital angular-momentum mixing in paraxial high-finesse cavities

Numerical calculation of vector electromagnetic modes of plano-concave microcavities reveals that the polarization-dependent reflectivity of a flat Bragg mirror can lead to unexpected cavity field distribution for nominally paraxial modes. Even in a rotationally symmetric resonator, certain pairs of orbital angular momenta are necessarily mixed in an excitation-independent way to form doublets. A characteristic mixing angle is identified, which even in the paraxial limit can be designed to have large values. This correction to Gaussian theory is of zeroth order in deviations from paraxiality. We discuss the resultant nonuniform polarization fields. Observation will require small cavities with sufficiently high Q. Possible applications are proposed.

Spatial and polarization structure in microdome resonators: effects of a Bragg mirror

Micro-domes based on a combination of metallic and dielectric multilayer mirrors are studied using a fully vectorial numerical basis-expansion method that accurately accounts for the effects of an arbitrary Bragg stack and can efficiently cover a large range of dome shapes and sizes. Results are examined from three different viewpoints: (i) the ray-optics limit, (ii) the (semi-) confocal limit for which exact wave solutions are known, and (iii) the paraxial approximation using vectorial Gaussian beams.

Degenerate perturbation theory describing the mixing of orbital angular momentum modes in Fabry-Perot cavity resonators

We present an analytic perturbation theory which extends the paraxial approximation for a common cylindrically symmetric stable optical resonator and incorporates the differential, polarization-dependent reflectivity of a Bragg mirror. The degeneracy of Laguerre-Gauss modes with distinct orbital angular momentum (OAM) and polarization, but identical transverse order

Dome-shaped microresonators and the Born-Oppenheimer method

N

Classical spin-orbit coupling of light in micro-dome cavities with Bragg mirrors

, will become observably lifted at sufficiently small size and high finesse. The resulting paraxial eigenmodes possess two distinct OAM components, the fractional composition subtly depending on mirror structure.

Highly directional emission from nearly spherical resonators

Numerical studies of the vector electromagnetic fields in plano-concave microresonators have recently revealed that a photonic analogue of spin-orbit coupling can occur in paraxial geometries. Laguerre-Gauss modes with circular polarization are then no longer the correct eigenstates, even if the resonator is axially symmetric. A crucial role in this effect is played by the presence of a boundary (e.g., a Bragg mirror) whose reflectivity at non-normal incidence is polarization-dependent. Aiming for an analytical treatment that can incorporate both form birefringence and non-paraxiality, we explore the Born-Oppenheimer method as an alternative to the paraxial approximation. The conditions for the validity of these two approaches are different, but in a regime where they overlap we show that all the major results of paraxial theory can also be derived from the Born-Oppenheimer method. We discuss how this new approach can incorporate the Bragg stack physics in a way that can overcome the limitations of paraxial theory.

Toward cavity-QED strong coupling of a semiconductor quantum dot to an external optical micro-cavity

We study vectorial modes in dome-shaped high-finesse microcavities in which one of the mirrors is a planar DBR. Its birefringence leads to an externally controllable, classical spin-orbit coupling of light.

Methods for 3-D vector microcavity problems involving a planar dielectric mirror

We report highly directional light emission from nearly spherical fused-silica resonators. It is found that non-perturbative phase space structure in the internal ray dynamics profoundly affects evanescent leakage of the whispering-gallery modes.

Goos-Hänchen induced vector eigenmodes in a dome cavity

A hemispherical cavity containing interface-fluctuation GaAs quantum dots was constructed to achieve cavity-QED strong coupling between a cavity mode and a single QD. It consists of a 50-micron radius-of-curvature mirror and a semiconductor DBR mirror.