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.
We present an analytical study of surface plasmon polariton (SPP) propagation about a circular bend formed by the interface between a metal and a dielectric with the metal occupying the inner volume. It is shown that in the short wavelength limit, the problem is essentially analogous to scattering from a 1D finite potential well, with standard expressions for the transmittance and reflectance. In certain cases, we find that propagation on nonplanar interfaces may result in lower losses than on flat surfaces, contrary to expectation. We also show that the same approach is valid when the metal occupies the outer volume, such that in the 1D approximation SPPs propagating around such bends do not radiate. An upper bound for the transmittance, valid even when our approximation breaks down, is also derived. This is found to depend nonmonotonically on the bend radius, allowing increased transmission with decreasing radius. We further present a numerical study using the finite-
difference time-domain method and show that it is consistent with theoretical predictions. We also show that the introduction of a microcavity plasmon resonator could significantly enhance the transmission.
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.