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

We develop and demonstrate two numerical methods for solving the class of open cavity problems which involve a curved, cylindrically symmetric conducting mirror facing a planar dielectric stack. Such dome-shaped cavities are useful due to their tight focusing of light onto the flat surface. The first method uses the Bessel wave basis. From this method evolves a two-basis method, which ultimately uses a multipole basis. Each method is developed for both the scalar field and the electromagnetic vector field and explicit “end user” formulas are given. All of these methods characterize the arbitrary dielectric stack mirror entirely by its 2 × 2 transfer matrices for sand p-polarization. We explain both theoretical and practical limitations to our method. Non-trivial demonstrations are gi ven, including one of a stackinduced effect (the mixing of near-degenerate Laguerre-Gaussian modes) that may persist arbitrarily far into the paraxial limit. Cavities as large as 50λ are treated, far exceeding any vectorial solutions previously reported.