Highly Efficient Boundary Element Analysis of Whispering Gallery Microcavities

We demonstrate that the efficiency of the boundary element method, as applied to whispering gallery microcavity analyses, can be improved by orders of magnitude with the inclusion of the Fresnel technique. Using a scalar formulation, simulations of a microdisk with wavenumber-radius product as large as kR ≈ 8000 are achieved in contrast to a previous record of kR ≈ 100. In addition to its high accuracy for computing the modal field distributions and resonant wavelength, this technique yields a relative error of 10% when employing a direct root searching approach to calculate quality factors as high as 10¹¹ (which are otherwise unattainable by a conventional boundary element method, due to computational limitations). Quadrupole-shaped and double disk cavities as large as 100 μm in diameter are also modeled by employing as few as 512 boundary elements, where simulations of such cavities using the conventional boundary element method have yet to be reported.