Highly Efficient Boundary Element Analysis of Whispering Gallery Microcavities

We demonstrate that the efficiency of the boundary element whispering gallery microcavity analysis can be improved by orders of magnitude with the inclusion of Fresnel approximation. Using this formulation, simulation of a microdisk with wave-number-radius product as large as $kR\approx8,000$ was demonstrated in contrast to a previous record of $kR\approx100$. In addition to its high accuracy on computing the modal field distribution and resonance wavelength, this method yields a relative error of $10%$ in calculating the quality factor as high as $10^{11}$ through a direct root searching method where the conventional boundary element method failed to achieve. Finally, quadrupole shaped cavities and double disks as large as $100 {\mu}m$ in diameter were modeled by employing as few as $512$ boundary elements whilst the simulation of such large cavities using conventional boundary element method were not reported previously.