Simulating robust far-field coupling to traveling waves in large three-dimensional nanostructured high-Q microresonators

Ultra-high quality (Q) whispering gallery mode (WGM) microtoroid optical resonators have demonstrated highly sensitive biomolecular detection down to the single molecule limit; however, the lack of a robust coupling method has prevented their widespread adoption outside the laboratory. We demonstrate through simulation that a phased array of nanorods can enable free-space coupling of light both into and out of a microtoroid while maintaining a high Q. To simulate large nanostructured WGM resonators, we developed a new approach known as FloWBEM, which is an efficient and compact 3D wedge model with custom boundary conditions that accurately simulate the resonant Fano interference between the traveling WGM waves and a nanorod array. Depending on the excitation conditions, we find loaded Q factors of the driven system as high as 2.1 × 10⁷ and signal-to-background ratios as high as 3.86%, greater than the noise levels of many commercial detectors. These results can drive future experimental implementation.