Numerical Study on Optical Coupling by Whispering Gallery Modes

Coupled Resonator Optical Waveguides (CROWs) is a new way of integrating coupled cavities onto a single chip. To numerically study the optical coupling by evanescent whispering gallery modes (WGMs) between two microspheres, we introduce a high- order time-domain discontinuous spectral element method to the 3D Maxwell's equations, and propose a mesh generation method for optical coupled spherical resonators with well conditioned mass matrices. A Legendre orthogonal polynomial basis is used on cubes, cuboids, and truncated square pyramids with a spherical surface. A general multidomain scheme is developed to simulate scattering of plane wave by a dielectric sphere, and the corresponding numerical results demonstrate the exponential convergence of the discontinuous spectral element method (DSEM) with increasing expansion order. The numerical results of WGMs show the successful optical coupling of WGMs between two microspheres, and validate our numerical method and algorithms. Finally, an algorithm for improving the efficiency of DSEM is proposed, and a theorem to estimate the maximum error, introduced by this algorithm, is proved.