Simulation of optical resonators using DGTD and FDTD

We present a comparative analysis of the finite-difference time-domain method (FDTD) and the discontinuous Galerkin time-domain (DGTD) method for the simulation of integrated optical microresonators. It is found that FDTD suffers from phase errors and is limited by the staircasing approximation. A further restriction stems from only second-order accuracy which limits the geometrical problem size that can be analysed with given computational hardware. Particularly for simulations of high- Q optical resonators, those problems prevent sufficient convergence with reasonable grid spacing. The DGTD method, on the other hand, allows for the approximation of curved surfaces with high accuracy using triangular elements. Combined with the exponential convergence, the DGTD approach outperforms the FDTD method and is thus a suitable candidate for large-scale simulations.