FDTD-modelling of dispersive nonlinear ring resonators: Accuracy studies and experiments

The accuracy of nonlinear finite-difference time-domain (FDTD) methods is investigated by modeling nonlinear optical interaction in a ring resonator. We have developed a parallelized 3-D FDTD algorithm which incorporates material dispersion, χ⁽³⁾-nonlinearities and stair-casing error correction. The results of this implementation are compared with experiments, and intrinsic errors of the FDTD algorithm are separated from geometrical uncertainties arising from the fabrication tolerances of the device. A series of progressively less complex FDTD models is investigated, omitting material dispersion, abandoning the stair-casing error correction, and approximating the structure by a 2-D effective index model. We compare the results of the different algorithms and give guidelines as to which degree of complexity is needed in order to obtain reliable simulation results in the linear and the nonlinear regime. In both cases, incorporating stair-casing error correction and material dispersion into a 2-D effective index model turns out to be computationally much cheaper and more effective than performing a fully three-dimensional simulation without these features.