Abstract:
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, (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.
