Three dimensional finite-difference frequency-domain method in modeling of photonic nanocavities

The finite-difference frequency-domain (FDFD) method is a counterpart of the finite-difference time-domain (FDTD) technique in the frequency domain. The FDFD method with the 3D perfectly matched layers appears to be a powerful tool in modeling of nanophotonic cavities, e.g. in extraction of resonance wavelengths (λ) and quality factors (Q) of single or degenerate modes. A single simulation run to get mode's eigenfrequency and field profile takes from several minutes up to an hour in a 3D case. Thus, the main FDTD bottlenecks: long execution time and intensive postprocessing to find λ and Q, are overcome with the FDFD employment. In the benchmarking stage as a reference system we use a dipole resonance of a dielectric sphere with known analytical solution. The FDFD-method provides valid results starting from low resolution and exhibits good convergence to analytic values with improvement of discretization. The critical problem of high memory requirements for the FDFD technique can be partly mitigated with use of space reduction through symmetry planes. We also report on modeling ultra high-Q cavities, like single or coupled photonic crystal nanobeams.