Positional Dependence of Mode Detection in FDTD based Photonic Crystal Simulations

We have developed an algorithm for evaluating the accuracy and reliability of photonic crystal simulations, and used this to analyze the influence of excitation and detector placement in FDTD simulations. We generate a map of locations where mode detection fails, and show that this is equivalent to a map of the node densities of the system. In addition to the expected high nodal densities at the symmetry points of the system, we find more difficult to characterize patterns of high nodal density for the higher order modes. Based on the observed behavior we are able to provide concrete suggestions for the optimal detection and excitation of modes in FDTD simulations of photonic crystal systems. modes can occur. We then detail our algorithm for evaluating the accuracy and reliability of photonic crystal simulations. In section III we use the algorithm to analyze the spatial dependence of the excitation and detection of modes in a canonical problem, the band-gap diagram (BGD) of a PhC consisting of a square lattice of dielectric rods. We present maps showing the spatial sensitivity of mode detection, and show that we have in fact derived a map of the density of nodes in a PhC. For the lower order modes, we find that the node densities are easily predicted, being trivially dependent on the symmetries of the system. We find however that for the higher order modes more interesting behavior occurs. This gives us some general insight into the choice of detector positioning, and some preliminary insight regarding systems with high densities of modes.