Positional dependence of FDTD mode detection in photonic crystal systems
We have developed an algorithm for evaluating the accuracy and reliability of photonic crystal (PhC)simulations, and used it to analyze the influence of excitation and detector placement in finite-difference time-domain algorithm (FDTD) simulations of two canonical PhC systems. In order to perform this computationally expensive analysis, we evaluated the use of filter diagonalization as an alternative to the Fourier Transform for mode detection, and developed a parallelization algorithm to take advantage of the inherent concurrency in simulating periodic systems. A map of locations where mode detection fails was generated, and we 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 areas of each 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 rules to optimize the detection and excitation of modes in FDTD simulations of PhC systems. Although PhCs were studied, the presented strategies and results apply to the much broader class of all computational time-domain problems where Bloch–Floquet boundary conditions are used.
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