Positional dependence of FDTD mode detection in photonic crystal systems

Abstract

SUMMARYWe 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.

Electromagnetic Modeling of Metamaterials

“…It is noted here that the Filter Diagonalization Method (FDM) is more efficient than the FFT for detecting the peaks of the spectrum, for both the computational accuracy and the requited computational time [29], [30]. It is also noted that we cannot distinguish whether the mode is the degenerated one or not, only from the spectrum as shown in Fig.…”

Transfer-matrix approach for finite-difference time-domain simulation of periodic structures

“…III, while calculation for nonzero q is a trivial extension, which requires applying Bloch-periodic boundary conditions (29). The hybrid FDTD transfer-matrix technique is a good alternative to common way to calculate eigenmodes in FDTD where eigenmodes are extracted from peaks in spectral response to some excitation pulse [39][40][41].…”

The application of a high-order discontinuous Galerkin time-domain method for the computation of electromagnetic resonant modes

“…For instance, if a monitor point coincides with a symmetry point of a particular mode, the frequency associated to this mode will not be extracted when applying the signal processing algorithm to the recorded signal. This effect can be utilised to avoid exciting undesired modes [42]. In all the examples a fourth order explicit time marching scheme is considered.…”