Frequency‐dependent finite‐difference time‐domain method based on iterated Crank–Nicolson scheme

Abstract

The finite-difference time-domain (FDTD) method based on the iterated Crank-Nicolson (ICN) scheme is extended to a frequencydependent version. The Drude model is used to express a metal dispersion, which is incorporated into the iterated Crank-Nicolson formulation with the trapezoidal recursive convolution technique. The validity of the present finite-difference time-domain method with convolutional perfectly matched layers is discussed through the analysis of a metalinsulator-metal plasmonic waveguide. Numerical results obtained from a two-iteration technique are found to agree well with those from the traditional explicit finite-difference time-domain method.

Numerical Dispersion Analysis of the One-Dimensional Iterated Crank-Nicolson-Based FDTD Method

“…Unfortunately, only the ICN-FDTD method is slightly dissipative resulting from the attenuation factor, since the iterative calculation terminates the series expansion of the CN procedure. Nevertheless, the ICN-FDTD method yields almost the same numerical results as those from the explicit FDTD method when analyzing optical devices [10], [14].…”

“…Note that the ICN-FDTD method is constrained by the CFL condition as the explicit FDTD method [10]. Recently, the ICN-FDTD method has been extended with the domain decomposition [12], body-of-revolution technique [13] and frequency-dependent formulation [14]. Although the validity of the ICN-FDTD method has been demonstrated, its numerical dispersion property has not yet been discussed.…”

Numerical Dispersion Analysis of the Iterated Crank-Nicolson-Based FDTD Method

“…To alleviate this difficulty of the CN-FDTD method, we have proposed the explicit FDTD method based on the iterated CN (ICN) scheme [4], in which an implicit CN procedure can be replaced with an explicit iteration process. Very recently, the ICN-FDTD method has been extended to a frequency-depended version [5]. Although the validity of the ICN-FDTD method has been discussed, the numerical dispersion analysis has not yet been performed.…”