Direct-Splitting-Based CN-FDTD for Modeling 2D Material Nanostructure Problems

Abstract

Incorporating a truncation of the complex-frequencyshifted perfectly matched layer (CFS-PML), the direct-splittingbased Crank-Nicolson finite-difference time-domain (CNDS-FDTD) is developed and applied to the infrared two-dimensional layered material (2DLM) black phosphorous (BP) metasurface implementations on the all-dielectric nanostructure. To improve extremely low efficiencies in solving infrared terahertz (THz) problems with the few-atomic-layer thickness of 2DLMs, the CFS-CNDS-FDTD is proposed in demand due to the fact that it possesses capabilities of implicit FDTD method and unsplit-field CFS-PML truncation, respectively, in completely conquering the Courant-Friedrich-Levy condition (CFL) limit and holding good performance. The temporal incremental in the CFS-CNDS-FDTD can reach 1000 times larger than that in the regular FDTD for infrared nanoscale problems centered at the 2.5 THz and then keep accurate. Three-dimensional (3D) numerical cases have been carried out to corroborate the proposed method. The CFS-CNDS-FDTD can not only achieve high accuracies and then saves several dozen times of CPU time as compared to the regular FDTD, but also pave the way for designing all-dielectric nanostructures with other 2DLM metasurfaces. Index Terms-Black phosphorous (BP), Crank-Nicolson finitedifference time-domain (CN-FDTD), complex-frequency-shifted perfectly matched layer (CFS-PML), direct-splitting (DS), metasurface, two-dimensional layered material (2DLM).

Comments on “Direct-Splitting-Based CN-FDTD for Modeling 2-D Material Nanostructure Problems”

“…The formulas shown in [1] is completely wrong on closer inspection. To be more specifically, for example, eqs.…”

“…The authors claimed that they have developed the CNDS-FDTD algorithms along with its PML implementation in [1], while it is not the truth. These two studies can be respectively found in [2] and [42].…”

“…Here, the authors proposed CNDS-PML for 2D material nanostructure. In a word, as numerical examples look like more sophisticated are used to instead of those in [42] but based on the same CNDS methods, any innovations can be found compared with [1].…”

“…To be more specifically, for example, eqs. (1) to (38) shown in [1] are in terms of PML implementations, while eqs.…”

“…HE authors proposed an unconditionally stable perfectly matched layer (PML) based on the Crank-Nicolson direct-splitting (CNDS) method to analyze nanostructure problems in [1]. However, it has been found that there are some concerns at the correctness and validity of the mathematical derivations and numerical results which were shown in the original manuscript, which can be summarized into the following three aspects.…”