Incorporating a truncation of the complex-frequency-shifted perfectly matched layer (CFS-PML), the direct-splitting- based 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.

中文翻译：

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基于直接分裂的CN-FDTD用于二维材料纳米结构问题的建模

结合了截断复频完美匹配层（CFS-PML），开发了基于直接分离的Crank-Nicolson时差有限域（CNDS-FDTD），并将其应用于红外二维分层全介电纳米结构上的材料（2DLM）黑色磷（BP）超表面实现。为了提高2DLM原子层厚度很少的红外太赫兹（THz）问题的解决效率极低，由于CFS-CNDS-FDTD具有隐式FDTD方法和非分割场的功能，因此提出了需求CFS-PML截断分别完全克服了Courant-Friedrich-Levy条件（CFL）限制并保持了良好的性能。对于以2.5 THz为中心的红外纳米级问题，CFS-CNDS-FDTD中的时间增量可以达到常规FDTD中的时间增量的1000倍，然后保持准确。已进行了三维（3D）数值计算，以证实所提出的方法。与常规FDTD相比，CFS-CNDS-FDTD不仅可以实现较高的精度，然后节省数十倍的CPU时间，而且还为设计具有其他2DLM超表面的全介电纳米结构铺平了道路。