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

Naixing Feng,Meisong Tong,Guo Ping Wang,Yuxian Zhang,William T Joines,Qingsheng Zeng

doi:10.1109/ojap.2020.3006842

Abstract

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.

Highlights

T HE METALLIC or dielectric metasurfaces [1]–[7] are composed of arrays of subwavelength-spaced optical scatters distributed atop the interface whose prime function is to allow for locally altering the phase of incident light, which have very recently drawn considerable attention due to the fact that a unique method can be provided to guide electromagnetic waves at will, and possess advanced optical technology adopted for implementing versatile functionalities in a planar structure [8]–[14]
The efficient direct-splittingbased CN-finite-difference time-domain (FDTD) (CNDS-FDTD) method with the complex-frequency-shifted perfectly matched layer (CFS-PML) scheme is proposed based on the auxiliary differential equation (ADE) method to model 3D all-dielectric photonic nanostructures with monolayer black phosphorous (BP) metasurfaces in the infrared Terahertz range
The main contributions of this work include following: (1) The unconditionally-stable CNDS-based FDTD formulations is developed, different from the CNCSU-based FDTD which is conditionally stable in certain cases; (2) The 3D alldielectric nanostructures with BP metasurfaces in the infrared range are implemented using the CFS-CNDS-FDTD

Summary

INTRODUCTION

T HE METALLIC or dielectric metasurfaces [1]–[7] are composed of arrays of subwavelength-spaced optical scatters distributed atop the interface whose prime function is to allow for locally altering the phase of incident light, which have very recently drawn considerable attention due to the fact that a unique method can be provided to guide electromagnetic waves at will, and possess advanced optical technology adopted for implementing versatile functionalities in a planar structure [8]–[14]. At the central frequency of 1 terahertz (THz) in the all-dielectric nanostructure application, spatial and temporal sampling densities in air can be approximately 0.1 million points per wavelength (PPW) and 0.3 million points per period (PPP), separately To circumvent this problem, implicit FDTD methods [35]–[38] can be well used, which encounter no limit on time intervals arising from stability considerations. The BT-based CNDS-FDTD method is proposed and applied to solve FDTD problems in the microwave range, and further prove that the CNCSU-FDTD exists the instability in certain cases [42] In this systematic study, the efficient direct-splittingbased CN-FDTD (CNDS-FDTD) method with the CFS-PML scheme is proposed based on the auxiliary differential equation (ADE) method to model 3D all-dielectric photonic nanostructures with monolayer BP metasurfaces in the infrared Terahertz range. The main contributions of this work include following: (1) The unconditionally-stable CNDS-based FDTD formulations is developed, different from the CNCSU-based FDTD which is conditionally stable in certain cases; (2) The 3D alldielectric nanostructures with BP metasurfaces in the infrared range are implemented using the CFS-CNDS-FDTD

FORMULATION

NUMERICAL RESULTS

CONCLUSION