Research And Application Of Fast FDTD Algorithm For Nonlocal And Nonlinear Effects

The Finite-Difference Time-Domain(FDTD)method is a numerical method for solving the electromagnetic field variation with time.It approximates Maxwell’s equations by second-order accuracy finite differences in time and space and obtains iterative equations.The Yee grid is used to ensure that the differential equations always satisfy the Gauss law of electric and magnetic fields.FDTD has been widely used in the fields of micro-nano devices,electromagnetic compatibility,antenna design,gain materials,metamaterials,scattering and inverse scattering,and radar scattering cross-section.However,when the electromagnetic solver of micro-nano structures simulates nonlocal and nonlinear effects,there are still problems of spatial and temporal multiscale,which lead to low computational efficiency and large resource consumption of traditional FDTD methods.In order to solve the above problems,this paper aims to study the fast FDTD algorithm and its application for nonlocal and nonlinear effects.From the perspective of nonlocal and nonlinear effects of FDTD methods,the following specific research work is carried out in-depth:1.To avoid the time step limitations in fine grid regions imposed by the stability condition(Courant-Friedrich-Lewy,CFL)in subgridding techniques,a mixed explicit-implicit FDTD method is proposed.This method employs a fine grid for regions containing high refractive index objects or intricate small structures,and a coarse grid for other regions,reducing the memory usage during traditional FDTD grid generation.Explicit and implicit FDTD iterations are applied respectively to the coarse and fine grids,and the time step in the fine grid region is increased to ensure that the time step in the entire three-dimensional subgrid region is only limited by the CFL condition in the coarse grid,thereby improving the computational efficiency for three-dimensional space multiscale problems.2.Due to the larger number of fine grids than coarse grids in a three-dimensional subgrid,a CPU-GPU heterogeneous parallel FDTD method is proposed.This method combines the advantages of CPU and GPU in data-intensive and logic-intensive computing and designs a CPU-GPU heterogeneous parallel computing framework.The physical fields of coarse and fine grids are respectively assigned to the CPU and GPU for parallel computation of the electromagnetic fields in coarse and fine grid regions.During FDTD iterations,the physical fields at the coarse-fine grid interface are exchanged to enable data communication between CPU and GPU heterogeneous computations.Experimental results show that this method significantly reduces the computational complexity of time.3.To solve the spectrum shift and broadening of nonlocal effects,a generalized nonlocal optical nanoparticle response FDTD method is proposed.This method establishes an electromagnetic-fluid dynamics model for metallic structures with micro and nanoscale features to simulate the generalized nonlocal response spectrum shift and broadening under the action of electric and magnetic fields.The CPU-GPU heterogeneous parallel framework proposed in Chapter 3 is used to compute the physical fields in the coarse and fine grid regions of the 3D subgrid,reducing the time and space computational complexity caused by the excessively small Yee grid scale of the traditional FDTD method.Since the boundary interface of the coarse and fine grid will penetrate the metal,not only special treatment for the electric field but also for the free current term is needed on the boundary interface,resulting in higher complexity of subgrid techniques in nonlocal effects.4.A non-depleted time-domain model derived from the Maxwell-hydrodynamic model is proposed where linear and nonlinear responses in metallic structures under an intense excitation is separated.By using the proposed model,only linear and low-frequency DFG signals will be considered,which makes this model suitable for unconditional stable time-domain algorithms.Finite-difference time-domain method is employed to solve a set of multiphysics equations based on the proposed model.We validate our method by simulating THz generations from metallic nonlinear metasurfaces(NLMS)and benchmark the approach with previous numerical studies as well as recent experimental results.In addition,the implementation of solving the DFG response can be remarkably accelerated by using the unconditionally stable algorithm.Then,this method is applied to metasurfaces to study the effect of chiral coupling between metasurface structures on terahertz generation and realize terahertz metasurfaces sensitive to circular polarization excitation.