Quantum-Electromagnetic Computational Method Based On State-Controllable Terahertz Metamaterials

With the rapid development of terahertz technology and electromagnetic metamaterials,terahertz metamaterials which combine state-controllable materials and artificial metal microstructures have become a research hotspot,providing a practical scientific path for the free regulation of terahertz waves.In recent years,the development of terahertz wave generation and detection instruments has brought new experimental insights to many materials and devices,but the related theoretical research development is still slow.On the one hand,the terahertz response of many state-controllable materials under external excitation is still an unresolved problem in the field of condensed matter physics.On the other hand,terahertz metamaterial array devices combined with state-controllable materials are large and multi-scale complex structures.How to quickly and accurately model them poses challenges to traditional electromagnetic computational methods.In addition to terahertz metamaterials,the scale and complexity of electromagnetic equipment in national defense and industry are increasing,which puts forward higher requirements for the accuracy and efficiency of electromagnetic algorithms.In response to the above scientific problems,based on the emerging discontinuous Galerkin time domain（DGTD）electromagnetic algorithm,this dissertation proposes a low-memory solution and GPU parallel acceleration techniques,as well as a time step estimation method and a MPI+MPI CPU parallel algorithm.For large multiscale electromagnetic problems,excellent memory compression performance,accurate time step estimation and fast and accurate solution can be achieved.Based on the first principles calculations,the terahertz equivalent dispersion model of light-excited gallium arsenide（Ga As）and temperature-controlled vanadium dioxide（VO₂）are proposed,whose terahertz characteristics are effectively analyzed.After combined with the efficient DGTD parallel algorithm,high-precision simulation of state-controlled terahertz metamaterials can be achieved.The dissertation gives a large number of numerical simulations and experimental measurements to verify the correctness and effectiveness of the proposed quantum-electromagnetic computational method.The specific research content and innovation points include:1.A low-memory solution of the hybrid DGTD（HDGTD）method has been proposed by using the universal matrix technology.By performing hierarchical vector basis functions expansion and linear mapping to the basic matrices of the HDGTD method,the geometrically related basic matrices of each tetrahedral element have been decomposed into geometrically independent universal matrices in the reference tetrahedral element.After the memory analysis of the matrix,the expansion expressions of all the basic matrices and the definition of the general matrix have been deduced.So instead of storing basic matrices,each element only needs to store a small number of regeneration coefficients,resulting in a significant reduction in memory consumption.Numerical examples show that the application of universal matrix technology greatly reduces the memory usage compared with traditional HDGTD,and the memory compression ratio increases with the increase of the basis function order,and can be compressed up to 1/18 of traditional HDGTD.2.Two GPU parallel acceleration techniques based on local time stepping（LTS）HDGTD algorithm have been proposed,namely 1D-block and 2D-block parallel framework.When the problem scale is small and the memory usage is smaller than the GPU memory,the 1D-block framework is adopted.The matrices are reorganized and transferred to the GPU during preprocessing,and during time stepping,each thread is responsible for the multiplication and addition operation of the matrix and the vector.In addition,the application of the parallel reduction algorithm reduces the computational time complexity,making the 1D-block framework has excellent speedup ratio.When the problem scale is large and the memory usage is larger than the GPU memory,the 2D-block framework is used to accelerate the low-memory HDGTD solution.Each thread is responsible for matrix regeneration and matrix-vector multiplication.While reducing the amount of data transmission,the calculation time is appropriately increased,so that the time overlap of data transmission and calculation is high,and a considerable acceleration can be obtained while reducing memory consumption.Numerical examples show that compared with the traditional global time-stepping HDGTD method,the solutions of small and medium-scale complex problems achieve an outstanding speedup ratio of more than 590 times,and the solution of large-scale complex problems achieves a speedup ratio of more than 150 times and memory compression of 13 times.3.An accurate time-step estimation scheme of the DGTD method based on Maxwells equations（DGTD-ME）has been proposed,and an efficient element-by-element time step estimation algorithm has been established through local spectral radius analysis.After a stability analysis similar to that of the finite difference time domain（FDTD）method,the global spectral radius of the DGTD-ME system matrices is analyzed to obtain the analytical time step limit.Further analysis of the local system characteristics of DGTD-ME is performed,and the spectral radius of the global matrix is decomposed into the local system to obtain an element-by-element time step estimation scheme.When selecting the weight coefficients,the influence of the 2nd-layer adjacent elements is ignored to further reduce the dimension of the local matrix and improve the estimation efficiency.The proposed method has outstanding prediction accuracy due to only introducing 1 inequality scaling in the global matrix factorization.Numerical examples show that compared with the precise time step,the accuracy of the maximum time step estimated by the proposed method is as high as 0.95.Compared with the widely used local energy estimation method,the estimation accuracy of the proposed method increases to 3.83 times.4.The MPI+MPI large-scale CPU parallel algorithm of the DGTD-ME-LTS method has been proposed,as well as the corresponding two-layer load balancing and two-layer communication technology.Bind the CPU cores in the same node into groups,realize direct access to data through the MPI shared memory window,and use optimized MPI point-to-point communication between nodes,which greatly improves the speed of information transmission.Corresponding to the two-layer communication architecture,a two-layer mesh partition strategy and a corresponding two-layer load balancing method have been proposed.MPI+MPI greatly reduces the number of sub-domains through the shared memory mechanism inside the node.The load balance between cores is changed to the load balance between nodes,which improves the load balance and significantly improves parallel efficiency of LTS method.Numerical results show that for large multi-scale problems,the parallel efficiency of the proposed method is as high as 94%for 6400 cores.Even if the mesh scale ratio is as high as 3 orders of magnitude,the parallel efficiency is still above 90%,which greatly improves its parallel scalability.5.A quantum-electromagnetic terahertz equivalent dispersion model of light-excited Ga As has been proposed,which can effectively improve the simulation accuracy of light-controlled Ga As materials and terahertz metamaterials.The density functional theory（DFT）and hybrid functional have been used to calculate the band gap of Ga As insulating state,and the density functional perturbation theory（DFPT）has been employed to calculate the dielectric constant.The correctness of the results has been verified through experiments.When photo-excited Ga As exhibits the metallic state,the electron-phonon interactions method has been utilized to calculate the electron transport characteristics under different excitation intensities,whose results are consistent with published measurement data.Based on the characteristics of the first-principles analysis,the terahertz equivalent dispersion model of light-controlled Ga As has been established through Drude model,which then has been combined into the DGTD algorithm through the auxiliary equation method.With the numerical verification of light-controlled Ga As materials and metamaterials,the efficient and accurate simulation of light-controlled Ga As terahertz metamaterials has been realized.6.A quantum-electromagnetic terahertz equivalent dispersion model of temperature-controlled VO₂ has been proposed,which can effectively improve the simulation accuracy of temperature-controlled VO₂ materials and terahertz metamaterials.The U value of the M1-VO₂ insulating phase has been calculated by DFPT.With that,the band gap and dielectric constant of M1-VO₂ have been computed by DFT/DFPT+U.And the electron transport characteristics of the R-VO₂ metallic phase have been solved by the electron-phonon interactions method.Based on the characteristics of the first-principles analysis,the terahertz equivalent dispersion model of the whole process of temperature-controlled VO₂phase transition has been established by using the Drude model and the equivalent medium theory（EMT）,and the direct relationship of metallic volume fraction factor f and the terahertz transmission T_r has been derived.A VO₂ thin film sample based on the sapphire substrate has been fabricated and measured,and combined with the numerical results of various VO₂thin film materials and terahertz metamaterials,the accuracy and universality of the algorithm have been demonstrated.In summary,this dissertation proposes the quantum-electromagnetic computational methods from first-principles analysis to full-wave electromagnetic simulation for state-controlled materials,and develops efficient large-scale parallel electromagnetic simulation algorithms.It provides effective solutions for high-performance electromagnetic computing,simulation of terahertz metamaterials and devices,and terahertz modeling of state-controlled materials.