Research On Fast Simulation Method Of Multi-directional Extinction Characteristics Of Nanoparticles

The study on the extinction characteristics of plasmonic nanoparticles has a wide range of application prospects.This characteristic is affected by the structure,material,incident angle of the incident wave,wavelength and other elements of the nanoparticle.In practical applications,the extinction characteristics of different incident directions are often concerned.The electromagnetic numerical simulation method is not only suitable for most situations,but also the accuracy of the calculation results can meet the needs of engineering research,so it is widely used.Among them,the moment method and the finite element-boundary element method are two efficient electromagnetic numerical simulation algorithms.The former is based on the boundary integral equation,which can efficiently calculate nanoparticles of homogeneous materials and is very suitable for analyzing opendomain light scattering problems;the latter Then the advantages of the boundary element method and the finite element method are fully combined,and the boundary element method is used to deal with the external open area,and the finite element method is used to deal with the nanoparticles with nonuniform materials.However,in practical engineering,it is usually necessary to pay attention to the extinction characteristics of nanoparticles when incident light is irradiated from a direction.At this time,the iterative solution method on which the above-mentioned electromagnetic numerical simulation algorithm relies has the problem of a large number of redundant calculations,which greatly reduces the simulation efficiency.Based on this,this paper studies the introduction of an efficientH-matrix algorithm under the framework of the above two electromagnetic numerical simulation methods to achieve an efficient so LUtion to the multi-directional light scattering problem.This paper firstly analyzes the basic principle and computational complexity ofH-matrix.Then,the boundary elementH-matrix method is studied to analyze the multi-directional extinction characteristics.Based on the JMCFIE integral equation and the method of moments as the numerical solution of the boundary element method,the direct solution method based onH-matrix is introduced to replace the traditional iterative solution method when solving the matrix equation.The influence of the incident angle on the extinction characteristics of nanoparticles is mainly reflected in that the right-hand vector of the matrix equation changes with the change of the incident angle.Using the direct solution method,the impedance matrix can be decomposed by LU and the LU factor can be stored,and then the back and forth operation can be performed to obtain the solution of the equation,and then the extinction cross section of the nanoparticles can be extracted through the calculation formula of the extinction cross section.Because the LU factor is constant under different incident angles,it can avoid the repeated calculation of the iterative solution method when the right vector changes,and can greatly improve the solution efficiency when performing multi-directional analysis.Finally,a hybrid finite element-boundary elementH-matrix method is studied to analyze the multidirectional extinction characteristics.First,combine the boundary element part and the finite element part to generate a complete matrix equation.The external scattering field is obtained by introducing theH-matrix direct solution method to solve the equation,and the extinction cross section of the nanostructure is obtained by combining the calculation formula of the extinction cross section.Since only one LU decomposition needs to be performed for the matrix of FEM-BEM,it is very efficient in solving the extinction properties of multi-directional incidence of nanoparticles of complex materials.The effectiveness of the method in this paper is verified by the analysis of examples of nanoparticles with different structures.