Micro-nano structure extinction characteristic efficient simulation method and system based on time domain discontinuous Galerkin technology

Abstract

The invention discloses an efficient simulation method and system for extinction characteristics of a micro-nano structure based on a time domain discontinuous Galerkin technology, and the method comprises the steps: building an electromagnetic field discrete model of the micro-nano structure based on a Maxwell equation set in combination with the time domain discontinuous Galerkin technology; reasonable tetrahedron / hexahedron mixed grid discretization is adopted for a calculation area, and multi-scale high-efficiency time domain solution of the micro-nano structure is realized by introducing discontinuity of field quantities among numerical flux processing units. When the method is used for processing the multi-scale problem of the micro-nano structure, the number of subdivision grids can be well reduced, the calculation time complexity is O (N), the extinction characteristic in a wide frequency spectrum range can be efficiently calculated, and the method is suitable for analyzing the problem of a complex micro-nano light field.

Description

Technical Field

[0001] The present invention relates to a simulation method for the extinction characteristics of micro-nano structures in the field of micro-nano optics, and particularly to an efficient simulation method and system for the extinction characteristics of micro-nano structures based on the discontinuous Galerkin time domain technique. Background Art

[0002] With the rapid development of nanotechnology, micro-nano structures are increasingly widely used in the fields of optics, biomedicine, energy, etc. The optical properties of micro-nano structures, especially their extinction characteristics, are of great significance for the design and optimization of nano-photonic devices. The extinction characteristics reflect the absorption and scattering ability of micro-nano structures to incident light, and are one of the key parameters for evaluating their optical performance. Accurately simulating the extinction characteristics of micro-nano structures has important theoretical guiding significance for the development of high-performance nano-waveguides, surface-enhanced Raman scattering sensors, photothermal therapy devices, etc.

[0003] The discontinuous Galerkin time domain (DGTD) technique is an emerging time-domain numerical simulation method that combines the high geometric adaptability of the finite element method and the high computational efficiency of the finite difference time domain method. The DGTD method can achieve high-precision simulation in complex geometric structures by introducing numerical fluxes to handle the discontinuity of field quantities between elements. In addition, the DGTD method supports hybrid mesh meshing, which can significantly reduce the number of meshes and improve the computational efficiency, and is particularly suitable for the simulation of multi-scale micro-nano structures. In recent years, the DGTD technique has shown great potential in the fields of electromagnetic field simulation, photonic crystals, plasmon resonance, etc., but its application in the simulation of the extinction characteristics of micro-nano structures is still in the exploratory stage.

[0004] Currently, in the field of analysis of the extinction characteristics of micro-nano structures, the most commonly used numerical analysis methods mainly include the finite element in the frequency domain, the finite difference time domain, the method of moments, etc. When dealing with complex geometric structures or wide spectral ranges, the finite element method in the frequency domain often faces disadvantages such as high computational complexity (O(N 3 )) and a large number of conformal meshes for handling multi-scale problems. Therefore, developing an efficient simulation method for the extinction characteristics of micro-nano structures based on the discontinuous Galerkin time domain technique can provide a powerful tool for the design and optimization of nano-photonic devices, and has important scientific research value and application prospects. Summary of the Invention

[0005] The purpose of the present invention is to provide an efficient simulation method and system for the extinction characteristics of micro-nano structures based on the discontinuous Galerkin time domain technique. When dealing with multi-scale problems of micro-nano structures, it can well reduce the number of meshes for meshing, and the computational time complexity is O(N), which can efficiently calculate the extinction characteristics in a wide spectral range and is applicable to the analysis of complex micro-nano optical field problems.

[0006] The technical solution for achieving the object of the present invention is as follows: An efficient simulation method for the extinction characteristics of micro-nano structures based on the time-domain discontinuous Galerkin technique, comprising the steps of:

[0007] Step 1: Establish a simulation model for the micro-nano structure to be solved, discretize the corresponding region using tetrahedral and hexahedral elements to obtain all node information of the simulation model; use a mixed tetrahedral-hexahedral mesh for the micro-nano structure to reduce the number of meshes.

[0008] Step 2: Based on the simulation model, using Maxwell's equations as the basic governing equations, establish a matrix equation for the unknown electric and magnetic fields using the time-domain discontinuous Galerkin finite element method, then introduce a numerical flux to handle the discontinuity of field quantities between non-conformal surfaces, and select a time iteration formula for time discretization to obtain the matrix equation system for solving the electric and magnetic fields.

[0009] Step 3: Iteratively solve the matrix equation system to obtain the electric and magnetic field coefficients in the entire computational domain, extract any closed surface enclosing the micro-nano structure, obtain the electric and magnetic fields at the points on the surface, and then perform a discrete Fourier transform on the electric and magnetic fields to obtain the frequency-domain electric and magnetic fields at different frequencies.

[0010] Step 4: Based on the frequency-domain electric and magnetic fields, calculate the Poynting vectors of the scattered field and the total field on the closed surface.

[0011] Step 5: Perform a Gaussian surface integral on the Poynting vectors of the scattered field and the total field on the closed surface respectively to obtain the scattered light intensity and the absorbed light intensity at different frequency points.

[0012] Step 6: Calculate the incident light intensity according to the applied excitation source, obtain the scattering cross-section and the absorption cross-section by the ratio of the scattered light intensity and the absorbed light intensity to the incident light intensity, and further obtain the extinction cross-section to obtain the characteristics of the micro-nano structure.

[0013] The numerical flux described in Step 2 is the upwind flux.

[0014] Further, the specific steps of Step 3 are as follows: The calculated closed surface is composed of multiple triangular faces or quadrilateral faces. After obtaining the coefficients of the electric and magnetic fields by iteratively solving the matrix equation system, loop through the triangular faces or quadrilateral faces where the closed surface is located, combine the basis functions, the coefficients of the electric and magnetic fields, obtain the electric and magnetic fields at the Gaussian points on each loop surface, and then perform a frequency-domain conversion on the obtained electric and magnetic fields through a discrete Fourier transform.

[0015] Further, the closed surfaces enclosing the micro-nano structure are respectively in the total field region and the scattered field region, and the electric and magnetic fields at different frequencies can be obtained through a discrete Fourier transform.

[0016] Further, in the step 4: the Poynting vector of the total field is equal to the sum of the scattered field and the incident field, and the Poynting vector of the scattered field is equal to the cross product of the electric field and the conjugate of the magnetic field on the closed surface in the scattered field.

[0017] Further, the Poynting vector of the total field in the step 4 is equal to the cross product of the electric field and the conjugate of the magnetic field on the closed surface in the total field.

[0018] Further, the step 5 includes: looping over the small triangular faces on the closed surface, multiplying the Poynting vector of the Gauss points on the looped small triangular faces by the normal vector, then performing Gauss integration to obtain the scattered light intensity and the absorbed light intensity of the small triangular faces, and finally performing accumulation to obtain the scattered light intensity and the absorbed light intensity of the entire closed surface;

[0019] Further, in the step 6, the incident wave is a uniform plane wave, a modulated Gaussian pulse is used as the excitation source, the incident wave is subjected to discrete Fourier transform to obtain the incident intensity at different frequencies, the incident light intensity is a constant related to the wave impedance and the amplitude of the incident wave, and the extinction cross section is numerically the sum of the scattering cross section and the absorption cross section.

[0020] An efficient simulation system for the extinction characteristics of micro-nano structures based on the time-domain discontinuous Galerkin technique, comprising:

[0021] A simulation model establishment unit that establishes a simulation model for the micro-nano structure to be solved, spatially discretizes the corresponding region using tetrahedral and hexahedral elements, and obtains all node information of the simulation model;

[0022] A solution matrix equation construction unit that, based on the simulation model, uses the Maxwell's equations as the basic control equations, establishes a matrix equation for the unknown electric and magnetic fields using the time-domain discontinuous Galerkin finite element method, then introduces a numerical flux to handle the discontinuity of the field quantities between non-conformal surfaces, and selects a time iteration formula for time discretization to obtain the solution matrix equations for the electric and magnetic fields;

[0023] A frequency-domain electric and magnetic field solution unit that iteratively solves the matrix equations to obtain the electric and magnetic field coefficients of the entire computational domain, extracts any closed surface enclosing the micro-nano structure, obtains the electric and magnetic fields at the points on the surface, and then performs discrete Fourier transform on the electric and magnetic fields to obtain the frequency-domain electric and magnetic fields at different frequencies;

[0024] A Poynting vector calculation unit that calculates the Poynting vectors of the scattered field and the total field on the closed surface based on the frequency-domain electric and magnetic fields;

[0025] A scattered light intensity and absorbed light intensity calculation unit that performs Gauss surface integration on the Poynting vectors of the scattered field and the total field on the closed surface respectively to obtain the scattered light intensity and the absorbed light intensity at different frequency points;

[0026] The extinction cross-section calculation unit calculates the intensity of incident light according to the applied excitation source, obtains the scattering cross-section and absorption cross-section by the ratios of the scattered light intensity and absorption light intensity to the incident light intensity, and further obtains the extinction cross-section.

[0027] Compared with the prior art, the present invention has the following remarkable advantages: Based on Maxwell's equations and combined with the discontinuous Galerkin time-domain technique, the present invention constructs a discrete electromagnetic field model of micro-nano structures, discretizes the calculation region with a reasonable tetrahedron / hexahedron hybrid grid, and introduces a numerical flux to handle the discontinuity of field quantities between units, thereby realizing multi-scale and high-efficiency time-domain solution of micro-nano structures, enabling spatial multi-scale modeling, reducing the number of grids, and accelerating the calculation speed; the computational time complexity is O(N). Description of the Drawings

[0028] Figure 1 It is a schematic diagram of the division of the calculation region.

[0029] Figure 2 It is a schematic diagram of different situations of the interface between tetrahedrons and hexahedrons.

[0030] Figure 3 It is a schematic diagram of the processing of the surface integral of the non-conformal interface between one tetrahedron and four hexahedrons.

[0031] Figure 4 It is a schematic diagram of the realization of the surface integral of the non-conformal surface with five intersection points.

[0032] Figure 5 It is a schematic diagram of the computational time complexity of the algorithm of the present invention.

[0033] Figure 6 It is a tetrahedron / hexahedron hybrid meshing diagram of a gold nanosphere.

[0034] Figure 7 It is a comparison diagram of the extinction cross-section of a gold sphere with a radius of 100 nm and the results of the commercial software COMSOL. Detailed Implementation Modes

[0035] In order to handle the spatial multi-scale problem in solving the extinction characteristics of micro-nano structures, the present invention proposes an efficient simulation method for the extinction characteristics of micro-nano structures based on the discontinuous Galerkin time-domain technique, and uses tetrahedron / hexahedron hybrid meshing to reduce the number of grids and improve the calculation efficiency.

[0036] The following further describes the present invention in detail with reference to the drawings.

[0037] The present invention is an efficient simulation method for the extinction characteristics of micro-nano structures based on the discontinuous Galerkin time-domain technique, and the steps are as follows:

[0038] Step 1: Establish a simulation model for the micro-nano structure to be solved. Use tetrahedral and hexahedral elements to discretize the corresponding regions in space and obtain all the node information of the simulation model. Figure 1 The schematic diagram of the computational domain division is given.

[0039] Step 2: Take the Maxwell's equations as the basic governing equations, follow the standard analysis steps of the discontinuous Galerkin finite element method in time domain, and expand the unknown electric and magnetic fields using hierarchical vector basis functions:

[0040] E = ∑N j e e j (1)

[0041] H = ∑N j h h j (2)

[0042] where N j represents the hierarchical vector basis function, and e j , h j denote the unknown electric and magnetic field quantities to be solved.

[0043] Perform Galerkin tests on both sides of the equations respectively.

[0044]

[0045] For the treatment of discontinuous surfaces, it is necessary to introduce numerical fluxes to enforce the continuity of the fields. Introduce the upwind flux

[0046]

[0047] where e n is the normal vector of the surface, E and H are the electric and magnetic fields on the bulk element respectively, represents the intrinsic impedance of the bulk element, Y = 1 / Z represents the intrinsic admittance of the bulk element, and the adjacent element volume is marked by the superscript "+".

[0048] Substitute the upwind flux and formulas (1), (2) into (3), (4) to obtain:

[0049]

[0050] For the discontinuous Galerkin method with non-conformal meshes, only the continuity treatment of the surface integrals in the equations is required. For the interface between tetrahedra and hexahedra, it can be seen that there are multiple triangles on each quadrilateral at the interface. Figure 2 The schematic diagram of different situations of the tetrahedron-hexahedron interface is given.

[0051] For the area integral matrix generated by the discontinuous Galerkin method, in the case of non-conformal meshing, only the area integral on the interface needs to be processed, that is, the interaction between the main body and the adjacent bodies. Taking the matrix S eh + as an example,

[0052]

[0053] For Figure 3 the non-conformal surface in eh + , the processing of the matrix S

[0054]

[0055] The area integral used in this method is implemented on triangular Gaussian quadrature. When the interface is an irregular shape as shown in Figure 4 , when calculating the area integral, the irregular shape needs to be split into multiple triangles for integration and then accumulated. For a non-conformal pentagonal surface, it can be split into S1, S2, and S3, and then Gaussian area integration is performed on these three triangles and accumulated as the value of the area integral of the polygon.

[0056] Step 3: Iteratively solve the matrix equation system to obtain the electric and magnetic field coefficients in the entire computational domain, extract an arbitrary closed surface enclosing the micro-nano structure, obtain the electric and magnetic fields at the points on the surface, and then perform discrete Fourier transform on the electric and magnetic fields to obtain the frequency-domain electric and magnetic fields at different frequencies. Figure 1 The schematic diagram of the extracted closed surface is also given.

[0057]

[0058] where, Δt is the time-domain sampling interval, N is the number of sampling points, h(n) is the time-domain signal, and m is the frequency-domain index corresponding to the discrete frequency points.

[0059] Step 4: Calculate the Poynting vectors of the scattered field and the total field on the closed surface.

[0060] The Poynting vector of the scattered field is:

[0061]

[0062] E s ,H s* are the conjugates of the electric field and magnetic field of the scattered field respectively, and E x ,E y ,E z ,H x ,H y ,H z are the components of the electric and magnetic fields in three directions.

[0063] The Poynting vector of the total field is as follows:

[0064]

[0065] E, H * are the conjugates of the total-field electric field and the total-field magnetic field, respectively.

[0066] Step 5: Perform a Gauss surface integral on the Poynting vectors of the scattered field and the total field on a closed surface respectively to obtain the scattered light intensity and the absorbed light intensity at different frequencies.

[0067] The energies scattered and absorbed by the nanoparticle are respectively:

[0068] W sca = ∫ s S s ds (13)

[0069] W abs = -∫ s S ds (14)

[0070] The negative sign indicates that it points into the surface, making W abs > 0. W ext is the energy extinguished during the scattering process, and its physical meaning can be understood through the following energy relationship:

[0071] W ext = W abs + W sca (15)

[0072] is the total energy of scattering and absorption.

[0073] Perform a loop on the small triangular surfaces on the closed surface. Multiply the Poynting vector at the Gauss points on the looped small triangular surfaces by the normal vector, then perform a Gauss integral to obtain the scattered light intensity and the absorbed light intensity of the small triangular surfaces, and finally perform an accumulation to obtain the scattered light intensity and the absorbed light intensity of the entire closed surface;

[0074] Step 6: Calculate the incident light intensity according to the applied excitation source, and obtain the scattering cross-section and the absorption cross-section through the ratios of the scattered light intensity and the absorbed light intensity to the incident light intensity, and further obtain the extinction cross-section.

[0075] According to the applied excitation source, the incident field intensity E0 at different frequencies can be obtained. For a uniform plane wave, the incident light intensity is:

[0076]

[0077] where η is the wave impedance.

[0078] The scattering cross-section represents the ratio of the scattered light intensity of the nanostructure to the incident light intensity:

[0079]

[0080] The absorption cross-section represents the ratio of the light absorption intensity of the nanostructure to the incident light intensity:

[0081]

[0082] The extinction cross-section is numerically the sum of the scattering cross-section and the absorption cross-section:

[0083] σ ext = σ sca + σ abs (19)

[0084] To verify the correctness and effectiveness of the present invention, the extinction characteristics of a gold sphere with a radius of 100 nm are analyzed below.

[0085] The radius of the gold nanosphere is 100 nm, and a modulated Gaussian pulse is used as the excitation source, with a frequency range from 400 THz to 750 TH. Figure 5 The computational time complexity of the algorithm described in the present invention is given as O(N). Figure 6 A surface schematic diagram of the method described in the present invention using a tetrahedral and hexahedral hybrid meshing is given. The nanosphere part is meshed using tetrahedrons with a mesh size of 1 / 40λ, and the air part is meshed using hexahedrons with a mesh size of 1 / 8λ, where λ is the wavelength of the highest frequency of the incident wave in vacuum. Table 1 gives a comparison of the mesh discretization information and computational time between the method described in the present invention and the commercial software COMSOL (finite element in frequency domain). It can be found that the number of meshes after discretizing the model using the method described in the present invention is greatly reduced, and the computational efficiency is significantly improved, showing obvious advantages.

[0086] Table 1 Comparison results of mesh discretization information and computational time between the method of the present invention and COMSOL

[0087] Number of tetrahedrons Number of hexahedrons Solution time (s) COMSOL 294878 23277 DGTD 44094 7784 5495

[0088] Figure 7 A comparison graph of the calculation results of the method described in the present invention and the COMSOL results is given. It can be found that the curves fit well, indicating that the method described in the present invention has a high accuracy in calculating the extinction characteristics.

[0089] This embodiment also provides an efficient simulation system for the extinction characteristics of micro-nano structures based on the time-domain discontinuous Galerkin technique, including:

[0090] A simulation model establishment unit that establishes a simulation model for the micro-nano structure to be solved, spatially discretizes the corresponding regions using tetrahedral and hexahedral elements, and obtains all node information of the simulation model;

[0091] The matrix equation solving unit constructs a matrix equation for the unknown electric and magnetic fields based on the simulation model, using Maxwell's equations as the basic governing equations and adopting the discontinuous Galerkin finite element method in the time domain. Then, a numerical flux is introduced to handle the discontinuity of field quantities between non-conformal surfaces, and a time iteration formula is selected for time discretization to obtain the matrix equation systems for solving the electric and magnetic fields.

[0092] The frequency-domain electric and magnetic field solving unit iteratively solves the matrix equation systems to obtain the electric and magnetic field coefficients in the entire computational domain, extracts any closed surface enclosing the micro-nano structure, obtains the electric and magnetic fields at the points on the surface, and then performs a discrete Fourier transform on the electric and magnetic fields to obtain the frequency-domain electric and magnetic fields at different frequencies.

[0093] The Poynting vector calculation unit calculates the Poynting vectors of the scattered field and the total field on the closed surface based on the frequency-domain electric and magnetic fields.

[0094] The scattered light intensity and absorbed light intensity calculation unit performs Gaussian surface integrals on the Poynting vectors of the scattered field and the total field on the closed surface respectively to obtain the scattered light intensity and absorbed light intensity at different frequency points.

[0095] The extinction cross-section calculation unit calculates the incident light intensity according to the applied excitation source, obtains the scattering cross-section and absorption cross-section through the ratios of the scattered light intensity and absorbed light intensity to the incident light intensity, and further obtains the extinction cross-section.

[0096] The method of the present invention is based on Maxwell's equations and combines the discontinuous Galerkin technique in the time domain to construct a discrete electromagnetic field model of the micro-nano structure. A reasonable tetrahedron / hexahedron hybrid grid discretization is adopted for the computational region, and the discontinuity of field quantities between units is handled by introducing a numerical flux, thereby realizing multi-scale and high-efficiency time-domain solution of the micro-nano structure. When dealing with multi-scale problems of micro-nano structures, this method can well reduce the number of meshes, and the computational time complexity is O(N). It can efficiently calculate the extinction characteristics in a wide frequency spectrum range and is applicable to the analysis of complex micro-nano optical field problems.

[0097] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0098] Obviously, those skilled in the art can make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these modifications and variations.

Claims

1. An efficient simulation method for extinction characteristics of micro-nano structures based on time-domain discontinuous Galerkin technology, characterized in that: Includes steps: Step 1: establish a simulation model for the micro-nano structure to be solved, use tetrahedron and hexahedron units to spatially discretize the corresponding area, and obtain all node information of the simulation model; Step 2: Based on the simulation model, the Maxwell equations are used as the basic control equations, and the matrix equations for the unknown electric and magnetic fields are established by using the time-domain discontinuous Galerkin finite element method. Then, the numerical flux is introduced to deal with the discontinuity of the field quantities between the non-conformal surfaces, and the time iteration formula is selected for time discretization to obtain the matrix equations for the electric and magnetic fields. Step 3, iteratively solve the matrix equations to obtain the electric field and magnetic field coefficients of the entire calculation domain, extract any closed surface surrounding the micro-nano structure, obtain the electric field and magnetic field of the point on the surface, and then perform discrete Fourier transform on the electric field and magnetic field to obtain the frequency domain electric field and magnetic field at different frequencies; Step 4, based on the frequency domain electric field and magnetic field, calculate the Poynting vector of the scattered field and the total field on the closed surface; Step 5, performing Gaussian surface integration of the Poynting vector of the scattered field and the total field on the closed surface to obtain the scattered light intensity and the absorbed light intensity at different frequencies; Step 6, calculate the incident light intensity according to the added excitation source, obtain the scattering cross section and absorption cross section by the ratio of the scattered light intensity and the absorbed light intensity to the incident light intensity, further obtain the extinction cross section, and obtain the characteristics of the micro-nano structure.

2. The method for efficiently simulating extinction characteristics of micro-nano structures based on time-domain discontinuous Galerkin technology according to claim 1 is characterized in that: The numerical flux in step 2 adopts the upwind flux, which is: Among them, e n is the normal vector of the surface, E and H are the electric field and magnetic field on the main unit respectively, Z represents the intrinsic impedance of the main unit, Y=1 / Z represents the intrinsic admittance of the main unit, and the superscript "+" represents the body of the adjacent unit.

3. The method for efficiently simulating extinction characteristics of micro-nano structures based on time-domain discontinuous Galerkin technology according to claim 1 is characterized in that: The step 3 specifically includes: the calculated closed surface is composed of multiple triangular faces or quadrilateral faces, and after obtaining the coefficients of the electric field and the magnetic field by iteratively solving the matrix equation group, the triangular faces or quadrilateral faces where the closed surface is located are looped, and the electric field and magnetic field of the Gaussian points on each loop surface are obtained by combining the basis functions, the electric field and the magnetic field coefficients, and then the obtained electric field and magnetic field are converted into the frequency domain by discrete Fourier transform.

4. The method for efficiently simulating extinction characteristics of micro-nano structures based on time-domain discontinuous Galerkin technology according to claim 1 is characterized in that: The Poynting vector of the scattered field is the cross product of the electric field and the magnetic field conjugate on the closed surface in the scattered field, and the Poynting vector of the total field is the cross product of the electric field and the magnetic field conjugate on the closed surface in the total field.

5. The method for efficiently simulating extinction characteristics of micro-nano structures based on time-domain discontinuous Galerkin technology according to claim 1, characterized in that: The step 5 specifically includes: looping each small triangular face on the closed surface, multiplying the Poynting vector of the Gaussian point on the looped small triangular face by the normal vector, performing Gaussian integration to obtain the scattered light intensity and absorbed light intensity of the small triangular face, and finally accumulating to obtain the scattered light intensity and absorbed light intensity of the entire closed surface, wherein the small triangular face is a triangular face formed by cutting the quadrilateral face on the closed surface along the diagonal line.

6. The method for efficiently simulating extinction characteristics of micro-nano structures based on time-domain discontinuous Galerkin technology according to claim 1, characterized in that: The step 6 uses a modulated Gaussian pulse as an excitation source, and performs a discrete Fourier transform on the incident wave to obtain the incident light intensity at different frequencies.

7. The method for efficiently simulating extinction characteristics of micro-nano structures based on time-domain discontinuous Galerkin technology according to claim 1, characterized in that: The extinction cross section is numerically the sum of the scattering cross section and the absorption cross section.

8. An efficient simulation system for micro-nanostructure extinction characteristics showing any of the methods described in claims 1-7, characterized in that: include: A simulation model building unit is used to build a simulation model for the micro-nano structure to be solved, and the corresponding area is spatially discretized using tetrahedron and hexahedron units to obtain all node information of the simulation model; Solving the matrix equations to build a unit, based on the simulation model, using the Maxwell equations as the basic control equations, using the time domain discontinuous Galerkin finite element method to establish the matrix equations for the unknown electric and magnetic fields, then introducing the numerical flux to deal with the discontinuity of the field quantities between the non-conformal surfaces, selecting the time iteration formula for time discretization, and obtaining the matrix equations for the electric and magnetic fields; The frequency domain electric field and magnetic field solving unit iteratively solves the matrix equations to obtain the electric field and magnetic field coefficients of the entire calculation domain, extracts any closed surface surrounding the micro-nano structure, obtains the electric field and magnetic field of the point on the surface, and then performs discrete Fourier transform on the electric field and magnetic field to obtain the frequency domain electric field and magnetic field at different frequencies; Poynting vector calculation unit, which calculates the Poynting vector of the scattered field and the total field on the closed surface based on the frequency domain electric field and magnetic field; The scattered light intensity and absorbed light intensity calculation unit performs Gaussian surface integration of the Poynting vector of the scattered field and the total field on the closed surface to obtain the scattered light intensity and absorbed light intensity at different frequency points; The extinction cross section calculation unit calculates the incident light intensity according to the added excitation source, obtains the scattering cross section and the absorption cross section through the ratio of the scattered light intensity and the absorbed light intensity to the incident light intensity, and further obtains the extinction cross section.

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