Micro-nano structure extinction characteristic high-efficiency simulation method and system based on time domain discontinuous galerkin technique

Abstract

The application discloses a micro-nano structure extinction characteristic efficient simulation method and system based on a time domain discontinuous Galerkin technology, which is based on a Maxwell equation set, combines the time domain discontinuous Galerkin technology to construct an electromagnetic field discrete model of the micro-nano structure, adopts a reasonable tetrahedron / hexahedron mixed grid to disperse a calculation region, and introduces a numerical flux processing unit to process discontinuity of field quantities between units, so that multi-scale efficient time domain solving of the micro-nano structure is realized. When the method processes the multi-scale problem of the micro-nano structure, the number of split 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 complex micro-nano light field problem analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to a micro-nano structure extinction characteristic simulation method in the field of micro-nano optics, in particular to a micro-nano structure extinction characteristic efficient simulation method and system based on time domain discontinuous Galerkin technology. BACKGROUND

[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 nanophotonic devices. 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. Accurate simulation of the extinction characteristics of micro-nano structures has important theoretical guiding significance for the development of high-performance nanowires, surface-enhanced Raman scattering sensors, photothermal therapy devices, etc.

[0003] Discontinuous Galerkin Time Domain (DGTD) is a new time-domain numerical simulation method that combines the high geometric adaptability of the finite element method and the high computational efficiency of the time-domain finite difference method. The DGTD method can achieve high-precision simulation in complex geometric structures by introducing numerical flux to handle the discontinuity of field quantities between elements. In addition, the DGTD method supports mixed mesh partitioning, which can significantly reduce the number of meshes and improve computational efficiency, making it particularly suitable for simulation of multi-scale micro-nano structures. In recent years, DGTD technology has shown great potential in the fields of electromagnetic field simulation, photonic crystals, plasmonic resonance, etc., but its application in the simulation of micro-nano structure extinction characteristics is still in the exploratory stage.

[0004] Currently, in the field of analysis of micro-nano structure extinction characteristics, the most commonly used numerical analysis methods are frequency domain finite element, time domain finite difference, and moment method, etc. The frequency domain finite element method often faces high computational complexity (O(N 3 )) and a large number of conformal meshes for multi-scale problems when dealing with complex geometric structures or wide frequency spectrum. Therefore, developing a micro-nano structure extinction characteristic efficient simulation method based on time domain discontinuous Galerkin technology can provide a powerful tool for the design and optimization of nanophotonic devices, and has important scientific research value and application prospects. SUMMARY

[0005] The purpose of the present application is to provide a micro-nano structure extinction characteristic efficient simulation method and system based on time domain discontinuous Galerkin technology, which can effectively reduce the number of partitioned meshes when dealing with multi-scale problems of micro-nano structures, and has a computational time complexity of O(N), which can efficiently calculate the extinction characteristics in a wide frequency spectrum, and is suitable for complex micro-nano optical field problem analysis.

[0006] The technical solution for achieving the object of the application is a micro-nano structure extinction characteristic high-efficiency simulation method based on time-domain discontinuous Galerkin technology, comprising the following steps:

[0007] Step 1: a simulation model of the micro-nano structure to be solved is established, tetrahedron and hexahedron elements are used for spatial discretization of the corresponding regions to obtain all node information of the simulation model, and the micro-nano structure is subjected to four-hexahedron hybrid meshing to reduce the number of meshes;

[0008] Step 2: based on the simulation model, the Maxwell equation set is used as the basic control equation, the time-domain discontinuous Galerkin finite element method is used to establish a matrix equation for unknown electric field and magnetic field, the numerical flux is introduced to process the discontinuity of field quantities between non-conformal surfaces, a time iteration formula is selected for time discretization, and a matrix equation set for solving electric field and magnetic field is obtained;

[0009] Step 3: the matrix equation set is iteratively solved to obtain electric field and magnetic field coefficients of the entire calculation domain, a closed curved surface surrounding the micro-nano structure is extracted, electric field and magnetic field of points on the curved surface are obtained, and discrete Fourier transform is performed on the electric field and magnetic field to obtain frequency-domain electric field and magnetic field at different frequencies;

[0010] Step 4: based on the frequency-domain electric field and magnetic field, the Poynting vector of the scattering field and the total field on the closed curved surface is calculated;

[0011] Step 5: the Poynting vector of the scattering field and the total field on the closed curved surface is subjected to Gaussian area integration to obtain scattering light intensity and absorption light intensity at different frequency points;

[0012] Step 6: the incident light intensity is calculated according to the added excitation source, the scattering cross section and the absorption cross section are obtained by the ratio of the scattering light intensity and the absorption light intensity to the incident light intensity, and the extinction cross section is further obtained, thereby obtaining the characteristics of the micro-nano structure.

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

[0014] Further, the step 3 specifically comprises the following steps: the calculated closed curved surface is composed of multiple triangular surfaces or quadrilateral surfaces, after the coefficients of electric field and magnetic field are obtained by iteratively solving the matrix equation set, the triangular surfaces or quadrilateral surfaces on which the closed curved surface is located are cycled, the electric field and the magnetic field of the Gaussian points on each cycled surface are obtained in combination with the basis functions and the electric field and magnetic field coefficients, and the obtained electric field and magnetic field are subjected to frequency-domain conversion through discrete Fourier transform.

[0015] Further, the closed curved surface surrounding the micro-nano structure is respectively in the total field region and the scattering field region, and the electric field and the magnetic field at different frequencies can be obtained through discrete Fourier transform.

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

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

[0018] Further, the step 5 comprises: performing a loop on small triangular surfaces on the closed surface, multiplying the Poynting vector of the Gauss point on the looped small triangular surface by the normal vector, performing Gauss integration to obtain the scattering light intensity and the absorption light intensity of the small triangular surface, and finally accumulating to obtain the scattering light intensity and the absorption 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 an 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 incident wave amplitude, and the extinction cross section is numerically equal to the sum of the scattering cross section and the absorption cross section.

[0020] A micro-nano structure extinction characteristic high-efficiency simulation system based on a time-domain discontinuous Galerkin technique, comprising:

[0021] A simulation model establishing unit establishes a simulation model for a micro-nano structure to be solved, uses tetrahedron and hexahedron units to discretize corresponding regions in space, and obtains all node information of the simulation model;

[0022] A matrix equation set constructing unit, based on the simulation model, takes the Maxwell equation set as a basic control equation, uses a time-domain discontinuous Galerkin finite element method to establish a matrix equation for unknown electric field and magnetic field, introduces numerical flux to process the discontinuity of field quantities between non-conformal surfaces, selects a time iteration formula to perform time discretization, and obtains a solving matrix equation set of the electric field and the magnetic field;

[0023] A frequency-domain electric field and magnetic field solving unit, which iteratively solves the matrix equation set to obtain electric field and magnetic field coefficients of the entire calculation domain, extracts a closed surface surrounding the micro-nano structure, obtains electric field and magnetic field of points on the surface, and performs discrete Fourier transform on the electric field and the magnetic field to obtain frequency-domain electric field and magnetic field at different frequencies;

[0024] A Poynting vector calculating unit, which calculates Poynting vectors of a scattering field and a total field on the closed surface based on the frequency-domain electric field and the magnetic field;

[0025] A scattering light intensity and absorption light intensity calculating unit, which respectively performs Gauss area integration on the Poynting vectors of the scattering field and the total field on the closed surface to obtain scattering light intensity and absorption light intensity at different frequencies;

[0026] 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 scattering light intensity and the absorption light intensity to the incident light intensity, and further obtains the extinction cross section.

[0027] Compared with the prior art, the present application has the following advantages: the present application is based on Maxwell equations, combines time domain discontinuous Galerkin technology to construct the electromagnetic field discrete model of micro-nano structure, adopts reasonable tetrahedron / hexahedron mixed grid discretization for the calculation region, processes the discontinuity of field quantity between units by introducing numerical flux, thereby realizing multi-scale efficient time domain solution of micro-nano structure, realizing spatial multi-scale modeling, reducing the number of grids, and accelerating the calculation speed; and the calculation time complexity is O(N). BRIEF DESCRIPTION OF DRAWINGS

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

[0029] Figure 2 Fig. 2 is a schematic diagram of different situations of tetrahedron / hexahedron interface.

[0030] Figure 3 Fig. 3 is a processing schematic diagram of area integration of a non-conformal interface of one tetrahedron and four hexahedrons.

[0031] Figure 4 Fig. 4 is an implementation schematic diagram of area integration of a non-conformal surface of five intersection points.

[0032] Figure 5 Fig. 5 is a calculation time complexity schematic diagram of the algorithm of the present application.

[0033] Figure 6 Fig. 6 is a tetrahedron / hexahedron mixed partition grid diagram of gold nanospheres.

[0034] Figure 7 Fig. 7 is a comparison diagram of extinction cross sections of gold spheres with a radius of 100 nm and the results of commercial software COMSOL. DETAILED DESCRIPTION

[0035] In order to process and solve the spatial multi-scale problem in solving the extinction characteristics of micro-nano structure, the present application provides a high-efficiency simulation method for extinction characteristics of micro-nano structure based on time domain discontinuous Galerkin technology, which utilizes tetrahedron / hexahedron mixed grid partition to reduce the number of grids and improve the calculation efficiency.

[0036] The present application will be further described in detail below with reference to the drawings.

[0037] The present application is a high-efficiency simulation method for extinction characteristics of micro-nano structure based on time domain discontinuous Galerkin technology, and the steps are as follows:

[0038] Step 1, a simulation model of the micro-nano structure to be solved is established, tetrahedron and hexahedron elements are used to discretize the corresponding regions in space, and all node information of the simulation model is obtained. Figure 1 The calculation region division schematic diagram is given.

[0039] Step 2, based on the Maxwell equation group as the basic control equation, following the standard analysis steps of the discontinuous Galerkin time domain finite element method, the unknown electric field and magnetic field are expanded by using the laminated vector basis function:

[0040] E = ∑N j e e j (1)

[0041] H = ∑N j h h j (2)

[0042] Wherein, N j represents the laminated vector basis function, e j , h j represent the unknown electric field and magnetic field to be solved.

[0043] The Galerkin test is carried out on both sides of the equation.

[0044]

[0045] For the treatment of discontinuous surface, the continuity of numerical flux strong field needs to be introduced. The upwind flux

[0046]

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

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

[0049]

[0050] For the discontinuous Galerkin method of non-conformal grid, only the area integral in the equation needs to be processed for continuity. For the interface of tetrahedron and hexahedron, it can be seen that there will be multiple triangles on each quadrilateral on the interface. Figure 2 The schematic diagram of different cases of tetrahedron and hexahedron interface is given.

[0051] For the area integral matrix generated by the discontinuous Galerkin method, when the non-conforming partition exists, only the area integral on the interface needs to be processed, that is, the interaction between the body and the adjacent body. Taking the matrix S eh + as an example,

[0052]

[0053] For the non-conforming surface in the matrix S Figure 3 , the processing of the matrix S eh + is as follows:

[0054]

[0055] The area integral used in this method is realized on the triangular Gaussian integral. When the interface is irregular as shown in Figure 4 , the irregular figure needs to be split into multiple triangles for integration and then accumulation when calculating the area integral. The non-conforming surface of the pentagon can be split into S1, S2, and S3, and then Gaussian area integral is performed on the three triangles, and then the values are accumulated as the area integral of the polygon.

[0056] Step 3, iteratively solve the matrix equation to obtain the electric field and magnetic field coefficients of the entire calculation domain, extract the closed surface surrounding the micro-nano structure, obtain the electric field and magnetic field 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. 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 point.

[0059] Step 4, calculate the Poynting vector 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 scattered field electric field and the scattered field magnetic field, respectively, E x ,E y ,E z ,H x ,H y ,H z are the components of the electric field and the magnetic field in three directions.

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

[0064]

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

[0066] Step 5, the Gaussian surface integral of the Poynting vector of the scattering field and the total field on the closed surface is performed to obtain the scattering light intensity and the absorption light intensity at different frequencies.

[0067] The energy scattered and absorbed by the nanoparticles is:

[0068] W sca =∫ s S s ds (13)

[0069] W abs =-∫ s Sds (14)

[0070] The negative sign indicates the direction in the plane, so that W abs > 0. W ext is the energy of extinction in the scattering process, which can be understood by the following energy relationship:

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

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

[0073] The small triangular surface on the closed surface is cycled, and the Poynting vector of the Gaussian point on the cycled small triangular surface is multiplied by the normal vector, and then the Gaussian integral is performed to obtain the scattering light intensity and the absorption light intensity of the small triangular surface, and finally the scattering light intensity and the absorption light intensity of the entire closed surface are obtained by accumulation;

[0074] Step 6, the incident light intensity is calculated according to the added excitation source, the scattering cross section and the absorption cross section are obtained by the ratio of the scattering light intensity and the absorption light intensity to the incident light intensity, and further the extinction cross section can be obtained.

[0075] According to the added excitation source, the incident field intensity E0 at different frequencies can be obtained, and 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 scattering light intensity of the nanostructure to the incident light intensity:

[0079]

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

[0081]

[0082] The extinction cross section is the sum of the scattering cross section and the absorption cross section in value:

[0083] σ ext = σ sca + σ abs (19)

[0084] In order to verify the correctness and effectiveness of the present application, 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 calculation time complexity of the algorithm described in the present application is O(N). Figure 6 The surface diagram of the method described in the present application using tetrahedral-hexahedral hybrid subdivision is given. The nanosphere part is subdivided using tetrahedrons with a subdivision size of 1 / 40λ, and the air part is subdivided using hexahedrons with a subdivision size of 1 / 8λ, where λ is the wavelength of the highest frequency of the incident wave in vacuum. Table 1 gives the grid discretization information and calculation time comparison of the method described in the present application and the commercial software COMSOL (frequency domain finite element), and it can be found that the number of grids after discretizing the model using the method described in the present application is greatly reduced, and the calculation efficiency is greatly improved, which has obvious advantages.

[0086] Table 1 Comparison of grid discretization information and calculation time of the method of the present application and COMSOL

[0087] Tetrahedron count Hexahedron count Solving time (s) COMSOL 294878 23277 DGTD 44094 7784 5495

[0088] Figure 7 The comparison diagram of the calculation results of the method described in the present application and the COMSOL results is given, and it can be found that the curves agree well, indicating that the accuracy of the method described in the present application for calculating the extinction characteristics is high.

[0089] The embodiment also provides a high-efficiency simulation system for micro-nano structure extinction characteristics based on time-domain discontinuous Galerkin technology, comprising:

[0090] The simulation model establishing unit establishes a simulation model for the micro-nano structure to be solved, and uses tetrahedral and hexahedral elements to discretize the corresponding regions in space to obtain all node information of the simulation model;

[0091] The solving matrix equation set construction unit is based on a simulation model, takes the Maxwell equation set as basic control equations, adopts a time domain discontinuous Galerkin finite element method to establish matrix equations for unknown electric field and magnetic field, introduces numerical flux to process the discontinuity of field quantity between non-conformal surfaces, selects a time iteration formula to carry out time discretization, and obtains the solving matrix equation set of electric field and magnetic field;

[0092] The frequency domain electric field and magnetic field solving unit iteratively solves the matrix equation set to obtain electric field and magnetic field coefficients of the whole calculation domain, extracts a closed curved surface surrounding the micro-nano structure, obtains electric field and magnetic field of points on the curved surface, and then carries out discrete Fourier transform on the electric field and magnetic field to obtain frequency domain electric field and magnetic field under different frequencies.

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

[0094] The scattered light intensity and absorbed light intensity calculation unit carries out Gaussian area integration on the Poynting vector of the scattered field and the total field on the closed curved surface to obtain the scattered light intensity and the absorbed light intensity under different frequency points.

[0095] 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.

[0096] The method of the application is based on the Maxwell equation set, combines the time domain discontinuous Galerkin technology to construct the electromagnetic field discrete model of the micro-nano structure, adopts a reasonable tetrahedron / hexahedron mixed grid discretization to the calculation region, processes the discontinuity of field quantity between units by introducing numerical flux, and thus realizes the multi-scale high-efficiency time domain solving of the micro-nano structure. When the method is used to process the multi-scale problem of the micro-nano structure, the number of the divided grid can be well reduced, the time complexity of the calculation is O(N), the extinction characteristics in a wide frequency spectrum range can be efficiently calculated, and the method is suitable for the analysis of complex micro-nano light field problems.

[0097] Although the preferred embodiments of the application have been described, those skilled in the art who understand the basic creative concept can make additional changes and modifications to the embodiments. Therefore, the appended claims are intended to include the preferred embodiments and all changes and modifications falling within the scope of the application.

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

Claims

1. An efficient simulation method for the extinction properties of micro / nano structures based on time-domain discontinuous Galerkin technique, characterized in that, Including the following steps: Step 1: Establish a simulation model of the micro / nano structure to be solved, and use tetrahedral and hexahedral elements to spatially discretize the corresponding regions to obtain all node information of the simulation model; Step 2: Based on the simulation model, using Maxwell's equations as the basic governing equations, the time-domain discontinuous Galerkin finite element method is used to establish matrix equations for the unknown electric and magnetic fields. Then, numerical flux is introduced to handle the discontinuity of field quantities between non-conformal surfaces. The time iteration formula is selected for time discretization to obtain the solution matrix equations for the electric and magnetic fields. Step 3: Iteratively solve the matrix equations to obtain the electric and magnetic field coefficients of the entire computational domain, extract any closed surface surrounding the micro / nano structure, obtain the electric and magnetic fields at 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. Step 4: Calculate the Poynting vectors of the scattered field and the total field on the closed surface based on the frequency domain electric and magnetic fields; Step 5: Perform Gaussian surface integrals on the Poynting vectors of the scattered field and the total field on the closed surface to obtain the scattered light intensity and absorbed light intensity at different frequencies. Step 6: Calculate the incident light intensity based on the applied 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, and further obtain the extinction cross section to obtain the characteristics of the micro / nano structure.

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

3. The efficient simulation method for the extinction characteristics of micro / nano structures based on time-domain discontinuous Galerkin technology according to claim 1, characterized in that, Step 3 specifically includes: the calculated closed surface is composed of multiple triangular or quadrilateral surfaces. After obtaining the coefficients of the electric and magnetic fields by iteratively solving the matrix equations, the triangular or quadrilateral surfaces containing the closed surface are iterated. The electric and magnetic fields of the Gaussian points on each iterated surface are obtained by combining the basis functions, electric and magnetic field coefficients, and then the obtained electric and magnetic fields are frequency domain transformed by discrete Fourier transform.

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

5. The efficient simulation method for the extinction characteristics of micro / nano structures based on time-domain discontinuous Galerkin technology according to claim 1, characterized in that, Step 5 specifically includes: looping through each small triangular facet on the closed surface, multiplying the Poynting vector of the Gaussian point on the looped small triangular facet by the normal vector, and then performing Gaussian integration to obtain the scattered light intensity and absorbed light intensity of the small triangular facet, and finally summing them to obtain the scattered light intensity and absorbed light intensity of the entire closed surface. The small triangular facet is a triangular facet formed by cutting a quadrilateral facet along the diagonal on the closed surface.

6. The efficient simulation method for the extinction characteristics of micro / nano structures based on time-domain discontinuous Galerkin technology according to claim 1, characterized in that, Step 6 uses a modulated Gaussian pulse as the excitation source to perform a discrete Fourier transform on the incident wave to obtain the incident light intensity at different frequencies.

7. The efficient simulation method for the 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. A high-efficiency simulation system for the extinction properties of micro / nano structures exhibiting the method of any one of claims 1-7, characterized in that, include: The simulation model building unit establishes a simulation model of the micro / nano structure to be solved. Tetrahedral and hexahedral elements are used to spatially discretize the corresponding regions to obtain all node information of the simulation model. The matrix equations are solved by constructing a unit based on the simulation model. Maxwell's equations are used as the basic governing equations. The matrix equations for the unknown electric and magnetic fields are established using the time-domain discontinuous Galerkin finite element method. Numerical flux is then introduced to handle the discontinuity of field quantities between non-conformal surfaces. The time iteration formula is selected for time discretization to obtain the solution matrix equations for the electric and magnetic fields. The frequency domain electric and magnetic field solution unit iteratively solves the matrix equations to obtain the electric and magnetic field coefficients of the entire computational domain. It extracts any closed surface surrounding the micro-nano structure, obtains the electric and magnetic fields at 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. The Poynting vector calculation unit calculates the Poynting vector of the scattered field and the total field on a 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 integrals on the Poynting vectors 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 section calculation unit calculates the incident light intensity based on the applied excitation source, and obtains the scattering section and absorption section by the ratio of the scattered light intensity and the absorbed light intensity to the incident light intensity, and further obtains the extinction section.

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