Three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic field in graphene dispersive medium

Abstract

The invention discloses a three-dimensional (SBC-HIE-FDTD) method for efficiently calculating the propagation characteristics of electromagnetic waves in a graphene dispersive medium on the basis of a mixed explicit-implicit finite difference time domain (HIE-FDTD) method and a surface boundary condition (SBC) of the graphene, and the three-dimensional SBC-HIE-FDTD method is used for efficiently calculating the propagation characteristics of the electromagnetic waves in the graphene dispersive medium. According to the three-dimensional SBC-HIE-FDTD method for efficiently calculating the electromagnetic field in the graphene dispersive medium, the advantages of the HIE-FDTD method in thin dielectric layer modeling and the advantages of the SBC method in the aspect of zero-thickness graphene sheet modeling are fused, so that the size of a small grid caused by a graphene sheet or a thin dielectric layer does not limit the time step length any more; compared with other simulation methods based on a graphene structure, the method has the advantages that the calculation efficiency is better, and the method is particularly suitable for analysis and simulation of radio wave propagation characteristics in a terahertz graphene absorber structure.

Description

Technical Field

[0001] The present invention belongs to the field of computational electromagnetics technology, and specifically relates to a three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media. Background Art

[0002] In the field of terahertz devices, absorbers are a subject of considerable research interest. As key components capable of absorbing electromagnetic waves, absorbers play a vital role in radar stealth, electronic countermeasures, and electromagnetic interference. In the defense sector, military aircraft can use absorbers to efficiently absorb electromagnetic waves, shielding them from radar detection and enhancing combat capabilities. In the civilian sector, absorbers can be used in products such as wearable devices to effectively reduce electromagnetic radiation, mitigate potential harm to the human body, and ultimately reduce electromagnetic pollution. However, traditional absorbers suffer from numerous challenges, such as structural sizing issues, constant absorption frequency, low absorption rates, and unadjustable operating frequencies. To address these challenges, current research is focusing on developing novel absorber structures and materials to achieve miniaturization, frequency tunability, and optimized absorption rates. These efforts are expected to further advance absorber technology and open up new possibilities for practical applications.

[0003] Graphene absorbers have attracted widespread attention due to their many characteristics, such as wide bandwidth, thin layer thickness, strong absorption and easy design. In the simulation of the electromagnetic properties of graphene, commonly used computational electromagnetic methods include the Method of Moments (MoM), the Finite Element Method (FEM) and the Finite Difference Time Domain (FDTD). These methods have been widely used in the simulation of the electromagnetic properties of graphene. Among them, the FDTD method is one of the first choices because it is suitable for the calculation of broadband responses and has the ability to intuitively visualize electromagnetic responses. However, the CFL stability condition of the traditional FDTD method requires the use of fine grids and small time steps for the film, which increases the computational complexity and memory requirements of the simulation and reduces the simulation efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a three-dimensional SBC-HIE-FDTD method for calculating electromagnetic fields in graphene dispersive media that is more efficient than current methods. This method can combine the advantages of the HIE-FDTD method in modeling thin dielectric layers with the advantages of the SBC (Surface Boundary Condition, SBC) method in modeling zero-thickness graphene sheets. The small grid size caused by the graphene sheet or thin dielectric layer no longer limits the time step, and the meshing within the graphene sheet can be ignored. Compared with other simulation methods based on graphene structures, this algorithm is more computationally efficient and more suitable for simulating terahertz graphene absorber structures. This algorithm is then used to perform electromagnetic simulations of the designed graphene absorber to verify the effectiveness and efficiency of the method.

[0005] The technical solution adopted by the present invention is specifically implemented according to the following steps:

[0006] Step 1: Input model file;

[0007] Step 2: Initialize parameters and set parameters;

[0008] Step 3: Update the electric field components E in the x, y, and z directions of the graphene sheet and non-graphene sheet calculation area ζ ,ζ=x,y,z;

[0009] Step 4: Add the field source to the electric field component coefficient in the x direction;

[0010] Step 5: Update and calculate the auxiliary components of the electric field in the x, y, and z directions of the entire calculation area;

[0011] Step 6: Update the x, y, and z magnetic field components H in the calculation area of ​​the graphene sheet and non-graphene sheet ζ ,ζ=x,y,z;

[0012] Step 7: Update and calculate the auxiliary components of the magnetic field in the x, y, and z directions of the entire calculation area;

[0013] Step 8: Determine whether the number of time steps reaches the preset value. If not, return to step 3. If it reaches the preset value, output the calculation result.

[0014] The present invention is also characterized in that:

[0015] Step 1 Input the model file, specifically:

[0016] Calculate the area size N x ×N y ×N z , where N x is the number of grids in the x direction, N yis the number of grids in the y direction; N z is the number of grids in the z direction; the spatial step Δζ, ζ = x, y, z, where x is the horizontal coordinate, y is the vertical coordinate, and z is the vertical coordinate; the time step Δt; the electrical conductivity σ, magnetic permeability μ0, and dielectric constant ε0 in vacuum; the absorbing boundary SC-PML and related parameters κ ζmax ,σ ζmax , α ζmax ; Among them, κ ζmax Take an integer, κ ζmax The value range is [1, 60]; α ζmax The value range is [0, 1); the simulation calculation time T f ; Iteration number k, k ≥ 0 and is an integer; Observation point; Field source parameters; Graphene sheet addition position; Graphene sheet parameter σ0, external electromagnetic μ c ; Connection boundary adding position; dielectric layer starting position.

[0017] Step 2: Initialize and set parameters as follows:

[0018] The initialization parameters include:

[0019] The electromagnetic field components (E ζ ,H ζ ,ζ=x,y,z), the auxiliary electromagnetic field components of the entire calculation area (E ζξ ,H ζξ ,ζ=x,y,z,ξ=x,y,z,ζ≠ξ), the incident wave electromagnetic field component of the entire calculation area (E ζ，inc ,H ζ,inc ,ζ=x,y,z、E ζξ，inc ,H ζξ,inc ,ζ=x,y,z,ξ=x,y,z,ζ≠ξ), the electromagnetic field components on the upper and lower surfaces of the graphene sheet and the auxiliary electromagnetic field components ( θ E z , θ H ζ ,ζ=x,y,θ=1,2、 θ E zζ , θ H ζξ ,ζ=x,y,ζ=x,y,θ=1,2), the parameters of the SC-PML absorption boundary (α ζ ,σ ζ , ζ=x,y,z) are initialized to zero; the parameter κ of the SC-PML absorption boundary ζ ζ=x,y,z are initialized to 1;

[0020] The parameters to be set are:

[0021] Set the parameters of the SC-PML absorbing boundary, specifically:

[0022] σ ζ =σ ζmax |ζ-ζ0| m / d m

[0023] κ ζ =1+(κ ζmax -1)|ζ-ζ0| m / d m

[0024] α ζ =α ζmax ζ0 / d

[0025] Where ζ = x, y, z, ζ0 ​​is the position of the PML layer and the non-PML section, d is the thickness of the PML absorption boundary, κ ζmax Take an integer, κ ζmax The value range is [1, 60]; α ζmax The value range is [0, 1); σ ζmax According to σ opt To set, σ ζmax / σ opt The value range is (0, 12]; σ opt =(m+1) / 150πΔζ, where m ranges from [1, 20]. When m is 4, the absorption effect of the boundary is the best. The range of Δζ is λ is the wavelength of the source;

[0026] Set the parameters of auxiliary variables in the SC-PML framework, specifically:

[0027]

[0028] Where ζ=x,y,z,κ ζ , α ζ , σ ζ are all parameters of the SC-PML absorption boundary, ε represents the relative dielectric constant, and Δt represents the time step. Step 3 Update the electric field components E in the x, y, and z directions of the graphene sheet and non-graphene sheet calculation area ζ ,ζ=x,y,z, the specific update formula is as follows:

[0029] Non-graphene sheet calculation area:

[0030]

[0031]

[0032] Graphene sheet calculation area:

[0033]

[0034] Where i represents the i-th computational grid on the horizontal axis, j represents the j-th computational grid on the vertical axis, and k represents the k-th computational grid on the vertical axis. 0ζ , f 1ζ , f 2ζ are the parameters of the SC-PML absorbing boundary. ε0 is the dielectric constant in vacuum, and Δt represents the time step.

[0035] The field source added in step 4 is a Gaussian pulse plane wave excitation source, and its waveform is:

[0036]

[0037] Among them, T c =T d =0.0667ps, which is the field source parameter.

[0038] Step 5 updates and calculates the auxiliary components of the electric field in the x, y, and z directions of the entire calculation area. The specific update formula is as follows:

[0039]

[0040]

[0041] Step 6 Update the x, y, and z magnetic field components H in the calculation area of ​​the graphene sheet and non-graphene sheet ζ ,ζ=x,y,z, the specific update formula is as follows:

[0042] Non-graphene sheet calculation area:

[0043]

[0044] Graphene sheet calculation area:

[0045]

[0046]

[0047] The coefficients involved are:

[0048]

[0049] in e is the electron charge, τ = 1 / (2Γ) is the scattering time, Γ is the scattering rate, k B is the Boltzmann constant, T is the Kelvin temperature, is the reduced Planck constant. h is the Planck constant, is the cyclotron frequency, B0 is the external magnetic field strength, v F ≈106 m / s is the Fermi velocity, μ c For step 7 of the graphene chemical potential, the auxiliary magnetic field components in the x, y, and z directions of the entire calculation area are updated. The specific update formula is as follows:

[0050]

[0051]

[0052] The beneficial effects of the present invention are:

[0053] ① The present invention provides a three-dimensional SBC-HIE-FDTD method for efficiently calculating the electromagnetic field in graphene dispersive media. It has the advantages of the HIE-FDTD method in modeling thin dielectric layers, namely, it eliminates the CFL condition in the direction of thinner structures, thereby improving cost-effectiveness.

[0054] ② The present invention provides a three-dimensional SBC-HIE-FDTD method for efficiently calculating the electromagnetic field in graphene dispersive media. It also has the advantages of the SBC method in modeling zero-thickness graphene sheets. This method can ignore the division of fine grids inside the graphene, thereby improving the calculation efficiency.

[0055] ③ The present invention provides a three-dimensional SBC-HIE-FDTD method for efficiently calculating the electromagnetic field in graphene dispersive media. It has excellent electrical adjustability and can affect the absorption performance of graphene by adjusting the external electric field. Under a specific external electric field, optimal absorption of electromagnetic waves can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of the method used in the present invention;

[0057] Figure 2 is a schematic diagram of the structure of a calculation model in an embodiment of the present invention;

[0058] Figure 3 The electric field component E at the observation point is the same as that of the method of the present invention and the traditional FDTD method. x Time domain waveform comparison chart;

[0059] Figure 4 is the external electric field μ c =0.1eV using the method of the present invention and different FDTD methods and analytical methods to obtain the transmission coefficient amplitude comparison diagram;

[0060] Figure 5 Comparison of the calculation time between the method of the present invention and several other methods; DETAILED DESCRIPTION

[0061] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0062] The present invention is a three-dimensional SBC-HIE-FDTD method for efficiently calculating the electromagnetic field in a graphene dispersive medium. The principle is as follows: first, based on a schematic diagram of a graphene sheet, the Maxwell equations satisfied by the electromagnetic field in the graphene model are obtained; then, the graphene surface conductivity formula approximated by the Drude model in the absence of an external magnetic field and the magnetic field boundary conditions satisfied by the graphene surface are introduced to derive the electromagnetic field update equations for the upper and lower surfaces of the graphene. The electromagnetic field quantities not at the graphene position are updated using the traditional HIE-FDTD method; finally, the electromagnetic field components at the observation point are solved.

[0063] Assume that graphene is placed on On the xoy plane, due to the existence of current and net charge on its surface, there is a pair of tangential magnetic field components (H x and H y ) and a pair of normal electric field components (E z ) distribution. When discretizing using Faraday's law, Maxwell's equations need to be modified based on the location of the graphene. Considering that the graphene is located on a half-space grid in the z direction, a central difference scheme is used for the time and spatial derivatives along the x and y directions (parallel to the surface), and backward and forward difference schemes are used for the spatial derivative along the z direction (perpendicular to the surface).

[0064]

[0065] get:

[0066]

[0067] In order to implement the conductivity model in the HIE-FDTD method, the boundary conditions at the conductive sheet can be written in the frequency domain as:

[0068] represents the unit vector perpendicular to the sheet, 1 H, 2 H is the magnetic field on both sides of the sheet, E t is the tangential component of the electric field on the sheet, σ s is the surface conductivity. Substitute into (5) and convert the expression from frequency domain to time domain, that is, get:

[0069]

[0070] Below is E x Take the iterative formula of the algorithm as an example:

[0071]

[0072] The time step The electric field component value of is approximately represented by the average value of the field values ​​of n+1 and n. Substituting (7) into (1) and (2), we obtain the equation system:

[0073]

[0074] in

[0075]

[0076] Will The function of the field component at time step n+1 / 2 is defined as:

[0077]

[0078] The coefficients involved are as follows:

[0079]

[0080] get 1 H y and 2 H y The final iterative equation is:

[0081]

[0082] Similarly, 1 H x and 2 H x Update equation:

[0083]

[0084]

[0085] At the graphene location, 1 E z and 2 E z The update equation can be obtained by 1 H x 、 2 H x and 1 H y 、 2 H y Using the classic Yee method to obtain

[0086]

[0087] After the introduction of SC-PML, auxiliary variables are used to update the electromagnetic field, and the definition of the time grid of the HIE-FDTD method is used, that is, E is defined. z and H z At half time step, other variables are at full time step, so E x and E y The update equation needs to be adjusted as follows:

[0088]

[0089] There are unknowns on both sides of the equation, so it is initially determined that implicit updates are required. x For example, the auxiliary variables on the right side of the equation can be expanded into the following form

[0090]

[0091]

[0092] Substituting equations (21), (22) and (23) into equation (19), we can obtain E x The implicit update equation of :

[0093] Similarly, the implicit iterative form of Ey is:

[0094]

[0095] Finally, using the obtained graphene upper and lower surface components, the other electromagnetic field components in the calculation domain can be updated.

[0096] The algorithm introduces the graphene surface conductivity model into the three-dimensional HIE-FDTD algorithm, removing the limitation of fine grid in the z direction, so that the grid in the z direction no longer needs to be finely divided, thereby reducing the amount of calculation and improving the calculation efficiency.

[0097] The present invention provides a three-dimensional SBC-HIE-FDTD method for efficiently calculating the electromagnetic field in graphene dispersive media. The specific implementation steps are as follows:

[0098] Step 1 Input the model file, specifically:

[0099] Calculate the area size N x ×N y ×N z , where N x is the number of grids in the x direction, N y is the number of grids in the y direction; N zis the number of grids in the z direction; the spatial step Δζ, ζ = x, y, z, where x is the horizontal coordinate, y is the vertical coordinate, and z is the vertical coordinate; the time step Δt; the electrical conductivity σ, magnetic permeability μ0, and dielectric constant ε0 in vacuum; the absorbing boundary SC-PML and related parameters κ ζmax ,σ ζmax , α ζmax ; Among them, κ ζmax Take an integer, κ ζmax The value range is [1, 60]; α ζmax The value range is [0, 1); the simulation calculation time T f ; Iteration number k, k ≥ 0 and is an integer; Observation point; Field source parameters; Graphene sheet addition position; Graphene sheet parameter σ0, external electromagnetic μ c ; Connection boundary adding position; dielectric layer starting position.

[0100] Step 2: Initialize and set parameters as follows:

[0101] The initialization parameters include:

[0102] The electromagnetic field components (E ζ ,H ζ ,ζ=x,y,z), the auxiliary electromagnetic field components of the entire calculation area (E ζξ ,H ζξ ,ζ=x,y,z,ξ=x,y,z,ζ≠ξ), the incident wave electromagnetic field component of the entire calculation area (E ζ，inc ,H ζ,inc ,ζ=x,y,z、E ζξ，inc ,H ζξ,inc ,ζ=x,y,z,ξ=x,y,z,ζ≠ξ), the electromagnetic field components on the upper and lower surfaces of the graphene sheet and the auxiliary electromagnetic field components ( θ E z , θ H ζ ,ζ=x,y,θ=1,2、 θ E zζ , θ H ζξ ,ζ=x,y,ζ=x,y,θ=1,2), the parameters of the SC-PML absorption boundary (α ζ ,σ ζ , ζ=x,y,z) are initialized to zero; the parameter κ of the SC-PML absorption boundary ζ ζ=x,y,z are initialized to 1;

[0103] The parameters to be set are:

[0104] Set the parameters of the SC-PML absorbing boundary, specifically:

[0105] σ ζ =σ ζmax |ζ-ζ0| m / d m

[0106] κ ζ =1+(κ ζmax -1)|ζ-ζ0| m / d m

[0107] α ζ =α ζmax ζ0 / d

[0108] Where ζ = x, y, z, ζ0 ​​is the position of the PML layer and the non-PML section, d is the thickness of the PML absorption boundary, κ ζmax Take an integer, κ ζmax The value range is [1, 60]; α ζmax The value range is [0, 1); σ ζmax According to σ opt To set, σ ζmax / σ opt The value range is (0, 12]; σ opt =(m+1) / 150πΔζ, where m ranges from [1, 20]. When m is 4, the absorption effect of the boundary is the best. The range of Δζ is λ is the wavelength of the source;

[0109] Set the parameters of auxiliary variables in the SC-PML framework, specifically:

[0110]

[0111] Where ζ=x,y,z,κ ζ , α ζ , σ ζ are all parameters of the SC-PML absorption boundary, ε represents the relative dielectric constant, and Δt represents the time step. Step 3 Update the electric field components E in the x, y, and z directions of the graphene sheet and non-graphene sheet calculation area ζ ,ζ=x,y,z, the specific update formula is as follows:

[0112] Non-graphene sheet calculation area:

[0113]

[0114]

[0115] Graphene sheet calculation area:

[0116]

[0117] Where i represents the i-th computational grid on the horizontal axis, j represents the j-th computational grid on the vertical axis, and k represents the k-th computational grid on the vertical axis. 0ζ , f 1ζ , f 2ζ is the parameter of the SC-PML absorption boundary. ε0 is the dielectric constant in vacuum, and Δt represents the time step. The field source added in step 4 is a Gaussian pulse plane wave excitation source, and its waveform is:

[0118]

[0119] Among them, T c =T d =0.0667ps, which is the field source parameter.

[0120] Step 5 updates and calculates the auxiliary components of the electric field in the x, y, and z directions of the entire calculation area. The specific update formula is as follows:

[0121]

[0122]

[0123] Step 6 Update the x, y, and z magnetic field components H in the calculation area of ​​the graphene sheet and non-graphene sheet ζ ,ζ=x,y,z, the specific update formula is as follows:

[0124] Non-graphene sheet calculation area:

[0125]

[0126] Graphene sheet calculation area:

[0127]

[0128]

[0129] Step 7 updates and calculates the auxiliary components of the magnetic field in the x, y, and z directions of the entire calculation area. The specific update formula is as follows:

[0130]

[0131] Example

[0132] Simulating the propagation characteristics of radio waves in a single-layer graphene sheet

[0133] According to the method steps of the present invention, the model structure is as follows Figure 2As shown in the figure, the grid size is set to Δx = Δy = 100 Δz = 0.25 μm. For the FDTD, SBC-FDTD, HIE-FDTD, and SBC-HIE-FDTD methods, the corresponding time step values ​​are 7.37 × 10 -3 fs, 7.37×10 -3 fs, 0.59fs, and 0.59fs. Graphene is placed on the xy plane of the 200th grid in the z direction, with a chemical potential of 0.1eV, a temperature of Τ = 300K, a scattering time of τ = 29.96fs, and a Gaussian pulse plane wave excitation source with the waveform:

[0134]

[0135] Among them, T c =T d = 0.0667ps. The observation point is placed 10 grids away from the graphene sheet and is located at the center of the xy plane. Figure 3 The electric field components E at the observation point calculated by FDTD, SBC-FDTD, HIE-FDTD and SBC-HIE-FDTD methods are shown in the figure. x The time domain waveform.

[0136] from Figure 3 The results of the proposed dispersive SBC-HIE-FDTD method are consistent with those of the FDTD, SBC-FDTD, and HIE-FDTD methods, demonstrating the correctness and reliability of the dispersive SBC-HIE-FDTD method in graphene. This consistency verifies the accuracy of the new method in simulating electric field components. Furthermore, compared with traditional FDTD, SBC-FDTD, and HIE-FDTD methods, the dispersive SBC-HIE-FDTD method exhibits superior performance when accounting for dispersion effects in graphene. This consistent result provides a reliable foundation for further electromagnetic simulations and research on graphene material properties.

[0137] Figure 4 is in μ c = 0.1eV using different FDTD and analytical methods. The excellent agreement between these curves further demonstrates the validity of the dispersive SBC-HIE-FDTD method. This consistency validates the accuracy of the dispersive SBC-HIE-FDTD method for simulating electromagnetic wave propagation in graphene. Furthermore, compared to other methods and analytical methods, its calculated results demonstrate the validity of the frequency dependence of the transmission coefficient amplitude. This provides a solid foundation for the application of the dispersive SBC-HIE-FDTD method to studying the electromagnetic properties of materials such as graphene. Figure 5The calculation time of the proposed dispersion SBC-HIE-FDTD method and other FDTD methods is shown. It can be seen that the proposed method takes the shortest time and is highly efficient.

Claims

1. A three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media, characterized by The internal mesh of the graphene sheet can be ignored, the time stability condition can be relaxed, and the computational efficiency is high. The specific implementation steps are as follows: Step 1: Input model file; Step 2: Initialize parameters and set parameters; Step 3: Update the electric field components E in the x, y, and z directions of the graphene sheet and non-graphene sheet calculation area ζ ,ζ=x,y,z; Step 4: Add the field source to the electric field component coefficient in the x direction; Step 5: Update and calculate the auxiliary components of the electric field in the x, y, and z directions of the entire calculation area; Step 6: Update the x, y, and z magnetic field components H in the calculation area of ​​the graphene sheet and non-graphene sheet ζ ,ζ=x,y,z; Step 7: Update and calculate the auxiliary components of the magnetic field in the x, y, and z directions of the entire calculation area; Step 8: Determine whether the number of time steps reaches the preset value. If not, return to step 3. If it reaches the preset value, output the calculation result.

2. The three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media according to claim 1, characterized in that: The input model file in step 1 is as follows: Calculate the area size N x ×N y ×N z , where N x is the number of grids in the x direction, N y is the number of grids in the y direction; N z is the number of grids in the z direction; the spatial step Δζ, ζ = x, y, z, where x is the horizontal coordinate, y is the vertical coordinate, and z is the vertical coordinate; the time step Δt; the electrical conductivity σ, magnetic permeability μ0, and dielectric constant ε0 in vacuum; the absorbing boundary SC-PML and related parameters κ ζmax ,σ ζmax , α ζmax ; Among them, κ ζmax Take an integer, κ ζmax The value range is [1, 60]; α ζmax The value range is [0, 1); the simulation calculation time T f ; Iteration number k, k ≥ 0 and is an integer; Observation point; Field source parameters; Graphene sheet addition position; Graphene sheet parameter σ0, external electromagnetic μ c ; Connection boundary adding position; dielectric layer starting position.

3. The three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media according to claim 1, characterized in that: Step 2: Initialize and set parameters as follows: The initialization parameters include: The electromagnetic field components (E ζ ,H ζ ,ζ=x,y,z), the auxiliary electromagnetic field components of the entire calculation area (E ζξ ,H ζξ ,ζ=x,y,z,ξ=x,y,z,ζ≠ξ), the incident wave electromagnetic field component of the entire calculation area (E ζ，inc ,H ζ,inc ,ζ=x,y,z、E ζξ，inc ,H ζξ,inc ,ζ=x,y,z,ξ=x,y,z,ζ≠ξ), the electromagnetic field components on the upper and lower surfaces of the graphene sheet and the auxiliary electromagnetic field components ( θ E z , θ H ζ ,ζ=x,y,θ=1,2、 θ E zζ , θ H ζξ ,ζ=x,y,ζ=x,y,θ=1,2), the parameters of the SC-PML absorption boundary (α ζ ,σ ζ , ζ=x,y,z) are initialized to zero; the parameter κ of the SC-PML absorption boundary ζ ζ=x,y,z are initialized to 1; The parameters to be set are: Set the parameters of the SC-PML absorbing boundary, specifically: s ζ =s ζmax |ζ-ζ0| m / d m k ζ =1+(k ζmax -1)|ζ-ζ0| m / d m a ζ =a ζmax ζ0 / d Where ζ = x, y, z, ζ0 ​​is the position of the PML layer and the non-PML section, d is the thickness of the PML absorption boundary, κ ζmax Take an integer, κ ζmax The value range is [1, 60]; α ζmax The value range is [0, 1); σ ζmax According to σ opt To set, σ ζmax / σ opt The value range is (0, 12]; σ opt =(m+1) / 150πΔζ, where m ranges from [1, 20]. When m is 4, the absorption effect of the boundary is the best. The range of Δζ is λ is the wavelength of the source; Set the parameters of auxiliary variables in the SC-PML framework, specifically: Where ζ=x,y,z,κ ζ , α ζ , σ ζ are the parameters of the SC-PML absorption boundary, ε represents the relative permittivity, and Δt represents the time step.

4. The three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media according to claim 1, characterized in that: Step 3 Update the electric field components E in the x, y, and z directions of the graphene sheet and non-graphene sheet calculation area ζ ,ζ=x,y,z, the specific update formula is as follows: Non-graphene sheet calculation area: Graphene sheet calculation area: Where i represents the i-th computational grid on the horizontal axis, j represents the j-th computational grid on the vertical axis, and k represents the k-th computational grid on the vertical axis. 0ζ , f 1ζ , f 2ζ are the parameters of the SC-PML absorbing boundary. ε0 is the dielectric constant in vacuum, and Δt represents the time step.

5. The three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media according to claim 1, characterized in that: The field source added in step 4 is a Gaussian pulse plane wave excitation source, and its waveform is: Among them, T c =T d =0.0667ps, which is the field source parameter.

6. The three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media according to claim 1, characterized in that: Step 5 updates and calculates the auxiliary components of the electric field in the x, y, and z directions of the entire calculation area. The specific update formula is as follows:

7. According to the three-dimensional SBC-HIE-FDTD method for efficiently calculating the electromagnetic field in a graphene dispersive medium according to claim 1, step 6 updates the x, y, and z directions of the magnetic field components H in the calculation area of ​​the graphene sheet and the non-graphene sheet. ζ ,ζ=x,y,z, the specific update formula is as follows: Non-graphene sheet calculation area: Graphene sheet calculation area:

8. The three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media according to claim 1, characterized in that: Step 7 updates and calculates the auxiliary components of the magnetic field in the x, y, and z directions of the entire calculation area. The specific update formula is as follows:

9. The three-dimensional SBC-HIE-FDTD method for efficiently calculating electromagnetic fields in graphene dispersive media according to claim 1, characterized in that: Step 8 determines whether the total number of time steps reaches the preset value. If not, return to step 3. If it reaches the preset value, output the calculation result.

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