A method for calculating interfacial polarization charge and current distribution based on reflection coefficient

Abstract

The application provides a method for calculating interface polarization charge and current distribution based on reflection coefficient, and relates to the technical field of computational electromagnetics. The method comprises the following steps: establishing a reflection coefficient-dielectric parameter mapping, directly correlating the reflection characteristics of electromagnetic waves with the intrinsic parameters of the medium through a reflection coefficient formula, and laying a physical foundation for polarization analysis; interface electromagnetic field reconstruction, using boundary conditions and constitutive relations to determine the electric field distribution on both sides of the interface and the corresponding polarization intensity. The distribution rule of the electromagnetic field in the medium is determined, the macroscopic electric field is converted into the spatial description of the polarization intensity, and an intermediate variable is provided for charge and current calculation; polarization dynamic response quantification, through the spatial and temporal derivatives of the polarization intensity, the interface polarization charge density and the polarization current density are derived. The theoretical model is converted into actual physical quantities, and the dynamic response mechanism of charges and currents when electromagnetic waves interact with the medium is revealed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computational electromagnetics, and in particular to a method for calculating interface polarization charge and current distribution based on reflection coefficient. BACKGROUND

[0002] In the view of electromagnetics, the medium is also a system of charged particles, and the electromagnetic field formed by the micro-particles inside the medium is stored. Under the action of an external electric field, the polar molecules in the medium will be subjected to a force, and the positive and negative charges will be displaced due to the force, resulting in that the positive and negative charges cannot be completely canceled out, and macroscopic charges, called polarization charges, will be generated. When the medium is polarized, the positive and negative charges of the originally electrically neutral particles are pulled apart. During the pulling-apart process, the positive and negative charges are displaced, that is, there is a current, which is the polarization current.

[0003] At present, the calculation methods for interface charge and current distribution show a trend of "coexistence of multiple methods and still need to develop towards high precision". The most accurate method is to use the density functional theory or time-dependent density functional theory to solve the electron density rearrangement and polarization strength at the interface. Based on the non-equilibrium Green's function framework, the Hamiltonian calculated by the density functional theory is combined to simulate the transmission and reflection of carriers at the nanoscale interface to obtain the current density under the quantum state. However, in practical applications, each step of solving needs to process thousands to tens of thousands of atomic orbitals, and the overall calculation time is very long. In addition, the calculation requires a good command of electromagnetic simulation software and the like, and therefore a calculation method that can reduce the calculation complexity and improve the efficiency can help the engineering design and theoretical teaching to have more development directions for future polarization charge and current distribution.

[0004] The current several methods are mainly divided into different types: the analytical method plays a good role in basic theory and teaching research, but it is limited to simple boundaries and uniform material systems, and it is difficult to handle nonlinear materials and complex geometric device structures. Numerical simulation has become a mainstream tool and is widely used in electromagnetic software environments (such as COMSOL, ANSYS, Lumerical), but it is very dependent on experimental data fitting and does not have universality in unknown environments; the semi-empirical model can quickly predict the performance in engineering practice, and multi-scale simulation has gradually become a key means to understand new interface effects, but its technical threshold is high, the model parameters are complex, and it is difficult to verify the calculation. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides a method for calculating interface polarization charge and current distribution based on reflection coefficient. The method avoids complex microscopic polarization mechanism analysis, closely combines with the basic law of electromagnetic wave propagation while reducing the calculation complexity, and completes the calculation of interface polarization charge and current distribution.

[0006] A method for calculating interface polarization charge and current distribution based on reflection coefficient, comprising the following steps:

[0007] Step S101: Perform reflection coefficient-dielectric parameter mapping; based on the reflection law of electromagnetic waves at the medium interface, an explicit equation of reflection coefficient and medium intrinsic parameter is established, and reflection coefficient data is measured by a vector network analyzer or an optical interferometer.

[0008] Assuming that the two media are linear, uniform, isotropic and non-magnetic under the condition of vertical incidence, the reflection coefficient is calculated; comprising the following steps:

[0009] Step S11: Let the incident wave amplitude E i And the reflected wave amplitude E r The formula (1) is used to calculate the reflection coefficient: ;

[0010] Where E i is the incident wave amplitude, is the reflected wave amplitude;

[0011] Let the intrinsic impedance of the medium , assuming that the medium is non-magnetic, i.e. , then the reflection coefficient under vertical incidence is: ; wherein, μ is the permeability of the medium, ε is the dielectric constant of the medium, 、 is the impedance, is the permeability of medium 1, is the permeability of medium 2, is the value of the permeability, 、 is the dielectric constant of the medium on both sides of the interface;

[0012] Step S12: Refer to the material manual or measure the dielectric constant of the medium on both sides of the interface 、 by a dielectric spectrometer; combine the dielectric constant 、 with the measured reflected wave amplitude , and establish the quantitative relationship between the reflection coefficient and the medium parameters, i.e. formula (2).

[0013] Step S102: Interface electromagnetic field reconstruction;

[0014] First, the total electric field distribution on both sides of the interface is analyzed by using the electromagnetic boundary conditions to determine the superposition field strength characteristics of the incident wave and the reflected wave; then, the polarization intensity vector field at the interface is calculated according to the medium constitutive relation, and the macroscopic electric field distribution is mapped to the spatial gradient function of the polarization intensity;

[0015] Specifically, the total electric field distribution at the interface is analyzed based on the electromagnetic boundary conditions, the electric field components of the incident wave and the reflected wave are superimposed, and the continuity equation of the electric field intensity on both sides of the interface is established; the electric field vector is decomposed by using the medium constitutive relation to calculate the polarization intensity field, and the macroscopic electric field distribution is mapped to the function of the polarization intensity with respect to the electric field intensity and the reflection coefficient through the linear relationship between the polarization intensity and the total electric field.

[0016] The total electric field and the polarization intensity at the interface are calculated, including the following steps:

[0017] Step S21: Calculate the total electric field intensity on the incident side; the total electric field intensity on the incident side is the superposition of the incident wave and the reflected wave, and the total electric field intensity formula (3) on the incident side is obtained: ;

[0018] Step S22: Calculate the total electric field intensity on the transmission side; the total electric field intensity on the transmission side is set as , assuming vertical incidence, the electric field satisfies the boundary condition at the interface, and the normal component of the electric displacement D is continuous, then formula (4) is obtained:

[0019] ; wherein, , are the normal components of the electric displacement vector at the boundary of medium 1 and medium 2 respectively;

[0020] The total electric field intensity on the transmission side is obtained from the following formula (5): ; wherein, is the transmission wave electric field, is the incident wave electric field;

[0021] Step S23: Calculate the polarization intensity P of different media using the relationship formula (6) between the polarization intensity and the electric field: (6); wherein, is the dielectric constant in vacuum;

[0022] The polarization intensity P1 and P2 of medium 1 and medium 2 are obtained from the above formulas respectively, as shown in formulas (7) and (8): , .

[0023] Step S103: Polarization dynamic response quantification;

[0024] The interface polarization charge density distribution function is derived by spatially differentiating the polarization intensity vector field, and then the dynamic response of the polarization current density is calculated synchronously by combining the time derivative characteristics of the polarization intensity under the time-harmonic field condition.

[0025] Specifically, the interface polarization charge density is calculated based on the polarization intensity, the direct correlation between the charge distribution and the dielectric polarization state is established, the polarization current density is calculated by combining the time derivative characteristics of the polarization intensity under the time-harmonic field condition, and the frequency domain expression The dynamic response of the current is quantified synchronously, and the coupling law of the reflection coefficient and the polarization current is revealed.

[0026] The transmission coefficient in the polarization current density expression is converted into the reflection coefficient, and the obtained polarization current expression only contains the reflection coefficient, the dielectric parameters, the electric field and the incident angle information; the polarization charge density and the polarization current density at the interface are derived, which includes the following steps:

[0027] Step S31: The difference between the normal components of the polarization intensities on both sides of the interface is the surface polarization charge density , and the following formula (9) is obtained: ;

[0028] Wherein, n is the unit normal vector;

[0029] The formula (7) and the formula (8) are brought into the formula (9), and the following formula (10) is obtained: ;

[0030] The above formula is simplified to obtain the polarization charge density calculation formula based on the reflection coefficient: ;

[0031] Wherein, is the incident wave amplitude, is the reflection coefficient, and are the dielectric constants of the medium 1 and the medium 2, is the surface polarization charge density;

[0032] Step S32: The polarization current density is the time derivative of the polarization intensity P , that is , assuming that the time-harmonic field , wherein E0 is the complex amplitude of the electric field, then the polarization current is: ; the formula (7) and the formula (8) are brought into the formula (12) and simplified to obtain the polarization current density calculation formula based on the reflection coefficient: ;

[0033] Wherein, f is the frequency of the electromagnetic wave.

[0034] Step S104: Based on the vertical incidence obtained in steps S101-S103 and assuming that the two media are linear, homogeneous, isotropic and non-magnetic, the method for calculating the polarization charge and the polarization current is expanded to the case of oblique incidence of electromagnetic waves to the interface, and the distribution calculation method of the polarization charge and the current is expanded, which comprises the following steps:

[0035] Step S41: Assuming that the electromagnetic wave is incident at an angle Oblique incidence to the medium interface, i.e. from medium 1 to medium 2, assuming that the two media are linear, homogeneous, isotropic and non-magnetic, and according to the polarization direction, it is divided into two cases of transverse electric wave TE polarization and transverse magnetic wave TM polarization for analysis, and the electric field is decomposed into normal, i.e. z direction, and tangential, i.e. x-y plane component;

[0036] Step S42: Calculate the reflection coefficient under TE polarization and decompose the electric field, and the incident wave electric field is represented as: ;

[0037] The reflected wave electric field is represented as: ;

[0038] The transmitted wave electric field is represented as: ;

[0039] Wherein, is the initial electric field amplitude of the incident wave, is the unit vector of the electric field polarization direction, is the wave number in medium 1, is the wave number in medium 2, is the reflection angle, is the refraction angle;

[0040] According to the boundary condition, the tangential electric field is continuous, i.e. , combined with Snell's law , the reflection coefficient is derived as: ;

[0041] Step S43: Calculate the reflection coefficient under TM polarization and decompose the electric field, and the incident wave electric field is represented as: ;

[0042] The reflected wave electric field is represented as: ;

[0043] The transmitted wave electric field is represented as: ;

[0044] Wherein, is the unit vector along the interface direction, is the unit vector perpendicular to the interface direction;

[0045] According to the boundary conditions, the tangential electric field is continuous and the normal electric displacement is continuous, i.e.: ;

[0046] According to Snell's law, the reflection coefficient is: ;

[0047] Step S44: considering the decomposed electric field components, the polarization intensity is calculated; the relationship between the polarization intensity and the electric field intensity is known from formula (6), and in the TE polarization mode, only the tangential electric field The polarization intensities of medium 1 and medium 2 are respectively:

[0048] , ;

[0049] In the TM polarization mode, the relationship between the normal component E z and the tangential component E x is expressed by the polarization intensities P 1 and P 2:

[0050] , ;

[0051] Step S45: calculating the polarization charge and the polarization current; in the TE polarization case, the electric field only has a tangential component, and the normal component E z is 0, and the polarization charge is only generated by the jump of the normal polarization intensity, and the normal polarization charge is:

[0052] ;

[0053] wherein, , is the normal component of the polarization intensity P in the two media, is the normal component of the electric field intensity in the two media;

[0054] Therefore, the TE polarization does not generate an interface polarization charge;

[0055] In the TM polarization case, the electric field has a normal component and a tangential component , and the normal polarization surface charge density is: ;

[0056] Substituting the formula (19) and the formula (20) of the transmission and reflection electric field components, we obtain: ;

[0057] By using Snell's law and simplifying the reflection coefficient, we finally obtain: ;

[0058] wherein, the transmission coefficient , ;

[0059] Step S46: the polarization current of TE polarization and TM polarization is calculated by formula and formula (12);

[0060] In TE polarization mode, the polarization intensity only has a tangential component, and the polarization current is a tangential current, and formula (23) is brought into formula (12) to obtain the polarization current as: ;

[0061] In TM polarization mode, the electric field in the incident plane is divided into a normal component and a tangential component , and for the normal component, the polarization current density is: ;

[0062] Through boundary conditions and reflection coefficient analysis, the final normal polarization current density expression is: ;

[0063] Formula (28) is brought into formula (31) to obtain the complete expression of the normal polarization current density as: ;

[0064] For the tangential component, formula (24) is brought into formula , and the polarization current density is: ;

[0065] Wherein, the transmission coefficient , .

[0066] The beneficial effects generated by the above technical scheme are:

[0067] The application provides a method for calculating interface polarization charge and current distribution based on a reflection coefficient, and the application starts from the reflection coefficient and the dielectric constant, determines the polarization intensity by analyzing the electric field distribution on both sides according to the calculated reflection coefficient and dielectric constant data. Since the method can calculate the interface polarization charge and current distribution under various environments, the method can effectively expand the existing interface polarization charge and current distribution calculation method. Compared with the existing calculation method, the method is based on the dielectric constant and the reflection coefficient for analysis, the analysis process is more concise, has higher efficiency and accuracy, and at the same time, the method mainly calculates the interface polarization charge and current distribution, the experimental device requirement is not high, and the cost of setting the experiment is low.

[0068] Based on the above, the application can directly measure the reflection coefficient based on a vector network analyzer, an optical interferometer, etc., and then calculate the polarization charge and polarization current distribution on the interface in combination with the dielectric constant. Since the method directly relates the complex polarization problem to the interface electromagnetic parameters, it has the advantages of simple theory, friendly experiment and high efficiency of calculation, and therefore can provide a fast and intuitive tool for engineering design and theoretical teaching. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 Flow chart for deriving the polarization charge and current distribution on the interface of the vertically incident electromagnetic wave of the embodiment of the application;

[0070] Figure 2 Flow chart for deriving the polarization charge and current distribution on the interface of the obliquely incident electromagnetic wave;

[0071] Figure 3 Schematic diagram of oblique incidence of electromagnetic wave;

[0072] Wherein (a) is a schematic diagram of TM oblique incidence of parallel polarization wave, and (b) is a schematic diagram of TE oblique incidence of vertical polarization wave. DETAILED DESCRIPTION

[0073] The specific embodiments of the application will be further described in detail below in combination with the drawings and examples. The following examples are used to illustrate the application, but are not used to limit the scope of the application.

[0074] The interface polarization charge and current calculation method of the application directly relates the medium electromagnetic parameters to the reflection coefficient, and inversely calculates the interface polarization distribution based on the amplitude characteristics of the incident wave and the reflected wave. The method directly relates the parameters to the reflection coefficient 、 and the dielectric constant, avoiding the complex grid division and iterative calculation required by the traditional numerical simulation. By introducing the time-harmonic field assumption , the frequency variation characteristics of the polarization current under different frequencies can be quickly analyzed. Under the condition of known reflection coefficient and dielectric constant, only the parameters (dielectric constant or incident frequency) need to be adjusted, and the polarization effect analysis of complex interfaces such as multi-layer medium and composite material can be extended, thereby improving the efficiency and accuracy of engineering design.

[0075] In order to further illustrate the embodiments of the application, the steps of establishing the relationship between the reflection coefficient and the dielectric constant, calculating the total electric field and polarization intensity at the interface, and deriving the polarization charge and polarization current in the application will be divided into steps as shown in Figure 1 、 Figure 2 The specific implementation steps of the method of the application are as follows:

[0076] A method for calculating the interface polarization charge and current distribution based on the reflection coefficient, comprising the following steps:

[0077] Step S101: Perform reflection coefficient-dielectric parameter mapping;

[0078] Based on the reflection law of electromagnetic waves at the interface of the medium, the explicit equation of the reflection coefficient and the intrinsic parameters of the medium (dielectric constant ε, incident angle θ, frequency ω) is established, and the reflection coefficient data is measured by a vector network analyzer or an optical interferometer. Then, the validity of the parameter correlation model is verified by combining the time-harmonic field assumption, and a generalized polarization analysis framework is constructed, which can be extended to multi-layer media and composite materials;

[0079] Specifically, the explicit correlation between the reflection coefficient and the intrinsic parameters of the medium is established according to the Fresnel reflection equation, and the physical basis for polarization effect analysis is constructed. The model validity is verified by measuring the reflection coefficient data with a vector network analyzer or an optical interferometer, and the influence of dielectric parameter dispersion characteristics on the reflection coefficient is corrected to ensure the accuracy of parameter mapping. The explicit correlation between the reflection coefficient and the medium parameters under TE polarization and TM polarization is calculated respectively. From normal incidence to oblique incidence.

[0080] Assuming that the two media are linear, uniform, isotropic and non-magnetic under normal incidence, the reflection coefficient is calculated, which includes the following steps:

[0081] Step S11: Let the incident wave amplitude and the reflected wave amplitude , the reflection schematic diagram is shown in Figure 3 (a) and (b), and the reflection coefficient is calculated using formula (1): ; wherein is the incident wave amplitude, is the reflected wave amplitude;

[0082] Let the intrinsic impedance of the medium , and assume that the medium is non-magnetic, i.e. , then the reflection coefficient under normal incidence is: ; wherein, is the permeability of the medium (H / m), ε is the dielectric constant of the medium (F / m), , is the impedance, is the permeability of medium 1, is the permeability of medium 2, is the value of the permeability, , is the dielectric constant of the medium on both sides of the interface;

[0083] The greater the difference between the dielectric constants of medium 1 and medium 2, the stronger the reflection will be;

[0084] Step S12: Refer to the material manual or perform experimental measurement with a dielectric spectrometer to obtain the dielectric constants of the media on both sides of the interface , ; the dielectric constant , and the measured reflected wave amplitude are combined to establish a quantitative relationship between the reflection coefficient and the medium parameters, i.e., formula (2), to provide input conditions for polarization analysis.

[0085] Step S102: interface electromagnetic field reconstruction;

[0086] First, the total electric field distribution on both sides of the interface is analyzed using the electromagnetic boundary conditions to determine the superposition field intensity characteristics of the incident wave and the reflected wave; then, the polarization intensity vector field at the interface is calculated according to the medium constitutive relation, which maps the macroscopic electric field distribution to the spatial gradient function of the polarization intensity, providing intermediate variables for charge and current calculation.

[0087] Specifically, the total electric field distribution on both sides of the interface is analyzed based on the electromagnetic boundary conditions, the electric field components of the incident wave and the reflected wave are superimposed, and the continuity equation of the electric field intensity on both sides of the interface is established; the electric field vector is decomposed by calculating the interface polarization intensity field using the medium constitutive relation, and the macroscopic electric field distribution is mapped to the function of the polarization intensity with respect to the electric field intensity and the reflection coefficient through the linear relationship between the polarization intensity and the total electric field.

[0088] In the TE polarization mode, the function relationship of the reflection coefficient with respect to the dielectric parameters and the incident angle is derived based on the continuity condition of the tangential electric field combined with Snell's law; in the TM polarization mode, the function relationship of the reflection coefficient with respect to the dielectric parameters and the incident angle is derived based on the continuity conditions of the tangential electric field and the normal electric displacement combined with Snell's law.

[0089] The total electric field and the polarization intensity at the interface are calculated, including the following steps:

[0090] Step S21: calculating the total electric field intensity on the incident side; the total electric field intensity on the incident side is the superposition of the incident wave and the reflected wave, and the total electric field intensity formula (3) on the incident side is obtained:

[0091] ;

[0092] Step S22: calculating the total electric field intensity on the transmitted side; the total electric field intensity on the transmitted side is set as , assuming vertical incidence, the electric field satisfies the boundary conditions at the interface, and the normal component of the electric displacement D is continuous, then formula (4) is obtained: ;

[0093] wherein , are the normal components of the electric displacement vector at the boundary of medium 1 and medium 2, respectively.

[0094] The total electric field intensity on the transmitted side is obtained by the following formula (5): ;

[0095] wherein, is the transmission wave electric field, is the incident wave electric field.

[0096] Step S23: calculate the different medium polarization intensity P using the polarization intensity and electric field relationship formula (6): ;

[0097] wherein, is the dielectric constant in vacuum;

[0098] The polarization intensity P1 and P2 of medium 1 and medium 2 are obtained by the above formula respectively, as shown in formula (7), (8):

[0099] , ;

[0100] Step S103: polarization dynamic response quantization;

[0101] The polarization intensity vector field is subjected to spatial differentiation operation, and the interface polarization charge density distribution function is derived. Then, the polarization current density dynamic response is calculated synchronously in combination with the time derivative characteristics of the polarization intensity under the time-harmonic field condition, and the frequency variation mechanism of charges and currents in the electromagnetic wave and medium interaction process is revealed.

[0102] Specifically: based on the polarization intensity, the interface polarization charge density is calculated, and the direct correlation between the charge distribution and the polarization state of the medium is established; in combination with the time derivative characteristics of the polarization intensity under the time-harmonic field condition, the polarization current density is calculated, and the frequency domain expression synchronous quantization of current dynamic response, revealing the coupling law of reflection coefficient and polarization current;

[0103] The transmission coefficient in the polarization current density expression is converted into the reflection coefficient, and the obtained polarization current expression only contains the reflection coefficient, dielectric parameters, electric field and incident angle information; the polarization charge density and the polarization current density at the interface are derived, which contain the following steps:

[0104] Step S31: the difference between the normal components of the polarization intensities on both sides of the interface is the surface polarization charge density , obtaining the following formula (9): ;

[0105] wherein, n is the unit normal vector; formula (7) and formula (8) are brought into formula (9), obtaining: ;

[0106] Simplify the above formula to get the polarization charge density calculation formula based on the reflection coefficient: ;

[0107] wherein, is the incident wave amplitude, unit: V / m; is the reflection coefficient, dimensionless; and are the dielectric constants of medium 1 and medium 2, unit: F / m; is the surface polarization charge density, unit: C / m 2 ;

[0108] Step S32: Polarization current density is the time derivative of the polarization intensity P , that is , assuming a time-harmonic field , wherein E0 is the complex amplitude of the electric field, then the polarization current is: ;

[0109] Bring formula (7) and formula (8) into formula (12) and simplify to get the polarization current density calculation formula based on the reflection coefficient :

[0110] ;

[0111] wherein, is the electromagnetic wave frequency, unit: Hz.

[0112] Step S104: Based on the vertical incidence obtained in steps S101-S103 and assuming that the two media are linear, uniform, isotropic and non-magnetic, the method for calculating the polarization charge and the polarization current is expanded to the case where the electromagnetic wave is obliquely incident to the interface, and the distribution calculation method of the polarization charge and the current is included. The following steps:

[0113] Step S41: Assume that the electromagnetic wave is obliquely incident to the medium interface at an incident angle , that is, from medium 1 to medium 2, assuming that the two media are linear, uniform, isotropic and non-magnetic, and according to the polarization direction, it is divided into two cases of transverse electric wave TE polarization and transverse magnetic wave TM polarization. The electric field is decomposed into the normal direction, that is, the z direction, and the tangential direction, that is, the x-y plane component;

[0114] Step S42: Calculate the reflection coefficient under TE polarization and decompose the electric field, and the incident wave electric field is represented as: ;

[0115] The reflected wave electric field is represented as: ;

[0116] The transmitted wave electric field is represented as: ;

[0117] where, is the initial electric field amplitude of the incident wave, is the unit vector of the electric field polarization direction, is the wave number in medium 1, is the wave number in medium 2, is the reflection angle, is the refraction angle.

[0118] According to the boundary conditions, the tangential electric field is continuous, i.e. , combined with Snell's law , the reflection coefficient is: ;

[0119] Step S43: Calculate the reflection coefficient under TM polarization and decompose the electric field, the incident wave electric field is represented as: ;

[0120] The reflected wave electric field is represented as: ;

[0121] The transmitted wave electric field is represented as: ;

[0122] where, is the unit vector along the direction of the interface, is the unit vector perpendicular to the direction of the interface.

[0123] According to the boundary conditions, the tangential electric field is continuous and the normal electric displacement is continuous, i.e. ;

[0124] Combined with Snell's law, the reflection coefficient is: ;

[0125] Step S44: Considering the decomposed electric field components, calculate the polarization intensity; the relationship between the polarization intensity and the electric field intensity is known from formula (6), in the TE polarization mode, only the tangential electric field , the polarization intensity of medium 1 and medium 2 is respectively:

[0126] , ;

[0127] In the TM polarization mode, the relationship between the normal component and the tangential component is expressed through the polarization intensity P 1 and P 2:

[0128] , ;

[0129] Step S45: Calculate the polarization charge and the polarization current; the polarization charge density is caused by the abrupt change of the normal component of the polarization intensity according to formula (9). In the TE polarization case, the electric field only has a tangential component, the normal component is 0, and the polarization charge is only caused by the jump of the normal polarization intensity, and the normal polarization charge is: ;

[0130] wherein, , is the normal component of the polarization intensity P in the two media, is the normal component of the electric field intensity in the two media;

[0131] Therefore, the TE polarization does not generate the interface polarization charge.

[0132] In the TM polarization case, the electric field has a normal component and a tangential component , and the normal polarization surface charge density is:

[0133] ;

[0134] Substitute the formula (19) and the formula (20) of the transmission and reflection electric field components to obtain:

[0135] ;

[0136] Simplify by using the Snell's law and the reflection coefficient to finally obtain: ;

[0137] wherein, the transmission coefficient , ;

[0138] Step S46: Calculate the polarization current of the TE polarization and the TM polarization according to the formula and the formula (12);

[0139] In the TE polarization mode, the polarization intensity only has a tangential component, and the polarization current is the tangential current. Substitute the formula (23) into the formula (12) to obtain the polarization current as:

[0140] ;

[0141] In the TM polarization mode, the electric field is divided into a normal component and a tangential component in the incident plane. For the normal component, the polarization current density is:

[0142] ;

[0143] Through the boundary condition and the reflection coefficient analysis, the final normal polarization current density expression is:

[0144] ;

[0145] Substituting equation (28) into equation (31), the complete expression of the normal polarization current density is:

[0146] ;

[0147] For the tangential component, substituting equation (24) into equation , the polarization current density is:

[0148] ;

[0149] where the transmission coefficient , .

[0150] The above description is merely preferred embodiments of the present disclosure and a description of the principles of the technology used. It should be understood by those skilled in the art that the scope of the application involved in the embodiments of the present disclosure is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or equivalent features without departing from the above inventive concept. For example, the above features are replaced with each other to form a technical solution with similar functions disclosed in the embodiments of the present disclosure (but not limited to).

Claims

1. A method for calculating the distribution of interface polarization charge and current based on the reflection coefficient, characterized in that, Includes the following steps: Step S101: Perform reflection coefficient-dielectric parameter mapping; Based on the law of electromagnetic wave reflection at the interface of a medium, an explicit equation is established for the reflection coefficient and the intrinsic parameters of the medium. The reflection coefficient data is measured by a vector network analyzer or an optical interferometer. Step S102: Interface electromagnetic field reconstruction; First, the total electric field distribution on both sides of the interface is analyzed using electromagnetic field boundary conditions to determine the superposition field strength characteristics of the incident and reflected waves. Then, the polarization intensity vector field at the interface is calculated based on the constitutive relation of the medium, and the macroscopic electric field distribution is mapped to the spatial gradient function of the polarization intensity. Step S103: Polarization dynamic response quantization; Spatial differentiation is performed on the polarization intensity vector field to derive the interface polarization charge density distribution function; then, combined with the time derivative characteristics of polarization intensity under time-harmonic field conditions, the dynamic response of polarization current density is calculated simultaneously. Step S104: Based on the method obtained in steps S101-S103 for calculating polarization charge and polarization current under the assumption that the two media are linear, homogeneous, isotropic and nonmagnetic, this method extends the calculation method for the distribution of polarization charge and current when electromagnetic waves are obliquely incident on the interface.

2. The method for calculating interface polarization charge and current distribution based on reflection coefficient according to claim 1, characterized in that, In step S101, assuming the two media are linear, homogeneous, isotropic, and nonmagnetic under perpendicular incidence, the reflection coefficient is calculated; this includes the following steps: Step S11: Set the amplitude of the incident wave E i and reflected wave amplitude E r The reflection coefficient is calculated using formula (1): Γ= E r / E i (1); where E i The amplitude of the incident wave, E r The amplitude of the reflected wave; Let the intrinsic impedance of the medium Assuming the medium is non-magnetic, that is Then the reflection coefficient for perpendicular incidence is: (2); where, μ ε is the magnetic permeability of the medium, and ε is the dielectric constant of the medium. , For impedance, It is the permeability of medium 1. It is the permeability of medium 2. The value of permeability. , denoted as ν, where ν is the dielectric constant of the medium on both sides of the interface. Step S12: Consult the material handbook or perform experimental measurements using a dielectric spectrometer to obtain the dielectric constants of the media on both sides of the interface. , ; Dielectric constant , Compared with the measured amplitude of the reflected wave By combining these factors, a quantitative relationship between the reflection coefficient and the medium parameters is established, namely, formula (2).

3. The method for calculating interface polarization charge and current distribution based on reflection coefficient according to claim 2, characterized in that, Specifically, step S102 involves: analyzing the total electric field distribution at the interface based on electromagnetic boundary conditions; establishing a continuity equation for the electric field intensity on both sides of the interface by superimposing the electric field components of the incident and reflected waves; calculating the interface polarization intensity field using the constitutive relation of the medium; decomposing the electric field vector; and mapping the macroscopic electric field distribution to a function of the polarization intensity with respect to the electric field intensity and reflection coefficient through the linear relationship between the polarization intensity and the total electric field. The calculation of the total electric field and polarization intensity at the interface includes the following steps: Step S21: Calculate the total electric field intensity on the incident side; the total electric field intensity on the incident side is the superposition of the incident wave and the reflected wave, and the formula for the total electric field intensity on the incident side is (3): (3); Step S22: Calculate the total electric field intensity on the transmission side; The total electric field intensity on the transmission side is set as Assuming perpendicular incidence, the electric field satisfies the boundary conditions at the interface, and the normal component of the electric displacement D is continuous, then we have formula (4): (4); among which, , These are the electric displacement vectors at the boundaries of medium 1 and medium 2, respectively. The normal component; The total electric field intensity on the transmission side It can be obtained from the following formula (5): (5); among which, It is the electric field of the transmitted wave. It is the electric field of the incident wave; Step S23: Calculate the polarization intensity P of different media using the formula (6) relating polarization intensity to electric field: (6); among which, Dielectric constant in a vacuum; The polarization intensities P1 and P2 of medium 1 and medium 2 are obtained from formula (6), as shown in formulas (7) and (8): (7), (8).

4. The method for calculating interface polarization charge and current distribution based on reflection coefficient according to claim 3, characterized in that, Specifically, step S103 involves: calculating the interface polarization charge density based on the polarization intensity, establishing a direct correlation between charge distribution and dielectric polarization state; calculating the polarization current density by combining the time derivative characteristics of the polarization intensity under time-harmonic field conditions, and using frequency domain expressions to synchronously quantize the dynamic response of the current, revealing the coupling law between the reflection coefficient and the polarization current. The transmission coefficient in the polarization current density expression is converted into the reflection coefficient, resulting in a polarization current expression containing only the reflection coefficient, dielectric parameter, electric field, and incident angle information. The polarization charge density and polarization current density at the interface are derived, including the following steps: Step S31: The difference between the normal components of the polarization intensity on both sides of the interface is the surface polarization charge density, resulting in the following formula (9): (9); among which, n It is the unit normal vector; Substituting formulas (7) and (8) into formula (9), we get: (10); Simplifying the above equation, we obtain the formula for calculating polarization charge density based on the reflection coefficient: (11); among which, The amplitude of the incident wave, The reflection coefficient, and Let be the dielectric constants of dielectric 1 and dielectric 2. The surface polarization charge density; Step S32: Polarization current density J p polarization intensity P The time derivative, i.e. Assuming a time-harmonic field E=E 0 e j ωt Where E0 is the complex amplitude of the electric field, the polarization current is: (12); Substituting equations (7) and (8) into equation (12) and simplifying, we obtain the formula for calculating the polarization current density based on the reflection coefficient: (13); where f is the electromagnetic wave frequency.

5. The method for calculating interface polarization charge and current distribution based on reflection coefficient according to claim 4, characterized in that, Step S104 includes the following steps: Step S41: Assume that the electromagnetic wave is obliquely incident on the interface of the medium at the incident angle, that is, from medium 1 to medium 2. Assume that the two media are linear, homogeneous, isotropic and nonmagnetic. According to the polarization direction, the two cases are divided into transverse electric wave TE polarization and transverse magnetic wave TM polarization and analyzed separately. The electric field is decomposed into the normal direction, i.e. the z direction, and the tangential direction, i.e. the xy plane component. Step S42: Calculate the reflection coefficient under TE polarization and decompose the electric field. The incident wave electric field is expressed as: (14); The electric field of the reflected wave is expressed as: (15); The electric field of the transmitted wave is represented as: (16); among which, It is the initial electric field amplitude of the incident wave. The unit vector of the electric field polarization direction. Let be the wave number in medium 1. The wave number in medium 2, The angle of reflection, The angle of refraction; Based on the boundary conditions, the tangential electric field is continuous, i.e. Combined with Snell's Law The reflection coefficient was derived. for: (17); Step S43: Calculate the reflection coefficient under TM polarization and decompose the electric field. The incident wave electric field is expressed as: （18）； The electric field of the reflected wave is represented as: (19); The electric field of the transmitted wave is represented as: (20); in, It is a unit vector along the interface direction. It is a unit vector perpendicular to the interface direction; Based on the boundary conditions, the tangential electric field is continuous and the normal electric displacement is continuous, that is: (twenty one); According to Snell's law, the reflection coefficient is: (twenty two); Step S44: Consider the decomposed electric field components and calculate the polarization intensity; the relationship between polarization intensity and electric field intensity is known from formula (6). In the TE polarization mode, only the tangential electric field exists. The polarization intensities of medium 1 and medium 2 are respectively: ， （23）； In TM polarization mode, the normal component E z and tangential component E x The relationship is through polarization intensity P 1 and P 2. Expression: ， （24）； Step S45: Calculate the polarization charge and polarization current; in the case of TE polarization, the electric field has only a tangential component and a normal component E. z Since the polarization charge is 0, it is generated solely by the abrupt change in normal polarization intensity. The normal polarization charge is: (25); in, , Let P be the normal component of the polarization intensity P in the two media. These are the normal components of the electric field intensity in the two media; Therefore, TE polarization does not generate interfacial polarization charge; Under TM polarization, the electric field has a normal component. and tangential components The normal polarization surface charge density is: (26); Substituting into equations (19) and (20) for the transmission and reflection electric field components, we get: (27); Using Snell's law and the reflection coefficient for simplification, we finally obtain: (28); Among them, transmission coefficient , ; Step S46: From the formula The polarization currents for TE polarization and TM polarization modes are calculated using formula (12); In TE polarization mode, the polarization intensity has only a tangential component, and the polarization current is a tangential current. Substituting equation (23) into equation (12), we obtain the polarization current as follows: (29); In TM polarization mode, the electric field is divided into a normal component within the incident plane. and tangential components For the normal component, the polarization current density is: （30）； Based on boundary conditions and reflection coefficient analysis, the final expression for the normal polarization current density is: (31); Substituting equation (28) into equation (31), we obtain the complete expression for the normal polarization current density as follows: (32); For the tangential component, substitute equation (24) into the equation. The polarization current density is: (33); Among them, transmission coefficient , .

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