A method for calculating the electromagnetic wave reflection coefficient

Abstract

The present disclosure relates to a method for calculating the electromagnetic wave reflection coefficient. The method includes: dividing a non-uniform medium into multiple layers of uniform dielectric plates and establishing a layered dielectric model of the non-uniform medium, wherein the parameters of each layer of the layered dielectric model include: electron density, collision frequency, intrinsic wave impedance, thickness; calculating the electromagnetic wave refraction angle and wave vector in the layered dielectric model according to the parameters of each layer; based on the electromagnetic wave refraction angle and the wave vector of each layer of uniform dielectric, constructing an incident angle judgment vector and a wave vector judgment vector for each layer of uniform dielectric, and calculating the incident depth of the electromagnetic wave in the layered dielectric model. According to the total reflection effect of electromagnetic waves in the non-uniform medium, the present disclosure constructs an incident angle judgment vector and a wave vector judgment vector, introduces the physical effect into the calculation method, and the obtained calculation result is more in line with the actual situation. Especially in the case of sparse data grids and grazing incidence of electromagnetic waves, a robust and accurate method for calculating the reflection coefficient is provided.

Description

Technical Field

[0001] The present disclosure relates to the technical field of electromagnetic wave reflection calculation, and particularly to a method for calculating the electromagnetic wave reflection coefficient. Background Art

[0002] When an aircraft flies at hypersonic speed in the high-altitude atmosphere, the plasma sheath covering the aircraft will interfere with and shield the radar echo signal, resulting in distortion of the signal amplitude and phase, abnormal broadening of the Doppler spectrum, and increasing the difficulty of radar detection.

[0003] In order to analyze the influence degree of the plasma sheath on radar target detection, it is necessary to calculate the reflection coefficient of the plasma sheath to simulate the radar echo signal of the hypersonic aircraft covered by the plasma sheath. The plasma sheath belongs to a non-uniform time-varying charged medium, and it is difficult to obtain data and the data grid is often sparse, which leads to the need for the calculation of the reflection coefficient of the plasma sheath to be inclusive of data.

[0004] The analytical calculation method of the propagation equation is a calculation method for obtaining the propagation characteristics of electromagnetic waves by solving the wave equation of electromagnetic wave propagation. The wave equation is derived from Maxwell's equations and is a differential equation set used to describe the fluctuation characteristics of the electromagnetic field. Since the analytical method can only be applied to non-uniform media with a typical mathematical characteristic of electron density distribution, with the continuous deepening of practical application research, its limitations are increasing day by day. The analytical calculation method of the propagation equation is only applicable to non-uniform media with a typical mathematical characteristic of electron density and does not adapt to the actual application scenario.

[0005] Therefore, it is necessary to provide a new technical solution to improve one or more problems existing in the above solution.

[0006] It should be noted that the information disclosed in the above background art section is only used to strengthen the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0007] The purpose of the present disclosure is to provide a method for calculating the electromagnetic wave reflection coefficient, so as to at least overcome one or more problems caused by the limitations and defects of the related art to a certain extent.

[0008] A method for calculating the electromagnetic wave reflection coefficient provided according to an embodiment of the present disclosure includes:

[0009] Dividing the non-uniform medium into multiple layers of uniform dielectric plates and establishing a layered dielectric model of the non-uniform medium, where each layer parameter of the layered dielectric model includes: electron density, collision frequency, intrinsic wave impedance, thickness;

[0010] Calculate the electromagnetic wave refraction angle and wave vector in the stratified medium model according to the parameters of each layer;

[0011] Based on the electromagnetic wave refraction angle and wave vector of each layer of the homogeneous medium, construct the incident angle judgment vector and wave vector judgment vector of each layer of the homogeneous medium, and calculate the incident depth of the electromagnetic wave in the stratified medium model;

[0012] Obtain the total transmission matrix according to the incident depth;

[0013] Calculate the reflection coefficient of the electromagnetic wave according to the total transmission matrix.

[0014] In the embodiments of the present disclosure, the step of calculating the electromagnetic wave refraction angle and wave vector in the stratified medium model according to the parameters of each layer includes:

[0015] Calculate the oscillation angular frequency of the i-th layer of the homogeneous medium in the stratified medium model according to the electron density of the i-th layer of the homogeneous medium, where the calculation formula for the oscillation angular frequency of the i-th layer of the homogeneous medium in the stratified medium model is:

[0016]

[0017] In the formula, i = 1, 2,..., N, N represents the number of layers of the stratified medium model, e represents the unit charge, m e represents the electron mass, ε0 represents the vacuum permittivity, ω p,i represents the oscillation angular frequency of the i-th layer of the homogeneous medium in the stratified medium model, n e,i represents the electron density of the i-th layer of the homogeneous medium in the stratified medium model.

[0018] In the embodiments of the present disclosure, the step of calculating the electromagnetic wave refraction angle and wave vector in the stratified medium model according to the parameters of each layer includes:

[0019] Calculate the complex permittivity of the i-th layer of the homogeneous medium in the stratified medium model according to the collision frequency and oscillation angular frequency of the i-th layer of the homogeneous medium, where the calculation formula for the complex permittivity of the i-th layer of the homogeneous medium in the stratified medium model is:

[0020]

[0021] In the formula, ω represents the electromagnetic wave angular frequency, v e,i represents the collision frequency of the homogeneous medium of the i-th layer of the stratified medium model, j represents the displacement current density, represents the complex permittivity of the i-th layer of the homogeneous medium in the stratified medium model.

[0022] In an embodiment of the present disclosure, the step of calculating the electromagnetic wave refraction angle and the wave vector in the layered medium model according to the parameters of each layer includes:

[0023] According to the angular frequency and the oscillation angular frequency of the electromagnetic wave of the i-th layer of the homogeneous medium, calculate the refractive index of the i-th layer of the homogeneous medium in the layered medium model, where the calculation formula for the refractive index of the i-th layer of the homogeneous medium in the layered medium model is:

[0024]

[0025] In the formula, n p,i represents the refractive index of the i-th layer of the homogeneous medium in the layered medium model.

[0026] In an embodiment of the present disclosure, the step of calculating the electromagnetic wave refraction angle and the wave vector in the layered medium model according to the parameters of each layer includes:

[0027] According to the refractive index of the i-th layer of the homogeneous medium, calculate the total reflection critical angle and the electromagnetic wave refraction angle of the i-th layer of the homogeneous medium in the layered medium model,

[0028] where the calculation formula for the total reflection critical angle of the i-th layer of the homogeneous medium in the layered medium model is:

[0029]

[0030] In the formula, θ c,i represents the total reflection critical angle of the i-th layer of the homogeneous medium in the layered medium model, and n p,i-1 represents the refractive index of the (i - 1)-th layer of the homogeneous medium in the layered medium model;

[0031] The calculation formula for the electromagnetic wave refraction angle of the i-th layer of the homogeneous medium in the layered medium model is:

[0032]

[0033] In the formula, θ0 represents the electromagnetic wave incident angle, and θ i represents the electromagnetic wave refraction angle of the i-th layer of the homogeneous medium in the layered medium model, and θ i-1 represents the electromagnetic wave refraction angle of the (i - 1)-th layer of the homogeneous medium in the layered medium model.

[0034] In an embodiment of the present disclosure, the step of calculating the electromagnetic wave refraction angle and the wave vector in the layered medium model according to the parameters of each layer includes:

[0035] Calculate the wave vector of the homogeneous medium in the i-th layer of the layered medium model according to the complex dielectric constant of the homogeneous medium in the i-th layer, where the wave vector of the homogeneous medium in the i-th layer of the layered medium model is:

[0036]

[0037] Where represents the wave vector of the homogeneous medium in the i-th layer of the layered medium model, and u0 represents the vacuum permeability.

[0038] In an embodiment of the present disclosure, the incident angle judgment vector of the homogeneous medium in the i-th layer is constructed as:

[0039]

[0040] Where H J (i) represents the incident angle judgment vector of the homogeneous medium in the i-th layer;

[0041] The wave vector judgment vector of the homogeneous medium in the i-th layer is constructed as:

[0042]

[0043] Where K J (i) represents the wave vector judgment vector of the homogeneous medium in the i-th layer.

[0044] In an embodiment of the present disclosure, the calculation formula for the incident depth of the electromagnetic wave in the layered medium model is:

[0045]

[0046] Where L represents the incident depth. When H J (i)·K J (i) = 1, the electromagnetic wave can be incident.

[0047] In an embodiment of the present disclosure, the total transmission matrix is:

[0048]

[0049] Where the transmission matrix of the homogeneous medium in the i-th layer is:

[0050]

[0051] Where represents the propagation constant of the homogeneous medium in the i-th layer, d i represents the thickness of the homogeneous medium in the i-th layer, and Z i represents the intrinsic wave impedance of the i-th layer.

[0052] In an embodiment of the present disclosure, the formula for the reflection coefficient of the electromagnetic wave is as follows:

[0053]

[0054] where Z0 represents the wave impedance of air, and Z L+1 represents the intrinsic wave impedance of the (L + 1)-th layer.

[0055] The technical solution provided by the embodiment of the present disclosure may include the following beneficial effects:

[0056] In an embodiment of the present disclosure, by the above method, according to the parameters of each layer of the stratified medium model of the inhomogeneous medium, the refraction angle and wave vector of the electromagnetic wave of each layer of homogeneous medium are calculated, the incident angle judgment vector and wave vector judgment vector of each layer of homogeneous medium are constructed, the incident depth of the electromagnetic wave in the stratified medium model is calculated, and the total transmission matrix is obtained according to the incident depth, so as to calculate the reflection coefficient of the electromagnetic wave. According to the total internal reflection effect of the electromagnetic wave in the inhomogeneous medium, the incident angle judgment vector and wave vector judgment vector are constructed, and the physical effect is introduced into the calculation method, so that the obtained calculation result is more in line with the actual situation. Especially in the case of sparse data grid and grazing incidence of the electromagnetic wave, a robust and accurate calculation method for the reflection coefficient is provided. Moreover, by first judging the incident depth and then calculating the reflection coefficient, this method abandons unnecessary iterative calculations, greatly reduces the amount of calculation, and effectively improves the calculation performance of the reflection coefficient.

[0057] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present disclosure, and are used together with the specification to explain the principles of the present disclosure. Obviously, the accompanying drawings in the following description are only some embodiments of the present disclosure, and those of ordinary skill in the art can obtain other drawings without creative efforts based on these drawings.

[0059] Figure 1 Schematically showing a flowchart of a method for calculating the reflection coefficient of an electromagnetic wave in an exemplary embodiment of the present disclosure;

[0060] Figure 2 Schematically showing a schematic diagram of the reflection intensity distribution of an electromagnetic wave incident on a plasma sheath obtained by using an equivalent transmission method in a simulation experiment in an exemplary embodiment of the present disclosure;

[0061] Figure 3 Schematically showing a schematic diagram of the reflection intensity distribution of an electromagnetic wave incident on a plasma sheath obtained by using the present invention in a simulation experiment in an exemplary embodiment of the present disclosure;

[0062] Figure 4 Schematically show the reflectivity curves of electromagnetic waves incident on the plasma sheath obtained by using the equivalent transmission line method and the method of the present invention in the simulation experiment in the exemplary embodiments of the present disclosure. Detailed implementation manners

[0063] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be more thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0064] Multiple internal reflections of electromagnetic waves in a multi-layer structure will generate a standing wave pattern in the normal direction. Therefore, the multi-layer structure is equivalent to a cascade of transmission lines with different effective impedances in the normal direction. The equivalent transmission line calculation method is based on a layered model. The non-uniform medium is approximately cut into multiple uniform dielectric plates with different thicknesses according to the electron density distribution profile. These uniform dielectric plates are stacked to form a layered dielectric model. Assuming that each uniform dielectric plate is an impedance, the cascading of multiple impedances is equivalent to the total impedance of the entire layered model, and then the total transmission matrix of the entire layered model is obtained, and finally the reflection coefficient of the electromagnetic wave is obtained. Since the equivalent transmission line calculation method can only give the reflection coefficient of the entire layered dielectric model and cannot reflect the reflection position of the electromagnetic wave in the model, and cannot reflect the total reflection of the electromagnetic wave on the outermost layer when the electromagnetic wave is grazing incident. Therefore, the equivalent transmission line calculation method is not applicable to the grazing incidence phenomenon often occurring in the field of signal processing. The calculation results of the equivalent transmission line calculation method are inaccurate when the data grid is sparse and the electromagnetic wave is grazing incident. Therefore, in the process of calculating the electromagnetic wave reflection coefficient of a non-uniform medium, due to the limitations of the data grid and the incident angle of the electromagnetic wave, the existing various electromagnetic reflection calculation methods have great limitations and are no longer applicable.

[0065] In the present example embodiment, a method for calculating the electromagnetic wave reflection coefficient is first provided. This method is an improved calculation method for the electromagnetic wave reflection coefficient based on the equivalent transmission line. Refer to Figure 1 as shown, this method may include:

[0066] Step S101: Divide the non-uniform medium into multiple uniform dielectric plates and establish a layered dielectric model of the non-uniform medium, where each parameter of the layered dielectric model includes: electron density, collision frequency, intrinsic wave impedance, thickness, electron density.

[0067] Step S102: Calculate the refraction angle and wave vector of the electromagnetic wave in the layered dielectric model according to each parameter.

[0068] Step S103: Based on the refraction angle and wave vector of the electromagnetic wave in each layer of the homogeneous medium, construct the incident angle judgment vector and wave vector judgment vector for each layer of the homogeneous medium, and calculate the incident depth of the electromagnetic wave in the stratified medium model.

[0069] Step S104: Obtain the total transmission matrix according to the incident depth.

[0070] Step S105: Calculate the reflection coefficient of the electromagnetic wave according to the total transmission matrix.

[0071] Through the above method, according to the parameters of each layer of the stratified medium model of the inhomogeneous medium, calculate the refraction angle and wave vector of the electromagnetic wave in each layer of the homogeneous medium, construct the incident angle judgment vector and wave vector judgment vector for each layer of the homogeneous medium, calculate the incident depth of the electromagnetic wave in the stratified medium model, and obtain the total transmission matrix according to the incident depth, so as to calculate the reflection coefficient of the electromagnetic wave. This method constructs the incident angle judgment vector and wave vector judgment vector according to the total reflection effect of the electromagnetic wave in the inhomogeneous medium, introduces the physical effect into the calculation method, and the obtained calculation results are more in line with the actual situation. Especially in the case of sparse data grids and grazing incidence of electromagnetic waves, a robust and accurate method for calculating the reflection coefficient is provided. Moreover, this method first judges the incident depth and then calculates the reflection coefficient, discards unnecessary iterative calculations, greatly reduces the amount of calculation, and effectively improves the calculation performance of the reflection coefficient.

[0072] Next, reference will be made to Figure 1 to describe each step of the above method in the exemplary embodiment in more detail.

[0073] In step S101, the inhomogeneous medium is divided into multiple layers of homogeneous dielectric slabs, and a stratified medium model of the inhomogeneous medium is established. Among them, the parameters of each layer of the stratified medium model include: electron density, collision frequency, intrinsic wave impedance, thickness, electron density. Specifically, according to the electron density distribution of the inhomogeneous medium, it is divided into multiple layers of homogeneous dielectric slabs, and a stratified medium model of the inhomogeneous medium is established. Let i = 1, 2,..., N, where N represents the number of layers of the stratified medium model, and they are arranged in sequence according to the propagation direction of the electromagnetic wave. The parameters of the i-th layer of the stratified medium model include electron density n e,i collision frequency v e,i , intrinsic wave impedance Z i , thickness d iAmong them, electron density, also known as electron ray density, refers to the density of the material where electron rays are scattered. When observing materials with a transmission electron microscope, the denser the material with stronger electron ray scattering ability, the darker it appears in the observation. These parts are generally called high electron density regions. Electron density can reflect the ability of an atom to attract positively charged ions or atomic groups. Electron density represents the probability of finding electrons at specific positions around an atom or molecule. Usually, it is easier to find electrons in regions with high electron density. An atom or group with lower electron density means that certain aspects of the molecular structure are shifting negative charges away. The collision frequency refers to the sum of the number of collisions between electrons and other particles in the ionosphere per unit time. The intrinsic wave impedance, also known as the characteristic impedance, is generally defined as the ratio of the complex amplitudes of the electric field and magnetic field of a uniform plane wave.

[0074] In step S102, calculate the electromagnetic wave refraction angle and wave vector in the stratified medium model according to the parameters of each layer.

[0075] Specifically, according to the electron density n in the parameters of the i-th layer e,i , the collision frequency v e,i , the intrinsic wave impedance Z i , and the thickness d i , calculate the electromagnetic wave refraction angle θ of the i-th layer in the stratified medium model i and the wave vector This is convenient for constructing the incident angle judgment vector and wave vector judgment vector of the homogeneous medium subsequently. The specific calculation method of the electromagnetic wave refraction angle and wave vector of the i-th layer in the stratified medium model will be elaborated later. When an electromagnetic wave is incident on the medium interface, reflection and refraction phenomena will occur. The wave vector is a vector representation of a wave, whose magnitude represents the wave number and whose direction represents the direction of wave propagation.

[0076] In step S103, based on the electromagnetic wave refraction angle and wave vector of each layer of the homogeneous medium, construct the incident angle judgment vector and wave vector judgment vector of each layer of the homogeneous medium, and calculate the incident depth of the electromagnetic wave in the stratified medium model.

[0077] Specifically, through the above calculations, the electromagnetic wave refraction angle θ of the i-th layer of the homogeneous medium i and the wave vector are used to construct the corresponding incident angle judgment vector H of the i-th layer of the homogeneous medium J (i) and the wave vector judgment vector K J (i). Only when both are 1 can the electromagnetic wave be incident. The incident depth L of the electromagnetic wave in the stratified medium model is obtained through a summation operation. And by constructing the incident angle judgment vector H J (i) and the wave vector judgment vector K J(i), introducing physical effects into the calculation method, the obtained calculation results are more in line with the actual situation. Especially in the case of sparse data grids and grazing incidence of electromagnetic waves, the calculation method of the electromagnetic wave reflection coefficient is more robust and accurate during calculation.

[0078] In step S104, according to the incident depth, the total transmission matrix is obtained.

[0079] Specifically, based on the incident depth L of the electromagnetic wave in the stratified medium model obtained above, the total transmission matrix Q of the electromagnetic wave is obtained.

[0080] In step S105, according to the total transmission matrix, the reflection coefficient of the electromagnetic wave is calculated.

[0081] Specifically, through the obtained total transmission matrix Q, the reflection coefficient of the electromagnetic wave in the stratified medium model is calculated This method for calculating the electromagnetic wave reflection coefficient first determines the incident depth L and then calculates the reflection coefficient Unnecessary iterative calculations are discarded, greatly reducing the amount of calculation and effectively improving the calculation performance of the reflection coefficient. Among them, the reflection coefficient is the ratio of the intensity of the reflected light on the surface to the intensity of the incident light when light (incident light) is projected onto an object.

[0082] Optionally, in some embodiments, in the step of calculating the refraction angle and wave vector of the electromagnetic wave in the stratified medium model according to the parameters of each layer, it includes:

[0083] According to the electron density of the i-th layer of the homogeneous medium, the oscillation angular frequency of the i-th layer of the homogeneous medium in the stratified medium model is calculated. Among them, the calculation formula for the oscillation angular frequency of the i-th layer of the homogeneous medium in the stratified medium model is:

[0084]

[0085] In the formula, i = 1, 2,..., N, N represents the number of layers of the stratified medium model, e represents the unit charge, m e represents the electron mass, ε0 represents the vacuum permittivity, ω p,i represents the oscillation angular frequency of the i-th layer of the homogeneous medium in the stratified medium model, n e,i represents the electron density of the i-th layer of the homogeneous medium in the stratified medium model.

[0086] Specifically, according to the electron density n e,i of the i-th layer of the homogeneous medium in the stratified medium model, the electron mass m e unit charge e and vacuum permittivity ε0, the oscillation angular frequency ω of the i-th layer of the homogeneous medium in the stratified medium model is calculated p,i, the angular oscillation frequency ω of the i-th layer of homogeneous medium in the specific stratified medium model p,i The calculation formula is shown in Formula (1). Among them, the vacuum permittivity is an electromagnetic physical constant. In the International System of Units, the value of the vacuum permittivity is: ε0 = 8.854187817×10 -12 F / m (approximate value).

[0087] Optionally, in some embodiments, in the step of calculating the electromagnetic wave refraction angle and wave vector in the stratified medium model according to the parameters of each layer, it includes:

[0088] According to the collision frequency and angular oscillation frequency of the i-th layer of homogeneous medium, calculate the complex permittivity of the i-th layer of homogeneous medium in the stratified medium model. Among them, the calculation formula for the complex permittivity of the i-th layer of homogeneous medium in the stratified medium model is:

[0089]

[0090] In the formula, ω represents the electromagnetic wave angular frequency, v e,i represents the collision frequency of the homogeneous medium of the i-th layer of the stratified medium model, j represents the displacement current density, represents the complex permittivity of the i-th layer of homogeneous medium in the stratified medium model.

[0091] Specifically, according to the angular oscillation frequency ω of the i-th layer of homogeneous medium in the stratified medium model p,i , the electromagnetic wave angular frequency ω, the collision frequency v of the i-th layer of homogeneous medium e,i , the vacuum permittivity ε0 and the displacement current density j, calculate the complex permittivity of the i-th layer of homogeneous medium in the stratified medium model The complex permittivity of the i-th layer of homogeneous medium in the specific stratified medium model The calculation formula is shown in Formula (2).

[0092] Optionally, in some embodiments, in the step of calculating the electromagnetic wave refraction angle and wave vector in the stratified medium model according to the parameters of each layer, it includes:

[0093] According to the electromagnetic wave angular frequency and angular oscillation frequency of the i-th layer of homogeneous medium, calculate the refractive index of the i-th layer of homogeneous medium in the stratified medium model. Among them, the calculation formula for the refractive index of the i-th layer of homogeneous medium in the stratified medium model is:

[0094]

[0095] In the formula, n p,i represents the refractive index of the i-th layer of homogeneous medium in the stratified medium model.

[0096] Specifically, based on the angular frequency ω of the electromagnetic wave and the oscillation angular frequency ω of the i-th layer of homogeneous medium, p,i calculate the refractive index n of the i-th layer of homogeneous medium in the stratified medium model p,i , where the refractive index n of the i-th layer of homogeneous medium in the stratified medium model p,i is calculated according to formula (3) as shown below.

[0097] Optionally, in some embodiments, the step of calculating the refraction angle and wave vector of the electromagnetic wave in the stratified medium model according to the parameters of each layer includes:

[0098] Calculate the total reflection critical angle and the refraction angle of the electromagnetic wave of the i-th layer of homogeneous medium in the stratified medium model according to the refractive index of the i-th layer of homogeneous medium,

[0099] where the calculation formula for the total reflection critical angle of the i-th layer of homogeneous medium in the stratified medium model is:

[0100]

[0101] In the formula, θ c,i represents the total reflection critical angle of the i-th layer of homogeneous medium in the stratified medium model, and n p,i-1 represents the refractive index of the (i - 1)-th layer of homogeneous medium in the stratified medium model;

[0102] The calculation formula for the refraction angle of the electromagnetic wave of the i-th layer of homogeneous medium in the stratified medium model is:

[0103]

[0104] In the formula, θ0 represents the incident angle of the electromagnetic wave, θ i represents the refraction angle of the electromagnetic wave of the i-th layer of homogeneous medium in the stratified medium model, and θ i-1 represents the refraction angle of the electromagnetic wave of the (i - 1)-th layer of homogeneous medium in the stratified medium model.

[0105] Specifically, when i = 1, calculate the refraction angle θ of the electromagnetic wave of the i-th layer of homogeneous medium according to the refractive index n p,i of the i-th layer of homogeneous medium in the stratified medium model; when i > 1, according to the incident angle θ0 of the electromagnetic wave, the refraction angle of the electromagnetic wave of the (i - 1)-th layer of homogeneous medium, the refractive index n i of the i-th layer of homogeneous medium in the stratified medium model and the refractive index n p,i of the (i - 1)-th layer of homogeneous medium, calculate the refraction angle θ p,i-1 of the i-th layer of homogeneous medium, where the refraction angle θ i of the i-th layer of homogeneous medium corresponding to i = 1 and i > 1 iThe calculation formula is as shown in Formula (5).

[0106] Optionally, in some embodiments, in the step of calculating the electromagnetic wave refraction angle and wave vector in the stratified medium model according to the parameters of each layer, it includes:

[0107] According to the complex dielectric constant of the i-th layer of the homogeneous medium, calculate the wave vector of the i-th layer of the homogeneous medium in the stratified medium model, where the wave vector of the i-th layer of the homogeneous medium in the stratified medium model is:

[0108]

[0109] Wherein, represents the wave vector of the i-th layer of the homogeneous medium in the stratified medium model, and u0 represents the vacuum permeability.

[0110] Specifically, according to the angular frequency ω of the electromagnetic wave, the complex dielectric constant of the i-th layer of the homogeneous medium in the stratified medium model, and the vacuum permeability u0, calculate the wave vector of the i-th layer of the homogeneous medium in the stratified medium model. Wherein, when ω > ω p,i the i-th layer of the homogeneous medium is sparser than the vacuum, indicating that the electromagnetic wave can pass through the i-th layer of the homogeneous medium smoothly. At this time, the wave vector of the i-th layer of the homogeneous medium in the stratified medium model. When ω ≤ ω p,i set the wave vector of the i-th layer of the homogeneous medium in the stratified medium model to 0, indicating that the electromagnetic wave cannot propagate in the i-th layer of the homogeneous medium.

[0111] Optionally, in some embodiments, the constructed incident angle judgment vector of the i-th layer of the homogeneous medium is:

[0112]

[0113] Wherein, H J (i) represents the incident angle judgment vector of the i-th layer of the homogeneous medium;

[0114] The constructed wave vector judgment vector of the i-th layer of the homogeneous medium is:

[0115]

[0116] Wherein, K J (i) represents the wave vector judgment vector of the i-th layer of the homogeneous medium.

[0117] Specifically, according to the refraction angle θ i of the electromagnetic wave in the i-th layer of the homogeneous medium and the critical angle θ c,i of total reflection, construct the incident angle judgment vector of the i-th layer of the homogeneous medium. When cosθ i> cosθ c,i When, θ i < θ c,i , that is, the refraction angle θ of the electromagnetic wave in the i-th layer of homogeneous medium i is less than the total reflection critical angle θ of the i-th layer of homogeneous medium c,i , at this time, the electromagnetic wave can continue to propagate in the medium, and the incident angle judgment vector H of the i-th layer of homogeneous medium J (i) is 1, that is, the judgment factor is 1; when cosθ i ≤ cosθ c,i When, θ i ≥ θ c,i , that is, the refraction angle θ of the electromagnetic wave in the i-th layer of homogeneous medium i is greater than or equal to the total reflection critical angle θ of the i-th layer of homogeneous medium c,i , at this time, the electromagnetic wave undergoes total reflection, and the incident angle judgment vector H of the i-th layer of homogeneous medium J (i) is 0, that is, the judgment factor is 0.

[0118] According to the wave vector of the i-th layer of homogeneous medium in the stratified medium model Construct the wave vector judgment vector K of the i-th layer of homogeneous medium J (i). When the wave vector of the i-th layer of homogeneous medium in the stratified medium model is not equal to 0, at this time, the wave vector judgment vector K of the i-th layer of homogeneous medium J (i) is 1; when the wave vector of the i-th layer of homogeneous medium in the stratified medium model is equal to 0, at this time, the wave vector judgment vector K of the i-th layer of homogeneous medium J (i) is 0.

[0119] Optionally, in some embodiments, the calculation formula for the incident depth of the electromagnetic wave in the stratified medium model is:

[0120]

[0121] where L represents the incident depth. When H J (i)·K J (i) = 1, the electromagnetic wave can be incident.

[0122] Specifically, by summing the incident angle judgment vector H of the i-th layer of homogeneous medium J (i) and the wave vector judgment vector K J (i), the incident depth L of the electromagnetic wave in the stratified medium model is obtained. For the i-th layer of homogeneous medium, when the incident angle judgment vector H of the i-th layer of homogeneous medium J (i) and the wave vector judgment vector K J (i) are both 1 at the same time, the electromagnetic wave can be incident, that is, H J (i)·KJ When (i) = 1, electromagnetic waves can be incident, and thus the incident depth L of the electromagnetic waves in the stratified medium model is obtained through summation operation.

[0123] Optionally, in some embodiments, the total transmission matrix is:

[0124]

[0125] Among them, the transmission matrix of the i-th layer of homogeneous medium is:

[0126]

[0127] Among them, represents the propagation constant of the i-th layer of the homogeneous medium, d i represents the thickness of the i-th layer of the homogeneous medium, Z i represents the intrinsic wave impedance of the i-th layer.

[0128] Specifically, according to the propagation constant of the i-th layer of homogeneous medium, the thickness d i of the i-th layer of homogeneous medium, the intrinsic wave impedance Z i of the i-th layer, and the displacement current density j, the transmission matrix of the i-th layer of homogeneous medium is obtained. Based on the transmission matrix of the i-th layer of homogeneous medium, the total transmission matrix Q of the electromagnetic waves in the stratified medium model is obtained.

[0129] Optionally, in some embodiments, the formula for the reflection coefficient of the electromagnetic waves is:

[0130]

[0131] Among them, Z0 represents the wave impedance of air, and Z L+1 represents the intrinsic wave impedance of the (L + 1)-th layer.

[0132] Specifically, according to the total transmission matrix Q of the electromagnetic waves in the stratified medium model, the wave impedance Z0 of air, and the intrinsic wave impedance Z L+1 of the (L + 1)-th layer, the reflection coefficient of the electromagnetic waves is calculated. Since when H J (i)·K JWhen (i) = 1, the electromagnetic wave can be incident, and then the incident depth L of the electromagnetic wave in the stratified medium model can be calculated. During the transmission of the electromagnetic wave, there may be two situations: one is that the product of the incident angle judgment vector and the wave vector judgment vector of each layer is not 1. That is, during the transmission of the electromagnetic wave, in some layers, the electromagnetic wave can pass through the homogeneous medium of that layer smoothly, while in some layers, it cannot propagate in the homogeneous medium of that layer. In this case, the incident depth L of the electromagnetic wave in the stratified medium model is not equal to the number of layers N of the stratified medium model; the other is that the product of the incident angle judgment vector and the wave vector judgment vector of the electromagnetic wave in each layer is 1, that is, during the transmission of the electromagnetic wave, it can pass through smoothly in the homogeneous medium of each layer. In this case, the incident depth L in the stratified medium model is equal to the number of layers N of the stratified medium model. Among them, when the incident depth L in the stratified medium model is not equal to the number of layers N of the stratified medium model, the reflection coefficient of the electromagnetic wave is calculated according to the corresponding formula is When the incident depth L in the stratified medium model is equal to the number of layers N of the stratified medium model, the reflection coefficient of the electromagnetic wave is calculated according to the corresponding formula is

[0133] Through the above method, according to the parameters of each layer of the stratified medium model of the inhomogeneous medium, the refraction angle and wave vector of the electromagnetic wave of each layer of homogeneous medium are calculated, and the incident angle judgment vector and wave vector judgment vector of each layer of homogeneous medium are constructed. The incident depth of the electromagnetic wave in the stratified medium model is calculated, and the total transmission matrix is obtained according to the incident depth, so as to calculate the reflection coefficient of the electromagnetic wave. Based on the total reflection effect of the electromagnetic wave in the inhomogeneous medium, this method constructs the incident angle judgment vector and wave vector judgment vector, introduces the physical effect into the calculation method, and the obtained calculation results are more in line with the actual situation. Especially in the case of sparse data grids and grazing incidence of electromagnetic waves, a robust and accurate method for calculating the reflection coefficient is provided. Moreover, this method first judges the incident depth and then calculates the reflection coefficient, discards unnecessary iterative calculations, greatly reduces the amount of calculation, and effectively improves the calculation performance of the reflection coefficient

[0134] The following further illustrates the embodiments of the present disclosure through simulation experiments

[0135] Simulation experiment 1

[0136] 1) Simulation conditions

[0137] During the simulation process, the frequency of the electromagnetic wave is f = 10 GHz, and the data of the stagnation point of the plasma sheath with a flight altitude of 30 km and a speed of 25 Ma is used

[0138] 2) Simulation content

[0139] The reflection intensity distributions of electromagnetic waves in the plasma sheath are obtained by using the equivalent transmission line method and the present invention respectively. Refer toFigure 2 , which is a schematic diagram of the reflection intensity distribution of electromagnetic waves incident on the plasma sheath obtained by using the equivalent transmission line method in the simulation experiment. Figure 2 In, the horizontal axis represents the incident depth of electromagnetic waves (from 1 to 18), and the vertical axis represents the incident angle of electromagnetic waves (from 0° to 90°), with the unit being degrees. Refer to Figure 3 , which is a schematic diagram of the reflection intensity distribution of electromagnetic waves incident on the plasma sheath obtained by using the present invention in the simulation experiment. Figure 3 In, the horizontal axis represents the incident depth of electromagnetic waves (from 1 to 18), and the vertical axis represents the incident angle of electromagnetic waves (from 0° to 90°), with the unit being degrees. By comparing Figure 2 and Figure 3 , it can be obtained that the present invention can obtain the incident depth of electromagnetic waves in the inhomogeneous medium and the position of the strongest reflection of electromagnetic waves.

[0140] Simulation experiment two:

[0141] 1) Simulation conditions

[0142] During the simulation process, the frequency of electromagnetic waves is f = 10Gz, the incident angle of electromagnetic waves is θ0 = 30°, and the data in the middle section of the plasma sheath with a flight altitude of 30km and a speed of 25Ma is used.

[0143] 2) Simulation content

[0144] The reflection rate curves of electromagnetic waves in the plasma sheath are obtained by using the equivalent transmission line method and the present invention respectively. Refer to Figure 4 , which is the reflection rate curve of electromagnetic waves incident on the plasma sheath obtained by using the equivalent transmission line method and the method of the present invention in the simulation experiment. Figure 4 In, the horizontal axis represents the incident depth of electromagnetic waves (from 1 to 46), and the vertical axis represents the electromagnetic wave reflection rate (from 0 to 1). It can be seen from Figure 4 that the present invention can reflect the electromagnetic shielding phenomenon of the plasma sheath, that is, total reflection occurs at the electromagnetic shielding surface, and the reflection rate is zero behind the shielding surface; in the calculation result of the equivalent transmission line method, the reflection rate no longer changes behind the electromagnetic shielding surface, but the total reflection of electromagnetic waves cannot be reflected, and the shielding effect on electromagnetic waves cannot be reflected.

[0145] Those skilled in the art will readily think of other embodiments of the present disclosure after considering the specification and the practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure, which follow the general principles of the present disclosure and include the common general knowledge or conventional technical means in the technical field not disclosed in the present disclosure. The specification and the embodiments are only regarded as exemplary, and the true scope and spirit of the present disclosure are pointed out by the appended claims.

Claims

1. A method for calculating the electromagnetic wave reflection coefficient, characterized in that, The method includes: Dividing the inhomogeneous medium into multiple homogeneous medium plates and establishing a layered medium model of the inhomogeneous medium. Among them, the parameters of each layer of the layered medium model include: electron density, collision frequency, intrinsic wave impedance, thickness; Calculating the electromagnetic wave refraction angle and wave vector in the layered medium model according to the parameters of each layer; Based on the electromagnetic wave refraction angle and the wave vector of each layer of the homogeneous medium, constructing the incident angle judgment vector and wave vector judgment vector of each layer of the homogeneous medium, and calculating the incident depth of the electromagnetic wave in the layered medium model; Among them, the constructed incident angle judgment vector of the i-th layer of the homogeneous medium is: where \(i = 1, 2, \ldots, N\), \(N\) represents the number of layers of the layered medium model, \(H\) J (i) represents the incident angle judgment vector of the \(i\)-th homogeneous medium, \(\theta\) i represents the electromagnetic wave refraction angle of the \(i\)-th homogeneous medium of the layered medium model, \(\theta\) c,i represents the total reflection critical angle of the \(i\)-th homogeneous medium of the layered medium model; The constructed wave vector judgment vector of the i-th layer of the homogeneous medium is: where, K J (i) represents the wave vector judgment vector of the i-th layer of homogeneous medium, represents the wave vector of the i-th layer of homogeneous medium in the stratified medium model; The calculation formula for the incident depth of the electromagnetic wave in the layered medium model is: Among them, L represents the incident depth, H J (i) represents the incident angle judgment vector of the i-th homogeneous medium, K J (i) represents the wave vector judgment vector of the i-th homogeneous medium. When H J (i)·K J (i) = 1, the electromagnetic wave can be incident; Obtaining the total transmission matrix according to the incident depth; Calculating the reflection coefficient of the electromagnetic wave according to the total transmission matrix.

2. The calculation method of the electromagnetic wave reflection coefficient according to claim 1, wherein, The step of calculating the electromagnetic wave refraction angle and wave vector in the layered medium model according to the parameters of each layer includes: Calculating the oscillation angular frequency of the i-th layer of the homogeneous medium in the layered medium model according to the electron density of the i-th layer of the homogeneous medium. Among them, the calculation formula for the oscillation angular frequency of the i-th layer of the homogeneous medium in the layered medium model is: where \(i = 1, 2, \cdots, N\), \(N\) represents the number of layers of the layered medium model, \(e\) represents a unit charge, \(m\) e represents the electron mass, \(\varepsilon_0\) represents the vacuum permittivity, \(\omega\) p,i represents the angular oscillation frequency of the \(i\)-th homogeneous medium of the layered medium model, \(n\) e,i represents the electron density of the \(i\)-th homogeneous medium of the layered medium model.

3. The calculation method of the electromagnetic wave reflection coefficient according to claim 2, wherein The step of calculating the electromagnetic wave refraction angle and wave vector in the layered medium model according to the parameters of each layer includes: Calculating the complex dielectric constant of the i-th layer of the homogeneous medium in the layered medium model according to the collision frequency and oscillation angular frequency of the i-th layer of the homogeneous medium. Among them, the calculation formula for the complex dielectric constant of the i-th layer of the homogeneous medium in the layered medium model is: Where ω represents the angular frequency of the electromagnetic wave, and v e,i represents the collision frequency of the homogeneous medium of the i-th layer of the stratified medium model, j represents the displacement current density, represents the complex permittivity of the homogeneous medium of the i-th layer of the stratified medium model.

4. The calculation method of the electromagnetic wave reflection coefficient according to claim 3, wherein The step of calculating the electromagnetic wave refraction angle and wave vector in the layered medium model according to the parameters of each layer includes: Calculating the refractive index of the i-th layer of the homogeneous medium in the layered medium model according to the electromagnetic wave angular frequency and oscillation angular frequency of the i-th layer of the homogeneous medium. Among them, the calculation formula for the refractive index of the i-th layer of the homogeneous medium in the layered medium model is: where n p,i represents the refractive index of the i-th homogeneous medium of the layered medium model.

5. The calculation method of the electromagnetic wave reflection coefficient according to claim 4, characterized in that The step of calculating the electromagnetic wave refraction angle and wave vector in the layered medium model according to the parameters of each layer includes: Calculating the total reflection critical angle and electromagnetic wave refraction angle of the i-th layer of the homogeneous medium in the layered medium model according to the refractive index of the i-th layer of the homogeneous medium, Among them, the calculation formula for the total reflection critical angle of the i-th layer of the homogeneous medium in the layered medium model is: where θ c,i represents the total reflection critical angle of the i-th layer of the homogeneous medium in the layered medium model, and n p,i-1 represents the refractive index of the (i - 1)-th layer of the homogeneous medium in the layered medium model; The calculation formula for the electromagnetic wave refraction angle of the i-th layer of the homogeneous medium in the layered medium model is: Where, θ0 represents the incident angle of the electromagnetic wave, and θ i represents the refraction angle of the electromagnetic wave of the i-th layer of the homogeneous medium in the layered medium model, and θ i-1 represents the refraction angle of the electromagnetic wave of the (i-1)-th layer of the homogeneous medium in the layered medium model.

6. The calculation method of the electromagnetic wave reflection coefficient according to claim 5, wherein The step of calculating the electromagnetic wave refraction angle and wave vector in the layered medium model according to the parameters of each layer includes: Calculating the wave vector of the i-th layer of the homogeneous medium in the layered medium model according to the complex dielectric constant of the i-th layer of the homogeneous medium. Among them, the wave vector of the i-th layer of the homogeneous medium in the layered medium model is: Among them, represents the wave vector of the i-th layer of the homogeneous medium in the layered medium model, and u0 represents the vacuum permeability.

7. The calculation method of the electromagnetic wave reflection coefficient according to claim 1, characterized in that The total transmission matrix is: Among them, the transmission matrix of the i-th layer of the homogeneous medium is: wherein, represents the propagation constant of the i-th layer of the homogeneous medium, d i represents the thickness of the i-th layer of the homogeneous medium, Z i represents the intrinsic wave impedance of the i-th layer, and j represents the displacement current density.

8. The calculation method of the electromagnetic wave reflection coefficient according to claim 7, characterized in that The formula for the reflection coefficient of the electromagnetic wave is: Among them, Z0 represents the wave impedance of air, and Z L+1 represents the intrinsic wave impedance of the (L + 1)-th layer.

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