Optical transmission characteristics analysis method and system for uniaxial magnetoelectric coupled atomic gas multilayer structure

Abstract

The present invention relates to an analysis method and system for the optical transmission characteristics of a uniaxial magnetoelectrically coupled atomic gas multilayer structure, the method comprising the following steps: S1, establishing a multilayer periodic structure model of a coherently driven atomic gas medium and a common medium; S2, calculating the expression of the effective parameters of the coherently driven atomic gas medium; S3, using a quaternion vector to represent the electromagnetic wave in the common medium layer, and determining the boundary conditions at the interface of the two material layers; S4, calculating the transmission matrix of the multilayer periodic structure; S5, obtaining the reflection and transmission spectrum of the multilayer periodic structure of the atomic gas medium and the common medium. The coherently driven magnetoelectrically coupled atomic gas medium and the common medium multilayer structure of the present invention has application value as a test model; at the same time, the present invention provides an optical method for analyzing multilayer metamaterial structures based on the transmission matrix calculation method and the quaternion vector method, producing beneficial technical effects.

Description

Technical Field

[0001] The present invention belongs to the field of optical information technology, and in particular relates to an optical transmission characteristic analysis method and system for a uniaxial magnetoelectrically coupled atomic gas multilayer structure. Background Art

[0002] Electromagnetically induced transparency is a coherent optical nonlinear effect. Based on the destructive quantum interference of the transition probability amplitude between atomic states, it allows light to propagate through opaque atomic media. Atomic media are transparent within a narrow spectral window within the absorption line. Extreme dispersion will also occur in the transparent window, which can lead to slow light. In recent years, coherently driven atomic gas media with electromagnetically induced transparency mechanism have attracted extensive attention from researchers at home and abroad. The principle of coherently driven atomic gas media is also to use the quantum coherence between atomic energy levels to produce magnetoelectric cross-coupling and strong chirality. For atomic gas media of multi-level systems (such as five-level energy levels), the sign of the refractive index of the medium can be regulated and its loss absorption can be suppressed at the same time by coherently coupling the electric dipole and the magnetic dipole. The most obvious feature of coherently driven atomic gas media is magnetoelectric cross-coupling. By adjusting the parameters of the coherent driving field, the degree of magnetoelectric cross-coupling can be adjusted, affecting the transmission characteristics of the medium. The atomic gas medium exhibits electromagnetic properties that are significantly different from those of ordinary media for electromagnetic waves, producing a special reflection and transmission spectrum. So far, existing studies have only involved simple interface properties of isotropic atomic gas media. However, if magnetoelectrically coupled atomic gas with uniaxial anisotropy is involved and its complex multilayer structure is used, the reflection and transmission characteristics can be improved, as well as the polarization deflection angle can be increased. Therefore, it is very necessary to analyze the transmission characteristics of the uniaxial anisotropic multilayer structure of magnetoelectrically coupled atomic gas.

[0003] In view of the above technical problems, it is necessary to improve them. Summary of the invention

[0004] Based on the above-mentioned deficiencies in the prior art, the present invention provides a method and system for analyzing the optical transmission characteristics of a uniaxial magneto-electrically coupled atomic gas multilayer structure.

[0005] The coherently driven atomic gas medium and ordinary medium construct a multilayer structure in the present invention, and the process involves a transfer matrix calculation method and a quaternion vector method, which provides a new technical solution for analyzing multilayer metamaterial structures.

[0006] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0007] The optical transmission characteristics analysis method of a uniaxial magnetoelectric coupled atomic gas multilayer structure comprises the following steps:

[0008] S1. Establish a multi-layer periodic structure model of coherently driven atomic gas medium and ordinary medium;

[0009] S2. Calculate the effective parameter expressions in the coherently driven atomic gas medium;

[0010] S3, using quaternion vectors to represent electromagnetic waves in ordinary media and determine the boundary conditions at the interface between two material layers;

[0011] S4, calculating the transmission matrix of the multi-layer periodic structure;

[0012] S5. Solve the reflection and transmission spectra of the multilayer periodic structure constructed by atomic gas medium and ordinary medium.

[0013] As a preferred embodiment, S1, establishing a multi-layer periodic structure model of a coherently driven atomic gas medium and a common medium;

[0014] The structure of the model is a multi-layer periodic structure constructed by anisotropic coherently driven atomic gas medium and ordinary medium. For the sake of convenience, the ordinary medium layer is arranged periodically from left to right, taking the vacuum layer as an example (see Figure 2 ), but the method is still general.

[0015] Among them, the constitutive equation of uniaxial anisotropic atomic gas medium is:

[0016]

[0017]

[0018] in, are the dielectric constant tensor and magnetic permeability tensor of the atomic gas medium, and is the magnetoelectric coupling tensor of the atomic gas medium. For the sake of convenience, the present invention takes the case where the magnetoelectric coupling tensor only contains the longitudinal component as an example for detailed description, that is,

[0019] Constitutive equation in vacuum:

[0020]

[0021] Preferably, S2, an expression for calculating effective parameters of a coherently driven atomic gas medium;

[0022] Using the five-level structure scheme, the Hamiltonian of the system is:

[0023]

[0024] in, and is the electric dipole moment and magnetic dipole moment, E and B are in ω p are the electric and magnetic field components of the weak detection field at the oscillation frequency. Ω1, Ω2 and Ω cThe Rabi frequencies of strongly coupled laser fields are ω1, ω2, ω c .

[0025] The direct polarizability and cross-coupling polarizability are obtained by solving the equations. The detailed expressions are as follows:

[0026]

[0027] Among them, γ ij =(γ i +γ j ) / 2,ΔE=ω 34 -ω p ,ΔB=ω 21 -ω p ,δ c =ω 32 -ω c ,ω uv =ω u -ω v It represents the transition frequency between the energy levels |u> and |v>.

[0028] After considering linear response, non-radiative broadening and local field correction, the dielectric constant and permeability as well as the longitudinal elements of the magneto-electric coupling tensor are:

[0029]

[0030]

[0031]

[0032] in:

[0033]

[0034] The transverse elements of the permittivity and permeability tensors are the permittivity and permeability values ​​of the atomic gas medium environment background, respectively.

[0035] As a preferred embodiment, S3, using quaternion vectors to represent electromagnetic waves in ordinary media, and writing boundary conditions at the interface between two material layers;

[0036] Electromagnetic waves in a vacuum are represented by:

[0037]

[0038] Where, φ = k·r, the superscript + / - indicates the positive / negative direction along the z coordinate, and θ is the incident angle. x represents the electric field component in the x-axis direction, H x represents the magnetic field component in the x-axis direction, E yrepresents the electric field component in the y-axis direction, H y Represents the magnetic field component in the y-axis direction.

[0039] Wave number k in atomic gas medium + and k - The expression is as follows:

[0040]

[0041] Among them, θ + and θ - It is the angle between the transmitted wave and the normal. Combined with the continuity of the electric and magnetic fields on the dielectric interface, k0sinθ=k ± sinθ ± , θ± can be calculated.

[0042] From the electromagnetic field boundary conditions, we know that at the interface junction, the tangential components of the electric field and magnetic field are conserved, so the first interface (z = 0) can be written in matrix form:

[0043]

[0044] The boundary conditions at the second interface (z = d) are written in matrix form:

[0045]

[0046] in,

[0047] As a preferred embodiment, S4, calculate the transmission matrix of the multilayer periodic structure; write the transmission matrix according to the boundary conditions, and the boundary conditions at the first interface of step S4 can be obtained.

[0048]

[0049] The transmission matrix of interface 1 can be defined as:

[0050]

[0051]

[0052] The matrix form of the second interface boundary condition is:

[0053]

[0054]

[0055] It can be concluded that Ψ2=MP c M -1 Ψ1. Where P c is the medium propagation matrix of the atomic gas medium:

[0056]

[0057] Therefore, the transmission matrix of the atomic gas medium single layer structure is: T=MP c M -1 .

[0058] Another way is from Ψ(z=d)=P N Ψ(z=0) can obtain the propagation matrix in vacuum medium:

[0059]

[0060] Among them, k ⊥ =k0cosθ.

[0061] Then it is extended to the multi-layer periodic structure of vacuum-atomic gas medium:

[0062] Ψ n =M n-1 P Cn-1 M n-1 -1 P N M n-1 P Cn-2 M n-1 -1 P N …M1P C1 M1 -1 Ψ1 (21)

[0063] Among them, M n-1 is the transmission matrix from the n-1th layer of medium to the nth layer of medium, P cn-1 is the transfer matrix within the n-1th layer of atomic gas medium.

[0064] Therefore, there is a vacuum-atomic gas medium multilayer periodic structure transmission matrix:

[0065] Τ=M n-1 P Cn-1 M n-1 -1 P N M n-1 P Cn-2 M n-1 -1 P N …M1P C1 M1 -1 (twenty two).

[0066] As a preferred embodiment, S5, find the reflection and transmission spectrum of the multilayer periodic structure constructed by the atomic gas medium and the ordinary medium; taking the transmission matrix when the TE wave is incident as an example, then Substituting into the general vacuum quaternion vector expression, we can get the electromagnetic wave quaternion vector expression of vacuum 1:

[0067]

[0068] In vacuum n, if we only consider the transmitted wave along the +z direction, we can use the four-element vector representation:

[0069]

[0070] According to the Ψ obtained in step 5 t =TΨ1, known transmission matrix:

[0071]

[0072] List the equation:

[0073]

[0074] It can be solved Then r ss 、r sp Substituting back to the right side of the equation, we can get the transmission parameter t ss ,t sp .in:

[0075]

[0076] Similarly, when only the incident TM wave is considered, we can solve Then r ps 、r pp Substituting back to the right side of the equation, we can get the transmission parameter t ps ,t pp .in:

[0077]

[0078] The present invention also discloses an optical transmission characteristic analysis system of a uniaxial magnetoelectrically coupled atomic gas multilayer structure, comprising the following modules:

[0079] Multi-layer periodic structure model building module: build a multi-layer periodic structure model of coherently driven atomic gas medium and ordinary medium structure;

[0080] Calculation module: calculates the effective parameter expressions in the coherently driven atomic gas medium;

[0081] Boundary condition determination module: uses quaternion vectors to represent electromagnetic waves in ordinary media and determines the boundary conditions at the interface between two material layers;

[0082] Transfer matrix calculation module: calculates the transfer matrix of multi-layer periodic structure;

[0083] Reflection and transmission spectrum solving module: solves the reflection and transmission spectrum of multi-layer periodic structures constructed by atomic gas medium and ordinary medium.

[0084] The beneficial effects of the present invention are:

[0085] The uniaxial magneto-electrically coupled atomic gas medium and ordinary medium construct a multilayer structure, which has application value as a test model; at the same time, the present invention involves a calculation method based on a transmission matrix and a quaternion vector method, which provides a new idea for analyzing multilayer metamaterial structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is a flow chart of the analysis method according to an embodiment of the present invention;

[0087] Figure 2 A multi-layer structure model of a coherently driven atomic medium and a vacuum layer according to an embodiment of the present invention;

[0088] Figure 3 The five-level energy structure used in the embodiment of the present invention;

[0089] Figure 4 is a system input and output diagram of an embodiment of the present invention;

[0090] FIG5( a ) is a graph showing the transformation of the reflection coefficient at different incident angles according to an embodiment of the present invention;

[0091] FIG5( b ) is a graph showing the transformation of the transmission coefficient at different incident angles according to an embodiment of the present invention;

[0092] FIG6( a ) is a graph showing the transformation of the reflection coefficient under different numbers of layers according to an embodiment of the present invention;

[0093] FIG6( b ) is a graph showing the transformation of the transmission coefficient under different numbers of layers according to an embodiment of the present invention;

[0094] FIG. 7( a ) is a transformation curve diagram of the reflection coefficient under different control field amplitudes according to an embodiment of the present invention;

[0095] FIG. 7( b ) is a graph showing the transformation of the transmission coefficient under different control field amplitudes according to an embodiment of the present invention;

[0096] Figure 8 4 is a block diagram of an analysis system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0097] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0098] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0099] Embodiment 1:

[0100] like Figure 1 As shown, the analysis method of optical topological transformation based on anisotropic materials and common media to construct a multi-layer periodic structure in this embodiment includes the following steps:

[0101] S1. Establish a multi-layer periodic structure model of coherently driven atomic gas medium and ordinary medium;

[0102] The structure of the model is a multi-layer periodic structure constructed by anisotropic coherently driven atomic gas medium and ordinary medium. In order to facilitate the explanation of this method, the ordinary medium layer is arranged periodically from left to right, taking the vacuum layer as an example, as shown in the figure below: Figure 2 However, the method is still general.

[0103] The constitutive equation of the uniaxial anisotropic atomic gas medium is:

[0104]

[0105]

[0106] in, are the dielectric constant tensor and magnetic permeability tensor of the atomic gas medium, and is the magnetoelectric coupling tensor of the atomic gas medium. For the sake of convenience, the present invention takes the case where the magnetoelectric coupling tensor only contains the longitudinal component as an example for detailed description, that is,

[0107] Constitutive equation in vacuum:

[0108]

[0109] S2. Calculate the expression of effective parameters of coherently driven atomic gas medium;

[0110] like Figure 3 As shown, this embodiment adopts a five-level structure scheme, and the Hamiltonian of the system is:

[0111]

[0112] in, and is the electric dipole moment and magnetic dipole moment, E and B are in ω p are the electric and magnetic field components of the weak detection field at the oscillation frequency. Ω1, Ω2 and Ω c The Rabi frequencies of strongly coupled laser fields are ω1, ω2, ω c .

[0113] The direct polarizability and cross-coupling polarizability are obtained by solving the equations. The detailed expressions are as follows:

[0114]

[0115] Among them, γ ij =(γ i +γ j ) / 2,ΔE=ω 34 -ω p ,ΔB=ω 21 -ω p ,δ c =ω 32 -ω c ,ω uv =ω u -ω v It represents the transition frequency between the energy levels |u> and |v>.

[0116] After considering linear response, non-radiative broadening and local field correction, the dielectric constant and permeability as well as the longitudinal elements of the magneto-electric coupling tensor are:

[0117]

[0118]

[0119]

[0120] in:

[0121]

[0122] The transverse elements of the permittivity and permeability tensors are the permittivity and permeability values ​​of the atomic gas medium environment background, respectively.

[0123] S3. Use quaternion vectors to represent electromagnetic waves in ordinary media and write the boundary conditions at the interface between two material layers;

[0124] Electromagnetic waves in a vacuum are represented by:

[0125]

[0126] Where, φ = k·r, the superscript + / - indicates the positive / negative direction along the z coordinate, and θ is the incident angle. x represents the electric field component in the x-axis direction, H x represents the magnetic field component in the x-axis direction, E y represents the electric field component in the y-axis direction, H y Represents the magnetic field component in the y-axis direction.

[0127] Wave number k in atomic gas medium + and k - The expression is as follows:

[0128]

[0129] Among them, θ + and θ - It is the angle between the transmitted wave and the normal. Combined with the continuity of the electric and magnetic fields on the dielectric interface, k0sinθ=k ± sinθ ± , θ± can be calculated.

[0130] From the electromagnetic field boundary conditions, we know that at the interface junction, the tangential components of the electric field and magnetic field are conserved, so the first interface (z = 0) can be written in matrix form:

[0131]

[0132] The boundary conditions at the second interface (z = d) are written in matrix form:

[0133]

[0134] in,

[0135] S4, calculate the transmission matrix of the multilayer periodic structure; write the transmission matrix according to the boundary conditions, and from the boundary conditions at the first interface of step S4, we can get

[0136]

[0137] The transmission matrix of interface 1 can be defined as:

[0138]

[0139]

[0140] The matrix form of the second interface boundary condition is:

[0141]

[0142]

[0143] It can be concluded that Ψ2=MP c M -1 Ψ1. Where P c is the medium propagation matrix of the atomic gas medium:

[0144]

[0145] Therefore, the transmission matrix of the atomic gas medium single layer structure is: T=MP c M -1 .

[0146] Another way is from Ψ(z=d)=P N Ψ(z=0) can obtain the propagation matrix in vacuum medium:

[0147]

[0148] Among them, k ⊥ =k0cosθ.

[0149] Then it is extended to the multi-layer periodic structure of vacuum-atomic gas medium:

[0150] Ψ n =M n-1 P Cn-1 M n-1 -1 P N M n-1 P Cn-2 M n-1 -1 P N …M1P C1 M1 -1 Ψ1 (21)

[0151] Among them, M n-1 is the transmission matrix from the n-1th layer of medium to the nth layer of medium, P cn-1 is the transfer matrix within the n-1th layer of atomic gas medium.

[0152] Therefore, there is a vacuum-atomic gas medium multilayer periodic structure transmission matrix:

[0153] Τ=M n-1 P Cn-1 M n-1-1 P N M n-1 P Cn-2 M n-1 -1 P N …M1P C1 M1 -1 (twenty two)

[0154] S5. Calculate the reflection and transmission spectrum of the multilayer periodic structure constructed by atomic gas medium and ordinary medium; taking the transmission matrix when TE wave is incident as an example, Substituting into the general vacuum quaternion vector expression, we can get the electromagnetic wave quaternion vector expression of vacuum 1:

[0155]

[0156] In vacuum n, if we only consider the transmitted wave along the +z direction, we can use the four-element vector representation:

[0157]

[0158] According to the Ψ obtained in step 5 t =TΨ1, known transmission matrix:

[0159]

[0160] List the equation:

[0161]

[0162] It can be solved Then r ss 、r sp Substituting back to the right side of the equation, we can get the transmission parameter t ss ,t sp .in:

[0163]

[0164] Similarly, when only the incident TM wave is considered, we can solve Then r ps 、r pp Substituting back to the right side of the equation, we can get the transmission parameter t ps ,t pp .in:

[0165]

[0166] In this embodiment, the system Figure 4As shown, the A end inputs the layer number parameter, the B end inputs the incident angle parameter, the C end inputs the control field amplitude parameter, the D end inputs the frequency, the E end inputs the material thickness, the F end outputs the relationship between the reflection coefficient and each parameter, and the G end outputs the relationship between the transmission coefficient and each parameter.

[0167] In this embodiment, the atomic gas medium parameter is set to ε t =3,μ t =1; atomic density N = 5×10 10 m -3 , detuning amount Δ E =Δ B =Δ=-0.01*γ2, the attenuation rate is γ1=γ4=0, γ3=γ5=137 2 γ2,γ2=10 3 / s, considering the case where the incident wave is a TE wave.

[0168] In Figure 5(a) and Figure 5(b), the number of input layers at the A end is 3, and the input control field at the C end is The frequency range of the incident wave at the D terminal is Input the atomic gas medium thickness d = 10mm at the E end. Input the incident angles θ = 10°, 30°, 60°, and 90° at the B end, and obtain the curves of reflection coefficient and transmission coefficient changing with frequency at different incident angles. As the incident angle increases, the reflection coefficient also increases until the incident angle reaches 90°, the direct reflection coefficient is 1, and the cross reflection coefficient is 0, at which time no polarization deflection occurs; as the incident angle increases, the direct transmission coefficient decreases, and the cross reflection coefficient increases, until the incident angle reaches 90°, and the transmission coefficients are both 0. At a certain frequency, the direct reflection coefficient is 0, while the direct transmission coefficient is close to 1.

[0169] In Figure 6(a) and Figure 6(b), the input incident angle at the B end is θ = 30°, and the input control field at the C end is The frequency range of the incident wave at the D terminal is The thickness of the atomic gas medium input at the E end is d=10mm. The number of layers input at the A end is 1, 3, 5, and 7, respectively, and the reflection coefficient and transmission coefficient change curves with frequency under different numbers of layers are obtained. As the frequency increases, the overall trend of the reflection coefficient increases, and the overall trend of the transmission coefficient decreases. As the number of layers increases, the frequency points where the reflection coefficient appears to be 0 and the direct transmission coefficient appears to be 1 increase, and the frequency points where zero-loss transmission can be achieved increase.

[0170] In Figure 7(a) and Figure 7(b), the number of input layers at end A is 3, the input incident angle at end B is θ=30°, and the frequency range of the input incident wave at end D is The thickness of the atomic gas medium at the E end is d = 10 mm. The amplitude of the control field at the C end is changed to Thus, the magnetoelectric coupling parameters of the material are changed, and the reflection coefficient and transmission coefficient curves with different control field amplitudes are obtained. Under the three-layer structure, as the control field amplitude increases, the cross reflection coefficient and cross transmission coefficient both increase, while the direct reflection coefficient curves and direct transmission coefficient curves with different amplitudes are very close.

[0171] Embodiment 2

[0172] like Figure 8 As shown, this embodiment discloses an optical transmission characteristic analysis system of a uniaxial magnetoelectrically coupled atomic gas multilayer structure, comprising the following modules connected in sequence:

[0173] Multi-layer periodic structure model building module: build a multi-layer periodic structure model of coherently driven atomic gas medium and ordinary medium structure;

[0174] Calculation module: calculates the effective parameter expressions in the coherently driven atomic gas medium;

[0175] Boundary condition determination module: uses quaternion vectors to represent electromagnetic waves in ordinary media and determines the boundary conditions at the interface between two material layers;

[0176] Transfer matrix calculation module: calculates the transfer matrix of multi-layer periodic structures;

[0177] Reflection and transmission spectrum solving module: solves the reflection and transmission spectrum of multi-layer periodic structures constructed by atomic gas medium and ordinary medium.

[0178] In summary, the present invention proposes a technical solution for calculating the reflection and transmission spectra of a uniaxial magneto-electrically coupled atomic gas medium multilayer structure based on the transmission matrix and the quaternion vector method. The present invention relates to a new technical solution for analyzing multilayer and anisotropic metamaterial structures based on the transmission matrix calculation method and the quaternion vector method.

[0179] The above description is only a detailed description of the preferred embodiments and analytical calculations of the present invention. For ordinary technicians in this field, based on the ideas provided by the present invention, the above embodiments can be combined or there may be changes in the specific implementation methods, and these changes should also be regarded as the scope of protection of the present invention.

Claims

1. A method for analyzing the optical transmission characteristics of a uniaxial magnetoelectrically coupled atomic gas multilayer structure, characterized in that: The following steps are involved: S1. Establish a multi-layer periodic structure model of coherently driven atomic gas medium and ordinary medium; S2. Calculate the effective parameter expressions in the coherently driven atomic gas medium; S3, using quaternion vectors to represent electromagnetic waves in ordinary media and determine the boundary conditions at the interface between two material layers; S4, calculating the transmission matrix of the multi-layer periodic structure; S5. Solve the reflection and transmission spectra of the multilayer periodic structure constructed by atomic gas medium and ordinary medium; Step S1 specifically includes: the constitutive equation of the uniaxial anisotropic atomic gas medium is: in, are the dielectric constant tensor and magnetic permeability tensor of the atomic gas medium, and is the magnetoelectric coupling tensor of the atomic gas medium; taking the case where the magnetoelectric coupling tensor only contains the longitudinal component as an example, that is, Constitutive equation in vacuum: Step S2 specifically includes: using a five-level structure scheme, the Hamiltonian of the system is: in, and is the electric dipole moment and magnetic dipole moment, E and B are in ω p are the electric and magnetic field components of the weak detection field at the oscillation frequency; Ω1, Ω2 and Ω c The Rabi frequencies of strongly coupled laser fields are ω1, ω2, ω c ; The direct polarizability and cross-coupling polarizability are obtained by solving the equations. The detailed expressions are as follows: Among them, γ ij =(γ i +γ j ) / 2,ΔE=ω 34 -ω p ,ΔB=ω 21 -ω p ,δ c =ω 32 -ω c ,ω uv =ω u -ω v represents the transition frequency between energy levels |u> and |v>; After considering linear response, non-radiative broadening and local field correction, the dielectric constant and permeability as well as the longitudinal elements of the magneto-electric coupling tensor are: in: The transverse elements of the permittivity and permeability tensors are the permittivity and permeability values ​​of the atomic gas medium environment background, respectively; Step S3 specifically includes: the electromagnetic wave in vacuum is represented by: Where φ = k·r, the superscript + / - indicates the positive / negative direction along the z coordinate, and θ is the incident angle; E x represents the electric field component in the x-axis direction, H x represents the magnetic field component in the x-axis direction, E y represents the electric field component in the y-axis direction, H y represents the magnetic field component in the y-axis direction; Wave number k in atomic gas medium + and k - The expression is as follows: Among them, θ + and θ - is the angle between the transmitted wave and the normal; combined with the continuity requirements of the electric and magnetic fields on the dielectric interface, k0sinθ=k ± sinθ ± , find θ ± ; From the electromagnetic field boundary conditions, we know that at the interface junction, the tangential components of the electric field and magnetic field are conserved, so the first interface, z = 0, is written in matrix form: The boundary condition at the second interface, z = d, is written in matrix form: in, Step 4 specifically includes: writing out the transfer matrix according to the boundary conditions, and obtaining from the boundary conditions at the first interface in step S4: The transmission matrix of interface 1 is defined as: The matrix form of the second interface boundary condition is: It turns out that Ψ2=MP c M -1 Ψ1; where P c is the medium propagation matrix of the atomic gas medium: Therefore, the transmission matrix of the atomic gas medium single layer structure is: T=MP c M -1 ; From z＝d =P N Ψ z＝0 , we get the propagation matrix in vacuum medium: Among them, k ⊥ = k0cosθ; Then it is extended to the multi-layer periodic structure of vacuum-atomic gas medium: Ψ n =M n-1 P Cn-1 M n-1 -1 P N M n-1 P Cn-2 M n-1 -1 P N …M1P C1 M1 -1 Ψ1 (21) Among them, M n-1 is the transmission matrix from the n-1th layer of medium to the nth layer of medium, P cn-1 is the transfer matrix in the n-1th layer of atomic gas medium; Therefore, there is a vacuum-atomic gas medium multilayer periodic structure transmission matrix: T=M n-1 P Cn-1 M n-1 -1 P N M n-1 P Cn-2 M n-1 -1 P N …M1P C1 M1 -1 (22) Step S5 specifically includes: taking the transmission matrix when TE wave is incident as an example, then Substituting into the general vacuum quaternion vector expression, we get the electromagnetic wave quaternion vector expression of vacuum 1: In vacuum n, if we only consider the transmitted wave along the +z direction, we can use the four-element vector representation: According to the Ψ obtained in step 5 t =TΨ1, known transmission matrix: List the equation: Solved Then r ss 、r sp Substituting back to the right side of the equation, we get the transmission parameter t ss ,t sp ;in: Similarly, when only the incident TM wave is considered, the solution is Then r ps 、r pp Substituting back to the right side of the equation, we get the transmission parameter t ps ,t pp ,in:

2. Optical transmission characteristics analysis system of uniaxial magnetoelectric coupled atomic gas multilayer structure, characterized by: Includes the following modules: Multi-layer periodic structure model building module: build a multi-layer periodic structure model of coherently driven atomic gas medium and ordinary medium structure; Calculation module: calculates the effective parameter expressions in the coherently driven atomic gas medium; Boundary condition determination module: uses quaternion vectors to represent electromagnetic waves in ordinary media and determines the boundary conditions at the interface between two material layers; Transfer matrix calculation module: calculates the transfer matrix of multi-layer periodic structures; Reflection and transmission spectrum solving module: solves the reflection and transmission spectrum of multi-layer periodic structures constructed by atomic gas medium and ordinary medium; The multi-layer periodic structure model establishment module is as follows: The constitutive equation of uniaxial anisotropic atomic gas medium is: in, are the dielectric constant tensor and magnetic permeability tensor of the atomic gas medium, and is the magnetoelectric coupling tensor of the atomic gas medium; taking the case where the magnetoelectric coupling tensor only contains the longitudinal component as an example, that is, Constitutive equation in vacuum: The calculation modules are as follows: Using the five-level structure scheme, the Hamiltonian of the system is: in, and is the electric dipole moment and magnetic dipole moment, E and B are in ω p are the electric and magnetic field components of the weak detection field at the oscillation frequency; Ω1, Ω2 and Ω c The Rabi frequencies of strongly coupled laser fields are ω1, ω2, ω c ; The direct polarizability and cross-coupling polarizability are obtained by solving the equations. The detailed expressions are as follows: Among them, γ ij =(γ i +γ j ) / 2,ΔE=ω 34 -ω p ,ΔB=ω 21 -ω p ,δ c =ω 32 -ω c ,ω uv =ω u -ω v represents the transition frequency between energy levels |u> and |v>; After considering linear response, non-radiative broadening and local field correction, the dielectric constant and permeability as well as the longitudinal elements of the magneto-electric coupling tensor are: in: The transverse elements of the permittivity and permeability tensors are the permittivity and permeability values ​​of the atomic gas medium environment background, respectively; The boundary condition determination module is as follows: Electromagnetic waves in a vacuum are represented by: Where φ = k·r, the superscript + / - indicates the positive / negative direction along the z coordinate, and θ is the incident angle; E x represents the electric field component in the x-axis direction, H x represents the magnetic field component in the x-axis direction, E y represents the electric field component in the y-axis direction, H y represents the magnetic field component in the y-axis direction; Wave number k in atomic gas medium + and k - The expression is as follows: Among them, θ + and θ - is the angle between the transmitted wave and the normal; combined with the continuity requirements of the electric and magnetic fields on the dielectric interface, k0sinθ=k ± sinθ ± , find θ ± ; From the electromagnetic field boundary conditions, we know that at the interface junction, the tangential components of the electric field and magnetic field are conserved, so the first interface, z = 0, is written in matrix form: The boundary condition at the second interface, z = d, is written in matrix form: in, The transfer matrix calculation module is as follows: Write out the transfer matrix based on the boundary conditions, obtained from the boundary conditions at the first interface of the transfer matrix calculation module: The transmission matrix of interface 1 is defined as: The matrix form of the second interface boundary condition is: It turns out that Ψ2=MP c M -1 Ψ1; where P c is the medium propagation matrix of the atomic gas medium: Therefore, the transmission matrix of the atomic gas medium single layer structure is: T=MP c M -1 ; From z＝d =P N Ψ z＝0 , we get the propagation matrix in vacuum medium: Among them, k ⊥ = k0cosθ; Then it is extended to the multi-layer periodic structure of vacuum-atomic gas medium: Ψ n =M n-1 P Cn-1 M n-1 -1 P N M n-1 P Cn-2 M n-1 -1 P N …M1P C1 M1 -1 Ψ1 (21) Among them, M n-1 is the transmission matrix from the n-1th layer of medium to the nth layer of medium, P cn-1 is the transfer matrix in the n-1th layer of atomic gas medium; Therefore, there is a vacuum-atomic gas medium multilayer periodic structure transmission matrix: T=M n-1 P Cn-1 M n-1 -1 P N M n-1 P Cn-2 M n-1 -1 P N …M1P C1 M1 -1 (22) The reflection and transmission spectrum solution module is as follows: Taking the transmission matrix when TE wave is incident as an example, Substituting into the general vacuum quaternion vector expression, we get the electromagnetic wave quaternion vector expression of vacuum 1: In vacuum n, if we only consider the transmitted wave along the +z direction, we can use the four-element vector representation: According to the reflection and transmission spectrum solution module, Ψ t =TΨ1, known transmission matrix: List the equation: Solved Then r ss 、r sp Substituting back to the right side of the equation, we get the transmission parameter t ss ,t sp ;in: Similarly, when only the incident TM wave is considered, the solution is Then r ps 、r pp Substituting back to the right side of the equation, we get the transmission parameter t ps ,t pp ,in:

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