阅读说明：本技术 基于有限厚度手征原子媒质的Faraday偏振转换分析方法 (Finite thickness chiral atomic medium-based Faraday polarization conversion analysis method ) 是由 曾然 黄佳莹 张明月 陈伟强 李浩珍 杨淑娜 李齐良 胡淼 于 2020-07-31 设计创作，主要内容包括：本发明属于光学技术领域,具体涉及基于有限厚度手征原子媒质的Faraday偏振转换分析方法。包括如下步骤：建立有限厚度手征原子媒质的模型；确定电磁波在有限厚度手征原子媒质的电磁特性；确定边界和初始条件；利用传输矩阵法求得电磁波从真空入射到有限厚度手征原子媒质的透射系数；求解有限厚度手征原子媒质模型下的Faraday旋转角。本发明能准确地分析有限厚度手征原子媒介界面的Faraday偏振转换特性。能够准确地反映出手征特性、厚度、入射角、失谐量等对有限手征原子媒介界面的Faraday偏振转换的影响,从而控制电磁波的偏振转换。(The invention belongs to the technical field of optics, and particularly relates to a finite-thickness chiral atomic medium-based Faraday polarization conversion analysis method. The method comprises the following steps: establishing a model of a chiral atomic medium with limited thickness; determining the electromagnetic property of the electromagnetic wave in a chiral atomic medium with limited thickness; determining boundaries and initial conditions; obtaining the transmission coefficient of electromagnetic waves from vacuum to a chiral atomic medium with limited thickness by using a transmission matrix method; and solving the Faraday rotation angle under the finite thickness chiral atomic medium model. The method can accurately analyze the Faraday polarization conversion characteristic of the chiral atomic medium interface with limited thickness. The influence of the chiral characteristics, the thickness, the incident angle, the detuning amount and the like on the Faraday polarization conversion of the finite chiral atomic medium interface can be accurately reflected, so that the polarization conversion of the electromagnetic wave is controlled.)

1. The Faraday polarization conversion analysis method based on the chiral atomic medium with limited thickness is characterized by comprising the following steps of:

s1, establishing a model of chiral atomic media with limited thickness;

s2, determining the electromagnetic property of the chiral atomic medium with limited thickness;

s3, determining a boundary and an initial condition;

s4, obtaining the transmission coefficient of the electromagnetic wave from the vacuum to the chiral atomic medium with finite thickness by using a transmission matrix method;

and S5, solving the Faraday rotation angle under the finite thickness chiral atomic medium model.

2. The Faraday polarization conversion analysis method based on chiral atomic media with finite thickness as claimed in claim 1, wherein step S1 comprises the following steps:

probe light from vacuum: (₁,μ₁) Oblique incidence on a chiral atomic medium of thickness d ((ii))_c,μ_c,κ_EH,κ_HE) An interface xoy plane;

wherein the content of the first and second substances,₁、μ_cis dielectric constant, mu₁、μ_cIs magnetic permeability, κ_EH、κ_HEIs a chiral coefficient; the energy level of the chiral atomic medium adopts a five-energy-level atomic structure, and a control field acts on the chiral atomic medium.

3. The Faraday polarization conversion analysis method based on chiral atomic media with finite thickness as claimed in claim 2, wherein step S2 comprises the following steps:

the constitutive equation of the chiral atomic medium is expressed by adopting a linear relation, and the constitutive equation is as follows:

and (3) correcting the density of the atomic gas by using a Clausius-Mossotti local field, wherein the corrected related parameters are as follows:

wherein N is atomic gas density, alpha_EE,α_EB,α_BEIs a direct poleConversion rate, α_BBIs the cross-coupling polarizability.

4. The Faraday polarization conversion analysis method based on chiral atomic media with finite thickness as claimed in claim 3, wherein step S3 comprises the following steps:

the initial conditions are as follows:

vacuum (₁,μ₁) The medium incident, reflected electric and magnetic field components are:

at the z-0 interface, the refracted and reflected electric and magnetic field components are:

wherein, the superscript ± of E, H indicates that the propagation direction is positive or negative in the z-axis, the subscript c indicates an electromagnetic wave in a chiral atomic medium, the subscript 01 indicates a right-hand circularly polarized wave, and the subscript 02 indicates a left-hand circularly polarized wave;

the electric and magnetic field components of the transmitted wave are as follows:

wherein the content of the first and second substances,

omega is the angular frequency of the incident light, c is the speed of light, theta_i、θ_rAnd theta is the incident angle, the reflection angle and the transmission angle, respectively_±Two refraction angles; the electric field of linearly polarized light is divided into perpendicular and parallel components.

5. The Faraday polarization conversion analysis method based on finite thickness chiral atomic media according to claim 4, wherein the boundary conditions in step S3 are specifically:

wherein the content of the first and second substances,

6. The Faraday polarization conversion analysis method based on finite thickness chiral atomic media according to claim 5, wherein the step S4 comprises the steps of:

the electric field components of incident and reflected electromagnetic waves in the medium are represented by multiplying a Q matrix and the electric field components of the transmitted electromagnetic waves from the chiral atomic medium by using a transmission matrix method, the relation of the electric field components on two sides of the medium is represented by elements of the matrix, and the transmission matrix is obtained:

from the relationship between the incident light and the reflected and transmitted light, the transmission coefficient is calculated as shown in equation (19):

wherein, is₁₁m₂₂-m₁₂m₂₁，t_ijThe first subscript in (1) is the transmitted light polarization mode, t_ijThe second subscript in (1) is the incident light polarization mode.

7. The Faraday polarization conversion analysis method based on finite thickness chiral atomic media according to claim 6, wherein the step S5 comprises the steps of:

when s-polarized light is incident, the angle between the p-component and the s-component of the transmitted light, expressed as matrix elements, is the Faraday rotation angle θ_sFAngle of rotation theta of the Faraday_sFThe tangent value of (A) is:

when p-polarized light is incident, the angle between the s-component and the p-component of the transmitted light expressed by the matrix elements, i.e., the Faraday rotation angle θ_pFAngle of rotation theta of the Faraday_pFThe tangent value of (A) is:

substituting the calculation result of the step S4 into the equations (20) and (21) to obtain the Faraday rotation angle, so as to analyze the Faraday polarization conversion characteristic of the interface of the chiral atomic medium with limited thickness.

Technical Field

The invention belongs to the technical field of optics, and particularly relates to a finite-thickness chiral atomic medium-based Faraday polarization conversion analysis method.

Background

Polarization conversion of electromagnetic waves is a key issue in electromagnetic wave research. Electromagnetic fields can manipulate properties of matter such as absorption, dispersion, and various nonlinear characteristics by controlling the external field. Among various devices for manipulating polarization, a polarization transformer that rotates the polarization state of electromagnetic waves to its cross polarization state is widely used in microwave and optical research, for example, various polarization manipulation devices and circularly polarized antennas. In practical applications, most of the reported efforts to achieve polarization conversion are based on mechanisms that employ anisotropic or chiral structures.

The most obvious feature of the chiral material is that there is cross-coupling between the electric field and the magnetic field, which makes the electromagnetic wave pass through the chiral medium to generate polarized waves with different phase velocities: the left-hand circular polarized wave and the right-hand circular polarized wave generate strong optical rotation. The chiral atomic medium acts on the atomic gas together through the strong laser field and the weak detection field, so that the atomic gas has the similar property with the chiral material. The current research on the optical properties of chiral atomic media focuses on the GH and IF beam displacement effects, the Casimir effect, etc.

For example, the Kerr polarization deflection analysis method based on the aged insulator-chiral medium interface described in chinese patent application No. CN201910226828.1 is performed as follows: s1: establishing a model of an aged insulator-chiral medium interface; s2: determining the electromagnetic characteristics of electromagnetic waves at an insulator-chiral medium interface; s3: determining boundaries and initial conditions; s4: solving a transmission matrix by using the boundary and the initial condition; s5: obtaining the reflection coefficient of the electromagnetic wave from the common medium to the interface of the aged insulator-chiral medium by using a transmission matrix method; s6: and solving the Kerr angle, the polarization deflection rate and the reflected light phase difference under the aged insulator-chiral medium interface model. Although the Kerr polarization deflection characteristic of the aged insulator-chiral medium interface can be accurately analyzed by a method for analyzing the Kerr polarization deflection of the aged insulator-chiral medium interface according to the Kerr angle, the polarization deflection rate and the phase difference of reflected light, the method has the defect that the research object is limited to the insulator-chiral medium rather than a simple chiral medium, and has limitation in application, and in addition, the reflected data influence cannot achieve the purpose of accurately controlling the polarization conversion of electromagnetic waves through the analysis of the Kerr polarization deflection characteristic.

Disclosure of Invention

The invention provides a Faraday polarization conversion analysis method based on a chiral atomic medium with limited thickness, which has flexibility and practicability and can control Faraday polarization conversion, and aims to solve the problems that in the prior art, the optical characteristic research of a chiral medium is concentrated on GH and IF beam displacement effect, Casimir effect and the like, but the polarization property research of the chiral medium is lacked.

In order to achieve the purpose, the invention adopts the following technical scheme:

the Faraday polarization conversion analysis method based on the chiral atomic medium with limited thickness comprises the following steps:

s1, establishing a model of chiral atomic media with limited thickness;

s2, determining the electromagnetic property of the chiral atomic medium with limited thickness;

s3, determining a boundary and an initial condition;

s4, obtaining the transmission coefficient of the electromagnetic wave from the vacuum to the chiral atomic medium with finite thickness by using a transmission matrix method;

and S5, solving the Faraday rotation angle under the finite thickness chiral atomic medium model.

Preferably, step S1 includes the steps of:

probe light from vacuum: (₁,μ₁) Oblique incidence on a chiral atomic medium of thickness d ((ii))_c,μ_c,κ_EH,κ_HE) An interface xoy plane;

wherein the content of the first and second substances,₁、_cis dielectric constant, mu₁、μ_cIs magnetic permeability, κ_EH、κ_HEIs a chiral coefficient; the energy level of the chiral atomic medium adopts a five-energy-level atomic structure, and a control field acts on the chiral atomic medium.

Preferably, step S2 includes the steps of:

the constitutive equation of the chiral atomic medium is expressed by adopting a linear relation, and the constitutive equation is as follows:

and (3) correcting the density of the atomic gas by using a Clausius-Mossotti local field, wherein the corrected related parameters are as follows:

wherein N is atomic gas density, alpha_EE,α_EB,α_BEFor direct polarizability, alpha_BBIs the cross-coupling polarizability.

Preferably, step S3 includes the steps of:

the initial conditions are as follows:

vacuum (₁,μ₁) The medium incident, reflected electric and magnetic field components are:

at the z-0 interface, the refracted and reflected electric and magnetic field components are:

wherein, the superscript ± of E, H indicates that the propagation direction is positive or negative in the z-axis, the subscript c indicates an electromagnetic wave in a chiral atomic medium, the subscript 01 indicates a right-hand circularly polarized wave, and the subscript 02 indicates a left-hand circularly polarized wave;

the electric and magnetic field components of the transmitted wave are as follows:

wherein the content of the first and second substances,

omega is the angular frequency of the incident light, c is the speed of light, theta_i、θ_rAnd theta is the incident angle, the reflection angle and the transmission angle, respectively_±Two refraction angles; the electric field of linearly polarized light is divided into perpendicular and parallel components.

Preferably, the boundary conditions in step S3 are specifically:

wherein the content of the first and second substances,is the normal vector of the surface of the chiral atomic medium.

Preferably, step S4 includes the steps of:

the electric field components of incident and reflected electromagnetic waves in the medium are represented by multiplying a Q matrix and the electric field components of the transmitted electromagnetic waves from the chiral atomic medium by using a transmission matrix method, the relation of the electric field components on two sides of the medium is represented by elements of the matrix, and the transmission matrix is obtained:

from the relationship between the incident light and the reflected and transmitted light, the transmission coefficient is calculated as shown in equation (19):

wherein, is₁₁m₂₂-m₁₂m₂₁，t_ijThe first subscript in (1) is the transmitted light polarization mode, t_ijThe second subscript in (1) is the incident light polarization mode.

Preferably, step S5 includes the steps of:

when s-polarized light is incident, the angle between the p-component and the s-component of the transmitted light, expressed as matrix elements, is the Faraday rotation angle θ_sFAngle of rotation theta of the Faraday_sFThe tangent value of (A) is:

when p-polarized light is incident, the angle between the s-component and the p-component of the transmitted light expressed by the matrix elements, i.e., the Faraday rotation angle θ_pFAngle of rotation theta of the Faraday_pFThe tangent value of (A) is:

substituting the calculation result of the step S4 into the equations (20) and (21) to obtain the Faraday rotation angle, so as to analyze the Faraday polarization conversion characteristic of the interface of the chiral atomic medium with limited thickness.

Compared with the prior art, the invention has the beneficial effects that: (1) the method for analyzing the Faraday polarization conversion of the finite-thickness chiral atomic medium interface according to the Faraday rotation angle can analyze the change of the Faraday angle of the finite-thickness chiral atomic medium interface during s polarization and p polarization; (2) the method can accurately analyze the change trend of finite thickness chiral atomic medium interface Faraday polarization conversion reflected by the chiral characteristics and the thickness change. (3) The method can analyze the condition that the Faraday rotation angle of the chiral atomic medium interface with limited thickness changes along with the incident angle; (4) the method can accurately reflect the detuning amount and the negative extinction coefficient, and has influence on Faraday polarization conversion of the chiral atomic medium interface with limited thickness.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a schematic diagram of a finite thickness chiral atomic media interface model according to the present invention;

FIG. 3 is a diagram of input and output of a system corresponding to the Faraday polarization transformation analysis method based on chiral atomic media with finite thickness according to the present invention;

FIG. 4 is a graph showing the simulation of the Faraday rotation angle varying with the incident angle when s-polarized light with different thicknesses is incident;

FIG. 5 is a graph showing the simulation of the Faraday rotation angle varying with the incident angle when p-polarized light with different thicknesses is incident;

FIG. 6 is a graph showing the simulation of the Faraday rotation angle varying with the incident angle when s-polarized light is incident, with different negative extinction ratio coefficients;

FIG. 7 is a graph showing the simulation of the Faraday rotation angle varying with the incident angle when p-polarized light is incident, with different negative extinction ratio coefficients;

FIG. 8 is a graph showing the simulation of the Faraday rotation angle varying with the incident angle for different detuning amounts of the present invention when s-polarized light is incident;

FIG. 9 is a graph showing the simulation of the Faraday rotation angle with the incident angle when p-polarized light is incident, according to the present invention, with different detuning amounts.

Detailed Description

In order to more clearly illustrate the embodiments of the present invention, the following description will explain the embodiments of the present invention with reference to the accompanying drawings. It is obvious that the drawings in the following description are only some examples of the invention, and that for a person skilled in the art, other drawings and embodiments can be derived from them without inventive effort.