Application method and system of non-reciprocity polarized light analysis in weak magnetic field measurement

Abstract

The invention discloses an application method and system of non-reciprocity polarized light analysis in weak magnetic field measurement, and mainly relates to the technical field of weak magnetic field measurement. Comprising the following steps: establishing a propagation model of an optical path in a magneto-optical medium based on nonreciprocity of a Faraday magnetic rotation effect; based on the Faraday magneto-optical effect, parallel components of the magnetic field are calculated through the rotation angle in the uniform magnetic field; measuring the spatial distribution of the non-uniform magnetic field by adopting an approximation method; analyzing and judging the polarization property of the light path to obtain elliptically polarized light; and calculating the rotation angle in the elliptically polarized light based on the Malus law. The beneficial effects of the invention are that the method achieves the improvement of the measurement precision, has a wider linear interval, and solves the limitation of directivity.

Description

Technical Field

[0001] The present invention relates to the technical field of weak magnetic field measurement, and in particular to an application method and system of polarized light analysis based on non-reciprocity of Faraday effect in weak magnetic field measurement. Background Art

[0002] Magnetic field is an indispensable physical quantity in modern industrial production, experiments and life. A weak magnetic field refers to a magnetic field generated when the magnetic field strength is small. A weak magnetic field can be generated by current flowing through a conductor or magnet, or by other objects. There is no specific range and definition for a weak magnetic field, but in physical research and daily life, we usually consider a magnetic field below 10mT to be a weak magnetic field.

[0003] The measurement of weak magnetic fields plays a vital role in high-precision experiments and instrument development. Magnetic field sensors, as tools for studying space magnetic fields, play a huge role in the medical field, car navigation, aerospace, industrial automation and other fields. When using the non-reciprocity of the Faraday effect to measure weak magnetic field strength, polarized light undergoes multiple reflections and transmissions, which will cause it to become elliptically polarized light during the propagation process, resulting in inaccurate measurement results of weak magnetic field strength.

[0004] Therefore, a method and system for applying polarization light analysis based on the non-reciprocity of the Faraday effect in weak magnetic field measurement is proposed to solve the above problems. Summary of the invention

[0005] The purpose of the present invention is to provide an application method and system of polarization light analysis based on the non-reciprocity of the Faraday effect in weak magnetic field measurement, which solves the problem of inaccurate measurement results of weak magnetic field intensity caused by elliptically polarized light.

[0006] In order to achieve the above object, the present invention is implemented through the following technical solutions: On the one hand, a method for applying non-reciprocal polarization light analysis in weak magnetic field measurement is provided, comprising the following steps: Based on the non-reciprocity of Faraday magneto-optical effect, a propagation model of light path in magneto-optical medium is established; Based on the Faraday magneto-optical effect, the parallel component of the magnetic field is calculated by the rotation angle in a uniform magnetic field; The spatial distribution of the non-uniform magnetic field is measured using the approximation method; Analyze and judge the polarization properties of the light path itself to obtain elliptically polarized light; The rotation angle in elliptically polarized light is calculated based on Malus's law.

[0007] Preferably, the establishment of the propagation model of the light path in the magneto-optical medium is specifically: using multiple reflections of the light path to increase the propagation distance of the light path in the magneto-optical medium, so as to increase the effective length of the light path and reduce the requirement for the length of the magneto-optical medium.

[0008] Preferably, the rotation angle is recorded as , (1) in, is the magnetic field strength along the propagation direction of linearly polarized light; It is the effective length for the magnetic field to interact with polarized light; It is the Verdet constant of magneto-optical media, which is used to measure the rotation angle of linearly polarized light when it passes through different materials of the same length under the same magnetic field; According to the different directions of the magnetic deflection angle, the deflection angle is based on the right-hand spiral rule to distinguish between positive and negative. Among them, the polarized light rotates clockwise along the propagation direction as positive, that is, ; Polarized light rotates counterclockwise along the propagation direction to be negative, that is .

[0009] Preferably, the method of measuring the spatial distribution of the non-uniform magnetic field by using an approximation method is specifically as follows: Calculate the Faraday rotation angle, which is the weighted integral of the non-uniform magnetic field along the optical path, where the weight coefficient is recorded as , the deflection angle is recorded as , then the relationship between the deflection angle and the non-uniform magnetic field satisfies the formula: (2) Among them, the weight function Satisfy the normalized expression conditions: (3) Calculate the cross-sectional induction angle: (4) in, From the magnetic field, it is circular birefringence; From the stress field, it is linear birefringence; like ;but The calculation of the magnetic field satisfies: (5) like It is not always equal to 0. The medium induction angle and the cross-sectional induction angle satisfy: (6) in, is the weight coefficient function of the medium induction angle, which satisfies the normalization condition. , the magnetic field distribution of the non-uniform magnetic field can be obtained.

[0010] Preferably, the obtaining of elliptically polarized light is specifically: In a non-uniform magnetic field, the medium at different positions has different rotation effects on light, and the two perpendicular components of the light wave obtain different phase delays. The difference in phase delays causes the polarization waveform of the plane to become elliptical, that is, linear polarized light is converted into elliptically polarized light; Construct a rectangular coordinate system to make the two perpendicular components of the elliptically polarized light, and obtain polarized light in the major axis and minor axis directions, where the polarized light in the major axis direction is the x-axis and the light intensity is , the polarized light in the short axis direction is the y axis, and the light intensity is recorded as ; The electric vector amplitude of the x-axis is: (7) The electric vector amplitude of the y-axis is: (8) in, is the angular velocity of the linearly polarized photoelectric vector, is the time that linear polarized light acts in magneto-optical glass; The formula for the synthesized elliptically polarized light is as follows: (9) The intensity relationship of elliptically polarized light is as follows: (10) in, is the vacuum permittivity, is the speed of light, is the magnitude of the electric field vector; Substituting formula (9) into formula (10), the intensity of elliptically polarized light can be expressed as: (11).

[0011] On the other hand, a system for applying non-reciprocal polarization analysis in weak magnetic field measurement is provided, comprising: Model building module, used to: establish the propagation model of the optical path in magneto-optical media based on the non-reciprocity of the Faraday magneto-optical effect; The model analysis module is used to calculate the parallel component of the magnetic field through the rotation angle in a uniform magnetic field based on the Faraday magneto-optical effect, measure the spatial distribution of the non-uniform magnetic field using the approximation method, analyze and judge the polarization properties of the optical path itself, and obtain elliptically polarized light: The model output module calculates the rotation angle in elliptically polarized light based on Malus's law and outputs the result.

[0012] Compared with the prior art, the beneficial effects of the present invention are: The present invention calculates the rotation angle of elliptically polarized light formed by the propagation of polarized light in a non-reciprocal medium, thereby reversely deducing the weak magnetic field strength, thereby solving the problem of inaccurate measurement results of the weak magnetic field strength caused by elliptically polarized light and improving the measurement accuracy of the weak magnetic field strength. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the method of the present invention; Figure 2 Schematic diagram of the non-reciprocity of the Faraday optical rotation effect of the present invention, wherein (a) is a forward schematic diagram and (b) is a reverse schematic diagram; Figure 3 1 is a non-reciprocal demonstration diagram of the Faraday optical rotation effect of the present invention, wherein (a) is a forward demonstration diagram and (b) is a reverse demonstration diagram; Figure 4 is a schematic diagram of the Faraday effect of the present invention; Figure 5 is a schematic diagram of the Fresnel effect of the present invention; Figure 6 It is a schematic diagram of the system structure of the present invention. DETAILED DESCRIPTION

[0014] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the application equally.

[0015] Example: After being emitted by the laser generator, the light passes through the polarizer and becomes linearly polarized light. When the linearly polarized light propagates in the medium, the polarized light passes through the medium for the first time and is reflected by the plane reflector. When it passes through the medium again, the propagation direction of the reflected light is opposite to that of the incident light. According to the non-reciprocity of the Faraday effect, that is, under the action of the magnetic field, the rotation direction of the polarization plane of the light wave is only determined by the direction of the magnetic field, and has nothing to do with the propagation direction of the light. Therefore, the deflection angle direction of the polarized light remains unchanged. After reflection again, there are three light paths in the medium, which is equivalent to an effective length three times the length of the medium. Due to multiple refractions and reflections, the two perpendicular components of the linearly polarized light are affected differently by the medium and produce corresponding phase differences, thereby converting into elliptically polarized light.

[0016] like Figure 1 As shown, this embodiment provides a method for analyzing the polarization of interface reflected light based on the Faraday effect, comprising the following steps: Based on the non-reciprocity of Faraday magneto-optical effect, a propagation model of light path in magneto-optical medium is established; Based on the Faraday magneto-optical effect, the parallel component of the magnetic field is calculated by the rotation angle in a uniform magnetic field; The spatial distribution of the non-uniform magnetic field is measured using the approximation method; Analyze and judge the polarization properties of the light path itself to obtain elliptically polarized light; The rotation angle in elliptically polarized light is calculated based on Malus's law.

[0017] Among them, Figure 2 As shown in the figure, for a left-handed naturally polarized light medium, the linear polarized light is left-handed in both forward and reverse propagation. Then, after the linear polarized light is reflected by the optical medium and returns to the initial position, the vibration direction of the linear polarized light will return to the initial direction. In the Faraday magneto-optical rotation effect, the relationship between the left-handed and right-handed properties of the Faraday magneto-optical rotation and the parallel component of the magnetic field is constant. If the direction of the magnetic field remains unchanged, the direction of the optical rotation remains unchanged. That is, if it is left-handed in forward propagation, it is right-handed in reverse propagation, and the value of the optical rotation angle is the same. This means that under the condition of unchanged magnetic field, if the linear polarized light is reflected after passing through the magneto-optical medium and returns to the initial position, the optical rotation angle of the linear polarized light doubles, as shown in the figure below. Figure 3 As shown, in this embodiment, the theoretical basis for using reflection to increase the number of optical paths is the non-reciprocity of the Faraday magneto-optical effect. Through multiple reflections, the propagation distance of the optical path in the magneto-optical medium is indirectly increased, thereby reducing the length requirement for the magneto-optical medium, providing the possibility to meet the magnetic field at a certain point in the measurement space while reducing the experimental cost.

[0018] The Faraday effect refers to the change in the electromagnetic properties of an optical medium with an inherent magnetic moment under the action of an external magnetic field, which changes the transmission characteristics of light waves inside it. When linearly polarized light passes through a magneto-optical medium placed in a magnetic field along the direction of the magnetic field, its polarization plane rotates, such as Figure 4 As shown, When the propagation distance is fixed, the rotation angle is linearly related to the magnetic field strength, and the rotation angle θ satisfies the formula (1) in, is the magnetic field strength along the propagation direction of linearly polarized light; It is the effective length for the magnetic field to interact with polarized light; It is the Verdet constant of magneto-optical media, which is used to measure the rotation angle of linearly polarized light when it passes through different materials under the same magnetic field. According to the direction of the magnetic deflection angle, the deflection angle is based on the right-hand screw rule and can be positive or negative. The clockwise rotation of polarized light along the propagation direction is positive ( ), counterclockwise along the propagation direction is negative ( ) The Faraday effect describes the phenomenon that the polarization plane of linearly polarized light rotates when passing through a medium under the influence of a magnetic field. In an inhomogeneous magnetic field, this rotation is no longer a simple linear relationship, but is affected by the linear birefringence caused by the stress field in the magneto-optical medium. Without considering the stress field, the equation is satisfied. (2) Since the Faraday magneto-optical effect must include stress field in actual implementation, the phenomenon of birefringence caused by stress field It is inevitable, therefore, the Faraday rotation angle is the weighted integral of the non-uniform magnetic field along the optical path, assuming is the weight coefficient, then the deflection angle The relationship with the non-uniform magnetic field satisfies: (3) Weight function Satisfy the normalized expression conditions: (4) In the calculation of non-uniform magnetic field, the calculation formula of cross-sectional induction angle is: (5) in, From the magnetic field, it is circular birefringence; From the stress field, it is linear birefringence. ;but , indicating that the medium is uniform and the calculation of the magnetic field satisfies formula (2); It is not always equal to 0. The medium induction angle and the cross-sectional induction angle satisfy the relationship: (6) in, is the weight coefficient function of the medium induction angle, which satisfies the normalization condition. , the magnetic field distribution of the non-uniform magnetic field can be obtained.

[0019] Since magneto-optical glass has a certain length, it is impossible to measure the magnetic field strength at a certain point in an absolute sense, so an equivalent magnetic field is introduced. The concept of is used to describe the equivalent magnetic field intensity within the length range of magneto-optical glass: the overall input and output relationship of this physical system under non-uniform magnetic field and equivalent magnetic field is equivalent. The calculation method is as follows: As shown in formula (5), the cross-sectional induction angle is the parallel component of the magnetic field at coordinate x is a function of, so the equivalent circular birefringence It also comes from the magnetic field and is expressed as a function of the magnetic field, namely: (7) in, is the magnetic field coefficient, and the magnetic field In the same direction as the light wave, the phase shift difference and the medium induction angle satisfy the following formula: (8) (9) Combining formulas (8) and (9), we can get that the medium induction angle is a function of the equivalent magnetic field: (10) In this embodiment, the equivalent circular birefringence is calculated by measuring Linear birefringence The equivalent magnetic field within the range of the magneto-optical glass can be obtained by combining formulas (7)-(10). In this embodiment, the magneto-optical glass is moved 0.5 cm or less in the non-uniform magnetic field each time, and the approximation method can be used to measure the spatial distribution of the non-uniform magnetic field.

[0020] In an inhomogeneous magnetic field, due to the inhomogeneity of the magnetic field, the medium at different positions has different rotation effects on light, resulting in different phase delays for the two perpendicular components of the light wave. This difference in phase delay causes the original plane polarization waveform to become elliptical, that is, linear polarization light is converted into elliptically polarized light. By constructing a rectangular coordinate system, the two perpendicular components of the elliptically polarized light, that is, the linear polarization photoelectric vectors in the major axis and minor axis directions, vibrate along the x-axis and y-axis respectively, and they propagate along the z-axis. The two linearly polarized light waves have the same frequency, but they have different amplitudes and phase differences. The polarized light represented by the long axis has a vibration direction that is not in the same plane as the propagation direction of light. The speed and refractive index of the polarized light will change with the change of the vibration direction. Here we set it as the x-axis and record the light intensity as ; The polarized light represented by the short axis has a vibration direction in the same plane as the propagation direction of light. The speed and refractive index will not change with the change of the vibration direction. Here we set it as the y-axis and record the light intensity as , the electric vector amplitudes in these two directions are described by formulas (11) and (12): (11) (12) in, is the angular velocity of the linearly polarized photoelectric vector, is the time that linear polarized light acts in magneto-optical glass. Since the separated electric vectors can be synthesized to represent elliptically polarized light, the formula for synthesized elliptically polarized light is as follows: (13) The intensity relationship formula of elliptically polarized light is shown as follows: (14) in, is the vacuum permittivity, is the speed of light, is the modulus of the electric field vector. Substituting formula (13) into formula (14), the intensity of elliptically polarized light can be expressed as: (15) Based on the assumption that light is a transverse wave, the incident light is orthogonally decomposed into two components: one is the linearly polarized light with the vibration plane parallel to the incident plane, recorded as s polarization; the other is the linearly polarized light with the vibration plane perpendicular to the incident plane, recorded as p polarization, such as Figure 5 As shown in the figure, the light intensity is represented by the electric vector, and the electric vector amplitudes of the incident light, reflected light, and refracted light are respectively expressed as , , The corresponding components parallel to the incident plane (p light) and perpendicular to the incident plane (s light) are expressed as , , and , , ,use , , Mark the angle of incidence, angle of reflection, and angle of refraction. According to the boundary conditions and the laws of reflection and refraction of light, the Fresnel formula is as follows: (16) (17) (18) (19) Formulas (16) and (17) represent the ratio of the vertical and horizontal components of the electric vector amplitude corresponding to the reflected light to the vertical and horizontal components of the electric vector amplitude corresponding to the incident light; Formulas (18) and (19) represent the ratio of the vertical and horizontal components of the electric vector amplitude corresponding to the refracted light to the vertical and horizontal components of the electric vector amplitude corresponding to the incident light. Since the incident angle is not the Brewster angle, the reflection coefficient of the p-wave is not 0, which causes a phase change at the interface. The polarization angle between the interfaces caused by reflection and refraction is It can be calculated by the following formula: (20) The phase difference between the two components have: (twenty one) In addition, after mirror reflection, the p component will suffer a half-wave loss, that is, the phase of the p component will lag behind the s component. Because the ZF6 glass medium used in this embodiment is uniform and has weak magnetic permeability, it can be determined that there is no light intensity loss when the polarized light propagates in the ZF6 glass. The polarization angle is only related to the light intensity and phase relationship of the s and p components. Therefore, it can be considered that the deflection angle caused by the Faraday effect of the polarized light in the ZF6 glass is independent of the deflection angle caused by the reflection.

[0021] Malus's law states that when the intensity is After the linearly polarized light passes through the analyzer, the intensity of the transmitted light satisfies: (twenty two) in, It is the angle between the light vibration direction of the incident linear polarized light and the polarization direction of the polarizer. In this embodiment, since the linear polarized light undergoes multiple reflections and transmissions at different interfaces during propagation, the polarized light before passing through the analyzer is no longer linearly polarized light in the ideal state, but elliptically polarized light. There is a certain difference between the light intensity passing through the analyzer and the light intensity passing through the ideal linear polarized light, and its calculation formula no longer satisfies formula (22).

[0022] In this embodiment, the elliptically polarized light is orthogonally decomposed into two linearly polarized light beams along the major axis and the minor axis, and the light intensity of the two linearly polarized light beams passing through the analyzer is calculated respectively. A simple calculation can be obtained: (twenty three) in, is the light intensity when the major axis of the elliptically polarized light coincides with the polarization direction of the analyzer, is the light intensity when the minor axis of the elliptically polarized light coincides with the polarization direction of the analyzer, is the angle between the major axis of the elliptically polarized light and the polarization direction of the analyzer. According to Malus’s law and its variant (23), the value of the rotation angle can be deduced from the numerical value of the analog voltage, and the problem of the influence of elliptically polarized light on the experimental results can be successfully solved.

[0023] This embodiment further provides an analysis system for the polarization analysis method of the interface reflected light based on the Faraday effect, including: Model building module, used to: establish the propagation model of the optical path in magneto-optical media based on the non-reciprocity of the Faraday magneto-optical effect; The model analysis module is used to calculate the parallel component of the magnetic field through the rotation angle in a uniform magnetic field based on the Faraday magneto-optical effect, measure the spatial distribution of the non-uniform magnetic field using the approximation method, analyze and judge the polarization properties of the optical path itself, and obtain elliptically polarized light: The model output module calculates the rotation angle in elliptically polarized light based on Malus's law and outputs the result.

[0024] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the described embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. The application method of non-reciprocal polarization analysis in weak magnetic field measurement is characterized by: The following steps are involved: Based on the non-reciprocity of Faraday magneto-optical effect, a propagation model of light path in magneto-optical medium is established; Based on the Faraday magneto-optical effect, the parallel component of the magnetic field is calculated by the rotation angle in a uniform magnetic field; The spatial distribution of the non-uniform magnetic field is measured using the approximation method; Analyze and judge the polarization properties of the light path itself to obtain elliptically polarized light; Calculates the rotation angle in elliptically polarized light based on Malus's law and outputs the result.

2. The method for applying non-reciprocal polarization analysis in weak magnetic field measurement according to claim 1, characterized in that: The establishment of the light path propagation model in the magneto-optical medium specifically includes: using multiple reflections of the light path to increase the propagation distance of the light path in the magneto-optical medium, so as to increase the effective length of the light path and reduce the requirement for the length of the magneto-optical medium.

3. The method for applying non-reciprocal polarization analysis to weak magnetic field measurement according to claim 2, characterized in that: The rotation angle is recorded as , （1） in, is the magnetic field strength along the propagation direction of linearly polarized light; It is the effective length for the magnetic field to interact with polarized light; It is the Verdet constant of magneto-optical media, which is used to measure the rotation angle of linearly polarized light when it passes through different materials of the same length under the same magnetic field; According to the different directions of the magnetic deflection angle, the deflection angle is based on the right-hand spiral rule to distinguish between positive and negative. Among them, the polarized light rotates clockwise along the propagation direction as positive, that is, ; Polarized light rotates counterclockwise along the propagation direction to be negative, that is .

4. The method for applying non-reciprocal polarization analysis to weak magnetic field measurement according to claim 3, characterized in that: The method of using the approximation method to measure the spatial distribution of the non-uniform magnetic field is specifically as follows: Calculate the Faraday rotation angle, which is the weighted integral of the non-uniform magnetic field along the optical path, where the weight coefficient is recorded as , the deflection angle is recorded as , then the relationship between the deflection angle and the non-uniform magnetic field satisfies the formula: （2） Among them, the weight function Satisfy the normalized expression conditions: （3） Calculate the cross-sectional induction angle: （4） in, is the medium induction angle, From the magnetic field, it is circular birefringence; From the stress field, it is linear birefringence; like ;but The calculation of the magnetic field satisfies: （5） like It is not always equal to 0. The medium induction angle and the cross-sectional induction angle satisfy: （6） in, is the weight coefficient function of the medium induction angle, which satisfies the normalization condition. , the magnetic field distribution of the non-uniform magnetic field can be obtained.

5. The method for applying non-reciprocal polarization analysis to weak magnetic field measurement according to claim 4, characterized in that: The elliptically polarized light is obtained, specifically: In a non-uniform magnetic field, the medium at different positions has different rotation effects on light, and the two perpendicular components of the light wave obtain different phase delays. The difference in phase delays causes the polarization waveform of the plane to become elliptical, that is, linear polarized light is converted into elliptically polarized light; Construct a rectangular coordinate system to make the two perpendicular components of the elliptically polarized light, and obtain polarized light in the major axis and minor axis directions, where the polarized light in the major axis direction is the x-axis and the light intensity is , the polarized light in the short axis direction is the y axis, and the light intensity is recorded as ; The electric vector amplitude of the x-axis is: （7） The electric vector amplitude of the y-axis is: （8） in, is the angular velocity of the linearly polarized photoelectric vector, is the time that linear polarized light acts in magneto-optical glass; The synthetic elliptically polarized light formula is as follows: （9） The intensity relationship of elliptically polarized light is as follows: （10） in, is the vacuum permittivity, is the speed of light, is the magnitude of the electric field vector; Substituting formula (9) into formula (10), the intensity of elliptically polarized light can be expressed as: （11）。 6. The method for applying non-reciprocal polarization analysis to weak magnetic field measurement according to claim 5, characterized in that: The calculation of the rotation angle in the elliptically polarized light based on Malus's law is specifically as follows: According to Malus's law, the elliptically polarized light is orthogonally decomposed into two linearly polarized light beams along the major axis and the minor axis, and the light intensity of the two linearly polarized light beams passing through the analyzer is calculated respectively. The calculation formula is: （12） in, is the light intensity when the major axis of the elliptically polarized light coincides with the polarization direction of the analyzer, is the light intensity when the minor axis of the elliptically polarized light coincides with the polarization direction of the analyzer, is the angle between the major axis of the elliptically polarized light and the polarization direction of the analyzer. The rotation angle is calculated according to Malus’ law and its variant (12).

7. An application system based on the application method of non-reciprocal polarization analysis in weak magnetic field measurement according to claim 1, characterized in that: include: Model building module, used to: establish the propagation model of the optical path in magneto-optical media based on the non-reciprocity of the Faraday magneto-optical effect; The model analysis module is used to calculate the parallel component of the magnetic field through the rotation angle in a uniform magnetic field based on the Faraday magneto-optical effect, measure the spatial distribution of the non-uniform magnetic field using the approximation method, analyze and judge the polarization properties of the optical path itself, and obtain elliptically polarized light: The model output module calculates the rotation angle in elliptically polarized light based on Malus's law and outputs the result.

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