A method for measuring and analyzing electric field based on electro-optical effect

Abstract

The present invention relates to the technical field of electric field measurement, and specifically to an electric field measurement and analysis method based on the electro-optical effect, comprising: S1, determining the initial light signal injected during measurement; S2, determining the angle of the propagation direction of the initial light signal, injecting the initial light signal into the electro-optical crystal at multiple angles, and determining the calculated value of the electric field effect when the direction and magnitude of the electric field change; S3, determining the corresponding coordinates and path coordinates during light propagation according to the calculated value of the electric field effect in each propagation direction of the initial light signal, and superimposing the path through which the light passes; S4, determining the coupling amount at each angle when overlap occurs after the path is superimposed, and determining the influence of overlap and secondary refraction; S5, determining the change in the magnitude and direction of the electric field corresponding to the initial light signal when superimposed according to the influence of overlap and secondary refraction, and determining the factors affecting the measurement of the electro-optical effect. The accuracy and efficiency of electric field measurement are improved.

Description

Technical Field

[0001] The invention relates to the technical field of electric field measurement, and in particular to an electric field measurement and analysis method based on electro-optical effect. Background Art

[0002] In recent years, electric field sensors have been widely used to meet the needs of large-scale and large-capacity power systems, especially the special needs of remote control, telemetry and artificial intelligence research and development. Traditional electric field sensors are made based on electrical principles and have been relatively mature. However, the metal material of the metal probe in the traditional electric field sensor will cause the electric field to be distorted, thus affecting the measurement accuracy. The sensor cannot work under strong magnetic fields. With the vigorous development of photonics in recent years, optical electric field measurement technology has gradually aroused people's research interest. Optical electric field sensors can realize the non-metallization of the entire measuring probe, thereby avoiding interference with the measured electric field. They have the advantages of small size, good insulation, strong anti-interference ability, high precision and fast response speed, and have been widely used.

[0003] Optical electric field sensors use the Pockels effect of electro-optical modulation crystals to achieve voltage measurement. The Pockels effect refers to the change in the refractive index of certain crystals when an external electric field is applied to them. The optical effect caused by this refractive index change can be accurately measured by the method of polarization interference, thereby achieving the purpose of measuring voltage.

[0004] However, in the prior art, when measuring, if the incident light signal interferes, it will cause the electric field and the refractive index of the corresponding electro-optical crystal to change. At this time, the changes need to be quantified to improve the accuracy of the electric field measurement. Summary of the invention

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A method for measuring and analyzing an electric field based on an electro-optical effect, comprising:

[0007] S1, determines the initial light signal injected during measurement.

[0008] S2, determining the angle of the propagation direction of the initial light signal, emitting the initial light signal into the electro-optical crystal at multiple angles, and determining the calculated value of the electric field effect when the direction and magnitude of the electric field change.

[0009] S3, according to the calculated value of the electric field effect in each propagation direction of the initial optical signal, the corresponding coordinates and path coordinates of the light propagation are determined, and the paths through which the light passes are superimposed.

[0010] S4, determining the coupling amount at each angle when overlap occurs after path superposition, and determining the impact of overlap and secondary refraction.

[0011] S5, according to the influence of overlap and secondary refraction, determine the change of the magnitude and direction of the electric field corresponding to the initial light signal when it is superimposed, and determine the factors affecting the measurement of the electro-optical effect.

[0012] The beneficial effects of the present invention are as follows: the present invention significantly improves the accuracy of electric field measurement through a measurement method based on the electro-optical effect, combined with a precise description and calculation of the optical signal propagation path; by injecting initial optical signals at different angles and observing their propagation and changes in the electro-optical crystal, real-time measurement of the direction and size of the electric field is achieved, meeting the needs of actual application scenarios; through the calculation of path superposition and coupling amount, the complexity of the optical signal propagation path is effectively solved, providing a more accurate and reliable basis for electric field measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0014] Figure 1 It is a flow chart of an electric field measurement and analysis method based on the electro-optical effect. DETAILED DESCRIPTION

[0015] The embodiments of the present invention are described in detail below. The embodiments described below are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. If no specific techniques or conditions are specified in the embodiments, the techniques or conditions described in the literature in the art or the product specifications are used.

[0016] See also Figure 1 , an electric field measurement and analysis method based on electro-optical effect, comprising:

[0017] S1, determining the initial light signal incident during measurement. The input initial light signal is obtained through a polarizing prism or a polarizing plate. The polarization direction or phase of the initial light signal is known and is preset.

[0018] S2, determining the angle of the propagation direction of the initial light signal, emitting the initial light signal into the electro-optical crystal at multiple angles, and determining the calculated value of the electric field effect when the direction and magnitude of the electric field change.

[0019] S3, according to the calculated value of the electric field effect in each propagation direction of the initial optical signal, the corresponding coordinates and path coordinates of the light propagation are determined, and the paths through which the light passes are superimposed.

[0020] S4, determining the coupling amount at each angle when overlap occurs after path superposition, and determining the impact of overlap and secondary refraction.

[0021] S5, according to the influence of overlap and secondary refraction, determine the change of the magnitude and direction of the electric field corresponding to the initial light signal when it is superimposed, and determine the factors affecting the measurement of the electro-optical effect.

[0022] Electro-optic crystal: It is the core component for measuring the electro-optic effect. When an electric field acts on an electro-optic crystal, the refractive index of the crystal changes, causing the polarization state or phase of the light signal passing through the crystal to change. This change is proportional to the intensity of the electric field, so the intensity of the electric field can be inferred by measuring the change in the light signal.

[0023] First, a light source emits a laser and couples it into an optical fiber. The laser is coupled to the position to be measured through a fiber collimator, and a polarizing prism is set at the position to be measured to convert the light into polarized light. A phase delay glass is used for the polarized light to change the phase of the polarized light to determine the state of the polarized light at different phases. At the same time, the corresponding refractive index of the electro-optical crystal when the polarized light passes into the electro-optical crystal is determined. According to the refractive index of the electro-optical crystal, the corresponding electric field size can be calculated. At the same time, a polarizer is used to measure the corresponding light intensity to determine the state of light polarization and convert the corresponding light intensity change into the size and direction of the electric field measurement.

[0024] Then use a polarizing plate or a polarizing prism to set the polarization direction of the light beam; for example, the polarization direction of the light beam can be set along the x-axis, so that all subsequent measurements will be performed around this polarization direction; the light beam is incident on the electro-optical crystal at different angles, and the angle can be gradually increased from 0° to a certain maximum value, such as 90°, each time increasing by a fixed angle, such as 5°; while the light beam passes through the crystal, change the voltage at both ends of the crystal, thereby changing the size and direction of the electric field; for example, you can first apply an electric field perpendicular to the propagation direction of the light beam, and then gradually increase the electric field strength to observe the changes in the polarization state or intensity of the light beam; record the changes in the light beam at different The output position and direction under the angle and electric field strength, which can be achieved by placing a position-sensitive detector at the receiving end; when two or more paths overlap, analyze the light intensity distribution between these paths to determine their coupling degree; this can be achieved by measuring the intensity distribution of the output light and comparing the difference with the non-overlapping case; consider the multiple refractions and reflections of light in the crystal, especially in the case of path overlap, which may cause additional phase delay or polarization rotation; based on the results of the above steps, identify and quantify the various factors that affect the measurement of the electro-optic effect, including the uniformity of the electric field, the quality of the crystal, the accuracy of the polarizer, the stability of the light beam, etc.

[0025] Suppose you are measuring the electro-optical effect of a lithium niobate (LiNbO3) crystal. Use a linearly polarized laser beam with the polarization direction along the x-axis to hit the crystal at different angles. Apply an electric field perpendicular to the x-axis and gradually increase its intensity. Use a position-sensitive detector to record the exit position and intensity distribution of the beam.

[0026] At angle = 30°, it was noted that the intensity of the outgoing beam changed significantly with the increase in the electric field strength; this indicates that the electric field changes the refractive index of the crystal, thus affecting the propagation of the beam; further analysis shows that when the electric field strength reaches a certain threshold, path overlap occurs, which leads to complex changes in the light intensity distribution, including the effect of secondary refraction. By comparing the light intensity distribution under different electric field strengths, it is possible to determine the specific impact of the electric field on the electro-optical effect and which factors have a significant impact on the measurement results.

[0027] In this way, the electro-optic effect can be deeply understood and the performance of electro-optic devices can be optimized in practical applications.

[0028] The calculated value of the electric field effect in step S2 is expressed as follows: when the crystal refracts, the electro-optic coefficient and the electric field of the electro-optic crystal are obtained, and the refractive index change value corresponding to the electro-optic crystal is determined:

[0029] Δn=rE; wherein Δn is the refractive index change value, r is the electro-optic coefficient, and E is the electric field.

[0030] The obtained refractive index is used to determine how the refractive index of the currently input light is affected when the electric field changes, and the relationship between the electric field and the refractive index at this time is determined to determine whether the currently used electro-optical crystal has a linear or proportional relationship with the electric field.

[0031] Apply electric fields of different intensities to the current electro-optical crystal, and use an interferometer or other precision optical instruments to measure the change in the refractive index of the crystal under different electric field intensities; draw a scatter plot with the obtained refractive index change value as the ordinate and the electric field intensity as the abscissa; perform linear fitting on the points in the scatter plot, and the slope of the straight line obtained after fitting is the electro-optic coefficient; thereby determining that there is a linear relationship between the electric field and the refractive index change during measurement at this time.

[0032] When calculating the refractive index change value of the electro-optical crystal, it is also necessary to determine the change value of the set electric field, and based on the change value of the electric field, determine the relative relationship between the electric field and the propagation direction of the optical signal; the direction and magnitude of the electric field will affect the refractive index, but this effect is usually related to the relative relationship between the electric field and the propagation direction of the optical signal. Therefore, it is necessary to clarify the angle or relative position between the electric field vector and the propagation direction of the optical signal.

[0033] The method for determining the relative relationship between the electric field and the propagation direction of the optical signal includes using the ratio of the change value of the refractive index of the electro-optical crystal to the change value of the light propagation direction as the relative relationship between the electric field and the propagation direction of the optical signal.

[0034] For determining the coordinates and path coordinates corresponding to light propagation in step S3, the incident light is set according to the incident angle and the exit angle based on the principal axis (x, y, z) of the crystal to determine the path corresponding to the light before and after entering the electro-optical crystal.

[0035] For each propagation path, define its starting point, end point and point on the path to determine the main direction of light propagation.

[0036] The method for superimposing the paths in step S3 includes counting the refractive index change value and phase accumulation on each path.

[0037] The phase accumulation is expressed as:

[0038] Among them, φ total is the total phase accumulation, φ j is the phase accumulation on the jth path, j = 1, 2,,,m.

[0039] φ j =∫k(z)dz; where k(z) is the wave number of the jth path.

[0040] Where π is the circumference of a circle, λ is the wavelength of light, and n(z) is the refractive index along each path.

[0041] Therefore, the refractive index change value on each path at this time is expressed as obtaining the initial incident angle and refraction angle, calculating the linear refractive index generated by the first harmonic, obtaining the second harmonic intensity generated after the light passes through the electro-optical crystal, and inverting the second-order nonlinear polarization rate of the electro-optical crystal; the third-order nonlinear polarization rate is obtained by obtaining the third harmonic intensity generated after the light passes through the electro-optical crystal, and inverting the third-order nonlinear polarization rate of the electro-optical crystal; the b-order nonlinear polarization rate is obtained by obtaining the b-order harmonic intensity generated after the light passes through the electro-optical crystal, and inverting the b-order nonlinear polarization rate of the electro-optical crystal:

[0042] n(z)=n 0 +x (2) E 2 +x (3) E 3 +...+x (b) E b ; where n 0 is the linear refractive index, x (2) is the second-order nonlinear polarizability, x (3) is the third-order nonlinear polarizability, x(b) is the b-order nonlinear polarizability, E is the electric field, and n(z) is the refractive index change.

[0043] At this time, by calculating each incident light ray, it is determined how the hard-measured light rays overlap and interfere when the electric field changes or the light angle changes; and the nonlinear optical effect of the electro-optical crystal under the action of a strong electric field is directly measured, thereby inferring the nonlinear polarization rate.

[0044] Based on the identified paths of image overlap, the corresponding overlapping positions on the paths where the overlap occurs are confirmed, as well as the change in refractive index on each path when the overlapping position changes. Based on the change in refractive index, the corresponding slope when the refractive index changes is determined, and the slope is used as the basic path for identifying the current electric field.

[0045] The path with the maximum slope of the refractive index change is identified as the currently identified basic path, and other overlapping paths are superimposed on the path with the largest refractive index change, and the superimposed path is used as the path for calculating overlap and secondary effects.

[0046] The coupling amount for each angle in step S4 is expressed as:

[0047] Get the coupling modes A(t) and B(t) corresponding to the optical signals at two angles:

[0048]

[0049] Where A(t) and B(t) represent the changes in the complex amplitudes of the two coupled modes over time t. In optical waveguides or integrated photonic devices, they can be two light fields of different modes, such as TE and TM modes, or the coupling of the same mode between different waveguides. i represents the imaginary unit. k is the coupling constant, which characterizes the rate of energy transfer between the two modes. It is a complex number, whose real part represents the efficiency of energy exchange between the modes and the imaginary part reflects any possible non-reciprocity (for example, due to magneto-optical effects). These two terms represent the phase factor due to the phase mismatch Δβ between the two modes. Δβ is defined as the difference in the wave numbers of the two modes. That is, Δβ = β A -β B , where β A and β B are the wave numbers (or phase constants) of the two modes respectively. The phase mismatch Δβ affects the effectiveness of energy coupling between the two modes. If Δβ ​​= 0, it is called the phase matching condition, and the coupling efficiency is the highest at this time; t is a time variable that describes the evolution of the mode amplitude over time, z represents the spatial coordinate along the propagation direction of the waveguide or crystal, and the coupling process occurs along this direction, e is an exponential constant, B represents the initial amplitude of the coupling mode corresponding to A(t), and A represents the initial amplitude of the coupling mode corresponding to B(t).

[0050] The judgment of secondary refraction is to double the wave number of the originally refracted light to determine the corresponding wave number after secondary refraction.

[0051] When determining the influence of overlap and secondary refraction in step S4, it is necessary to determine the phase difference calculated after the secondary refraction of the light based on the refracted light.

[0052] The phase difference after the second refraction is expressed as follows: the interference light intensity after the second refraction and the initial light intensity of the two coherent lights that produce the refraction are obtained to determine the phase difference after the second refraction:

[0053]

[0054] Among them, I init is the interference intensity, I 1 and I 2 They represent the initial light intensities of the two coherent light beams, and Δφ is the phase difference after secondary refraction.

[0055] The interference light intensity obtained at this time is used to determine the interference light intensity value of the corresponding light when overlap and influence occur, so as to quantify the degree to which the two coherent light beams are affected at this time.

[0056] The effect of overlap and secondary refraction in step S4 is expressed as:

[0057] Determine the phase matching condition and the efficiency of secondary refraction after the initial optical signals are superimposed. The phase matching condition needs to satisfy that the amount of the second harmonic after the initial optical signals are superimposed is the sum of the wave vectors of the two fundamental frequency lights.

[0058] The efficiency of the double refraction is:

[0059] P 2ω ∝|x (2) | 2 sin 2 (τL / 2);

[0060] Among them, P 2ω is the efficiency of the secondary refraction, x (2) is the second-order nonlinear polarizability, τ is the phase mismatch factor, which is determined by the dispersion characteristics of the material and the phase matching conditions; L is the length of the electro-optical crystal.

[0061] The implementation of determining the factors affecting the electro-optical effect measurement in step S5 includes:

[0062] When determining the efficiency of secondary refraction, the phase matching condition, and the phase difference caused by the secondary refraction, the currently measured optical signal is analyzed to obtain the actual measurement value during the measurement, and the measurement error between the actual measurement value and the preset measurement value is determined, the measurement error includes the error caused by the measurement when the efficiency of secondary refraction and the phase matching condition are obtained, the angle of the optical signal in the propagation direction, and the corresponding electric field direction and magnitude when the measurement error occurs are determined, the probability distribution of the angle of the optical signal in the propagation direction, and the corresponding electric field direction and magnitude when the measurement error occurs is obtained, and the maximum likelihood value corresponding to the angle of the optical signal in the propagation direction, and the corresponding electric field direction and magnitude when the measurement error occurs is determined.

[0063] The way to obtain the maximum likelihood value is expressed as:

[0064]

[0065] Among them, L(θ|y) is the likelihood function, which means that the data y is observed under the parameter θ. l The probability of θ is the parameter of the likelihood function, f(θ) is the predicted measurement value, σ is the variance of the measurement error, and y v is the actual measured value, π is the ratio of pi, e is the exponential constant, and V represents the number of actual measured values, v=1,2,,,V.

[0066] The current measurement error is continuously calculated until the obtained value of L(θ|y) reaches the maximum value, that is, the maximum likelihood value is obtained, the parameter combination that produces the maximum likelihood value is recorded, and the corresponding parameter combination is used as the parameter combination for measuring the electro-optical effect.

[0067] At this time, after limiting the current measurement scene, determine how to handle light when it is superimposed and in corresponding situations, so that you can understand how the accuracy of the current measurement changes when the light and magnetic field change, and get the corresponding calculation results. According to the calculation results, find out the errors that occur during the calculation, and further verify the factors that affect the measurement, so that you can find a parameter combination suitable for the current scene calculation.

[0068] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention and they are still covered by the protection scope of the present invention.

Claims

1. A method for measuring and analyzing electric field based on electro-optical effect, characterized in that: include: S1, determines the initial light signal injected during measurement; S2, determining the angle of the propagation direction of the initial light signal, sequentially emitting the initial light signal into the electro-optical crystal at multiple angles, and determining the calculated value of the electric field effect when the direction and magnitude of the electric field change; S3, determining the corresponding coordinates and path coordinates of the light propagation according to the calculated values ​​of the electric field effect in each propagation direction of the initial light signal, and superimposing the paths through which the light passes; S4, determining the coupling amount at each angle when overlap occurs after path superposition, and determining the impact of overlap and secondary refraction; S5, determining the change in magnitude and direction of the electric field corresponding to the initial optical signals when they are superimposed based on the influence of overlap and secondary refraction, and determining the factors affecting the measurement of the electro-optical effect; The calculated value of the electric field effect in step S2 is expressed as follows: when the crystal refracts, the electro-optic coefficient and the electric field of the electro-optic crystal are obtained, and the refractive index change value corresponding to the electro-optic crystal is determined: ;in, is the refractive index change, is the electro-optic coefficient, It is the electric field; The method of superimposing the paths in step S3 includes statistically accumulating phase and the refractive index change value on each path; The phase accumulation is expressed as: ;in, is the total phase accumulation, is the phase accumulation on the jth path, ; ;in, is the wave number of the jth path; ,in, is pi, is the wavelength of light, is the refractive index on each path; Based on the identified overlapping paths, the corresponding overlapping positions on the overlapping paths are confirmed, and when the overlapping positions change, the change values ​​of the refractive index on each path are determined, and based on the change values ​​of the refractive index, the corresponding slope when the refractive index changes is determined, and the slope is used as the basic path for identifying the current electric field; The path with the maximum slope of the refractive index change is identified as the currently identified basic path, and other overlapping paths are superimposed on the path with the maximum refractive index change, and the superimposed path is used as the path for calculating overlap and secondary influence; The coupling amount for each angle in step S4 is expressed as: Get the coupling mode corresponding to the optical signals at two angles and : ； ； in, and Respectively represent the changes of the complex amplitudes of the two coupled modes with time t; represents the imaginary unit; is the coupling constant; is defined as the difference in wave numbers between the two modes; i.e. ,in and are the wave numbers of the two modes respectively; z represents the spatial coordinate along the propagation direction of the waveguide or crystal, t is the time variable, e is the exponential constant, and B represents The initial amplitude of the corresponding coupling mode, A represents The initial amplitude of the corresponding coupling mode; Determining the influence of overlap and secondary refraction in step S4 also includes determining, based on the refracted light, a phase difference calculated after the light is secondary refracted; The phase difference after the second refraction is expressed as follows: the interference light intensity after the second refraction and the initial light intensity of the two coherent lights that produce the refraction are obtained to determine the phase difference after the second refraction: ； in, is the interference intensity, and They represent the initial intensity of the two coherent light beams, is the phase difference after double refraction; The effect of overlap and secondary refraction in step S4 is expressed as: Determine the phase matching condition and the efficiency of secondary refraction after the initial optical signals are superimposed; the phase matching condition satisfies that the second harmonic amount after the initial optical signals are superimposed is the sum of the wave vectors of the two fundamental frequency lights; The efficiency of the double refraction is: ； in, is the efficiency of the secondary refraction, is the second-order nonlinear polarizability, is the phase mismatch factor; is the length of the electro-optic crystal; The implementation of determining the factors affecting the electro-optical effect measurement in step S5 includes: When determining the efficiency of secondary refraction, the phase matching condition, and the phase difference caused by the secondary refraction, the currently measured optical signal is analyzed to obtain the actual measurement value during the measurement, and the measurement error between the actual measurement value and the preset measurement value is determined, the measurement error includes the error caused by the measurement when the efficiency of secondary refraction and the phase matching condition are obtained, the angle of the optical signal in the propagation direction, and the corresponding electric field direction and magnitude when the measurement error occurs are determined, the probability distribution of the angle of the optical signal in the propagation direction, and the corresponding electric field direction and magnitude when the measurement error occurs is obtained, and the maximum likelihood value corresponding to the angle of the optical signal in the propagation direction, and the corresponding electric field direction and magnitude when the measurement error occurs is determined.

2. The electric field measurement and analysis method based on the electro-optical effect according to claim 1, characterized in that: The refractive index change value on each path is expressed as: ;in, is the linear refractive index, is the second-order nonlinear polarizability, is the third-order nonlinear polarizability, is the b-order nonlinear polarizability, is the electric field, is the refractive index change.

3. The electric field measurement and analysis method based on the electro-optical effect according to claim 1, characterized in that: The way to obtain the maximum likelihood value is expressed as: ； in, is the likelihood function, which means that The data observed below The probability of are the parameters of the likelihood function, is the predicted measured value, is the variance of the measurement error, is the actual measured value, is pi, is the exponential constant, represents the actual number of measurements, .

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