Classical entanglement-based beam axial rotation measurement method and system

Abstract

The application provides a kind of classical entanglement-based optical beam axial rotation measurement method and system, comprising: after single-frequency laser light source is expanded, the phase diagram corresponding to Hermite-Gaussian light beam is modulated, and higher purity Hermite-Gaussian light source is generated after filtering system;The horizontal component and vertical component of the polarization state of the light beam are introduced by pre-selection, and the axial rotation in opposite directions is introduced, and then the polarization state of the light beam is passed through post-selection, so that the optical beam axial rotation parameter is carried by spatial mode entanglement state;The phase diagram corresponding to the mode entanglement state carrying parameter of the light beam after post-selection is modulated, Fourier lens is passed through, and fiber tail fiber is used for receiving;Projection measurement converts optical beam axial rotation parameter into light intensity information, measures the light intensity obtained by projection measurement, converts into electrical signal and inputs into spectrum analyzer, and demodulates the size of optical beam axial rotation.The application has higher measurement accuracy compared with the existing optical beam axial rotation measurement scheme.

Description

Technical Field

[0001] This invention relates to the field of laser measurement, specifically to a method and system for measuring the axial rotation of a beam based on classical entanglement, and more specifically to a method and system for measuring the axial rotation of a tiny beam based on classical entanglement technology. Background Technology

[0002] In laser measurement, the beam profile is typically a standard Gaussian distribution with rotational symmetry, thus it cannot carry any information about the beam's axial rotation. Recent research has generally employed quantum resources, such as quantum entanglement, introduced into beams carrying orbital angular momentum (e.g., Laguerre Gaussian beams), to measure the beam's axial rotation.

[0003] While this type of quantum resource-based measurement technology can solve the problem of measuring beam axial rotation, it faces significant technical challenges in practical implementation. For example: 1. Quantum resources such as quantum entanglement remain difficult to prepare, and entangled states are highly susceptible to decoherence in noisy environments, affecting measurement accuracy. 2. Quantum resource-based measurement schemes generally require single-photon sources and signal measurement under single-photon conditions, which limits further improvements in measurement accuracy. 3. Currently, this type of scheme requires introducing quantum resources into extremely high-order orbital angular momentum eigenstates (orbital angular momentum topological charge exceeding 100) to achieve μrad-level accuracy in beam axial rotation measurement, which is a significant challenge in practical implementation. 4. This type of scheme has a low detection bandwidth, making it unable to measure high-frequency rotation signals. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this invention is to provide a method and system for measuring beam axial rotation based on classical entanglement.

[0005] A method for measuring the axial rotation of a beam based on classical entanglement, provided by the present invention, includes:

[0006] Step S1: After the single-frequency laser source is expanded, the phase diagram corresponding to the Hermitian beam is modulated, and a high-purity Hermitian light source is generated through a filtering system.

[0007] Step S2: Select the polarization state of the Hermigasaurus beam through pre-selection, introduce axial rotations in opposite directions to the horizontal and vertical components of the beam polarization state, and then pass the beam polarization state through post-selection so that the beam axial rotation parameter is carried by the entangled state of the spatial mode.

[0008] Step S3: The selected beam is incident on the spatial light modulator and the phase diagram corresponding to the mode entanglement state carrying parameters is modulated on it. After passing through the Fourier lens, the beam is received by an optical fiber pigtail at the focal point behind the lens to realize projection measurement.

[0009] Step S4: Projection measurement converts the beam axial rotation parameter into light intensity information. The light intensity obtained from the projection measurement is measured, converted into an electrical signal, and input into the spectrum analyzer to demodulate the magnitude of the beam axial rotation.

[0010] Preferably, in step S1:

[0011] After the single-frequency laser source is expanded by the beam expander coupling head, it is incident on the spatial light modulator and modulated on the spatial light modulator to generate the phase diagram corresponding to the m×n order Hermitian Gaussian beam. After the output light passes through the 4f filter system, a high-purity m×n order Hermitian Gaussian source is generated.

[0012] The phase diagram corresponding to the m×n order Hermitian Gaussian beam was obtained through numerical calculation, specifically as follows:

[0013] Let the beam distribution of the input spatial light modulator be denoted as... in This represents the amplitude intensity distribution of the beam input to the spatial light modulator. The input beam spatial phase distribution; i is the imaginary unit, x is the horizontal coordinate of the cross-section, and y is the vertical coordinate of the cross-section;

[0014] The phase diagram loaded onto the spatial light modulator is denoted as H. A (x,y); The output beam distribution of the spatial light modulator is as follows: Where ψ mn (x,y) represents the desired m×n order Hermitian beam distribution, and the amplitude intensity and spatial phase of the output beam from the spatial light modulator are respectively... and

[0015] Let the relative phase be denoted as in It is the phase of the blazed grating loaded on the spatial light modulator;

[0016] Let the relative amplitude be denoted as

[0017] Phase diagram loaded onto the spatial light modulator:

[0018]

[0019] in It is the inverse function of the first-order Bessel function;

[0020] The 4f filtering system is specifically as follows:

[0021] A Fourier lens with a focal length of f1 is placed at a position f1 behind the spatial light modulator. A small aperture is placed at a position f1 behind the Fourier lens. The beam modulated by the spatial light modulator is focused at the small aperture after passing through the Fourier lens. Due to the blazed grating added to the phase diagram, the focal points of the image plane will be periodically arranged in the horizontal direction. The aperture is used to filter out the first-order diffraction spot. A lens with a focal length of f2 is placed at a position f2 behind the Fourier lens, resulting in a high-purity m×n-order Hermitian beam. The spatial distribution of this Hermitian beam is denoted as |m,n>, and the symbol |·> represents the Dirac right vector.

[0022] |m,n>=∫∫dxdyψ mn (x,y)|x,y>

[0023] Where, ψ mn (x,y) is the wave function of an m×n order Hermitian Gaussian beam.

[0024] Preferably, in step S2:

[0025] The Hermigass beam is pre-selected to be linearly polarized at 45 degrees. In the weakly coupled module, an interferometer is used to introduce axial rotations in opposite directions to the horizontal component H and the vertical component V of the beam polarization state. Then, the beam polarization state is post-selected so that the beam axial rotation parameter is carried by a spatial mode entangled state.

[0026] The beam is pre-selected to have its polarization state set to 45-degree linearly polarized light, specifically:

[0027] A Hermetic beam generated by a spatial light modulator and a 4f filter system is oriented by a mirror and then incident on a Glan Taylor polarizing prism with its optical axis horizontal. After passing through a half-wave plate with its optical axis at a 22.5° angle to the horizontal plane, the polarization state of the output beam is preselected as follows:

[0028]

[0029] Where i represents the preselection state, H represents horizontally polarized light, and V represents vertically polarized light;

[0030] The opposite axial rotation specifically refers to:

[0031] In an interferometer, an axial rotation with a relative angle of 2α is applied to the horizontal and vertical polarization components of the beam, which can be represented by the evolution operator as follows:

[0032]

[0033] in, Let this be the unitary evolution operator representation of the rotation process; For Pauli operators acting on polarization states, is the angular momentum operator acting on the spatial mode of the beam, representing axial rotation, and <·| is the Dirac left vector symbol;

[0034] In practice, the beam is first input into the polarization interferometer through a beam splitter. The main body of the polarization interferometer consists of a polarization beam splitter and three mirrors. A linear polarizer and a half-wave plate are inserted into the interferometer. The optical axis of the linear polarizer is perpendicular to the horizontal plane, and the half-wave plate is at a 45-degree angle to the horizontal plane. In addition, the axial rotation of the beam is achieved by inserting a Dowell prism into the interferometer.

[0035] The input state of the interferometer is denoted as: |Ψ in >=|i>|ψ i >, where |ψ i >=|m,n> represents the initial spatial mode of the beam; therefore, the output state of the interferometer is denoted as:

[0036]

[0037] The subsequent selection specifically refers to:

[0038] The beam emitted from the interferometer passes through an optical axis that is perpendicular to the horizontal direction. A half-wave plate with an angle of 60° passes through a Glan Taylor polarizing prism with its optical axis horizontal, and the polarization state of the output beam is subsequently selected as follows:

[0039]

[0040] Where ε is the post-selection angle, 0.05 < ε < 1;

[0041] Before passing through the half-wave plate, the beam is pre-compensated by a Sorel-Barbinje phase compensator to compensate for the phase difference between the horizontal and vertical polarization components in the interferometer. After passing through the half-wave plate, the beam is oriented by a mirror and then incident on a spatial light modulator for projection measurement.

[0042] Preferably, the spatial mode entangled state specifically comprises:

[0043] The state vector of the selected beam is denoted as follows:

[0044]

[0045] Where: f represents the post-selection state, and <·|·> represents the inner product operation;

[0046]

[0047] A wThe weak value is considered, taking into account the approximate condition for weak measurement: α << 1. The resulting beam spatial mode is denoted as:

[0048]

[0049] The axial rotation information of the beam is completely controlled by the spatial mode. Bear, and

[0050]

[0051] The pattern states in the x and y directions are inseparable, which is equivalent to an entangled form and is a classic entangled state of a spatial pattern.

[0052] The quantum precision limit for estimating the unknown parameter α is:

[0053]

[0054] Where N is the number of photons received by the detector;

[0055] Due to the introduction of classical entangled states, the limiting accuracy for beam axis rotation measurement will be obtained through a factor proportional to the mode number. Enhancement;

[0056] The phase diagram corresponding to the entangled state of the modulation-carrying parameters is specifically as follows:

[0057] The beam distribution modulated by the spatial light modulator is denoted as in Entangled states of modes carrying rotation parameters The corresponding two-dimensional spatial wave function distribution, the amplitude intensity and spatial phase of the beam distribution modulated by the spatial light modulator are denoted here as... and When calculating the phase diagram of the spatial light modulator, the input beam is pre-set to be parallel light. The input beam amplitude intensity is preset when calculating the phase diagram of the spatial light modulator. The spatial phase of the input beam is preset when calculating the phase diagram of the spatial light modulator;

[0058] Let the relative phase be denoted as in It is the phase of the blazed grating loaded on the spatial light modulator;

[0059] Let the relative amplitude be denoted as

[0060] Therefore, the phase diagram loaded on the spatial light modulator is:

[0061]

[0062] The use of fiber optic pigtail receivers to achieve projection measurement specifically involves:

[0063] A Fourier lens is used behind the spatial light modulator to perform a Fourier transform on the projected light field. Since the light field distribution modulated by the spatial light modulator is... The light field input to the spatial light modulator is ψ f (x,y), i.e., the final state of the pointer |ψ f The corresponding two-dimensional optical field distribution is transformed into a transformed optical field at the focal length behind the Fourier lens. This transformed optical field is then directly received at the center of the transformed optical field via a single-mode fiber. Since the mode field diameter of the single-mode fiber is much smaller than the size of the transformed optical field, the receiving efficiency of the single-mode fiber is expressed as:

[0064]

[0065] in, for The conjugate representation of .

[0066] Preferably, in step S4:

[0067] Projection measurement converts the beam axial rotation parameter into light intensity information. The light intensity obtained from the projection measurement is measured using an avalanche photodiode detector, converted into an electrical signal, and input into a spectrum analyzer to demodulate the magnitude of the beam axial rotation.

[0068] Step S4.1: Input the light intensity received by the single-mode fiber into the avalanche photodiode detector to convert the received weak light intensity signal into an electrical signal;

[0069] Step S4.2: Input the electrical signal of the avalanche photodiode detector into the frequency analyzer, read the peak frequency and corresponding intensity of the frequency analyzer, and demodulate the amplitude and frequency of the beam axial rotation signal;

[0070] The process of inputting the light intensity received by the single-mode fiber into the avalanche photodiode detector specifically involves:

[0071] The light intensity received by the avalanche photodiode detector is proportional to the projected probability, i.e.

[0072]

[0073] Among them, I det Let P be the light intensity received by the avalanche photodiode detector, and P be the final state of the photon |ψ f >In the spatial mode carrying rotation information Projection probability on;

[0074] Under the same rotating signal intensity, the received light intensity will be increased by a factor 2mn+m+n related to the spatial mode number of the Hermetic beam;

[0075] The amplitude and frequency of the demodulated beam axial rotation signal are specifically as follows:

[0076] The electrical signal output by the avalanche photodiode detector is a voltage signal amplified by a built-in transimpedance amplifier, which is proportional to the received light intensity, i.e., V. det ∝I det The voltage signal is input into a frequency analyzer to determine the frequency and amplitude of the beam axial rotation signal.

[0077] A beam axial rotation measurement system based on classical entanglement according to the present invention includes:

[0078] Module M1: After expanding the single-frequency laser source, modulates the phase diagram corresponding to the Hermitian beam, and generates a high-purity Hermitian light source through a filtering system;

[0079] Module M2: The Hermetic Gaussian beam is preselected to select the polarization state, and the horizontal and vertical components of the beam polarization state are introduced to undergo axial rotation in opposite directions. The beam polarization state is then postselected so that the beam axial rotation parameter is carried by the entangled state of the spatial mode.

[0080] Module M3: After the beam has been selected, it is incident on the spatial light modulator and modulated onto it the phase diagram corresponding to the mode entanglement state carrying parameters. After passing through the Fourier lens, it is received by an optical fiber pigtail at the focal point behind the lens to realize projection measurement.

[0081] Module M4: Projection measurement converts the beam axial rotation parameters into light intensity information, measures the light intensity obtained from projection measurement, converts it into an electrical signal, and inputs it into a spectrum analyzer to demodulate the magnitude of the beam axial rotation.

[0082] Preferably, in module M1:

[0083] After the single-frequency laser source is expanded by the beam expander coupling head, it is incident on the spatial light modulator and modulated on the spatial light modulator to generate the phase diagram corresponding to the m×n order Hermitian Gaussian beam. After the output light passes through the 4f filter system, a high-purity m×n order Hermitian Gaussian source is generated.

[0084] The phase diagram corresponding to the m×n order Hermitian Gaussian beam was obtained through numerical calculation, specifically as follows:

[0085] Let the beam distribution of the input spatial light modulator be denoted as... in This represents the amplitude intensity distribution of the beam input to the spatial light modulator. The input beam spatial phase distribution; i is the imaginary unit, x is the horizontal coordinate of the cross-section, and y is the vertical coordinate of the cross-section;

[0086] The phase diagram loaded onto the spatial light modulator is denoted as H. A (x,y); The output beam distribution of the spatial light modulator is as follows: Where ψ mn (x,y) represents the desired m×n order Hermitian beam distribution, and the amplitude intensity and spatial phase of the output beam from the spatial light modulator are respectively... and

[0087] Let the relative phase be denoted as in It is the phase of the blazed grating loaded on the spatial light modulator;

[0088] Let the relative amplitude be denoted as

[0089] Phase diagram loaded onto the spatial light modulator:

[0090]

[0091] in It is the inverse function of the first-order Bessel function;

[0092] The 4f filtering system is specifically as follows:

[0093] A Fourier lens with a focal length of f1 is placed at a position f1 behind the spatial light modulator. A small aperture is placed at a position f1 behind the Fourier lens. The beam modulated by the spatial light modulator is focused at the small aperture after passing through the Fourier lens. Due to the blazed grating added to the phase diagram, the focal points of the image plane will be periodically arranged in the horizontal direction. The aperture is used to filter out the first-order diffraction spot. A lens with a focal length of f2 is placed at a position f2 behind the Fourier lens, resulting in a high-purity m×n-order Hermitian beam. The spatial distribution of this Hermitian beam is denoted as |m,n>, and the symbol |·> represents the Dirac right vector.

[0094] |m,n>=∫∫dxdyψ mn (x,y)|x,y>

[0095] Where, ψ mn (x,y) is the wave function of an m×n order Hermitian Gaussian beam.

[0096] Preferably, in module M2:

[0097] The Hermigass beam is pre-selected to be linearly polarized at 45 degrees. In the weakly coupled module, an interferometer is used to introduce axial rotations in opposite directions to the horizontal component H and the vertical component V of the beam polarization state. Then, the beam polarization state is post-selected so that the beam axial rotation parameter is carried by a spatial mode entangled state.

[0098] The beam is pre-selected to have its polarization state set to 45-degree linearly polarized light, specifically:

[0099] A Hermetic beam generated by a spatial light modulator and a 4f filter system is oriented by a mirror and then incident on a Glan Taylor polarizing prism with its optical axis horizontal. After passing through a half-wave plate with its optical axis at a 22.5° angle to the horizontal plane, the polarization state of the output beam is preselected as follows:

[0100]

[0101] Where i represents the preselection state, H represents horizontally polarized light, and V represents vertically polarized light;

[0102] The opposite axial rotation specifically refers to:

[0103] In an interferometer, an axial rotation with a relative angle of 2α is applied to the horizontal and vertical polarization components of the beam, which can be represented by the evolution operator as follows:

[0104]

[0105] in, Let this be the unitary evolution operator representation of the rotation process; For Pauli operators acting on polarization states, is the angular momentum operator acting on the spatial mode of the beam, representing axial rotation, and <·| is the Dirac left vector symbol;

[0106] In practice, the beam is first input into the polarization interferometer through a beam splitter. The main body of the polarization interferometer consists of a polarization beam splitter and three mirrors. A linear polarizer and a half-wave plate are inserted into the interferometer. The optical axis of the linear polarizer is perpendicular to the horizontal plane, and the half-wave plate is at a 45-degree angle to the horizontal plane. In addition, the axial rotation of the beam is achieved by inserting a Dowell prism into the interferometer.

[0107] The input state of the interferometer is denoted as: |Ψ in >=|i>|ψ i >, where |ψ i >=|m,n> represents the initial spatial mode of the beam; therefore, the output state of the interferometer is denoted as:

[0108]

[0109] The subsequent selection specifically refers to:

[0110] The beam emitted from the interferometer passes through an optical axis that is perpendicular to the horizontal direction. A half-wave plate with an angle of 60° passes through a Glan Taylor polarizing prism with its optical axis horizontal, and the polarization state of the output beam is subsequently selected as follows:

[0111]

[0112] Where ε is the post-selection angle, 0.05 < ε < 1;

[0113] Before passing through the half-wave plate, the beam is pre-compensated by a Sorel-Barbinje phase compensator to compensate for the phase difference between the horizontal and vertical polarization components in the interferometer. After passing through the half-wave plate, the beam is oriented by a mirror and then incident on a spatial light modulator for projection measurement.

[0114] Preferably, the spatial mode entangled state specifically comprises:

[0115] The state vector of the selected beam is denoted as follows:

[0116]

[0117] Where: f represents the post-selection state, and <·|·> represents the inner product operation;

[0118]

[0119] A w The weak value is considered, taking into account the approximate condition for weak measurement: α << 1. The resulting beam spatial mode is denoted as:

[0120]

[0121]

[0122] The axial rotation information of the beam is completely controlled by the spatial mode. Bear, and

[0123]

[0124] The pattern states in the x and y directions are inseparable, which is equivalent to an entangled form and is a classic entangled state of a spatial pattern.

[0125] The quantum precision limit for estimating the unknown parameter α is:

[0126]

[0127] Where N is the number of photons received by the detector;

[0128] Due to the introduction of classical entangled states, the limiting accuracy for beam axis rotation measurement will be obtained through a factor proportional to the mode number. Enhancement;

[0129] The phase diagram corresponding to the entangled state of the modulation-carrying parameters is specifically as follows:

[0130] The beam distribution modulated by the spatial light modulator is denoted as in Entangled states of modes carrying rotation parameters The corresponding two-dimensional spatial wave function distribution, the amplitude intensity and spatial phase of the beam distribution modulated by the spatial light modulator are denoted here as... and When calculating the phase diagram of the spatial light modulator, the input beam is pre-set to be parallel light. The input beam amplitude intensity is preset when calculating the phase diagram of the spatial light modulator. The spatial phase of the input beam is preset when calculating the phase diagram of the spatial light modulator;

[0131] Let the relative phase be denoted as in It is the phase of the blazed grating loaded on the spatial light modulator;

[0132] Let the relative amplitude be denoted as

[0133] Therefore, the phase diagram loaded on the spatial light modulator is:

[0134]

[0135] The use of fiber optic pigtail receivers to achieve projection measurement specifically involves:

[0136] A Fourier lens is used behind the spatial light modulator to perform a Fourier transform on the projected light field. Since the light field distribution modulated by the spatial light modulator is... The light field input to the spatial light modulator is ψ f (x,y), i.e., the final state of the pointer |ψ f The corresponding two-dimensional optical field distribution is transformed into a transformed optical field at the focal length behind the Fourier lens. This transformed optical field is then directly received at the center of the transformed optical field via a single-mode fiber. Since the mode field diameter of the single-mode fiber is much smaller than the size of the transformed optical field, the receiving efficiency of the single-mode fiber is expressed as:

[0137]

[0138] in, for The conjugate representation of .

[0139] Preferably, in module M4:

[0140] Projection measurement converts the beam axial rotation parameter into light intensity information. The light intensity obtained from the projection measurement is measured using an avalanche photodiode detector, converted into an electrical signal, and input into a spectrum analyzer to demodulate the magnitude of the beam axial rotation.

[0141] Module M4.1: Inputs the light intensity received by the single-mode fiber into the avalanche photodiode detector, and converts the received weak light intensity signal into an electrical signal;

[0142] Module M4.2: Inputs the electrical signal from the avalanche photodiode detector into the frequency analyzer, reads the peak frequency and corresponding intensity from the frequency analyzer, and demodulates the amplitude and frequency of the beam axial rotation signal;

[0143] The process of inputting the light intensity received by the single-mode fiber into the avalanche photodiode detector specifically involves:

[0144] The light intensity received by the avalanche photodiode detector is proportional to the projected probability, i.e.

[0145]

[0146] Among them, I det Let P be the light intensity received by the avalanche photodiode detector, and P be the final state of the photon |ψ f >In the spatial mode carrying rotation information Projection probability on;

[0147] Under the same rotating signal intensity, the received light intensity will be increased by a factor 2mn+m+n related to the spatial mode number of the Hermetic beam;

[0148] The amplitude and frequency of the demodulated beam axial rotation signal are specifically as follows:

[0149] The electrical signal output by the avalanche photodiode detector is a voltage signal amplified by a built-in transimpedance amplifier, which is proportional to the received light intensity, i.e., V. det ∝I det The voltage signal is input into a frequency analyzer to determine the frequency and amplitude of the beam axial rotation signal.

[0150] Compared with the prior art, the present invention has the following beneficial effects:

[0151] 1. Compared with existing beam axis rotation measurement schemes, the present invention has higher measurement accuracy, and the measurement accuracy can be further improved by increasing the number of Hermetic Gaussian spatial modes.

[0152] 2. This invention, combined with weak value amplification technology, can effectively resist the detection power saturation of avalanche detectors;

[0153] 3. This invention does not require the preparation of a single-photon source or the reception of single photons, thus enabling a larger detection bandwidth;

[0154] 4. The measurement end of this invention only requires one spatial light modulator to achieve projection measurement, making it more convenient. Attached Figure Description

[0155] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0156] Figure 1 This is a schematic diagram of the novel beam axial rotation measurement method based on classical entanglement in this invention.

[0157] Figure 2 The signal-to-noise ratio and minimum detectable rotation signal amplitude of the rotating signals obtained under different Hermetic Gaussian modes in this invention are measured.

[0158] In the picture:

[0159] 1 is a single-frequency laser source;

[0160] 2 is the beam expander coupling head;

[0161] 3 is a spatial light modulator;

[0162] 4 is a lens;

[0163] 5 represents a small hole;

[0164] 6 represents a reflecting mirror;

[0165] 7 is a Glan Taylor polarizing prism;

[0166] 8 is a half-wave plate;

[0167] 9 represents a beam splitter;

[0168] 10 is a polarization beam splitter;

[0169] 11 is a linear polarizer;

[0170] 12 is a Dowley prism;

[0171] 13 is the Sourir-Barbingé phase compensator;

[0172] 14 represents single-mode fiber;

[0173] 15 is an avalanche photodiode detector;

[0174] 16 is a frequency analyzer. Detailed Implementation

[0175] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0176] Example 1:

[0177] This invention provides a novel method for measuring the axial rotation of a light beam based on classical entanglement, comprising: a Hermitian Gaussian light source generation module, a weak coupling module, a projection measurement module, an electrical module, and a data processing module. The Hermitian Gaussian light source generation module generates a high-order Hermitian Gaussian light source. The weak coupling module introduces axial rotation of the light beam and generates a classically entangled state to improve measurement accuracy. This module also incorporates weak value amplification technology via post-selection to further amplify the weak axial rotation signal of the light beam and improve the system's noise immunity. The projection measurement module demodulates the weak axial rotation signal of the light beam into a light intensity signal. The electrical module converts the optical signal into an electrical signal to obtain and store measurement data. The data processing module analyzes and processes the measured data to calculate the axial rotation angle of the light beam. This invention utilizes classical entanglement and weak value amplification technology to achieve precise measurement of the axial rotation angle of a light beam. Furthermore, this scheme uses classical entanglement instead of quantum entanglement, achieving the same theoretical accuracy improvement while simplifying the implementation, improving stability, and achieving even higher accuracy when combined with weak value amplification technology. Therefore, it can effectively solve related problems in fields such as optical measurement, sensing, and navigation.

[0178] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for measuring the axial rotation of a tiny beam based on classical entanglement, which is suitable for systems with higher requirements for rotation measurement accuracy and easier implementation.

[0179] According to the present invention, a novel method for measuring the axial rotation of a beam based on classical entanglement is provided, such as... Figures 1-2 As shown, it includes:

[0180] Step 1: After the single-frequency laser source 1 is expanded by the beam expander coupling head 2, it is incident on the spatial light modulator 31 and modulated on it the phase diagram corresponding to the m×n order Hermit-Gaussian beam. After the outgoing light passes through the 4-f filter system, a high-purity m×n order Hermit-Gaussian source is generated.

[0181] Step 2: Select the polarization state of the Hermigass beam as 45-degree linearly polarized light through pre-selection. In the weakly coupled module, use an interferometer to introduce axial rotations in opposite directions for the horizontal component (H-light) and vertical component (V-light) of the beam polarization state. Then, perform post-selection on the beam polarization state so that the beam axial rotation parameter is carried by a spatial mode entangled state.

[0182] Step 3: The selected beam is incident on the spatial light modulator 32 and the phase diagram corresponding to the mode entanglement state carrying parameters is modulated on it. After the outgoing light passes through a Fourier lens 4, it is received by an optical fiber pigtail at the focal point behind the lens 4 to realize projection measurement.

[0183] Step 4: The projection measurement converts the beam axial rotation parameter into light intensity information. The light intensity obtained by the projection measurement is measured using the avalanche photodiode detector 15, converted into an electrical signal, and input into the spectrum analyzer 16 to demodulate the magnitude of the beam axial rotation.

[0184] Preferably, the phase diagram corresponding to the m×n order Hermitian Gaussian beam in step 1 is obtained through numerical calculation, specifically as follows:

[0185] The beam distribution input to the spatial light modulator 31 is denoted as... in The amplitude intensity distribution of the beam input to the spatial light modulator 31 The input beam spatial phase distribution; i is the imaginary unit, x is the horizontal coordinate of the cross-section, and y is the vertical coordinate of the cross-section;

[0186] The phase diagram loaded on the spatial light modulator 31 is denoted as H. A (x,y). The output beam distribution of the spatial light modulator 31 is as follows: Where ψ mn (x,y) represents the desired m×n order Hermitian beam distribution. The amplitude intensity and spatial phase of the output beam from the spatial light modulator 31 are denoted here as... and

[0187] Let the relative phase be denoted as in It is the phase of the blazed grating loaded on the spatial light modulator 31.

[0188] Let the relative amplitude be denoted as

[0189] The phase diagram loaded on the spatial light modulator 31 is given by the formula

[0190]

[0191] Given, among which It is the inverse function of the first-order Bessel function.

[0192] Preferably, the 4-f filtering system described in step 1 is specifically:

[0193] A Fourier lens 41 with a focal length of f1 is placed at a position f1 behind the spatial light modulator 31. A small aperture 5 is placed at a position f1 behind the Fourier lens 41. The beam modulated by the spatial light modulator is focused at the small aperture after passing through the Fourier lens 41. Because a blazed grating is added to the phase diagram, the focal points of the image plane will be periodically arranged in the horizontal direction. The aperture filters out the light spot at the first-order diffraction point. A Fourier lens 42 with a focal length of f2 is placed at a position f2 behind the modulator. The output beam is a high-purity m×n-order Hermitian Gaussian beam. The spatial distribution state of this Hermitian Gaussian beam can be denoted as |m,n>, where |·> represents the Dirac right vector.

[0194] |m,n>=∫∫dxdyψ mn (x,y)|x,y)

[0195] Where, ψ mn (x,y) is the wave function of an m×n order Hermitian Gaussian beam;

[0196] Preferably, in step 2, the beam's polarization state is selected as 45-degree linearly polarized light through pre-selection, specifically as follows:

[0197] The Hermetic Gaussian beam generated by the spatial light modulator 31 and the 4-f filter system is oriented by a reflector 61 and then incident on a Glan Taylor polarizing prism 7A with its optical axis along the horizontal direction. After passing through a half-wave plate 8A with its optical axis at an angle of 22.5° to the horizontal plane, the polarization state of the output beam is preselected as follows:

[0198]

[0199] Where i represents the preselection state, H represents horizontally polarized light, and V represents vertically polarized light.

[0200] Preferably, the axial rotation in opposite directions described in step 2 specifically refers to:

[0201] In an interferometer, an axial rotation with a relative angle of 2α is applied to the horizontal and vertical polarization components of the beam, which can be represented by the evolution operator as follows:

[0202]

[0203] in, Let this be the unitary evolution operator representation of the rotation process;

[0204] in For Pauli operators acting on polarization states, Let _ ...

[0205] It is easy to see that the input state of the interferometer can be denoted as: |Ψ in >=|i>|ψ i >, where |ψ i >=|m,n> represents the initial spatial pattern of the beam. Therefore, the output state of the interferometer can be denoted as:

[0206]

[0207] Preferably, the subsequent selection in step 2 specifically refers to:

[0208] The beam emitted from the interferometer passes through an optical axis that is perpendicular to the horizontal direction. A half-wave plate 83, after passing through a Glan Taylor polarizing prism 72 with its optical axis in the horizontal direction, has its output beam polarization state subsequently selected as:

[0209]

[0210] Where ε is the post-selection angle, 0.05 < ε < 1. Before passing through the half-wave plate, the beam is pre-compensated for the phase difference between the horizontal and vertical polarization components in the interferometer by a Sorel-Barbinegren phase compensator 13. Then, the post-selected beam is oriented by a spatial light modulator 32 after being incident on the interferometer by a mirror 65.

[0211] Preferably, the spatial mode entangled state mentioned in step 2 is specifically:

[0212] The available state vector of the selected beam is denoted as:

[0213]

[0214] Where f represents the post-selection state, and <·|·> represents the inner product operation.

[0215]

[0216] This is denoted as a weak value, and here we consider the approximate condition for weak measurement: α << 1. Therefore, the beam spatial mode after selection can be denoted as:

[0217]

[0218] It is evident that the axial rotation information of the beam is completely influenced by the spatial mode. Bear, and

[0219]

[0220] The pattern states in the x and y directions are inseparable, which is equivalent to an entangled form and is a classic entangled state of a spatial pattern.

[0221] Furthermore, the quantum precision limit for estimating the unknown parameter α can be calculated as follows:

[0222]

[0223] Where N is the number of photons received by the detector;

[0224] Due to the introduction of classical entangled states, the limiting accuracy of our beam axis rotation measurement will be obtained through the mode number as a factor proportional to the mode number. The enhancement is similar to the Heisenberg-scale enhancement of phase estimation in quantum interference.

[0225] Preferably, the phase diagram corresponding to the entangled state of the modulation-carrying parameters in step 2 is specifically as follows:

[0226] The principle of phase diagram calculation is the same as that described in claim 2. Here, the beam distribution modulated by the spatial light modulator 32 is denoted as... in Entangled states of modes carrying rotation parameters The corresponding two-dimensional spatial wave function distribution, the amplitude intensity and spatial phase of the beam distribution modulated by the spatial light modulator 32 are denoted here as... and When calculating the phase diagram of the spatial light modulator 32, the preset input beam is parallel light, i.e.

[0227] The input beam amplitude intensity is preset for calculating the phase diagram of the spatial light modulator 32. The spatial phase of the input beam is preset for calculating the phase diagram of the spatial light modulator 32;

[0228] Let the relative phase be denoted as in It is the phase of the blazed grating loaded on the spatial light modulator 32.

[0229] Let the relative amplitude be denoted as

[0230] Therefore, the phase diagram loaded on the spatial light modulator 32 is given by the formula

[0231]

[0232] Provided.

[0233] Preferably, the use of fiber optic pigtails to receive and perform projection measurement in step 2 specifically involves:

[0234] A Fourier lens 43 is used behind the spatial light modulator 32 to perform a Fourier transform on the projected light field. Since the light field distribution modulated by the spatial light modulator 32 is... The light field of the input spatial light modulator 32 is ψ f (x,y), i.e., the final state of the pointer |ψ f The corresponding two-dimensional optical field distribution is transformed at the focal length behind the Fourier lens 4C (the first-order diffraction position). This transformed optical field is then directly received at the center of the transformed optical field via a single-mode fiber 14. Since the mode field diameter of the single-mode fiber 14 is much smaller than the size of the transformed optical field, the receiving efficiency of the single-mode fiber 14 can be expressed as…

[0235]

[0236] in, for The conjugate representation of .

[0237] Preferably, step 4 includes the following steps:

[0238] Step 401: Input the light intensity received by the single-mode fiber into the avalanche photodiode detector 15 to convert the received weak light intensity signal into an electrical signal.

[0239] Step 402: Input the electrical signal of the avalanche photodiode detector 15 into the frequency analyzer 16, read the peak frequency and corresponding intensity of the frequency analyzer 16, and demodulate the amplitude and frequency of the beam axial rotation signal.

[0240] Preferably, the step of inputting the light intensity received by the single-mode fiber 14 into the avalanche photodiode detector 15 specifically involves:

[0241] The light intensity received by the avalanche photodiode detector 15 is proportional to the projected probability, i.e.

[0242]

[0243] Among them, I det Let P be the light intensity received by the avalanche photodiode detector 15, and let P be the final state of the photon |ψf >In the spatial mode carrying rotation information Projection probability on;

[0244] Under the same rotating signal intensity, the received light intensity will be increased by a factor 2mn+m+n, which is related to the spatial mode number of the Hermetic beam.

[0245] Preferably, the amplitude and frequency of the demodulated beam axial rotation signal are specifically as follows:

[0246] The electrical signal output by the avalanche photodiode detector 15 is a voltage signal amplified by the built-in transimpedance amplifier, which is proportional to the received light intensity, i.e., V. det ∝I det By inputting this voltage signal into the frequency analyzer 16, the frequency and amplitude of the beam axial rotation signal can be determined.

[0247] Example 2:

[0248] Example 2 is a preferred embodiment of Example 1, and is used to illustrate the present invention in more detail.

[0249] In this embodiment, a Hermitogaussian light source generation module, a weak coupling module, a projection measurement module, an electrical module, and a data processing module are deployed. The Hermitogaussian light source generation module is used to generate a high-order Hermitogaussian light source. The weak coupling module is used to introduce axial rotation of the beam and generate a classical entangled state to improve measurement accuracy. In this module, a weak value amplification technique is also introduced through post-selection to further amplify the weak axial rotation signal of the beam and improve the noise immunity of the system. The projection measurement module is used to demodulate the weak axial rotation signal of the beam into a light intensity signal. The electrical module is used to convert the optical signal into an electrical signal to obtain and store measurement data. The data processing module is used to analyze and process the measured data and calculate the axial rotation angle of the beam.

[0250] Specifically, the novel beam axial rotation method based on classical entanglement includes the following steps:

[0251] Step A1: After beam expansion, the Gaussian source of the single-frequency laser is incident on the spatial light modulator A;

[0252] Step A2: Modulate the phase diagram corresponding to the m×n order Hermitian Gaussian beam on the spatial light modulator A, specifically as follows:

[0253] Let the beam distribution input to spatial light modulator A be denoted as... in The amplitude intensity distribution of the beam input to spatial light modulator A. The spatial phase distribution of the input beam is given. The phase diagram loaded onto the spatial light modulator A is denoted as H.A (x, y). The output beam distribution of spatial light modulator A is as follows: Where ψ mn (x,y) represents the desired m×n order Hermitian Gaussian beam distribution, whose amplitude and spatial phase are denoted here as... and

[0254] Let the relative phase be denoted as in It is the phase of the blazed grating loaded on the spatial light modulator A.

[0255] Let the relative amplitude be denoted as

[0256] The phase diagram loaded on spatial light modulator A is given by the formula

[0257]

[0258] Given, among which It is the inverse function of the first-order Bessel function.

[0259] Step A3: The output light from spatial light modulator A is filtered by a 4-f filter system to generate a high-purity m×n-order Hermitian Gaussian light source, specifically as follows:

[0260] A Fourier lens A with a focal length of f1 is placed f1 behind the spatial light modulator A. A small aperture is placed f1 behind the Fourier lens A. The beam modulated by the spatial light modulator is focused at the small aperture after passing through the Fourier lens A. Due to the blazed grating added to the phase diagram, the focal points of the image plane will be periodically arranged in the horizontal direction. The aperture filters out the first-order diffraction spot. A lens with a focal length of f2 is placed f2 behind the modulator A, resulting in a high-purity m×n-order Hermitian Gaussian beam. The spatial distribution of this Hermitian Gaussian beam can be denoted as |m,n>, where |·> represents the Dirac right vector.

[0261] |m,n>=∫∫dxdyψ mn (x,y)|x,y>

[0262] Step B1: Select the polarization state of the Hermetic Gaussian beam as 45-degree linearly polarized light through pre-selection, specifically:

[0263] A Hermetic beam generated by a spatial light modulator and a 4-f filter system is incident on a polarizer with its optical axis aligned horizontally. After passing through a half-wave plate A with its optical axis at a 22.5° angle to the horizontal plane, the polarization state of the output beam is preselected as follows:

[0264]

[0265] Where i represents the preselection state, H represents horizontally polarized light, and V represents vertically polarized light.

[0266] Step B2: In the weakly coupled module, an interferometer is used to introduce axial rotations in opposite directions to the horizontal component (H-beam) and vertical component (V-beam) of the beam polarization state, specifically:

[0267] In an interferometer, an axial rotation with a relative angle of 2α is applied to the horizontal and vertical polarization components of the beam, which can be represented by the evolution operator as follows:

[0268]

[0269] in For Pauli operators acting on polarization states, Let be the angular momentum operator acting on the spatial mode of the beam, and represent axial rotation. It is easy to see that the input state of the interferometer can be denoted as: |Ψ in >=|i>|ψ i >, where |ψ i >=|m,n> represents the initial spatial pattern of the beam. Therefore, the output state of the interferometer can be denoted as:

[0270]

[0271] Step B3: Then, the beam polarization state is further selected, specifically as follows:

[0272] The beam emitted from the interferometer passes through an optical axis that is perpendicular to the horizontal direction. A half-angle waveplate B, after passing through an analyzer with its optical axis aligned horizontally, has its output beam polarization state subsequently selected as follows:

[0273]

[0274] Where ε is the post-selection angle, 0.05 < ε < 1.

[0275] Step B4: In the beam output from the weakly coupled module, the beam axial rotation parameter is carried by a spatial mode entangled state, specifically:

[0276] The available state vector of the selected beam is denoted as:

[0277]

[0278] in

[0279]

[0280] This is denoted as a weak value, and here we consider the approximate condition for weak measurement: α << 1. Therefore, the beam spatial mode after selection can be denoted as:

[0281]

[0282]

[0283] It is evident that the axial rotation information of the beam is completely influenced by the spatial mode. Bear, and

[0284]

[0285] The pattern states in the x and y directions are inseparable, which is equivalent to an entangled form and is a classic entangled state of a spatial pattern.

[0286] Furthermore, the quantum precision limit for estimating the unknown parameter α can be calculated as follows:

[0287]

[0288] Due to the introduction of classical entangled states, the limiting accuracy of our beam axis rotation measurement will be obtained through the mode number as a factor proportional to the mode number. The enhancement is similar to the Heisenberg-scale enhancement of phase estimation in quantum interference.

[0289] Step C1: The selected beam is incident on spatial light modulator B, and the phase diagram corresponding to the mode entanglement state carrying parameters is modulated on it, specifically:

[0290] Here, the beam distribution modulated by spatial light modulator B is denoted as... in Entangled states of modes carrying rotation parameters The corresponding two-dimensional spatial wave function distribution, whose amplitude and spatial phase are denoted here as... and When calculating the phase diagram of spatial light modulator B, the preset input beam is parallel light, i.e.

[0291] Let the relative phase be denoted as in It is the phase of the blazed grating loaded on the spatial light modulator B.

[0292] Let the relative amplitude be denoted as

[0293] Therefore, the phase diagram loaded on the spatial light modulator B is given by the formula.

[0294]

[0295] Provided.

[0296] Step C2: The outgoing light from the spatial light modulator B passes through a Fourier lens and is received by an optical fiber pigtail at the focal point behind the lens to achieve projection measurement. Specifically:

[0297] A Fourier lens is used behind the spatial light modulator B to perform a Fourier transform on the projected light field. Since the light field distribution modulated by the spatial light modulator B is... The light field input to spatial light modulator B is That is, the final state of the pointer |ψ f The corresponding two-dimensional optical field distribution is transformed into a transformed optical field at the focal length behind the Fourier lens (the first-order diffraction position). This transformed optical field is then directly received at the center of the transformed optical field via a single-mode fiber. Since the mode field diameter of the single-mode fiber is much smaller than the size of the transformed optical field, the receiving efficiency of the single-mode fiber can be expressed as…

[0298]

[0299] in It is exactly the final state of the beam in the classical entangled state. The projection probability on.

[0300] Step D1: Projection measurement converts the beam axial rotation parameters into light intensity information. The light intensity obtained from the projection measurement is then measured using an avalanche photodiode detector 15 and converted into an electrical signal. Specifically:

[0301] The light intensity received by the avalanche photodiode detector 15 is proportional to the projected probability, i.e.

[0302]

[0303] Under the same rotating signal intensity, the received light intensity will be increased by a factor 2mn+m+n, which is related to the spatial mode number of the Hermetic beam.

[0304] Step D2: Input the voltage signal of the avalanche photodiode detector 15 into the spectrum analyzer to demodulate the magnitude of the beam axial rotation, specifically:

[0305] The electrical signal output by the avalanche photodiode detector 15 is a voltage signal amplified by the built-in transimpedance amplifier, which is proportional to the received light intensity, i.e., V. det ∝I det By inputting this voltage signal into a frequency analyzer, the frequency and amplitude of the beam's axial rotation signal can be determined.

[0306] In the description of this application, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0307] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0308] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for measuring the axial rotation of a beam based on classical entanglement, characterized in that, include: Step S1: After the single-frequency laser source (1) is expanded, the phase diagram corresponding to the Hermetic Gaussian beam is modulated, and a high-purity Hermetic Gaussian source is generated through the filtering system; Step S2: Select the polarization state of the Hermigasaurus beam through pre-selection, introduce axial rotations in opposite directions to the horizontal and vertical components of the beam polarization state, and then pass the beam polarization state through post-selection so that the beam axial rotation parameter is carried by the entangled state of the spatial mode. Step S3: The selected beam is incident on the spatial light modulator (32) and the phase diagram corresponding to the mode entanglement state carrying parameters is modulated on it. After passing through the Fourier lens (4), the beam is received by the fiber optic pigtail at the focal point behind the lens (4) to realize projection measurement. Step S4: Projection measurement converts the beam axial rotation parameter into light intensity information, measures the light intensity obtained by projection measurement, converts it into an electrical signal and inputs it into the frequency analyzer (16) to demodulate the magnitude of the beam axial rotation. In step S2: The Hermigass beam is pre-selected to be linearly polarized at 45 degrees. In the weakly coupled module, an interferometer is used to introduce axial rotations in opposite directions to the horizontal component H and the vertical component V of the beam polarization state. Then, the beam polarization state is post-selected so that the beam axial rotation parameter is carried by a spatial mode entangled state. The beam is pre-selected to have its polarization state set to 45-degree linearly polarized light, specifically: The Hermigasaurus beam generated by the spatial light modulator (31) and the 4f filter system is oriented by a mirror (61) and then incident on a Glan Taylor polarizing prism (71) whose optical axis is horizontal. The polarization state of the output beam is pre-selected by the half-wave plate (81) at the included angle: in, Indicates the pre-selection state. Indicates horizontally polarized light. Indicates vertically polarized light; The opposite axial rotation specifically refers to: In an interferometer, a relative angle of θ is applied to the horizontal and vertical polarization components of the light beam. The axial rotation of is represented by the evolution operator as: in, Let this be the unitary evolution operator representation of the rotation process; For Pauli operators acting on polarization states, Let be the angular momentum operator acting on the spatial mode of the beam, and represent axial rotation. The symbol for the left arrow of Dirac; Unknown parameter; In practice, the beam is first input into the polarization interferometer through a beam splitter (9). The main body of the polarization interferometer consists of a polarization beam splitter (10) and a three-sided mirror (6). A linear polarizer (11) and a half-wave plate (82) are inserted into the interferometer. The optical axis of the linear polarizer (11) is perpendicular to the horizontal plane, and the half-wave plate (82) is at a 45-degree angle to the horizontal plane. In addition, the axial rotation of the beam is achieved by inserting a Dowell prism (12) into the interferometer. The input state of the interferometer is denoted as: ,in The initial spatial mode of the beam is represented; therefore, the output state of the interferometer is denoted as: The subsequent selection specifically refers to: The beam emitted from the interferometer passes through an optical axis that is perpendicular to the horizontal direction. A half-wave plate (83) at an angle, after passing through a Glan Taylor polarizing prism (72) with its optical axis in the horizontal direction, has its output beam polarization state subsequently selected as: in To select the angle later, ; Before passing through the half-wave plate (8), the beam is pre-compensated by a Sorel-Barbinje phase compensator (13) to compensate for the phase difference between the horizontal and vertical polarization components in the interferometer. After passing through the half-wave plate (8), the beam is adjusted in direction by a mirror (65) and then incident on the spatial light modulator (32) for projection measurement.

2. The beam axial rotation measurement method based on classical entanglement according to claim 1, characterized in that, In step S1: The single-frequency laser source (1) is expanded by the beam expander coupling head (2) and then incident on the spatial light modulator (31) and modulated on the spatial light modulator (31). The phase diagram corresponding to the Hermitian beam shows that the emitted light, after passing through a 4f filter system, generates a higher purity beam. Hermigaussian light source; The The phase diagram corresponding to the Hermitian beam was obtained through numerical calculation, specifically as follows: The beam distribution of the input spatial light modulator (31) is denoted as... ,in The amplitude intensity distribution of the beam input to the spatial light modulator (31), The input beam spatial phase distribution; i is the imaginary unit, x is the horizontal coordinate of the cross-section, and y is the vertical coordinate of the cross-section; The phase diagram loaded on the spatial light modulator (31) is denoted as The output beam distribution of the spatial light modulator (31) is as follows: ,in For what is hoped to be obtained The Hermitian beam distribution, the amplitude intensity and spatial phase of the output beam of the spatial light modulator (31) are respectively... and ; Let the relative phase be denoted as ,in It is the phase of the blazed grating loaded on the spatial light modulator (31); Let the relative amplitude be denoted as ; Phase diagram loaded on the spatial light modulator (31): in It is the inverse function of the first-order Bessel function; The 4f filtering system is specifically as follows: Behind the spatial light modulator (31) Place a focal length at [location]. The Fourier lens (41), behind the Fourier lens (41) A small hole (5) is placed at the image plane. The light beam modulated by the spatial light modulator (31) will be focused at the small hole (5) after passing through the Fourier lens (41). Since a blazed grating is attached to the phase diagram, the focal point of the image plane will be periodically arranged in the horizontal direction. The small hole (5) is used to filter out the light spot at the first diffraction point and then filter it out in the rear. Place a focal length at [location]. The lens (42) produces a high purity beam. A Hermitian beam; the spatial distribution of this Hermitian beam is denoted as... ,symbol Indicates Dirac's right arrow, and in, for The wave function of a Hermitian beam.

3. The beam axial rotation measurement method based on classical entanglement according to claim 1, characterized in that: The spatial mode entangled state is specifically as follows: The state vector of the selected beam is denoted as follows: in: For the post-selection state, This is an inner product operation; Denoteed as a weak value, consider the approximate conditions for weak measurements: The selected beam spatial mode is denoted as: The axial rotation information of the beam is completely controlled by the spatial mode. Bear, and The pattern states in the x and y directions are inseparable, which is equivalent to an entangled form and is a classic entangled state of a spatial pattern. For unknown parameters The estimated limit of quantum precision is: in, The number of photons received by the detector; Due to the introduction of classical entangled states, the limiting accuracy for beam axis rotation measurement will be obtained through a factor proportional to the mode number. Enhancement; The phase diagram corresponding to the entangled state of the modulation-carrying parameters is specifically as follows: The beam distribution modulated by the spatial light modulator (32) is denoted as ,in Entangled states of modes carrying rotation parameters The corresponding two-dimensional spatial wave function distribution, the amplitude intensity and spatial phase of the beam distribution modulated by the spatial light modulator (32) are respectively denoted here as: and When calculating the phase diagram of the spatial light modulator (32), the preset input beam is parallel light. , ; The input beam amplitude intensity is preset when calculating the phase diagram of the spatial light modulator (32). The spatial phase of the input beam is preset when calculating the phase diagram of the spatial light modulator (32); Let the relative phase be denoted as ,in It is the phase of the blazed grating loaded on the spatial light modulator (32); Let the relative amplitude be denoted as , Therefore, the phase diagram loaded on the spatial light modulator (32) is: in It is the inverse function of the first-order Bessel function; The use of fiber optic pigtails for receiving and implementing projection measurements specifically involves: A Fourier lens (43) is used behind the spatial light modulator (32) to perform a Fourier transform on the projected light field. Since the light field distribution modulated by the spatial light modulator (32) is... The light field input to the spatial light modulator (32) is That is, the final state of the pointer The corresponding two-dimensional optical field distribution is transformed at the focal length behind the Fourier lens (43), and then directly received at the center of the transformed optical field through a single-mode fiber (14). Since the mode field diameter of the single-mode fiber (14) is much smaller than the size of the transformed optical field, the receiving efficiency of the single-mode fiber (14) is expressed as: in, for The conjugate representation of .

4. The beam axial rotation measurement method based on classical entanglement according to claim 1, characterized in that, In step S4: Projection measurement converts the beam axial rotation parameter into light intensity information. The light intensity obtained by projection measurement is measured using an avalanche photodiode detector (15), converted into an electrical signal, and input into a frequency analyzer to demodulate the magnitude of the beam axial rotation. Step S4.1: Input the light intensity received by the single-mode fiber (14) into the avalanche photodiode detector (15) to convert the received weak light intensity signal into an electrical signal; Step S4.2: Input the electrical signal of the avalanche photodiode detector (15) into the frequency analyzer (16), read the peak frequency and corresponding intensity of the frequency analyzer (16), and demodulate the amplitude and frequency of the beam axial rotation signal; The process of inputting the light intensity received by the single-mode fiber (14) into the avalanche photodiode detector (15) specifically involves: The light intensity received by the avalanche photodiode detector (15) is proportional to the projected probability, i.e. in, The light intensity received by the avalanche photodiode detector (15) is... Photon final state In the spatial mode that carries rotation information Projection probability on; Under the same rotating signal intensity, the received light intensity will be affected by a factor related to the spatial mode number of the Hermetic beam. And improve; The amplitude and frequency of the demodulated beam axial rotation signal are specifically as follows: The electrical signal output by the avalanche photodiode detector (15) is a voltage signal amplified by the built-in transimpedance amplifier, which is proportional to the received light intensity, i.e. The voltage signal is input into the frequency analyzer (16) to determine the frequency and amplitude of the beam axial rotation signal.

5. A beam axial rotation measurement system based on classical entanglement, characterized in that, include: Module M1: After expanding the single-frequency laser source (1), the phase diagram corresponding to the Hermitian beam is modulated, and a high-purity Hermitian source is generated through the filtering system; Module M2: The Hermetic Gaussian beam is preselected to select the polarization state, and the horizontal and vertical components of the beam polarization state are introduced to undergo axial rotation in opposite directions. The beam polarization state is then postselected so that the beam axial rotation parameter is carried by the entangled state of the spatial mode. Module M3: The selected beam is incident on the spatial light modulator (32) and modulated on it the phase diagram corresponding to the mode entanglement state carrying parameters. After passing through the Fourier lens (4), the beam is received by the fiber optic pigtail at the focal point behind the lens (4) to realize projection measurement. Module M4: Projection measurement converts the beam axial rotation parameters into light intensity information, measures the light intensity obtained by projection measurement, converts it into an electrical signal and inputs it into the frequency analyzer (16) to demodulate the magnitude of the beam axial rotation; In module M2: The Hermigass beam is pre-selected to be linearly polarized at 45 degrees. In the weakly coupled module, an interferometer is used to introduce axial rotations in opposite directions to the horizontal component H and the vertical component V of the beam polarization state. Then, the beam polarization state is post-selected so that the beam axial rotation parameter is carried by a spatial mode entangled state. The beam is pre-selected to have its polarization state set to 45-degree linearly polarized light, specifically: The Hermigasaurus beam generated by the spatial light modulator (31) and the 4f filter system is oriented by a mirror (61) and then incident on a Glan Taylor polarizing prism (71) whose optical axis is horizontal. The polarization state of the output beam is pre-selected by the half-wave plate (81) at the included angle: in, Indicates the pre-selection state. Indicates horizontally polarized light. Indicates vertically polarized light; The opposite axial rotation specifically refers to: In an interferometer, a relative angle of θ is applied to the horizontal and vertical polarization components of the light beam. The axial rotation of is represented by the evolution operator as: in, Let this be the unitary evolution operator representation of the rotation process; For Pauli operators acting on polarization states, Let be the angular momentum operator acting on the spatial mode of the beam, and represent axial rotation. The symbol for the left arrow of Dirac; Unknown parameter; In practice, the beam is first input into the polarization interferometer through a beam splitter (9). The main body of the polarization interferometer consists of a polarization beam splitter (10) and a three-sided mirror (6). A linear polarizer (11) and a half-wave plate (82) are inserted into the interferometer. The optical axis of the linear polarizer (11) is perpendicular to the horizontal plane, and the half-wave plate (82) is at a 45-degree angle to the horizontal plane. In addition, the axial rotation of the beam is achieved by inserting a Dowell prism (12) into the interferometer. The input state of the interferometer is denoted as: ,in The initial spatial mode of the beam is represented; therefore, the output state of the interferometer is denoted as: The subsequent selection specifically refers to: The beam emitted from the interferometer passes through an optical axis that is perpendicular to the horizontal direction. A half-wave plate (83) at an angle, after passing through a Glan Taylor polarizing prism (72) with its optical axis in the horizontal direction, has its output beam polarization state subsequently selected as: in To select the angle later, ; Before passing through the half-wave plate (8), the beam is pre-compensated by a Sorel-Barbinje phase compensator (13) to compensate for the phase difference between the horizontal and vertical polarization components in the interferometer. After passing through the half-wave plate (8), the beam is adjusted in direction by a mirror (65) and then incident on the spatial light modulator (32) for projection measurement.

6. The beam axial rotation measurement system based on classical entanglement according to claim 5, characterized in that, In module M1: The single-frequency laser source (1) is expanded by the beam expander coupling head (2) and then incident on the spatial light modulator (31) and modulated on the spatial light modulator (31). The phase diagram corresponding to the Hermitian beam shows that the emitted light, after passing through a 4f filter system, generates a higher purity beam. Hermigaussian light source; The The phase diagram corresponding to the Hermitian beam was obtained through numerical calculation, specifically as follows: The beam distribution of the input spatial light modulator (31) is denoted as... ,in The amplitude intensity distribution of the beam input to the spatial light modulator (31), The input beam spatial phase distribution; i is the imaginary unit, x is the horizontal coordinate of the cross-section, and y is the vertical coordinate of the cross-section; The phase diagram loaded on the spatial light modulator (31) is denoted as The output beam distribution of the spatial light modulator (31) is as follows: ,in For what is hoped to be obtained The Hermitian beam distribution, the amplitude intensity and spatial phase of the output beam of the spatial light modulator (31) are respectively... and ; Let the relative phase be denoted as ,in It is the phase of the blazed grating loaded on the spatial light modulator (31); Let the relative amplitude be denoted as ; Phase diagram loaded on the spatial light modulator (31): in It is the inverse function of the first-order Bessel function; The 4f filtering system is specifically as follows: Behind the spatial light modulator (31) Place a focal length at [location]. The Fourier lens (41), behind the Fourier lens (41) A small hole (5) is placed at the image plane. The light beam modulated by the spatial light modulator (31) will be focused at the small hole (5) after passing through the Fourier lens (41). Since a blazed grating is attached to the phase diagram, the focal point of the image plane will be periodically arranged in the horizontal direction. The small hole (5) is used to filter out the light spot at the first diffraction point and then filter it out in the rear. Place a focal length at [location]. The lens (42) produces a high purity beam. A Hermitian beam; the spatial distribution of this Hermitian beam is denoted as... ,symbol Indicates Dirac's right arrow, and in, for The wave function of a Hermitian beam.

7. The beam axial rotation measurement system based on classical entanglement according to claim 5, characterized in that: The spatial mode entangled state is specifically as follows: The state vector of the selected beam is denoted as follows: in: For the post-selection state, This is an inner product operation; Denoteed as a weak value, consider the approximate conditions for weak measurements: The selected beam spatial mode is denoted as: The axial rotation information of the beam is completely controlled by the spatial mode. Bear, and The pattern states in the x and y directions are inseparable, which is equivalent to an entangled form and is a classic entangled state of a spatial pattern. For unknown parameters The estimated limit of quantum precision is: in, The number of photons received by the detector; Due to the introduction of classical entangled states, the limiting accuracy for beam axis rotation measurement will be obtained through a factor proportional to the mode number. Enhancement; The phase diagram corresponding to the entangled state of the modulation-carrying parameters is specifically as follows: The beam distribution modulated by the spatial light modulator (32) is denoted as ,in Entangled states of modes carrying rotation parameters The corresponding two-dimensional spatial wave function distribution, the amplitude intensity and spatial phase of the beam distribution modulated by the spatial light modulator (32) are respectively denoted here as: and When calculating the phase diagram of the spatial light modulator (32), the preset input beam is parallel light. , ; The input beam amplitude intensity is preset when calculating the phase diagram of the spatial light modulator (32). The spatial phase of the input beam is preset when calculating the phase diagram of the spatial light modulator (32); Let the relative phase be denoted as ,in It is the phase of the blazed grating loaded on the spatial light modulator (32); Let the relative amplitude be denoted as , Therefore, the phase diagram loaded on the spatial light modulator (32) is: in It is the inverse function of the first-order Bessel function; The use of fiber optic pigtails for receiving and implementing projection measurements specifically involves: A Fourier lens (43) is used behind the spatial light modulator (32) to perform a Fourier transform on the projected light field. Since the light field distribution modulated by the spatial light modulator (32) is... The light field input to the spatial light modulator (32) is That is, the final state of the pointer The corresponding two-dimensional optical field distribution is transformed at the focal length behind the Fourier lens (43), and then directly received at the center of the transformed optical field through a single-mode fiber (14). Since the mode field diameter of the single-mode fiber (14) is much smaller than the size of the transformed optical field, the receiving efficiency of the single-mode fiber (14) is expressed as: in, for The conjugate representation of .

8. The beam axial rotation measurement system based on classical entanglement according to claim 5, characterized in that, In module M4: Projection measurement converts the beam axial rotation parameter into light intensity information. The light intensity obtained by projection measurement is measured using an avalanche photodiode detector (15), converted into an electrical signal, and input into a frequency analyzer to demodulate the magnitude of the beam axial rotation. Module M4.1: Inputs the light intensity received by the single-mode fiber (14) into the avalanche photodiode detector (15) and converts the received weak light intensity signal into an electrical signal; Module M4.2: Input the electrical signal of the avalanche photodiode detector (15) into the frequency analyzer (16), read the peak frequency and corresponding intensity of the frequency analyzer (16), and demodulate the amplitude and frequency of the beam axial rotation signal; The process of inputting the light intensity received by the single-mode fiber (14) into the avalanche photodiode detector (15) specifically involves: The light intensity received by the avalanche photodiode detector (15) is proportional to the projected probability, i.e. in, The light intensity received by the avalanche photodiode detector (15) is... Photon final state In the spatial mode that carries rotation information Projection probability on; Under the same rotating signal intensity, the received light intensity will be affected by a factor related to the spatial mode number of the Hermetic beam. And improve; The amplitude and frequency of the demodulated beam axial rotation signal are specifically as follows: The electrical signal output by the avalanche photodiode detector (15) is a voltage signal amplified by the built-in transimpedance amplifier, which is proportional to the received light intensity, i.e. The voltage signal is input into the frequency analyzer (16) to determine the frequency and amplitude of the beam axial rotation signal.

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