CN-117664320-B - Classical entanglement-based light beam axial rotation measurement method and system

CN117664320BCN 117664320 BCN117664320 BCN 117664320BCN-117664320-B

Abstract

The invention provides a method and a system for measuring axial rotation of a light beam based on classical entanglement, wherein the method comprises the steps of expanding a single-frequency laser light source, modulating a phase diagram corresponding to an early Gaussian light beam, generating the early Gaussian light source with higher purity through a filtering system, introducing opposite axial rotation to horizontal components and vertical components of the polarization state of the light beam through pre-selection polarization state, carrying axial rotation parameters of the light beam by space mode entanglement state through post-selection of the polarization state of the light beam, modulating the phase diagram corresponding to the mode entanglement state carrying parameters of the light beam after post-selection, receiving the phase diagram through a Fourier lens by using an optical fiber tail fiber, converting the axial rotation parameters of the light beam into light intensity information through projection measurement, measuring the light intensity obtained through projection measurement, converting the light intensity into an electric signal, and inputting the electric signal into a spectrum analyzer to demodulate the axial rotation of the light beam. Compared with the existing beam axial rotation measurement scheme, the invention has higher measurement precision.

Inventors

HUANG JINGZHENG
Xia Binke
LI HONGJING
ZENG GUIHUA

Assignees

上海交通大学

Dates

Publication Date: 20260512
Application Date: 20220830

Claims (8)

1. A classical entanglement-based method for measuring axial rotation of a light beam, comprising: step S1, modulating a phase diagram corresponding to an early Gaussian beam after expanding a single-frequency laser light source (1), and generating an early Gaussian light source with higher purity through a filtering system; S2, enabling the hermitian Gaussian beam to pass through a pre-selection polarization state, introducing axial rotation with opposite directions to the horizontal component and the vertical component of the polarization state of the beam, and then enabling the axial rotation parameter of the beam to be carried by a space mode entanglement state after the polarization state of the beam passes through a post-selection; S3, the light beam after the selection is incident to a spatial light modulator (32) and modulated with a phase diagram corresponding to a mode entanglement state carrying parameters, and the light beam passes through a Fourier lens (4) and is received at a rear focal point of the lens (4) by using an optical fiber tail fiber, so that projection measurement is realized; S4, converting the axial rotation parameters of the light beam into light intensity information by projection measurement, measuring the light intensity obtained by the projection measurement, converting the light intensity into an electric signal, inputting the electric signal into a frequency analyzer (16), and demodulating the axial rotation of the light beam; in the step S2: the method comprises the steps of selecting a polarization state of an hermitian Gaussian beam to be 45-degree linearly polarized light before passing, respectively introducing axial rotation with opposite directions to horizontal component H light and vertical component V light of the polarization state of the beam by using an interferometer in a weak coupling module, and then selecting the polarization state of the beam after passing to enable an axial rotation parameter of the beam to be carried by a space mode entanglement state; The polarization state of the light beam is selected to be 45-degree linear polarized light before passing through the light beam, and the light beam is specifically: the Hermite Gaussian beam generated by the spatial light modulator (31) and the 4f filtering system is incident to a Gray Taylor polarizing prism (71) with an optical axis along the horizontal direction after being adjusted by a mirror (61), and forms a plane with the horizontal plane by the optical axis -An angled half-wave plate (81), the polarization state of the output beam being pre-selected as: Wherein, the The pre-selected state is indicated and the pre-selected state, Representing light of a horizontal polarization such as, Representing vertically polarized light; the opposite axial rotation is specifically as follows: In interferometers, a relative angle is applied to the horizontally polarized component and the vertically polarized component of a beam of light Is expressed by an evolution operator as: Wherein, the A unitary evolution operator representation for the rotation process; For the berkovich operator to act on polarization, For the angular momentum operator to act on the beam space pattern, axial rotation is represented, Is a dirac left-vector symbol; Is an unknown parameter; When the method is realized, firstly, a light beam is input into a polarization interferometer through a beam splitter (9), the polarization interferometer body consists of a polarization beam splitter (10) and a three-sided reflecting mirror (6), a linear polaroid (11) and a half-wave plate (82) are inserted into the interferometer, wherein the optical axis of the linear polaroid (11) is vertical to the horizontal plane, the half-wave plate (82) forms an included angle of 45 degrees with the horizontal plane, and in addition, the axial rotation of the light beam is realized by inserting a dove prism (12) into the interferometer; the input states of the interferometer are noted: wherein Representing the initial spatial mode of the beam, then the output state of the interferometer is noted as: the post-selection is specifically as follows: The beam emitted by the interferometer is led to be in a horizontal direction through an optical axis An angular half-wave plate (83), after passing through a grateiller polarizing prism (72) with an optical axis in the horizontal direction, the polarization state of the output beam is then selected to be: Wherein the method comprises the steps of For the purpose of the back-selection of the angle, ; Before passing through the half-wave plate (8), the phase difference of horizontal and vertical polarization components in the interferometer is compensated by a Sorbie Barbie phase compensator (13), and the light beam after selection is incident to a spatial light modulator (32) for projection measurement after the direction of the light beam is adjusted by a reflecting mirror (65).
2. The classical entanglement-based beam axial rotation measurement method according to claim 1, wherein in said step S1: after the single-frequency laser light source (1) is expanded by the beam expanding coupling head (2), the single-frequency laser light source is incident to the spatial light modulator (31) and modulated on the spatial light modulator (31) The emergent light passes through a 4f filtering system to generate a phase diagram corresponding to the order Mi Gaosi light beam with higher purity A step Mi Gaosi light source; the said The phase diagram corresponding to the order Mi Gaosi light beam is obtained through numerical calculation, and specifically comprises the following steps: the beam distribution of the input spatial light modulator (31) is recorded as Wherein For the amplitude intensity distribution of the light beam input to the spatial light modulator (31), I is imaginary unit, x is horizontal coordinate of cross section, y is vertical coordinate of cross section; The phase diagram loaded on the spatial light modulator (31) is denoted as The spatial light modulator (31) outputs a beam of light distributed as Wherein To be hoped for The order Mi Gaosi beam distribution, the amplitude intensity and the spatial phase of the output beam of the spatial light modulator (31) are respectively And ; Relative phase is noted as Wherein Is the blazed grating phase loaded on the spatial light modulator (31); Relative amplitude is noted as ; Phase diagram loaded on spatial light modulator (31): Wherein the method comprises the steps of Is the inverse of the first order Bessel function; the 4f filtering system specifically comprises: behind the spatial light modulator (31) A focal length is placed at Is behind the Fourier lens (41) An aperture (5) is arranged at the position, the light beam modulated by the spatial light modulator (31) is focused at the aperture (5) after passing through the Fourier lens (41), and the focusing point of the image plane is periodically arranged in the horizontal direction due to the blazed grating added on the phase diagram, the light spot at the first-order diffraction position is filtered out by the aperture (5) and is behind A focal length is placed at A lens (42) of higher purity of the outgoing beam The optical beam of order Ir Mi Gaosi is marked by the spatial distribution of the optical beam of Irpex Gaussian Symbol, symbol Represents the right vector of dirac, and Wherein, the Is that The wave function of the order Mi Gaosi beam.
3. The classical entanglement-based optical beam axial rotation measurement method according to claim 1, wherein: The space mode entangled state is specifically: the state vector of the light beam after the post-selection is recorded as: Wherein: in order to select the state of the post-selection, Is an inner product operation; recorded as weak values, consider the approximate condition of weak measurement: the beam space pattern after the post-selection is recorded as: The axial rotation information of the light beam is completely in a space mode state Is carried by and The mode number states in the x direction and the y direction are inseparable, are equivalent to entanglement forms, and are classical entanglement states of a space mode; For unknown parameters The estimated quantum precision limit is: Wherein, the The number of photons received for the detector; Due to the introduction of classical entanglement, the limiting accuracy of the axial rotation measurement of the beam is proportional to a factor by the number of modes Is improved; The phase diagram corresponding to the mode entanglement state of the modulation carrying parameter is specifically as follows: the beam profile modulated by the spatial light modulator (32) is noted as Wherein Mode entanglement for carrying rotational 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 predetermined input beam is parallel light, , ; For calculating the amplitude intensity of the input beam preset in the phase diagram of the spatial light modulator (32), The spatial phase of the input beam preset for calculating the phase diagram of the spatial light modulator (32); relative phase is noted as Wherein Is the blazed grating phase loaded on the spatial light modulator (32); Relative amplitude is noted as , The phase diagram loaded on the spatial light modulator (32) is then: Wherein the method comprises the steps of Is the inverse of the first order Bessel function; The use of optical fiber pigtail for receiving realizes projection measurement, specifically: Fourier transforming the projected light field behind the spatial light modulator (32) using a fourier lens (43), the light field modulated by the spatial light modulator (32) being distributed as The light field input to the spatial light modulator (32) is I.e. the last state of the pointer The corresponding two-dimensional light field distribution, the transformed light field is obtained at the focal length behind the Fourier lens (43), and then is directly received at the center of the transformed light field through a single-mode fiber (14), and the receiving efficiency of the single-mode fiber (14) is expressed as: Wherein, the Is that Is represented by the conjugate of (a).
4. The classical entanglement-based beam axial rotation measurement method according to claim 1, wherein in said step S4: The projection measurement converts the axial rotation parameters of the light beam into light intensity information, the light intensity obtained by the projection measurement is measured by utilizing an avalanche photodiode detector (15), the light intensity is converted into an electric signal, the electric signal is input into a frequency analyzer, and the axial rotation of the light beam is demodulated; s4.1, inputting the light intensity received by a single-mode fiber (14) into an avalanche photodiode detector (15), and converting the received weak light intensity signal into an electric signal; S4.2, inputting an electric signal of the avalanche photodiode detector (15) into a frequency analyzer (16), reading a peak frequency point and corresponding intensity of the frequency analyzer (16), and demodulating the amplitude and frequency of an axial rotation signal of the light beam; the light intensity received by the single-mode fiber (14) is input into the avalanche photodiode detector (15), specifically: the intensity of light received by the avalanche photodiode detector (15) is proportional to the probability of projection, i.e Wherein, the For the light intensity received by the avalanche photodiode detector (15), In the photon end state In a space mode carrying rotation information Probability of projection on; at the same rotation signal intensity, the received light intensity can be obtained by a factor related to the space mode number of the Er Mi Gaosi light beam Lifting; The amplitude and frequency of the demodulated beam axial rotation signal are specifically: the electrical signal output by the avalanche photodiode detector (15) is a voltage signal amplified by a built-in transimpedance amplifier, which is proportional to the received light intensity, i.e The voltage signal is input to a frequency analyzer (16) to determine the frequency and amplitude of the beam axial rotation signal.
5. A classical entanglement-based beam axial rotation measurement system, comprising: the module M1 is used for modulating a phase diagram corresponding to the hermitian Gaussian beam after the single-frequency laser light source (1) is subjected to beam expansion, and generating a hermitian Gaussian light source with higher purity through a filtering system; The module M2 is used for selecting a polarization state before passing through the hermitian Gaussian beam, introducing axial rotation with opposite directions to the horizontal component and the vertical component of the polarization state of the beam, and then selecting the polarization state of the beam after passing through to enable the axial rotation parameter of the beam to be carried by a space mode entanglement state; The module M3 is used for making the light beam after the selection incident to the spatial light modulator (32) and modulating a phase diagram corresponding to a mode entanglement state carrying parameters on the light beam, receiving the light beam by using an optical fiber tail fiber at a focus behind the lens (4) through the Fourier lens (4) and realizing projection measurement; The module M4 is used for converting the axial rotation parameters of the light beam into light intensity information by projection measurement, measuring the light intensity obtained by the projection measurement, converting the light intensity into an electric signal, inputting the electric signal into the frequency analyzer (16) and demodulating the axial rotation of the light beam; in the module M2: the method comprises the steps of selecting a polarization state of an hermitian Gaussian beam to be 45-degree linearly polarized light before passing, respectively introducing axial rotation with opposite directions to horizontal component H light and vertical component V light of the polarization state of the beam by using an interferometer in a weak coupling module, and then selecting the polarization state of the beam after passing to enable an axial rotation parameter of the beam to be carried by a space mode entanglement state; The polarization state of the light beam is selected to be 45-degree linear polarized light before passing through the light beam, and the light beam is specifically: the Hermite Gaussian beam generated by the spatial light modulator (31) and the 4f filtering system is incident to a Gray Taylor polarizing prism (71) with an optical axis along the horizontal direction after being adjusted by a mirror (61), and forms a plane with the horizontal plane by the optical axis -An angled half-wave plate (81), the polarization state of the output beam being pre-selected as: Wherein, the The pre-selected state is indicated and the pre-selected state, Representing light of a horizontal polarization such as, Representing vertically polarized light; the opposite axial rotation is specifically as follows: In interferometers, a relative angle is applied to the horizontally polarized component and the vertically polarized component of a beam of light Is expressed by an evolution operator as: Wherein, the A unitary evolution operator representation for the rotation process; For the berkovich operator to act on polarization, For the angular momentum operator to act on the beam space pattern, axial rotation is represented, Is a dirac left-vector symbol; Is an unknown parameter; When the method is realized, firstly, a light beam is input into a polarization interferometer through a beam splitter (9), the polarization interferometer body consists of a polarization beam splitter (10) and a three-sided reflecting mirror (6), a linear polaroid (11) and a half-wave plate (82) are inserted into the interferometer, wherein the optical axis of the linear polaroid (11) is vertical to the horizontal plane, the half-wave plate (82) forms an included angle of 45 degrees with the horizontal plane, and in addition, the axial rotation of the light beam is realized by inserting a dove prism (12) into the interferometer; the input states of the interferometer are noted: wherein Representing the initial spatial mode of the beam, then the output state of the interferometer is noted as: the post-selection is specifically as follows: The beam emitted by the interferometer is led to be in a horizontal direction through an optical axis An angular half-wave plate (83), after passing through a grateiller polarizing prism (72) with an optical axis in the horizontal direction, the polarization state of the output beam is then selected to be: Wherein the method comprises the steps of For the purpose of the back-selection of the angle, ; Before passing through the half-wave plate (8), the phase difference of horizontal and vertical polarization components in the interferometer is compensated by a Sorbie Barbie phase compensator (13), and the light beam after selection is incident to a spatial light modulator (32) for projection measurement after the direction of the light beam is adjusted by a reflecting mirror (65).
6. The classical entanglement-based beam axial rotation measurement system according to claim 5, wherein in said module M1: after the single-frequency laser light source (1) is expanded by the beam expanding coupling head (2), the single-frequency laser light source is incident to the spatial light modulator (31) and modulated on the spatial light modulator (31) The emergent light passes through a 4f filtering system to generate a phase diagram corresponding to the order Mi Gaosi light beam with higher purity A step Mi Gaosi light source; the said The phase diagram corresponding to the order Mi Gaosi light beam is obtained through numerical calculation, and specifically comprises the following steps: the beam distribution of the input spatial light modulator (31) is recorded as Wherein For the amplitude intensity distribution of the light beam input to the spatial light modulator (31), I is imaginary unit, x is horizontal coordinate of cross section, y is vertical coordinate of cross section; The phase diagram loaded on the spatial light modulator (31) is denoted as The spatial light modulator (31) outputs a beam of light distributed as Wherein To be hoped for The order Mi Gaosi beam distribution, the amplitude intensity and the spatial phase of the output beam of the spatial light modulator (31) are respectively And ; Relative phase is noted as Wherein Is the blazed grating phase loaded on the spatial light modulator (31); Relative amplitude is noted as ; Phase diagram loaded on spatial light modulator (31): Wherein the method comprises the steps of Is the inverse of the first order Bessel function; the 4f filtering system specifically comprises: behind the spatial light modulator (31) A focal length is placed at Is behind the Fourier lens (41) An aperture (5) is arranged at the position, the light beam modulated by the spatial light modulator (31) is focused at the aperture (5) after passing through the Fourier lens (41), and the focusing point of the image plane is periodically arranged in the horizontal direction due to the blazed grating added on the phase diagram, the light spot at the first-order diffraction position is filtered out by the aperture (5) and is behind A focal length is placed at A lens (42) of higher purity of the outgoing beam The optical beam of order Ir Mi Gaosi is marked by the spatial distribution of the optical beam of Irpex Gaussian Symbol, symbol Represents the right vector of dirac, and Wherein, the Is that The wave function of the order Mi Gaosi beam.
7. The classical entangled based beam axial rotation measurement system according to claim 5, characterized in that: The space mode entangled state is specifically: the state vector of the light beam after the post-selection is recorded as: Wherein: in order to select the state of the post-selection, Is an inner product operation; recorded as weak values, consider the approximate condition of weak measurement: the beam space pattern after the post-selection is recorded as: The axial rotation information of the light beam is completely in a space mode state Is carried by and The mode number states in the x direction and the y direction are inseparable, are equivalent to entanglement forms, and are classical entanglement states of a space mode; For unknown parameters The estimated quantum precision limit is: Wherein, the The number of photons received for the detector; Due to the introduction of classical entanglement, the limiting accuracy of the axial rotation measurement of the beam is proportional to a factor by the number of modes Is improved; The phase diagram corresponding to the mode entanglement state of the modulation carrying parameter is specifically as follows: the beam profile modulated by the spatial light modulator (32) is noted as Wherein Mode entanglement for carrying rotational 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 predetermined input beam is parallel light, , ; For calculating the amplitude intensity of the input beam preset in the phase diagram of the spatial light modulator (32), The spatial phase of the input beam preset for calculating the phase diagram of the spatial light modulator (32); relative phase is noted as Wherein Is the blazed grating phase loaded on the spatial light modulator (32); Relative amplitude is noted as , The phase diagram loaded on the spatial light modulator (32) is then: Wherein the method comprises the steps of Is the inverse of the first order Bessel function; The use of optical fiber pigtail for receiving realizes projection measurement, specifically: Fourier transforming the projected light field behind the spatial light modulator (32) using a fourier lens (43), the light field modulated by the spatial light modulator (32) being distributed as The light field input to the spatial light modulator (32) is I.e. the last state of the pointer The corresponding two-dimensional light field distribution, the transformed light field is obtained at the focal length behind the Fourier lens (43), and then is directly received at the center of the transformed light field through a single-mode fiber (14), and the receiving efficiency of the single-mode fiber (14) is expressed as: Wherein, the Is that Is represented by the conjugate of (a).
8. The classical entanglement-based beam axial rotation measurement system according to claim 5, wherein in said module M4: The projection measurement converts the axial rotation parameters of the light beam into light intensity information, the light intensity obtained by the projection measurement is measured by utilizing an avalanche photodiode detector (15), the light intensity is converted into an electric signal, the electric signal is input into a frequency analyzer, and the axial rotation of the light beam is demodulated; The module M4.1 is used for inputting the light intensity received by the single-mode fiber (14) into the avalanche photodiode detector (15) and converting the received weak light intensity signal into an electric signal; Inputting the electric signal of the avalanche photodiode detector (15) into a frequency analyzer (16), reading the peak frequency point and the corresponding intensity of the frequency analyzer (16), and demodulating the amplitude and the frequency of the axial rotation signal of the light beam; the light intensity received by the single-mode fiber (14) is input into the avalanche photodiode detector (15), specifically: the intensity of light received by the avalanche photodiode detector (15) is proportional to the probability of projection, i.e Wherein, the For the light intensity received by the avalanche photodiode detector (15), In the photon end state In a space mode carrying rotation information Probability of projection on; at the same rotation signal intensity, the received light intensity can be obtained by a factor related to the space mode number of the Er Mi Gaosi light beam Lifting; The amplitude and frequency of the demodulated beam axial rotation signal are specifically: the electrical signal output by the avalanche photodiode detector (15) is a voltage signal amplified by a built-in transimpedance amplifier, which is proportional to the received light intensity, i.e The voltage signal is input to a frequency analyzer (16) to determine the frequency and amplitude of the beam axial rotation signal.

Description

Classical entanglement-based light beam axial rotation measurement method and system Technical Field The invention relates to the field of laser measurement, in particular to a method and a system for measuring axial rotation of a light beam based on classical entanglement, and more particularly relates to a method and a system for measuring axial rotation of a micro light beam based on classical entanglement technology. Background Since in the field of laser measurement the profile of the beam is typically a standard gaussian distribution with rotational symmetry, it is not possible to carry any information about the axial rotation of the beam. In recent studies, measurement of the axial rotation of a beam is generally achieved by introducing quantum entanglement equivalent sub-resources into a beam carrying orbital angular momentum (e.g., a lager gaussian beam). Although the measuring technology based on the quantum resource can solve the measuring problem of axial rotation of the light beam, the measuring technology has obvious technical difficulty in practical implementation, for example, 1, quantum entanglement equivalent quantum resources are still difficult to prepare at present, and the quantum entanglement state is very easy to decoherence under a noise environment so as to influence the measuring precision. 2. Quantum resource-based measurement schemes generally require the use of single photon light sources and require the measurement of signals under single photon conditions, which also limits further improvement in measurement accuracy. 3. This type of solution currently requires the quantum resource to be introduced onto the very high order orbital angular momentum eigenstates (orbital angular momentum topological charge exceeds 100) to achieve the measurement of beam axial rotation with accuracy in the μrad level, which is a significant challenge in practical implementation. 4. The detection bandwidth of this type of scheme is low, and measurement of the high-frequency rotation signal cannot be performed. Disclosure of Invention Aiming at the defects in the prior art, the invention aims to provide a method and a system for measuring the axial rotation of a light beam based on classical entanglement. According to the invention, a classical entanglement-based light beam axial rotation measurement method comprises the following steps: Step S1, modulating a phase diagram corresponding to an hermitian Gaussian beam after a single-frequency laser light source is subjected to beam expansion, and generating a hermitian Gaussian light source with higher purity through a filtering system; S2, enabling the hermitian Gaussian beam to pass through a pre-selection polarization state, introducing axial rotation with opposite directions to the horizontal component and the vertical component of the polarization state of the beam, and then enabling the axial rotation parameter of the beam to be carried by a space mode entanglement state after the polarization state of the beam passes through a post-selection; s3, the selected light beam is incident to a spatial light modulator and modulated on the spatial light modulator to form a phase diagram corresponding to a mode entangled state carrying parameters, and the phase diagram is received by a Fourier lens at a focus position behind the lens by using an optical fiber tail fiber to realize projection measurement; And S4, converting the axial rotation parameters of the light beam into light intensity information by projection measurement, measuring the light intensity obtained by the projection measurement, converting the light intensity into an electric signal, inputting the electric signal into a spectrum analyzer, and demodulating the axial rotation of the light beam. Preferably, in said step S1: after a single-frequency laser light source is subjected to beam expansion through a beam expansion coupling head, the single-frequency laser light source is incident into a spatial light modulator and modulates a phase diagram corresponding to an m multiplied by n order early Mi Gaosi light beam on the spatial light modulator, and emergent light passes through a 4f filtering system to generate a higher-purity m multiplied by n order early Mi Gaosi light source; The phase diagram corresponding to the m multiplied by n order Mi Gaosi light beam is obtained through numerical calculation, specifically: the beam profile input to the spatial light modulator is noted as Wherein the method comprises the steps ofFor the beam amplitude intensity distribution input to the spatial light modulator,I is imaginary unit, x is horizontal coordinate of cross section, y is vertical coordinate of cross section; The phase diagram loaded on the spatial light modulator is marked as H A (x, y), and the distribution of the output light beam of the spatial light modulator is that Where ψ mn (x, y) is the desired m×n order early Mi Gaosi beam profile, the amplitude intensity and spatial phase