A measuring device and measuring method for the high-order topological charge number of a Laguerre-Gaussian beam

Abstract

The present invention discloses a measuring device and method for the high-order topological charge number of a Laguerre-Gaussian beam. A laser emits a beam, which passes through a beam splitter and reaches a spatial light modulator to generate a Laguerre-Gaussian beam to be measured. After passing through the beam splitter, this beam is divided into a transmitted Laguerre-Gaussian beam and a reflected Laguerre-Gaussian beam. The transmitted Laguerre-Gaussian beam is reflected by a plane mirror after being reflected by the beam splitter and serves as a mirror image beam of the Laguerre-Gaussian beam to illuminate the beam splitter, while the Laguerre-Gaussian beam transmitted through the beam splitter diffracts through an equilateral triangular aperture and enters a CCD camera for imaging; the reflected Laguerre-Gaussian beam is reflected by a mirror and then serves as the Laguerre-Gaussian beam to illuminate the beam splitter; the Laguerre-Gaussian beam and its mirror image beam interfere and superpose through the beam splitter; the light intensity of the interference superposition enters the CCD camera for imaging, and by analyzing the collected interference intensity pattern and diffraction intensity pattern, the magnitude and sign of the topological charge number of the vortex light can be obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of optical measurement, and particularly relates to a device and method for measuring the high-order topological charge number of a Laguerre-Gaussian beam. Background Technique

[0002] The Laguerre-Gaussian beam has a helical phase wavefront, and there is a phase singularity, that is, the central light intensity is zero. Its light field expression contains the Hilbert phase factor of exp(ilθ). The biggest difference between the Laguerre-Gaussian beam and the ordinary beam is that the Laguerre-Gaussian beam has orbital angular momentum, and each photon carries lħ of orbital angular momentum, where l is the topological charge number of the Laguerre-Gaussian beam, and ħ is the reduced Planck constant. The unique property of the Laguerre-Gaussian beam having orbital angular momentum has important applications and research significance in the fields of optical micro-manipulation, quantum information encoding, etc. At present, there are many methods for measuring the topological charge number of the Laguerre-Gaussian beam, but there are certain limitations in measuring the topological charge number of the high-order Laguerre-Gaussian beam, and only the order of the topological charge number can be obtained, and the magnitude of the topological charge number cannot be determined. And the presence of devices such as Dove prisms in the system makes the optical system have interference introduced by the devices and the system is complicated.

[0003] The high-order Laguerre-Gaussian beam has broad application prospects. Therefore, it is of great significance to propose a method for simply measuring the topological charge number of the high-order Laguerre-Gaussian beam. The Laguerre-Gaussian beam has mirror symmetry, and the interference with its mirror Laguerre-Gaussian beam can generate a circularly uniformly distributed chrysanthemum petal-like interference pattern. And there is a certain relationship between the light field distribution after the Laguerre-Gaussian beam passes through the diffraction of an equilateral triangular aperture and the sign of its topological charge number, but the topological charge number that can be measured only by observing the light field distribution after the diffraction of the equilateral triangular aperture is ±9. Based on the above characteristics, we propose a device and method for measuring the topological charge number of the high-order Laguerre-Gaussian beam. Summary of the Invention

[0004] Aiming at the above problems, the purpose of the present invention is to provide a device and method for measuring the high-order topological charge number of a Laguerre-Gaussian beam.

[0005] To achieve the object of the present invention, the technical solution provided by the present invention is a measuring device for the high-order topological charge number of a Laguerre-Gaussian beam, including a He-Ne laser 1, a beam splitter I 2, a spatial light modulator 3, a beam splitter II 4, a mirror I 5, a mirror II 6, a beam splitter III 7, a beam splitter IV 8, a CCD I camera 9, an equilateral triangular aperture stop 10, a CCD II camera 11, and a computer 12. The optical path structure of the measuring device is as follows: The fundamental mode Gaussian beam emitted by the He-Ne laser 1 passes through the beam splitter I 2 by transmission and is incident on the spatial light modulator 3 to generate the Laguerre-Gaussian beam to be measured. Then, the Laguerre-Gaussian beam reflected by the spatial light modulator 3 passes through the beam splitter I 2 and the beam splitter II 4. After passing through the beam splitter II 4, the Laguerre-Gaussian beam is divided into a transmitted Laguerre-Gaussian beam I and a reflected Laguerre-Gaussian beam I. The transmitted Laguerre-Gaussian beam I is reflected by the beam splitter III 7, then reflected by the mirror II 6 and transmitted by the beam splitter III 7 as the mirror image beam of the Laguerre-Gaussian beam and enters the beam splitter IV 8. After the transmitted Laguerre-Gaussian beam I passes through the beam splitter III 7 by transmission, it is diffracted by the equilateral triangular aperture stop 10 and enters the CCD II camera 11 for imaging and is stored in the computer 12. The reflected Laguerre-Gaussian beam I, after passing through the mirror I 5, enters the beam splitter IV 8 as the Laguerre-Gaussian beam II. Then, the mirror image beam of the Laguerre-Gaussian beam interferes with the Laguerre-Gaussian beam II, and the interference light enters the CCD I camera 9 for imaging and is stored in the computer 12;

[0006] The magnitude of the topological charge number is obtained by observing the interference pattern, and the sign of the topological charge number is obtained by observing the diffraction pattern.

[0007] Further, the observation of the interference pattern is as follows: The interference intensity diagrams of Laguerre-Gaussian beams with different high-order topological charge numbers stored in the computer 12. The interference intensity diagram is composed of a plurality of chrysanthemum petal-like shapes evenly distributed in a circle. The number of petals n is twice the magnitude of the topological charge number l, that is, n = 2l. The measurement of the high-order topological charge number of the Laguerre-Gaussian beam is realized by counting the number of petals in the interference intensity diagram.

[0008] Preferably, the observation of the diffraction pattern is as follows: The diffraction intensity diagrams of Laguerre-Gaussian beams with different high-order topological charge numbers stored in the computer 12. When the Laguerre-Gaussian beam is diffracted by the equilateral triangular aperture stop 10, the far-field diffraction spots are distributed in a triangular shape. When the Laguerre-Gaussian beams with opposite topological charge number signs are diffracted by the equilateral triangular aperture stop 10, the arrangement directions of their diffraction spots are opposite. The measurement of the sign of the high-order topological charge number of the Laguerre-Gaussian beam is realized by observing the arrangement direction of the diffraction spots in the diffraction intensity diagram.

[0009] Preferably, the He-Ne laser 1 is a He-Ne laser with a wavelength of 632.8 nm.

[0010] The present invention also provides a method for measuring the high-order topological charge of a Laguerre-Gaussian beam, which is characterized by comprising the following steps:

[0011] Step S1, arranging a measurement optical path of He-Ne laser 1, beam splitter I 2, spatial light modulator 3, beam splitter II 4, reflector I 5, reflector II 6, beam splitter III 7, beam splitter IV 8, CCD I camera 9, regular triangular aperture diaphragm 10, CCD II camera 11, and computer 12;

[0012] Step S2, turn on the He-Ne laser 1, the He-Ne laser 1 emits a basement Gaussian beam which is injected into the spatial light modulator 3 through the beam splitter Ⅰ2 to generate a Laguerre Gaussian beam to be measured, the Laguerre Gaussian beam is divided into a transmitted Laguerre Gaussian beam Ⅰ and a reflected Laguerre Gaussian beam Ⅰ through the beam splitter Ⅱ4, wherein the transmitted Laguerre Gaussian beam Ⅰ becomes a mirror beam of the Laguerre Gaussian beam through the beam splitter Ⅲ7 and the reflector Ⅱ6, the Laguerre Gaussian beam Ⅱ after the reflected Laguerre Gaussian beam Ⅰ passes through the reflector Ⅰ5 and its mirror beam interferes in the beam splitter Ⅳ8, the Laguerre Gaussian beam Ⅲ7 transmitted through the beam splitter Ⅲ is diffracted through the equilateral triangular aperture diaphragm 10, the interference image and the diffraction image are recorded by the CCDⅠ9 and CCDⅡ11 cameras, and stored in the computer 12;

[0013] Step S3, measuring the size of the high-order topological charge by counting the number of petals of the interference image, wherein the number of petals is twice the topological charge;

[0014] The step S3 is specifically as follows:

[0015] The complex amplitude of a Laguerre-Gaussian beam is,

[0016]

[0017] Where C is the normalization constant, is the beam waist radius, ;

[0018] r is the radial distance, is the azimuth, , , are the coordinates of the source plane,

[0019] The topological charge is and- The complex amplitude of the beam is expressed as,

[0020]

[0021]

[0022] After the Laguerre-Gaussian beam interferes with its mirror image beam, the interference intensity distribution recorded by the CCDⅠ9 camera is as follows:

[0023]

[0024] The interference petals have a circularly symmetric distribution structure, which is modulated by the cosine function in the formula. The first-order partial derivative and the second-order partial derivative of are used to calculate the angle between the two petals.

[0025]

[0026]

[0027] The angle between the two petals is

[0028]

[0029] The petals are evenly distributed on the circumference. From the angle between the two petals, the relationship between the number of petals and the topological charge number can be obtained as

[0030]

[0031] That is: the number of petals is twice the topological charge number.

[0032] By counting the number of petals in the interference intensity pattern, the measurement of the magnitude of the higher-order topological charge number of the Laguerre-Gaussian beam is obtained.

[0033] Step S5: Measure the sign of the higher-order topological charge number by the light field distribution of the diffraction image;

[0034] The specific content of the said step S5 is as follows:

[0035] The Laguerre-Gaussian beam is vertically incident on the diffraction aperture 10 of the equilateral triangular hole, and the position of the phase singularity corresponds to the center of the aperture; the light transmission aperture function of the diffraction aperture 10 of the equilateral triangular hole is expressed as

[0036]

[0037] In the formula, After the Laguerre-Gaussian beam irradiates the diffraction aperture 10 of the equilateral triangular hole and generates diffraction, the diffraction intensity recorded by the CCDⅡ12 camera is

[0038]

[0039] , , are the coordinates of the observation plane.

[0040] The sign of the higher-order topological charge number of the Laguerre-Gaussian beam is determined by the light field distribution of the diffraction intensity pattern.

[0041] Step S6, determine the magnitude and sign of the topological charge.

[0042] The beneficial effects of the present invention include:

[0043] 1. Without using complex optical elements, only a simple mirror is used to obtain the mirror image beam of the Laguerre-Gaussian beam. The measurement device has simple operation and low cost.

[0044] 2. Combine the interference and diffraction of the Laguerre-Gaussian beam. Measure the magnitude of the higher-order topological charge of the Laguerre-Gaussian beam by counting the number of petals in the interference intensity pattern, and measure the sign of the higher-order topological charge of the Laguerre-Gaussian beam by observing the direction of the light field distribution in the diffraction intensity pattern. The measurable topological charge can reach ±90. Description of the Drawings

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0046] Figure 1 It is a schematic structural diagram of the measurement device of the present invention;

[0047] Figure 2 It is the interference intensity pattern of the Laguerre-Gaussian beam with different topological charges obtained by using the improved Mach-Zehnder interferometer of the present invention;

[0048] Figure 3 It is the diffraction intensity pattern of the Laguerre-Gaussian beam with different topological charges obtained by using the improved Mach-Zehnder interferometer of the present invention;

[0049] Description of the Reference Numerals:

[0050] 1. He-Ne laser, 2. Beam splitter I, 3. Spatial light modulator, 4. Beam splitter II, 5. Mirror I, 6. Mirror II, 7. Beam splitter III, 8. Beam splitter IV, 9. CCD I camera, 10. Equilateral triangular aperture diaphragm, 11. CCD II camera, 12. Computer. Detailed Embodiments

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings.

[0052] As Figure 1As shown in the figure, the present invention is a measuring device for measuring the high-order topological charge number of a Laguerre-Gaussian beam. It is provided with a He-Ne laser 1 with a wavelength of 632.8 nm. The fundamental-mode Gaussian beam emitted by the He-Ne laser 1 passes through the beam splitter Ⅰ 2 and is incident on the spatial light modulator 3 to generate the Laguerre-Gaussian beam to be measured. Then, the Laguerre-Gaussian beam reflected by the spatial light modulator 3 passes through the beam splitter Ⅰ 2 and the beam splitter Ⅱ 4. After passing through the beam splitter Ⅱ 4, the Laguerre-Gaussian beam is divided into a transmitted Laguerre-Gaussian beam Ⅰ and a reflected Laguerre-Gaussian beam Ⅰ. The transmitted Laguerre-Gaussian beam Ⅰ is reflected by the beam splitter Ⅲ 7, then reflected by the mirror Ⅱ 6 and transmitted by the beam splitter Ⅲ 7 as the mirror image beam of the Laguerre-Gaussian beam and is incident into the beam splitter Ⅳ 8. After the transmitted Laguerre-Gaussian beam Ⅰ is transmitted by the beam splitter Ⅲ 7, it diffracts through the equilateral triangular aperture stop 10 and enters the CCD Ⅱ camera 11 for imaging and is stored in the computer 12. The reflected Laguerre-Gaussian beam Ⅰ, after passing through the mirror Ⅰ 5, is incident into the beam splitter Ⅳ 8 as the Laguerre-Gaussian beam Ⅱ. Then, the mirror image beam of the Laguerre-Gaussian beam interferes with the Laguerre-Gaussian beam Ⅱ, and the interference light enters the CCD Ⅰ camera 9 for imaging and is stored in the computer 12. Finally, the magnitude of the topological charge number is obtained by observing the interference pattern, and the sign of the topological charge number is obtained by observing the diffraction pattern.

[0053] As Figure 2 shown in the figure, the present invention uses the above-mentioned measuring device to obtain the interference intensity diagrams of Laguerre-Gaussian beams with different topological charge numbers. The interference intensity diagrams are composed of a plurality of chrysanthemum petal-like patterns evenly distributed on the circumference. The number of petals n is twice the magnitude of the topological charge number l, that is, n = 2l. The measurement of the magnitude of the high-order topological charge number of the Laguerre-Gaussian beam is realized by counting the number of petals in the interference intensity diagram.

[0054] As Figure 3 shown in the figure, the present invention uses the above-mentioned measuring device to obtain the diffraction intensity diagrams of Laguerre-Gaussian beams with different topological charge numbers. When the Laguerre-Gaussian beam diffracts through the equilateral triangular aperture stop, the far-field diffraction spots are distributed in a triangular shape. When the Laguerre-Gaussian beams with opposite topological charge number signs diffract through the equilateral triangular aperture stop, the arrangement directions of their diffraction spots are opposite. The measurement of the sign of the high-order topological charge number of the Laguerre-Gaussian beam is realized by observing the arrangement direction of the diffraction spots in the diffraction intensity diagram.

[0055] Combined Figure 2 with Figure 3 , the specific measurement method of the present invention is as follows:

[0056] It includes the following steps:

[0057] Step S1: Arrange the measurement optical path with a He-Ne laser 1, a beam splitter I 2, a spatial light modulator 3, a beam splitter II 4, a mirror I 5, a mirror II 6, a beam splitter III 7, a beam splitter IV 8, a CCD I camera 9, an equilateral triangular aperture diaphragm 10, a CCD II camera 11, and a computer 12.

[0058] Step S2: Turn on the He-Ne laser 1. The fundamental Gaussian beam emitted by the He-Ne laser 1 enters the spatial light modulator 3 through the beam splitter I 2, generating a Laguerre-Gaussian beam to be measured. The Laguerre-Gaussian beam is split by the beam splitter II 4 into a transmitted Laguerre-Gaussian beam I and a reflected Laguerre-Gaussian beam I. Among them, the transmitted Laguerre-Gaussian beam I becomes the mirror image beam of the Laguerre-Gaussian beam through the beam splitter III 7 and the mirror II 6. The reflected Laguerre-Gaussian beam I interferes with its mirror image beam after passing through the mirror I 5 at the beam splitter IV 8. The Laguerre-Gaussian beam III transmitted through the beam splitter III 7 is diffracted by the equilateral triangular aperture diaphragm 10. Use the CCD I 9 and CCD II 11 cameras to record the interference image and the diffraction image, and store them in the computer 12.

[0059] Step S3: Measure the magnitude of the high-order topological charge by counting the number of petals in the interference image, where the number of petals is twice the topological charge.

[0060] The specific content of Step S3 is as follows:

[0061] The complex amplitude of the Laguerre-Gaussian beam is

[0062]

[0063] where C is the normalization constant, is the beam waist radius, ;

[0064] r is the radial distance, is the azimuth angle, , , is the coordinate of the source plane,

[0065] The topological charge is and - The complex amplitude representation of the beam is

[0066]

[0067]

[0068] After the Laguerre-Gaussian beam interferes with its mirror image beam, the interference intensity distribution recorded by the CCD I 9 camera is

[0069]

[0070] The interference petals have a circularly symmetric distribution structure, modulated by the cosine function in the formula; The first-order partial derivative and the second-order partial derivative of are used to calculate the angle between the two petals.

[0071]

[0072]

[0073] The angle between the two petals is

[0074]

[0075] The petals are evenly distributed on the circumference. From the angle between the two petals, the relationship between the number of petals and the topological charge number can be obtained as

[0076]

[0077] That is: the number of petals is twice the topological charge number;

[0078] By counting the number of petals in the interference intensity pattern, the measurement of the magnitude of the high-order topological charge number of the Laguerre-Gaussian beam is obtained.

[0079] Step S4, by realizing the light field distribution of the diffraction image, the measurement of the sign of the high-order topological charge number is achieved;

[0080] The specific content of the described step S5 is as follows:

[0081] The Laguerre-Gaussian beam is perpendicularly incident on the diffraction aperture 10 of the regular triangular aperture. The position of the phase singularity corresponds to the center of the aperture. The light-transmitting aperture function of the diffraction aperture 10 of the regular triangular aperture is expressed as

[0082]

[0083] In the formula, After the Laguerre-Gaussian beam irradiates the diffraction aperture 10 of the regular triangular aperture and generates diffraction, the diffraction intensity recorded by the CCDⅡ12 camera is

[0084]

[0085] , , are the coordinates of the observation plane,

[0086] By realizing the light field distribution of the diffraction intensity pattern, the determination of the sign of the high-order topological charge number of the Laguerre-Gaussian beam is achieved.

[0087] Step S5, finally, the measurement of the magnitude and sign of the high-order topological charge number of the Laguerre-Gaussian beam is achieved.

[0088] The present invention provides a device for measuring the topological charge number of a high-order Laguerre-Gaussian beam. This device can not only measure the size of the Laguerre-Gaussian beam, but also measure the size of the topological charge number of the Laguerre-Gaussian beam, and the measurable topological charge number of the Laguerre-Gaussian beam can reach ±90. Since no complex devices are introduced, the measurement device is easy to operate.

[0089] The described embodiments are only a part of the embodiments of the present application, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts belong to the scope of protection of the present application.

Claims

1. A measuring device for the high-order topological charge number of a Laguerre-Gaussian beam, characterized in that, It includes a He-Ne laser (1), a beam splitter I (2), a spatial light modulator (3), a beam splitter II (4), a mirror I (5), a mirror II (6), a beam splitter III (7), a beam splitter IV (8), a CCD I camera (9), an equilateral triangular aperture diaphragm (10), a CCD II camera (11), and a computer (12). The optical path structure of the measuring device is as follows: The fundamental mode Gaussian beam emitted by the He-Ne laser (1) passes through the beam splitter I (2) by transmission and is incident on the spatial light modulator (3) to generate a Laguerre-Gaussian beam to be measured. Then, the Laguerre-Gaussian beam reflected by the spatial light modulator (3) passes through the beam splitter I (2) and the beam splitter II (4). After passing through the beam splitter II (4), the Laguerre-Gaussian beam is divided into a transmitted Laguerre-Gaussian beam I and a reflected Laguerre-Gaussian beam I. The transmitted Laguerre-Gaussian beam I is reflected by the beam splitter III (7), then reflected by the mirror II (6) and transmitted by the beam splitter III (7) to enter the beam splitter IV (8) as a mirror image beam of the Laguerre-Gaussian beam. The transmitted Laguerre-Gaussian beam I passes through the beam splitter III (7) by transmission, is diffracted by the equilateral triangular aperture diaphragm (10) and enters the CCD II camera (11) for imaging and is stored in the computer (12). The reflected Laguerre-Gaussian beam I enters the beam splitter IV (8) as the Laguerre-Gaussian beam II after passing through the mirror I (5). Then, the mirror image beam of the Laguerre-Gaussian beam interferes with the Laguerre-Gaussian beam II, and the interference light enters the CCD I camera (9) for imaging and is stored in the computer (12). The magnitude of the topological charge number is obtained by observing the interference pattern, and the sign of the topological charge number is obtained by observing the diffraction pattern; The measurement of the magnitude of the high-order topological charge number is realized by counting the number of petals in the interference image, where the number of petals is twice the topological charge number; The measurement of the sign of the high-order topological charge number is realized by the light field distribution of the diffraction image; Determine the magnitude and sign of the high-order topological charge number.

2. The measuring device for the high-order topological charge number of a Laguerre-Gaussian beam according to claim 1, wherein The observation of the interference pattern is as follows: The interference intensity diagrams of Laguerre-Gaussian beams with different high-order topological charge numbers stored in the computer (12). The interference intensity diagram is composed of multiple chrysanthemum-like petals evenly distributed on the circumference. The number of petals n is twice the magnitude of the topological charge number l, that is, n = 2l. The measurement of the high-order topological charge number of the Laguerre-Gaussian beam is realized by counting the number of petals in the interference light intensity diagram.

3. The measuring device for the high-order topological charge number of a Laguerre-Gaussian beam according to claim 1, characterized in that, The observation of the diffraction pattern is as follows: The diffraction intensity diagrams of Laguerre-Gaussian beams with different high-order topological charge numbers stored in the computer (12). When the Laguerre-Gaussian beam passes through the equilateral triangular aperture diaphragm (10) by diffraction, the far-field diffraction spots are distributed in a triangular shape. When the Laguerre-Gaussian beams with opposite topological charge signs pass through the equilateral triangular aperture diaphragm (10) by diffraction, the arrangement directions of their diffraction spots are opposite. The measurement of the sign of the high-order topological charge number of the Laguerre-Gaussian beam is realized by observing the arrangement direction of the diffraction spots in the diffraction light intensity diagram.

4. The measuring device for the high-order topological charge number of a Laguerre-Gaussian beam according to claim 1, characterized in that, The He-Ne laser (1) is a He-Ne laser with a wavelength of 632.8 nm.

5. A measuring method for the higher-order topological charge number of a Laguerre-Gaussian beam as described in claim 1, characterized in that It includes the following steps: Step S1: Arrange the measurement optical path with a He-Ne laser (1), a beam splitter I (2), a spatial light modulator (3), a beam splitter II (4), a mirror I (5), a mirror II (6), a beam splitter III (7), a beam splitter IV (8), a CCD I camera (9), an equilateral triangular aperture diaphragm (10), a CCD II camera (11), and a computer (12). Step S2: Turn on the He-Ne laser (1). The fundamental Gaussian beam emitted by the He-Ne laser (1) enters the spatial light modulator (3) through the beam splitter I (2), generating a Laguerre-Gaussian beam to be measured. The Laguerre-Gaussian beam is split by the beam splitter II (4) into a transmitted Laguerre-Gaussian beam I and a reflected Laguerre-Gaussian beam I. Among them, the transmitted Laguerre-Gaussian beam I becomes a mirror image beam of the Laguerre-Gaussian beam through the beam splitter III (7) and the mirror II (6). The reflected Laguerre-Gaussian beam I interferes with its mirror image beam at the beam splitter IV (8). The Laguerre-Gaussian beam III transmitted through the beam splitter III (7) diffracts through the equilateral triangular aperture diaphragm (10). Use the CCD I (9) and CCD II (11) cameras to record the interference image and the diffraction image, and store them in the computer (12). Step S3: Measure the magnitude of the high-order topological charge by counting the number of petals in the interference image, where the number of petals is twice the topological charge. Step S4: Measure the sign of the high-order topological charge through the light field distribution of the diffraction image. Step S5: Determine the magnitude and sign of the high-order topological charge.

6. The measuring method according to claim 5, characterized in that The specific content of the said Step S4 is as follows: The complex amplitude of the Laguerre-Gaussian beam is where C is the normalization constant, is the waist radius, L |l| is the Laguerre polynomial of l, r is the radial distance, θ is the azimuth angle, and x0, y0, z0 are the coordinates of the source plane. The complex amplitudes of the beams with topological charges l and -l are expressed as E l (r, θ) = R l (r)exp(ilθ) E -l (r, θ) = R l (r)exp(-ilθ) After the Laguerre-Gaussian beam interferes with its mirror image beam, the interference intensity distribution recorded by the CCD I (9) camera is I(r, θ) = 2|R l (r)| 2 (1 + cos(2lθ)) The interference petals have a circularly symmetric distribution structure, modulated by the cos function in the formula; the first-order partial derivative and the second-order partial derivative of θ are used to calculate the angle between two petals. The angle between two petals is The petals are evenly distributed on the circumference. From the angle between two petals, the relationship between the number of petals and the topological charge can be obtained as That is: the number of petals is twice the topological charge. Measure the magnitude of the high-order topological charge of the Laguerre-Gaussian beam by counting the number of petals in the interference intensity pattern.

7. The measurement method according to claim 5, characterized in that The specific content of the said Step S5 is as follows: The Laguerre-Gaussian beam is vertically incident on the equilateral triangular diffraction aperture diaphragm (10), and the position of the phase singularity corresponds to the center of the aperture diaphragm; the light-transmitting aperture function of the equilateral triangular diffraction aperture diaphragm (10) is expressed as In the formula, is a point set of (x0, y0). After the Laguerre-Gaussian beam irradiates the diffraction aperture of the equilateral triangular hole (10) to generate diffraction, the diffraction intensity recorded by the CCD II (11) camera is x, y, z are the coordinates of the observation plane. Determine the sign of the high-order topological charge of the Laguerre-Gaussian beam through the light field distribution of the diffraction intensity pattern.

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