CN109525310B - Apparatus and method for measuring the influence of transflective medium on photon orbital angular momentum - Google Patents

Abstract

The invention relates to a device and a method for measuring the influence of a transflective medium on photon orbital angular momentum. The device comprises a driving power supply (1), a laser head (2), a beam expander (3), a spiral phase plate (4), a reflection range-extending cavity (5), a double-slit baffle (6), a light screen (7), a measuring head (8), a CCD (charge coupled device) camera (9) and a computer (10). The laser head (2) sends out Laguerre gauss laser and expands the back through beam expander (3), and rethread spiral phase place board (4) give the spiral phase distribution, and pass through reflection and increase journey chamber (5) and constantly reflect, and rethread double slit baffle (6) produce two bundles of coherent light beams, and light screen (7) are interfered the result and are imaged to the double slit, measure the switching signal through measuring head (8) and CCD camera (9), show the measuring result on computer (10). The invention does not need a large-scale external field experiment, is simple, convenient and quick to measure, and reduces the uncertainty of measurement to about 6 percent.

Description

Apparatus and method for measuring the influence of transflective medium on photon orbital angular momentum

technical field

The invention relates to the field of physical optics, and relates to a device and method for measuring the influence of a transflective medium on photon orbital angular momentum

Background technique

In 1992, Allen et al. of Leidon University predicted the existence of Orbital Angular Momentum, OAM, of photon orbital angular momentum. It has played or is playing an unexpectedly important role in the research of basic physics, applied physics, astronomy, biology and other interdisciplinary subjects. In 1995, the research team of the University of Queensland observed the transfer of orbital angular momentum from the light beam to the CuO particle, and drove the latter to rotate, which directly verified the existence of the photon's orbital angular momentum. Photon orbital angular momentum is widely used in quantum radar target scattering characteristics research, target detection and identification, quantum stealth targets and many other fields. In addition, in the field of quantum communication, orbital angular momentum (OAM) has attracted much attention as a new technology. . However, in the process of studying the transmission characteristics of photon orbital angular momentum, it is easy for the vortex beam to carry a certain topological charge to have a special helical phase wavefront structure. Atmospheric turbulence, rain and fog, etc., destroy the spatial wavefront structure and interfere with the information transmission between different OAM modes.

SUMMARY OF THE INVENTION

The present invention provides a measuring device and method for the influence of the transflective medium on the photon orbital angular momentum, and provides the following technical solutions:

A measuring device for the influence of a transflective medium on the transmission characteristics of photon orbital angular momentum, comprising a driving power supply 1, a laser head 2, a beam expander 3, a spiral phase plate 4, a reflection range extension cavity 5, a double-slit baffle 6, a light The screen 7, the measuring head 8, the CCD camera 9 and the computer 10, except the power supply 1 and the computer 10, are all fixed on the support frame;

The driving power supply 1 is connected to the laser head 2. The outgoing end of the laser head 2 faces the incoming end of the beam expander 3, the outgoing end of the beam expander 3 faces the incoming end of the spiral phase plate 4, and the outgoing end of the spiral phase plate 4 faces the reflection range extender cavity. The incident end of 5, the outgoing end of the reflection range extension cavity 5 faces the incident end of the double-slit baffle 6, and the outgoing end of the double-slit baffle 6 faces the front of the light screen 7; the measuring end of the measuring head 8 faces the back of the light screen 7 , the CCD camera 9 is facing the output end of the measuring head 8 , and the CCD camera 9 is connected to the computer 10 .

Preferably, the laser head 2 outputs a continuous and stable Laguerre Gaussian laser with a laser wavelength range of 380nm-760nm, a spot diameter of 0.5-0.9mm, a transverse mode of TEM00, a polarization state of linear polarization, and a beam quality of less than 1.5.

Preferably, the Laguerre Gaussian laser generated by the laser head 2 passes through the center of the spiral phase plate 4 , and the spiral phase plate 4 makes the Laguerre Gaussian laser beam carry an orbital angular momentum with a topological charge of 1.

Preferably, the reflection range extender cavity 5 includes 5 mirrors connected end to end, the adjacent mirrors are perpendicular to each other, the length of the two emitting mirrors at the head and the end is 8cm-13cm, the length of the three mirrors in the middle is 20cm-30cm. The range extension cavity 5 is filled with a transflective medium.

Preferably, the double-slit spacing of the double-slit baffle 6 is 0.08 mm-0.4 mm, and the distance between the double-slit baffle 6 and the light screen 7 is 500 mm-800 mm.

A method for measuring the influence of a transflective medium on the transmission characteristics of photon orbital angular momentum, comprising the following steps:

Step 1: Fill the reflection-extending cavity 5 with a transflective medium and keep it at room temperature;

Step 2: Connect the driving power supply 1 to 220V AC, and the laser head 2 generates a continuous and stable Laguerre Gauss laser;

Step 2: Adjust the center points of the laser head 2, the beam expander 3 and the helical phase plate 4 to be on the same straight line, so that the incident beam emitted by the helical phase plate 4 and the reflection range extender cavity 5 are incident at 80°;

Step 3: Adjust the center points of the double-slit baffle 6, the light screen 7, the measuring head 8 and the CCD camera 9 to be on the same straight line, so that the double-slit baffle 6 and the outgoing beam from the reflection range extension cavity 5 are at 80° shoot out;

Step 4: After the Laguerre Gaussian laser passes through the beam expander 3, the spiral phase plate 4, the reflection range extension cavity 5, and the double-slit baffle 6 respectively, it is imaged through the optical screen 7, and the measuring head 8 quantitatively measures the interference fringes, and the CCD The camera 9 and the computer 10 display the measurement results of the interference fringes;

Step 5: Obtain the amount and direction of fringe bending by measuring the interference fringes, and reverse the topological charge of the orbital angular momentum of the laser beam under the action of the transflective medium.

Preferably, the laser head 2 outputs a continuous and stable Laguerre Gaussian laser with a laser wavelength range of 380nm-760nm, a spot diameter of 0.5-0.9mm, a transverse mode of TEM00, a polarization state of linear polarization, and a beam quality of less than 1.5.

Preferably, the Laguerre Gaussian laser generated by the laser head 2 passes through the center of the spiral phase plate 4 , and the spiral phase plate 4 makes the Laguerre Gaussian laser beam carry an orbital angular momentum with a topological charge of 1.

Preferably, the step 5 is specifically:

的光子轨道角动量光束波长为λ正入射双缝挡板，通过下式表示入射拉盖尔高斯激光光束的通用表达式：Step 1: A topological charge is

The photon orbital angular momentum beam wavelength of λ is the normal incidence double-slit baffle, and the general expression for the incident Laguerre Gaussian laser beam is expressed by the following equation:

为激光光束轨道角动量的拓扑荷数，i为虚数单位，exp(imr²)为额外的衍射项。Among them, E _in is the intensity of the incident Laguerre Gaussian laser beam, (r, θ) is the polar coordinate, A(r) is the characteristic complex amplitude,

is the topological charge of the orbital angular momentum of the laser beam, i is an imaginary unit, and exp(imr ² ) is an additional diffraction term.

第二个狭缝的相位表达为

两个狭缝的沿着方向的相位差分布δφ(y)通过下式表达：Step 2: Express the phase of the left slit as

The phase of the second slit is expressed as

The phase difference distribution δφ(y) of the two slits along the direction is expressed by the following formula:

Among them, δφ(y) is the phase distribution of the two slits along the direction, (x, y) is the rectangular coordinate on the light screen, and a is the double-slit spacing of the double-slit baffle 6 .

Step 3: According to the optical path difference theory and formula, when the laser beam is incident, the interference intensity distribution of the two slit arrays is expressed by the following formula:

When the fringes are equally spaced parallel fringes, the locus x of the central bright fringes is expressed by the following formula:

Among them, x is the trajectory of the central bright pattern, (x, y) is the rectangular coordinate on the light screen, λ is the wavelength of the laser beam, and d is the distance between the double-slit baffle 6 and the light screen 7 .

Step 4: The bending amount Δx of the stripes is obtained by the following formula:

On the contrary, according to the amount of fringe bending, the absolute value of the topological charge can be obtained by the following formula:

为激光光束轨道角动量的拓扑荷数的绝对值。Among them, Δx is the bending amount of the stripes,

is the absolute value of the topological charge of the orbital angular momentum of the laser beam.

Step 5: The positive or negative value of the topological charge of the orbital angular momentum of the laser beam is determined by the direction of the fringe bending. For the same fringe from top to bottom, if the fringe deviates to the right, the topological charge is negative, and if the fringe deviates to the left, the topological charge is positive. value.

The present invention has the following beneficial effects:

In order to study the influence of the transflective medium on the transmission characteristics of the photon orbital angular momentum, the device of the present invention modulates the Laguerre Gaussian beam by the wavefront, so that it carries the orbital angular momentum with a topological charge of 1, and increases through a reflection. The process system makes the transflective medium fully interact with the laser beam, and then generates curved fringes through double-slit interference. The CCD camera 9 and the computer 10 are used to display the interference pattern and its measurement results on the computer. The topological charge of the orbital angular momentum of the laser beam after the medium acts and its positive and negative, so that the influence of the transflective medium on the orbital angular momentum of the laser beam can be obtained.

The device for measuring the influence of the transflective medium on the transmission characteristics of the photon orbital angular momentum proposed by the invention is simple in structure and convenient in operation, and does not require complicated adjustment of the optical path. The device of the present invention is located in a small reflective range extender cavity 5, which increases the optical path by a hundred times, and does not require a large-scale external field experiment, so that the influence of the transflective medium on the transmission characteristics of the photon orbital angular momentum can be easily and quickly measured. The invention can quickly and efficiently measure the influence of the transflective medium on the orbital angular momentum of the laser beam, and at the same time has high scalability. Measurements can be made over a wide spectral range while reducing the measurement uncertainty to around 6%.

Description of drawings

Fig. 1 is a measuring device for the influence of transflective medium on photon orbital angular momentum.

FIG. 2 is a reflection schematic diagram of the reflection range extender cavity 5 .

Figure 3 is a graph of the measurement results when the laser beam carries the orbital angular momentum with a topological charge of 1

In the picture: 1-drive power supply, 2-laser head, 3-beam expander, 4-spiral phase plate, 5-reflection extender cavity, 6-double slit baffle, 7-light screen, 8-measurement head, 9 -CCD camera, 10-computer.

Detailed ways

The present invention is described in detail below with reference to specific embodiments.

Specific embodiment one:

As shown in FIG. 1 , the present invention provides a measuring device for the influence of a transflective medium on photon orbital angular momentum, including a driving power source 1, a laser head 2, a beam expander 3, a spiral phase plate 4, a reflection range extension cavity 5, The double-slit baffle 6, the light screen 7, the measuring head 8, the CCD camera 9 and the computer 10, except the power supply 1 and the computer 10, are all fixed on the support frame;

The driving power supply 1 is connected to the laser head 2. The outgoing end of the laser head 2 faces the incoming end of the beam expander 3, the outgoing end of the beam expander 3 faces the incoming end of the spiral phase plate 4, and the outgoing end of the spiral phase plate 4 faces the reflection range extender cavity. The incident end of 5, the outgoing end of the reflection range extension cavity 5 faces the incident end of the double-slit baffle 6, and the outgoing end of the double-slit baffle 6 faces the front of the light screen 7; the measuring end of the measuring head 8 faces the back of the light screen 7 , the CCD camera 9 is facing the output end of the measuring head 8 , and the CCD camera 9 is connected to the computer 10 .

The laser head 2 outputs a continuous and stable Laguerre Gaussian laser with a laser wavelength range of 380nm-760nm, a spot diameter of 0.5-0.9mm, a transverse mode of TEM00, a polarization state of linear polarization, and a beam quality of less than 1.5. The Laguerre Gaussian laser generated by the laser head 2 passes through the center of the spiral phase plate 4 , and the spiral phase plate 4 makes the Laguerre Gaussian laser beam carry an orbital angular momentum with a topological charge of 1.

The reflection range extender cavity 5 includes 5 mirrors connected end to end, and the adjacent mirrors are perpendicular to each other. 5 It can be filled with transmissive media, such as fog, turbulent atmosphere or ice crystals. The double-slit spacing of the double-slit baffle 6 is 0.08mm-0.4mm, and the distance between the double-slit baffle 6 and the light screen 7 is 500mm-800mm.

Specific embodiment two:

The device of the invention modulates the Laguerre Gaussian beam by the wavefront, so that it carries the orbital angular momentum with a topological charge of 1, makes the transflective medium and the laser beam fully interact through a reflection range extension system, and then passes through the double slit. The interference produces curved fringes, and the CCD camera 9 and the computer 10 are used to present the interference pattern and its measurement results on the computer. Finally, through the measurement results, the topological charge of the orbital angular momentum of the laser beam under the action of the transflective medium and its positive and negative can be obtained. , so that the influence of the transflective medium on the orbital angular momentum of the laser beam can be obtained.

Based on the above principles, a method for measuring the influence of a transflective medium on the transmission characteristics of photon orbital angular momentum is proposed, which includes the following steps:

Step 1: Fill the reflection-extending cavity 5 with a transflective medium and keep it at room temperature;

Step 2: Connect the driving power supply 1 to 220V AC, and the laser head 2 generates a continuous and stable Laguerre Gauss laser;

Step 2: Adjust the center points of the laser head 2, the beam expander 3 and the helical phase plate 4 to be on the same straight line, so that the incident beam emitted by the helical phase plate 4 and the reflection range extender cavity 5 are incident at 80°;

Step 3: Adjust the center points of the double-slit baffle 6, the light screen 7, the measuring head 8 and the CCD camera 9 to be on the same straight line, so that the double-slit baffle 6 and the outgoing beam from the reflection range extension cavity 5 are at 80° shoot out;

Step 4: After the Laguerre Gaussian laser passes through the beam expander 3, the spiral phase plate 4, the reflection range extension cavity 5, and the double-slit baffle 6 respectively, it is imaged through the optical screen 7, and the measuring head 8 quantitatively measures the interference fringes, and the CCD The camera 9 and the computer 10 display the measurement results of the interference fringes;

Step 5: Obtain the amount and direction of fringe bending by measuring the interference fringes, and reverse the topological charge of the orbital angular momentum of the laser beam under the action of the transflective medium.

The output end of the laser head 2 generates a continuous and stable Laguerre Gaussian laser, the output laser wavelength range is 380nm-760nm, the spot diameter is 0.5-0.9mm, the transverse mode is TEM00, the polarization state is linear polarization, and the beam quality is less than 1.5. The beam expander 3 can expand the laser beam by 10 times. The expanded laser beam passes through the center position of the spiral phase plate 4. The spiral phase plate 4 spatially modulates the Laguerre Gaussian laser, so that the laser beam can carry the topology Orbital angular momentum with a charge of 1.

The interference fringes and their measurement results are obtained through step 4. The interference fringes are curved fringes arranged at equal intervals. The amount and direction of fringe bending are related to the topological charge of the orbital angular momentum of the laser beam, and are also related to the double slits of the double slit baffle 6. The distance between the double-slit baffle 6 and the optical screen 7 is related to the distance between the two-slit baffle 6 and the optical screen 7. Therefore, the amount and direction of fringe bending can be obtained by measuring the interference fringes, and the topological charge of the orbital angular momentum of the laser beam after the action of the transflective medium can be reversed. The specific calculation process is as follows:

的光子轨道角动量光束波长为λ正入射双缝挡板，通过下式表示入射拉盖尔高斯激光光束的通用表达式：A topological charge is

The photon orbital angular momentum beam wavelength of λ is the normal incidence double-slit baffle, and the general expression for the incident Laguerre Gaussian laser beam is expressed by the following equation:

为激光光束轨道角动量的拓扑荷数，i为虚数单位，exp(imr²)为额外的衍射项。Among them, E _in is the intensity of the incident laser beam, (r, θ) is the polar coordinate, A(r) is the representative complex amplitude,

is the topological charge of the orbital angular momentum of the laser beam, i is an imaginary unit, and exp(imr ² ) is an additional diffraction term.

第二个狭缝的相位表达为

两个狭缝的沿着方向的相位差分布δφ(y)通过下式表达：Express the phase of the left slit as

The phase of the second slit is expressed as

The phase difference distribution δφ(y) of the two slits along the direction is expressed by the following formula:

Among them, (x, y) are the rectangular coordinates on the light screen, and a is the double-slit spacing of the double-slit baffle 6 .

According to the optical path difference theory and formula, when the laser beam is incident, the interference intensity distribution of the two slit arrays is expressed by the following formula:

Among them, (x, y) are the rectangular coordinates on the light screen, λ is the wavelength of the laser beam, and d is the distance between the double-slit baffle 6 and the light screen 7 .

Therefore, when the fringes are equally spaced parallel fringes, the locus x of the central bright fringes is expressed by the following formula:

The bending amount Δx of the stripes is obtained by the following formula:

为激光光束轨道角动量的拓扑荷数的绝对值。in,

is the absolute value of the topological charge of the orbital angular momentum of the laser beam.

On the contrary, according to the amount of fringe bending, the absolute value of the topological charge can be obtained by the following formula:

The positive and negative of the topological charge is determined by the direction of the stripe bending. For the same stripe from top to bottom, if the stripe deviates to the right, the topological load is negative, and if the stripe deviates to the left, the topological load is positive.

Specific embodiment three:

The driving power supply 1 generates a high-performance automatic ignition constant current power supply to supply power to the laser head 2 . The output end of the laser head 2 generates a continuous and stable Laguerre Gaussian laser, the output laser wavelength range is 632.8nm, the spot diameter is 0.68mm, the transverse mode is TEM00, the polarization state is linear polarization, and the beam quality is less than 1.5.

The beam expander 3 can expand the laser beam by 10 times, and the expanded laser beam passes through the center of the spiral phase plate 4 . The spiral phase plate 4 imparts a spiral phase distribution to the projected outgoing light beam, so that it carries a certain orbital angular momentum of a topological charge. The spiral phase plate 4 spatially modulates the Laguerre Gaussian laser, so that the laser beam can carry the topology The orbital angular momentum with a charge of 1, after the laser beam passes through the transflective medium, the measurement results are shown in Figure 3.

As shown in Fig. 2, the incident beam from the spiral phase plate 4 is incident at 80° to the reflection range extender cavity 5, and the double-slit baffle 6 and the outgoing beam from the reflection range extender cavity 5 emerge at an angle of 80°. Cavity 5 enables the Laguerre Gaussian laser to pass through the long-distance transflective medium region, and through continuous reflection, the action distance between the Laguerre Gaussian laser and the transflective medium is increased. The device of the present invention increases the optical path to 1021 cm in a cavity of 20cm*20cm, and the double-slit baffle 6 is a baffle with two slits, which can generate two coherent laser beams. The optical screen 7 images the double-slit interference results, the measuring head 8 quantitatively measures the imaging results, the CCD camera 9 converts the light into electric charges, converts them into digital signals through the analog-to-digital converter chip, and presents the measurement results through the computer 10 to achieve half-measurement. automated operation.

The device of the present invention is simple in structure and convenient to operate, and does not require complex adjustment of the optical path. The device of the present invention is located in a small reflective range extender cavity 5, which increases the optical path by a hundred times, and does not require a large-scale external field experiment. Quickly measure the effect of transflective medium on the transmission characteristics of photon orbital angular momentum. The invention can quickly and efficiently measure the influence of the transflective medium on the orbital angular momentum of the laser beam, and at the same time has high scalability. The measurement can be performed in a wide spectral range, and at the same time, the present invention reduces the measurement uncertainty to about 6%.

The above are only preferred embodiments of the device and method for measuring the influence of a transflective medium on the photon orbital angular momentum, and the protection scope of the device and method for measuring the influence of a transflective medium on the photon orbital angular momentum is not limited to the above-mentioned embodiments. , all the technical solutions under the idea belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and changes without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims (8)

1. A method for measuring the influence of a transflective medium on the transmission characteristic of the angular momentum of a photon orbit is based on a device for measuring the influence of the transflective medium on the transmission characteristic of the angular momentum of the photon orbit, the device comprises a driving power supply (1), a laser head (2), a beam expander (3), a spiral phase plate (4), a reflection range-extending cavity (5), a double-slit baffle (6), a light screen (7), a measuring head (8), a CCD (charge coupled device) camera (9) and a computer (10), and the rest parts except the power supply (1) and the computer (10) are fixed on a support frame;

the driving power supply (1) is connected with the laser head (2), the emergent end of the laser head (2) is over against the incident end of the beam expander (3), the emergent end of the beam expander (3) is over against the incident end of the spiral phase plate (4), the emergent end of the spiral phase plate (4) is over against the incident end of the reflection range-extending cavity (5), the emergent end of the reflection range-extending cavity (5) is over against the incident end of the double-slit baffle (6), and the emergent end of the double-slit baffle (6) is over against the front face of the light screen (7); the measuring end of the measuring head (8) is right opposite to the back surface of the light screen (7), the CCD camera (9) is right opposite to the result output end of the measuring head (8), and the CCD camera (9) is connected with the computer (10); the method is characterized in that: the method comprises the following steps:

the method comprises the following steps: filling a transflective medium into the reflection range-extending cavity (5) and keeping the room temperature state;

step two: the driving power supply (1) is connected with 220V alternating current, and the laser head (2) generates a continuous and stable Laguerre Gaussian laser beam;

step two: adjusting the central points of the laser head (2), the beam expander (3) and the spiral phase plate (4) to be on the same straight line, so that an incident beam emitted by the spiral phase plate (4) and the reflection range-extending cavity (5) are incident at an angle of 80 degrees;

step three: adjusting the central points of the double-slit baffle (6), the light screen (7), the measuring head (8) and the CCD camera (9) to be on the same straight line, so that emergent light beams emitted from the double-slit baffle (6) and the reflection range-extending cavity (5) are emergent at an angle of 80 degrees;

step four: laguerre Gaussian laser respectively passes through a beam expander (3), a spiral phase plate (4), a reflection range-extending cavity (5) and a double-slit baffle (6) and then is imaged through an optical screen (7), a measuring head (8) is used for quantitatively measuring interference fringes, and a CCD camera (9) and a computer (10) are used for displaying the measurement result of the interference fringes;

and fifthly, obtaining the bending amount and the bending direction of the fringes through interference fringe measurement, reversely deducing the topological charge number of the orbital angular momentum of the laser beam after the action of the transflective medium, and determining the influence of the transflective medium on the transmission characteristic of the photon orbital angular momentum through the reversely deduced topological charge number of the orbital angular momentum of the laser beam after the action of the transflective medium.

2. The method for measuring the influence of the transflective medium on the photon orbital angular momentum transfer characteristic according to claim 1, wherein the method comprises the following steps: the laser head (2) outputs continuous and stable Laguerre Gaussian laser, the laser wavelength range is 380nm-760nm, the spot diameter is 0.5-0.9mm, the transverse mode is TEM00, the polarization state is linear polarization, and the beam quality is less than 1.5.

3. The method for measuring the influence of the transflective medium on the photon orbital angular momentum transfer characteristic according to claim 1, wherein the method comprises the following steps: laguerre Gaussian laser generated by the laser head (2) passes through the central position of the spiral phase plate (4), and the spiral phase plate (4) enables Laguerre Gaussian laser beams to carry orbital angular momentum with topological load of l.

4. The method for measuring the influence of the transflective medium on the photon orbital angular momentum transfer characteristic according to claim 1, wherein the method comprises the following steps: the reflection range-extending cavity (5) comprises 5 reflectors which are connected end to end, the adjacent reflectors are mutually vertical, the lengths of the two reflectors at the end are 8cm-13cm, the lengths of the middle 3 reflectors are 20cm-30cm, and the reflection range-extending cavity (5) is filled with a transflective medium.

5. The method for measuring the influence of the transflective medium on the photon orbital angular momentum transfer characteristic according to claim 1, wherein the method comprises the following steps: the distance between the double slits of the double slit baffle (6) is 0.08mm-0.4mm, and the distance between the double slit baffle (6) and the light screen (7) is 500mm-800 mm.

6. The measurement method according to claim 1, wherein: the laser head (2) outputs continuous and stable Laguerre Gaussian laser, the laser wavelength range is 380nm-760nm, the spot diameter is 0.5-0.9mm, the transverse mode is TEM00, the polarization state is linear polarization, and the beam quality is less than 1.5.

7. The measurement method according to claim 1, wherein: laguerre Gaussian laser generated by the laser head (2) passes through the central position of the spiral phase plate (4), and the spiral phase plate (4) enables Laguerre Gaussian laser beams to carry orbital angular momentum with topological load of l.

8. The measurement method according to claim 1, wherein: the fifth step is specifically as follows:

the first step is as follows: a photon orbit angular momentum beam with topological charge number l has a lambda normal incidence double-slit baffle plate, and the general expression of an incident Laguerre Gaussian laser beam is expressed by the following formula:

E_in(r,θ)＝A(r)exp(ilθ)exp(imr²) (1)

wherein E is_inFor the incident Laguerre Gaussian laser beam intensity, (r, theta) are polar coordinates, A (r) is the characteristic complex amplitude, l is the topological charge number of the orbital angular momentum of the laser beam, i is the imaginary unit, exp (imr)²) In order for the additional diffraction term to be present,

the second step is that: the phase of the left slit is expressed as

The phase of the second slit is expressed as

The phase difference distribution δ Φ (y) along the direction of the two slits is expressed by the following equation:

wherein delta phi (y) is the phase distribution of the two slits along the direction, (x, y) is the rectangular coordinate on the light screen, a is the double-slit distance of the double-slit baffle (6),

the third step: according to the optical path difference theory and formula, when a laser beam is incident, the interference intensity distribution of two slit arrays is expressed by the following formula:

when the stripes are equally spaced parallel stripes, the locus x of the central bright stripe is represented by:

wherein x is the track of the central bright stripe, (x, y) are rectangular coordinates on the light screen, lambda is the wavelength of the laser beam, d is the distance between the double-slit baffle (6) and the light screen (7),

the fourth step: the amount of bending Δ x of the stripe is obtained by the following formula:

on the contrary, according to the bending amount of the stripe, the absolute value of the topological charge number can be obtained by the following formula:

wherein, Deltax is the bending amount of the stripe, | l | is the absolute value of the topological charge number of the orbital angular momentum of the laser beam,

the fifth step: the positive and negative of the topological charge value of the orbital angular momentum of the laser beam are determined by the bending direction of the stripes, and for the same stripe, from top to bottom, the deviation of the stripe to the right indicates that the topological charge is a negative value, and the deviation of the stripe to the left indicates that the topological charge is a positive value.

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