A method for measuring the topological charge of a vortex beam based on spatial self-phase modulation effect

Abstract

This invention discloses a method for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect. The apparatus, from left to right, consists of a laser, a spatial light modulator, a focusing lens, nonlinear optical materials, and a beam detection system. This invention provides a direct and accurate measurement of the topological charge of a vortex beam using nonlinear optics. Based on the spatial self-phase modulation effect of two-dimensional nanomaterials, a tailing phenomenon in the far-field self-diffraction intensity pattern was observed using an integer-order off-axis vortex beam; the number of tails is equal to the topological charge of the vortex beam. The far-field self-diffraction pattern excited by a fractional-order off-axis vortex beam exhibits a weaker tail intensity compared to the self-diffraction pattern of an integer-order vortex beam, which is related to the fractional topological charge. These experimental results provide a practical application: directly measuring the topological charge of a vortex beam using the spatial self-phase modulation effect. This method features a simple experimental setup, provides intuitive results, and offers reliable measurement results.

Description

Technical Field

[0001] This invention relates to a technique for measuring the topological charge of a vortex beam, belonging to the fields of optical field manipulation and nonlinear optics. Background Technology

[0002] As early as 1992, Allen et al. discovered that Laguerre-Gaussian beams carry a spiral phase structure of exp(ilφ), where φ is the azimuth angle and l is the topological charge [L. Allen, M.M. Beijersbergen, R.J. C. Preeuw, and J.P. Wördman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185 (1992)]. In a vortex beam, the orbital angular momentum carried by each photon around the optical axis is... in This is the reduced Planck constant. Therefore, the orbital angular momentum is determined by the spatial phase distribution of the light field. Compared to traditional Gaussian beams, vortex beams possess a definite orbital angular momentum, thus adding an optical degree of freedom. Vortex beams carrying orbital angular momentum have been widely applied in many fields, such as optical manipulation [M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343-384 (2011)], quantum information [A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits” Nat. Photonics 8, 234-238 (2014)], and free-space optical communication [Y. Yan, Y. Yue, H. Huang, Y. Ren, N. Ahmed, M. Tur, S. Dolinar, and A. Willner, “Multicasting in a spatial division multiplexing system based on optical orbital angular momentum photonic qubits”]. [Momentum, Opt. Lett. 38(19), 3930-3933(2013)] etc. In order to carry out relevant applications of vortex beams, it is very necessary to simply and accurately characterize the topological charge of vortex beams.

[0003] Based on interferometry [HISztul and RRAlfano, “Double-slit interference with Laguerre–Gaussian beams,” Opt. Lett. 31(7), 999-1001(2006)], diffraction [K. Dai, C. Gao, L. Zhong, Q. Na, and Q. Wang, “Measuring OAM states of light beams with gradually-changing-period gratings,” Opt. Lett. 40(4), 562-565(2015)], geometric coordinate transformation [Y. Wen, I. Chremmos, Y. Chen, J. Zhu, Y. Zhang, and S. Yu, “Spiral transformation for high-resolution and efficient sorting of optical vortex modes,” Phys. Rev. Lett. 120, 193904(2018)], and deep learning [Z. Liu, S. Yan, H. Liu, and Researchers have used various methods, including X. Chen, “Superhigh-resolution recognition of optical vortex modes assisted by a deep-learning method,” Phys. Rev. Lett. 123, 183902 (2019)], and surface plasmon resonances [J. Chen, X. Chen, T. Li, and S. Zhu, “On-chip detection of orbital angular momentum beam by plasmonic nanogratings,” Laser Photonics Rev. 12, 1700331 (2018)], to measure the topological charge of vortex beams. Interferometry, particularly using tilting and cylindrical lenses, directly yields the topological charge by counting the number of dark fringes in the focused beam. However, when the topological charge is high, the denser distribution of dark fringes affects the accurate measurement of the topological charge. Furthermore, these methods are not suitable for measuring the topological charge of fractional-order vortex beams.

[0004] Unlike previously reported methods for measuring topological charge, the innovation of this invention lies in its intuitive and simple method of measuring the topological charge of a vortex beam based on nonlinear optics. Specifically, integer-order off-axis vortex beams excited a tailing phenomenon in the far-field self-diffraction intensity pattern of a nonlinear optical sample, revealing that the number of tails is equal to the topological charge of the vortex beam. Fractional-order off-axis vortex beams, compared to the integer-order case, exhibited a tailing intensity change in the far-field self-diffraction intensity pattern, which is related to the fractional topological charge. Based on this, the topological charge of the vortex beam can be directly measured through the spatial self-phase modulation effect. Summary of the Invention

[0005] Technical Problem: To address the aforementioned problems, this invention proposes a device and method for measuring the topological charge of a vortex beam based on spatial self-phase modulation. This invention combines optical field manipulation techniques and nonlinear optical effects. By observing the tailing phenomenon in the far-field self-diffraction intensity pattern of a two-dimensional nanomaterial excited by an integer-order off-axis vortex beam, and finding that the number of tails equals the topological charge of the vortex beam, the topological charge of the vortex beam can be measured. This method can measure not only integer-order topological charges but also fractional-order topological charges.

[0006] Technical Solution: The device for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect of the present invention comprises, in sequence, a laser, a spatial light modulator, a focusing lens, a nonlinear optical material, and a beam detection system; the laser emits 1064nm infrared continuous laser light, the spatial light modulator operates at a wavelength of 650nm-1100nm, and its center coincides with the center of the incident Gaussian beam; the focusing lens is a positive lens with a focal length of 175mm, and the optical center of the focusing lens is coaxial with the beam; the nonlinear optical material is a two-dimensional black phosphorus nanosheet dispersed in a curing agent, which has the characteristics of wide-band nonlinear optical response; the nonlinear optical material is placed at a position slightly in front of the lens focal point; and the beam detection system is a CCD.

[0007] The laser output beam has a lateral intensity distribution of Gaussian or near-Gaussian incident beam, and its intensity can excite the spatial self-phase modulation effect of the material.

[0008] The spatial light modulator is coaxial with the incident beam, and by loading a vortex phase onto the spatial light modulator, vortex beams with different topological charges are generated.

[0009] The focusing lens is a weakly focusing positive lens.

[0010] The nonlinear optical material is a two-dimensional black phosphorus nanosheet dispersed in a curing agent, exhibiting a wide-band nonlinear optical response.

[0011] The beam detection system is a CCD, which can detect and record the transverse intensity distribution of the laser beam.

[0012] The method for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect of the present invention is as follows:

[0013] Step 1: Set the spatial light modulator and the laser output beam to be coaxial and concentric, with the beam propagating in the horizontal direction. Load a spiral phase onto the spatial light modulator to generate an on-axis vortex beam.

[0014] Step 2: Set up a focusing lens in the optical path, ensuring that the optical center of the lens is coaxial with the beam;

[0015] Step 3: Direct the focused beam onto the nonlinear optical material, which is positioned slightly in front of the lens focal point;

[0016] Step 4: By adjusting the displacement stage where the spatial light modulator is located, the spiral phase diagram loaded on the spatial light modulator is deviated from the center of the incident Gaussian light, generating an off-axis vortex beam.

[0017] Step 5: Record the far-field self-diffraction intensity pattern of the excited beam using a beam detection system;

[0018] Step 6: By loading spiral phases with different topological charges onto the spatial light modulator, the relationship between the far-field self-diffraction patterns and the topological charges of vortex beams with different topological charges can be obtained. By analyzing the tail number of the self-diffraction pattern, the topological charge of the vortex beam can be measured.

[0019] The relationship between the far-field self-diffraction patterns generated by vortex beams with different topological charges and the topological charge is determined by observing the tailing phenomenon of the far-field self-diffraction patterns using integer-order off-axis vortex beams. The number of tails is equal to the topological charge of the vortex beam. The self-diffraction patterns excited by fractional-order off-axis vortex beams show a tailing intensity change compared to the self-diffraction patterns of integer-order off-axis vortex beams, which is related to the fractional topological charge.

[0020] Beneficial Effects: Compared with existing technologies, the advantages of this invention are as follows: The proposed device and method for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect directly obtains the topological charge of the vortex beam by observing the tailing phenomenon of the self-diffraction intensity pattern of the off-axis vortex beam; and directly obtains the fractional topological charge by observing the tailing intensity change in the self-diffraction intensity pattern excited by a fractional-order off-axis vortex beam. This method is simple in principle, easy to use, exhibits obvious diffraction ring tailing phenomenon, is intuitive in measurement method, and provides reliable measurement results. The innovation of this invention patent lies in measuring the topological charge of a vortex beam based on a nonlinear optical method. Existing methods for measuring the topological charge of vortex beams are mainly based on linear optical methods, such as using tilting lenses and cylindrical lenses. These methods mainly count the number of dark fringes in the focused light field, which is the topological charge of the vortex beam. When the topological charge of the vortex beam is large, the dark fringes are densely distributed, thus affecting the accurate measurement of the topological charge of the vortex beam. Furthermore, these methods cannot measure the topological charge of fractional-order vortex beams. This paper innovatively proposes a method for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect. It combines optical field manipulation technology with nonlinear optics technology. By directly measuring the tail number in the far-field self-diffraction intensity pattern of the nonlinear optical material excited by the vortex beam, the topological charge of the vortex beam can be accurately obtained. This method is not only novel but also highly accurate. Attached Figure Description

[0021] Figure 1 This invention provides a device for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect.

[0022] Figure 2 The far-field self-diffraction intensity pattern is generated by an on-axis vortex beam with a topological charge of 3.

[0023] Figure 3 The diagram shows the far-field self-diffraction intensity patterns of an off-axis vortex beam with a topological charge of 3 and the off-axis vortex beam excited by the off-axis vortex beam. (a) and (b) are the far-field self-diffraction intensity patterns of the off-axis vortex beam with a topological charge of 3 and the off-axis vortex beam excited by the off-axis vortex beam, respectively.

[0024] Figure 4 The images show the far-field self-diffraction intensity patterns of an on-axis vortex beam and an off-axis vortex beam with a topological charge of 3.2, and the spatial self-phase modulation effect they excite. From left to right: intensity distribution of the on-axis vortex beam with a topological charge of 3.2, self-diffraction intensity pattern excited by the on-axis vortex beam with a topological charge of 3.2, intensity distribution of the off-axis vortex beam with a topological charge of 3.2, and self-diffraction intensity pattern excited by the off-axis vortex beam with a topological charge of 3.2.

[0025] Figure 5The images show the far-field self-diffraction intensity patterns of an on-axis and off-axis vortex beam with a topological charge of 3.5, and the spatial self-phase modulation effect excited by them. From left to right, the images show the intensity distribution of the on-axis vortex beam with a topological charge of 3.5, the self-diffraction intensity pattern excited by the on-axis vortex beam with a topological charge of 3.5, the intensity distribution of the off-axis vortex beam with a topological charge of 3.5, and the self-diffraction intensity pattern excited by the off-axis vortex beam with a topological charge of 3.5.

[0026] Figure 6 The images show the far-field self-diffraction intensity patterns of an on-axis and off-axis vortex beam with a topological charge of 3.8, and the spatial self-phase modulation effect they excite. From left to right: intensity distribution of the on-axis vortex beam with a topological charge of 3.8, self-diffraction intensity pattern excited by the on-axis vortex beam with a topological charge of 3.8, intensity distribution of the off-axis vortex beam with a topological charge of 3.8, and self-diffraction intensity pattern excited by the off-axis vortex beam with a topological charge of 3.8.

[0027] Among them: 1-laser, 2-spatial light modulator, 3-focusing lens, 4-nonlinear optical material, 5-beam detection system. Detailed Implementation

[0028] Experiments with vortex beams of different topological charges revealed that the far-field self-diffraction pattern excited by a fractional-order off-axis vortex beam exhibited a tailing intensity variation compared to that of an integer-order vortex beam, which is related to the fractional topological charge. Based on this, the topological charge of the vortex beam can be obtained by observing the far-field self-diffraction intensity pattern excited by the vortex beam in a nonlinear optical material.

[0029] To achieve the above functions, this invention employs a device and method for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect. The device comprises, in sequence, a laser, a spatial light modulator, a focusing lens, a nonlinear optical material, and an optical imaging recording system. The spatial intensity distribution of the laser beam emitted should be a fundamental mode Gaussian or near-Gaussian beam, and its output wavelength and intensity conditions should satisfy the requirement to excite the spatial self-phase modulation effect of the nonlinear material. The nonlinear optical material used can be a novel two-dimensional nanomaterial (for example, the two-dimensional nanomaterial used in this example is black phosphorus nanosheets dispersed in a curing agent). Under the illumination of the light source, a significant spatial self-phase modulation effect can be excited in the two-dimensional nanomaterial. This method is simple, intuitive, and produces good ring formation of the self-diffraction intensity pattern.

[0030] The example light source selected in this invention (the same below) is a 1064nm infrared continuous light laser.

[0031] The spatial light modulator used in this invention operates at a wavelength of 650nm-1100nm, with its center coinciding with the center of the Gaussian beam. This ensures that the spiral phase center loaded on the spatial light modulator coincides with the center of the incident Gaussian beam. In this way, the generated vortex light is relatively perfect and symmetrical, resulting in a symmetrical and clear far-field self-diffraction intensity pattern.

[0032] The focusing lens used in this invention is a positive lens with a focal length of 175mm. The function of a lens is to focus; if the focal length is too long, the focusing effect is not obvious and it is difficult to excite diffraction rings; if it is too short, the imaging effect is poor.

[0033] The nonlinear optical material selected in this invention is a two-dimensional black phosphorus nanosheet dispersed in a curing agent, which has the characteristics of a wide-band nonlinear optical response.

[0034] The beam detection system used in this invention is a CCD, which records the far-field self-diffraction intensity pattern of the excited beam.

[0035] This invention provides a device and method for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect. It can graphically represent the topological charge of the vortex beam by observing the trailing far-field self-diffraction intensity pattern of a nonlinear optical material excited by an integer-order off-axis vortex beam. Compared to the integer-order case, the far-field self-diffraction pattern excited by a fractional-order off-axis vortex beam exhibits a change in the brightness of the trailing light intensity, allowing for a direct measurement of the fractional topological charge of the vortex beam. The specific steps are as follows:

[0036] Step 1: According to the optical path Figure 1 Establish the optical path and adjust the position of the spatial light modulator to ensure that the spiral phase center loaded by the spatial light modulator is coaxial with the beam;

[0037] Step 2: Generate on-axis vortex beams with different topological charges by loading a spiral phase onto a spatial light modulator;

[0038] Step 3: Adjust the incident light power so that the light field can excite a significant spatial self-phase modulation effect in the nonlinear optical sample;

[0039] Step 4: By adjusting the displacement stage where the spatial light modulator is located, the spiral phase center is deviated from the beam center, thereby generating an off-axis vortex beam. The trailing self-diffraction intensity pattern of the off-axis vortex beam is observed and recorded using a beam analyzer.

[0040] Step 5: By changing the phase diagram loaded on the spatial light modulator, generate off-axis vortex beams with different topological charges, and repeat steps 3-4 above;

[0041] Step 6: Record the far-field self-diffraction intensity patterns of the off-axis vortex beam and the off-axis fractional-order vortex beam respectively, and analyze the relationship between the tail number in the self-diffraction pattern and the topological charge number of the vortex beam.

[0042] The following description, in conjunction with the accompanying drawings and specific embodiments, details the measurement of the topological charge of a vortex beam based on the spatial self-phase modulation effect. Examples of self-diffraction patterns excited by vortex beams with topological charges of 3, 3.2, 3.5, and 3.8 are provided for comparison.

[0043] Figure 1 This invention relates to an apparatus and method for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect. The apparatus comprises a laser 1, a spatial light modulator 2, a focusing lens 3, a nonlinear optical material 4, and a beam detection system 5. The laser beam emitted from the laser 1 has a spatial shape that is a fundamental mode Gaussian or near-Gaussian beam, and its intensity and wavelength satisfy the conditions for exciting the spatial self-phase modulation effect of the nonlinear optical material. The Gaussian beam emitted from the laser 1 is incident on the spatial light modulator, with an output power of 350 mW. By applying a helical phase to the spatial light modulator, a vortex beam with arbitrary topological charge can be generated. The generated vortex beam is focused by a lens with a focal length of 175 mm and then incident on the nonlinear optical material. In this example, the nonlinear optical sample is black phosphorus nanosheets dispersed in a curing agent, exhibiting a wide-band nonlinear optical response. Finally, a beam analyzer is used to record the generated far-field self-diffraction intensity pattern.

[0044] Figure 2 The figure shows the self-diffraction intensity pattern generated by the spatial self-phase modulation effect excited by an on-axis vortex beam with a topological charge of 3. The resulting self-diffraction intensity pattern consists of concentric rings, with the outer rings being wide and bright, and the inner rings being thin and dark, consistent with the basic characteristics of a self-diffraction intensity pattern. There is no tailing phenomenon, and the topological charge of the on-axis vortex beam cannot be determined from the figure.

[0045] Figure 3 Figure (a) shows an off-axis vortex beam with a topological charge of 3, and Figure (b) shows the self-diffraction intensity pattern excited by the off-axis vortex beam with a topological charge of 3. The experiment was conducted in... Figure 2 Based on the experiment, the displacement stage where the spatial light modulator is located was adjusted so that the loaded spiral phase gradually deviated from the center of the incident beam, generating an off-axis vortex beam. At this time, it can be seen that the diffraction ring gradually breaks inside the self-diffraction ring. As the off-axis amount increases, the breakage of the self-diffraction ring inside the ring gradually evolves to the outside of the ring and forms a tail, and the number of tails of the self-diffraction ring is the same as the topological charge of the excited spatial self-phase modulated vortex beam. (b) It can be seen from the figure that the number of tails of the self-diffraction ring is 3, which is the same as the topological charge of the excited spatial self-phase modulated vortex beam. It can be seen that the method is not only novel and simple, but also intuitive and highly accurate.

[0046] Figure 4From left to right, the figures show the self-diffraction intensity patterns generated by a fractional-order on-axis vortex beam with a topological charge of 3.2, the self-diffraction intensity patterns generated by a fractional-order on-axis vortex beam with a topological charge of 3.2 excited by spatial self-phase modulation, the self-diffraction intensity patterns generated by a fractional-order off-axis vortex beam with a topological charge of 3.2, and the self-diffraction intensity patterns generated by a fractional-order off-axis vortex beam with a topological charge of 3.2. It can be seen that the fractional-order on-axis vortex beam exhibits a certain degree of axisymmetry breaking compared to the integer-order on-axis vortex beam. The figure shows that the self-diffraction pattern generated by the fractional-order on-axis vortex beam with a topological charge of 3.2 consists of concentric rings without tailing. When the displacement stage of the spatial light modulator is adjusted, causing the loaded spiral phase to gradually deviate from the center of the incident beam, an off-axis vortex beam is generated. At this point, it can be seen that the diffraction rings gradually break inside the self-diffraction rings. As the amount of off-axis increases, the breaking of the self-diffraction rings inside the rings gradually evolves to the outside of the rings, forming a tail. It can be seen that the tail number generated by the self-diffraction ring is basically 3. However, unlike the off-axis vortex beam excited by the self-diffraction ring with a topological charge of 3, a slight break can be seen on the fourth ring of the tail. This is due to the fractional part of the fractional topological charge, which will also be the basis for us to judge the topological charge number of the vortex beam.

[0047] Figure 5 The figures, from left to right, represent the self-diffraction intensity patterns generated by a fractional-order on-axis vortex beam with a topological charge of 3.5, the self-diffraction intensity patterns generated by the spatial self-phase modulation effect excited by the fractional-order on-axis vortex beam with a topological charge of 3.5, the self-diffraction intensity patterns excited by the fractional-order off-axis vortex beam with a topological charge of 3.5, and the self-diffraction intensity patterns excited by the fractional-order off-axis vortex beam with a topological charge of 3.5. It can be seen from the figures that the self-diffraction pattern generated by the fractional-order on-axis vortex beam with a topological charge of 3.5 consists of concentric rings without tailing. When the displacement stage of the spatial light modulator is adjusted, causing the loaded spiral phase to gradually deviate from the center of the incident beam, an off-axis vortex beam is generated. At this point, it can be seen that the diffraction rings gradually break inside the rings. As the amount of off-axis increases, the breakage of the self-diffraction rings inside the rings gradually evolves to the outside of the rings, forming a tail. The number of tails generated by the self-diffraction rings is generally between 3 and 4. However, unlike the self-diffraction rings excited by the vortex beam with a topological charge of 3.2, there is a clear break in the fourth ring of the tail. This is because the larger the fractional part of the fractional topological charge, the more obvious the break in the internal tail self-diffraction rings.

[0048] Figure 6From left to right, the figures show the self-diffraction intensity patterns generated by a fractional-order on-axis vortex beam with a topological charge of 3.8, the self-diffraction intensity patterns generated by a fractional-order on-axis vortex beam with a topological charge of 3.8 excited by spatial self-phase modulation, the self-diffraction intensity patterns generated by a fractional-order off-axis vortex beam with a topological charge of 3.8, and the self-diffraction intensity patterns generated by a fractional-order off-axis vortex beam with a topological charge of 3.8. It can be seen from the figures that the self-diffraction intensity pattern generated by the fractional-order on-axis vortex beam with a topological charge of 3.8 is a concentric ring without tailing. When the displacement stage of the spatial light modulator is adjusted, causing the loaded spiral phase to gradually deviate from the center of the incident beam, an off-axis vortex beam is generated. At this time, it can be seen that the diffraction ring is gradually broken inside the self-diffraction ring. As the off-axis amount increases, the broken self-diffraction ring inside the ring gradually evolves to the outside of the ring, forming a tail. It can be seen that the number of tails generated by the self-diffraction ring is close to 4, but unlike the self-diffraction ring excited by the vortex beam with a topological charge of 3.5, the fourth tail has already basically formed.

[0049] Therefore, according to the apparatus and method provided by the present invention, the topological charge of a beam can be measured by exciting the spatial self-phase modulation effect of a nonlinear optical sample with a vortex beam. Specifically, the spatial self-phase modulation effect of a nonlinear optical material can be excited by an integer-order off-axis vortex beam, generating a tail number on the far-field self-diffraction intensity pattern, thereby accurately determining the topological charge of the excited spatial self-phase modulated vortex beam. For the self-diffraction intensity pattern generated by a fractional-order off-axis vortex beam, the fractional part of the topological charge of the excited fractional-order vortex beam can be determined based on the degree of breakage of the generated self-diffraction pattern tail. This is an advantage compared to the conventional tilting lens method and cylindrical lens method for measuring the topological charge of vortex beams. In summary, accurately determining the topological charge of a vortex beam by calculating the tail number in the self-diffraction intensity pattern excited by the vortex beam is not only novel and experimentally simple, but also provides intuitive and accurate results.

Claims

1. A device for measuring the topological charge of a vortex beam based on spatial self-phase modulation effect, characterized in that, The device consists of a laser (1), a spatial light modulator (2), a focusing lens (3), a nonlinear optical material (4), and a beam detection system (5). The laser emits a 1064 nm infrared continuous laser. The spatial light modulator operates at a wavelength of 650 nm-1100 nm, with its center coinciding with the center of the incident Gaussian beam. The focusing lens is a positive lens with a focal length of 175 mm, and its optical center is coaxial with the beam. The nonlinear optical material is a two-dimensional black phosphorus nanosheet dispersed in a curing agent, which has the characteristics of a wide-band nonlinear optical response. The nonlinear optical material is placed slightly in front of the lens focal point. The beam detection system is a CCD that can detect and record the transverse intensity distribution of the laser beam.

2. The apparatus for measuring the topological charge of a vortex beam based on spatial self-phase modulation effect according to claim 1, characterized in that, The laser (1) outputs a beam with a transverse intensity distribution that is Gaussian or near-Gaussian, and its intensity can excite the spatial self-phase modulation effect of the material.

3. The apparatus for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect according to claim 2, characterized in that, The spatial light modulator (2) is coaxial with the incident beam. By loading a vortex phase onto the spatial light modulator (2), vortex beams with different topological charges are generated.

4. The apparatus for measuring the topological charge of a vortex beam based on spatial self-phase modulation effect according to claim 3, characterized in that, The focusing lens (3) is a weak focusing positive lens.

5. A method for measuring the topological charge of a vortex beam based on the spatial self-phase modulation effect using the apparatus as described in claim 4, characterized in that, The method is as follows: Step 1: Set the spatial light modulator and the laser output beam to be coaxial and concentric, with the beam propagating in the horizontal direction. Load a spiral phase onto the spatial light modulator to generate an on-axis vortex beam. Step 2: Set up a focusing lens in the optical path, ensuring that the optical center of the lens is coaxial with the beam; Step 3: Direct the focused beam onto the nonlinear optical material, which is positioned slightly in front of the lens focal point; Step 4: By adjusting the displacement stage where the spatial light modulator is located, the spiral phase diagram loaded on the spatial light modulator is deviated from the center of the incident Gaussian light, generating an off-axis vortex beam. Step 5: Record the far-field self-diffraction intensity pattern of the excited beam using a beam detection system; Step 6: By loading spiral phases with different topological charges onto the spatial light modulator, the relationship between the far-field self-diffraction patterns and the topological charges of vortex beams with different topological charges can be obtained. By analyzing the tail number of the self-diffraction pattern, the topological charge of the vortex beam can be measured.

6. The method for measuring the topological charge of a vortex beam based on spatial self-phase modulation effect according to claim 5, characterized in that, The relationship between the far-field self-diffraction patterns generated by vortex beams with different topological charges and the topological charge is determined by observing the tailing phenomenon of the far-field self-diffraction patterns using integer-order off-axis vortex beams. The number of tails is equal to the topological charge of the vortex beam. The self-diffraction patterns excited by fractional-order off-axis vortex beams show a tailing intensity change compared to the self-diffraction patterns of integer-order off-axis vortex beams, which is related to the fractional topological charge.

Images