An experimental method and device for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry

Abstract

The present invention relates to the field of optical communication-related computing technologies, and specifically to an experimental method and apparatus for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry. The method comprises a helium-neon laser, a beam expansion and collimation system, a spectroscopic modulation component, a spatial light modulator, a phase polarization adjustment component, and a charge-coupled device (CCD) camera. The spatial light modulator is disposed on the optical path of the Gaussian beam output by the helium-neon laser, and a CCD camera is disposed at the end of the optical path of the beam modulated by the spatial light modulator. The beam expansion and collimation system and the spectroscopic modulation component are coaxially disposed in sequence on the optical path between the helium-neon laser and the spatial light modulator, and the phase polarization adjustment component is coaxially disposed on the optical path between the spatial light modulator and the CCD camera. The present invention utilizes a small amount of experimental equipment to achieve stable coaxial interferometry of a vortex beam and accurate measurement of the orbital angular momentum spectrum, greatly reducing the difficulty of constructing the experimental interferometric optical path.

Description

Technical Field

[0001] The present invention relates to the field of optical communication related computing technology, and in particular to an experimental method and device for measuring the orbital angular momentum spectrum of a vortex light beam based on coaxial interferometry. Background Art

[0002] With the explosive growth of the Internet and data traffic, people have put forward higher requirements for faster and more information transmission capabilities. Compared with traditional communication methods, optical communication has higher bandwidth and longer transmission distance, which is very conducive to the realization of large-scale data transmission. Vortex beams, as a kind of light beam with a spiral phase structure, carry orbital angular momentum (OAM). Vortex beams carrying different orbital angular momentum modes are spatially orthogonal to each other, which can greatly improve the channel capacity of optical communication and show great potential and development significance in the field of optical communication. Therefore, it is extremely important to accurately and efficiently identify the orbital angular momentum modes in vortex beams.

[0003] The orbital angular momentum spectrum is also called the spiral spectrum. It is similar to the spectrum and represents the energy proportion of different orbital angular momentum modes in the light beam. Because the orbital angular momentum of the vortex beam is closely related to its phase structure, the interferometer method has become an effective method to calculate the orbital angular momentum spectrum of the vortex beam. In the interferometer method, the interference of the light beam requires the introduction of a reference beam. The currently used Mach-Zehnder interferometer experimental scheme is as follows: Figure 2As shown in the figure, the experimental setup consists of a helium-neon laser (He-Ne laser), a beam expansion and collimation system consisting of a lens with a focal length of 5 cm (L1) and a lens with a focal length of 25 cm (L2), a polarizing beam splitter (PBS), a half-wave plate (HWP), a spatial light modulator (SLM), a quarter-wave plate (QWP), a mirror (M), a beam splitter (BS), a polarizer (P), and a CCD camera (CCD). The principle is to split the laser beam into two beams, one of which serves as a reference beam, and the other is modulated by a spatial light modulator to generate a vortex beam. The beams are then combined to achieve interference between the vortex beam and the reference beam. To obtain the light field intensity required for calculation, the reference beam path and the measured beam path need to be shielded to obtain the uninterfered reference beam intensity and vortex beam intensity. In addition, two different phase delays need to be introduced in the reference beam path or the vortex beam path to obtain the corresponding interference intensity of the reference beam and the vortex beam. Finally, the orbital angular momentum spectrum distribution of the vortex beam is calculated using the four light field intensities.

[0004] Therefore, existing interferometry-based methods for measuring the orbital angular momentum spectrum of vortex beams suffer from the following drawbacks: The optical path is difficult to adjust. Accurately measuring the orbital angular momentum spectrum of a vortex beam requires that the reference beam and the vortex beam be strictly coaxial (i.e., their propagation directions are identical to the beam centers). Achieving coaxial interference between the reference and vortex beams requires precise adjustment of the optical path. If a beam splitting and then combining scheme is employed, the beams pass through multiple reflectors, making adjustment of the optical path exponentially more difficult.

[0005] Therefore, it is necessary to provide an experimental method and device for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry to solve the above problems. Summary of the Invention

[0006] The present invention provides an experimental method and device for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry. By coaxially injecting a vertically polarized Gaussian reference beam and a horizontally polarized Gaussian beam of equal intensity into a spatial light modulator, the vortex beam generated after modulation by the spatial light modulator remains coaxial with the reference beam. Therefore, the reference beam and the vortex beam can be coaxially transmitted throughout the entire transmission process, ensuring that the measured interference intensity is always the coaxial interference intensity. This solves the following shortcomings of existing methods for measuring the orbital angular momentum spectrum of a vortex beam based on interferometry: the difficulty in adjusting the optical path. Accurate measurement of the orbital angular momentum spectrum of a vortex beam requires that the reference beam and the vortex beam be strictly coaxial (i.e., the propagation directions of the reference beam and the vortex beam are completely consistent with the center of the beam). To achieve coaxial interference between the reference beam and the vortex beam, precise adjustment of the optical path is required. If a solution of splitting and then combining the beams is adopted, the beams will pass through multiple reflective devices, resulting in an exponential increase in the difficulty of adjusting the optical path.

[0007] The present invention provides an experimental device for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry, which adopts the following technical solutions, including:

[0008] A spatial light modulator is provided on the optical path of the Gaussian beam output by a helium-neon laser, and a CCD camera is provided at the end of the optical path of the beam modulated by the spatial light modulator;

[0009] The beam expansion and collimation system and the light splitting and modulation components are coaxially arranged in the optical path between the He-Ne laser and the spatial light modulator.

[0010] and a phase polarization adjustment component, coaxially disposed on an optical path between the spatial light modulator and the CCD camera;

[0011] Among them, the beam expansion and collimation system is used to expand and collimate the Gaussian beam, the spectroscopic modulation component is used to modulate the expanded and collimated beam into a target Gaussian beam with equal light field intensity in the horizontal polarization direction and the vertical polarization direction; the spatial light modulator is used to modulate the horizontal polarization direction of the target Gaussian beam into a horizontally polarized vortex beam; and output an outgoing beam that is a superposition of the horizontally polarized vortex beam and the vertically polarized target Gaussian beam; the phase polarization adjustment component is used to introduce 0 or 0 between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing beam. phase difference; and adjusting the phase-adjusted light beam to a preset beam form, wherein the beam form includes: a vortex beam, a Gaussian beam, and an interference beam corresponding to the phase difference; a CCD camera is used to measure the light field intensity corresponding to different beam forms.

[0012] Preferably, when the introduced phase difference is 0, the phase polarization adjustment component includes: a polarizer, which is used to adjust the phase-adjusted light beam into a vortex beam, a Gaussian beam or an interference beam with a phase difference of 0; which is used to introduce a phase difference between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing light beam; when the introduced phase difference is The phase polarization adjustment component includes: a quarter wave plate and a polarizer. The quarter wave plate is set in the optical path between the polarizer and the spatial light modulator. The quarter wave plate is used to introduce a phase difference between the horizontally polarized vortex beam in the outgoing beam and the vertically polarized target Gaussian beam. Phase difference.

[0013] Preferably, the beam expansion and collimation system comprises: a first lens and a second lens, the first lens and the second lens are coaxially arranged, and the focal length of the second lens is greater than the focal length of the first lens.

[0014] Preferably, the focal length of the second lens is five times the focal length of the first lens.

[0015] Preferably, the optical splitting modulation component includes:

[0016] a polarization beam splitter for splitting the expanded and collimated light beam into a horizontally polarized light beam and a vertically polarized light beam perpendicular to each other, wherein the transmitted horizontally polarized light beam remains in the light path;

[0017] and a half-wave plate to adjust the polarization direction of the horizontally polarized light beam after being split by the polarization beam splitter, so that the outgoing light beam is a target Gaussian beam with equal light field intensity in the horizontal and vertical polarization directions.

[0018] Preferably, the spatial light modulator is a reflective modulator or a transmissive modulator.

[0019] The present invention provides an experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry, which adopts the following technical solutions, including:

[0020] Turn on the HeNe laser;

[0021] Turning on the spatial light modulator and loading the corresponding phase hologram onto the spatial light modulator to generate a vortex beam of a preset orbital angular momentum mode;

[0022] Turn on the CCD camera;

[0023] Adjust the polarizer so that the angle between the polarization direction and the horizontal direction is 0°, and use the CCD camera to collect the current first light field intensity;

[0024] Adjust the polarizer so that the angle between the polarization direction and the horizontal direction is 90°, and use the CCD camera to collect the current intensity of the second light field;

[0025] Adjust the polarizer so that the angle between the polarization direction and the horizontal direction is 0° to 90°, preferably 45°, and use a CCD camera to collect the current intensity of the first interference light field;

[0026] Add a quarter-wave plate and adjust the polarizer so that the angle between the polarization direction and the horizontal direction is 0° to 90°, preferably 45°, and the CCD camera collects the current second interference light field intensity;

[0027] The orbital angular momentum spectra of the vortex light beam corresponding to different orbital angular momentum modes are obtained according to the first light field intensity, the second light field intensity, the first interference light field intensity and the second interference light field intensity.

[0028] Preferably, the step of obtaining the orbital angular momentum spectrum of the vortex beam corresponding to the orbital angular momentum mode m is:

[0029]

[0030] Where, is the orbital angular momentum spectrum of the vortex beam corresponding to the orbital angular momentum mode m; is the expansion coefficient when the orbital angular momentum mode is m; is the sum of all orbital angular momentum modal energies contained in the vortex beam; An angle between the polarization direction of the polarizer and the horizontal direction when obtaining the first interference light field intensity and the second interference light field intensity; represents the phase difference introduced between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing beam; represents the intensity of the first light field; represents the intensity of the second light field; represents the intensity of the first interference light field; represents the intensity of the second interference light field is the complex amplitude of the horizontally polarized vortex beam light field; is the complex amplitude of the vertically polarized Gaussian beam light field; is the interference light field intensity received by the CCD camera; * indicates conjugation; It represents the phase difference between the expansion coefficient of orbital angular momentum mode m and the complex amplitude of Gaussian beam light field; represents an imaginary unit; Represents the azimuth in the polar coordinate system; represents the radius in polar coordinate system; represents the phase difference term introduced by the quarter-wave plate; represents the real part; Represents the interference term in the interference light field intensity; represents the interference term in the first interference light field intensity; Represents the interference term in the second interference light field intensity.

[0031] Preferably, before collecting the first interference light field intensity and the second interference light field intensity, the angle between the polarization direction of the polarizer and the horizontal direction is adjusted.

[0032] The beneficial effects of the present invention are:

[0033] 1. The present invention utilizes the polarization selection characteristic of the spatial modulator for the modulated light beam, and coaxially inputs the vertically polarized Gaussian reference beam and the horizontally polarized Gaussian beam into the spatial light modulator, so that the vortex beam generated after modulation by the spatial light modulator remains coaxial with the reference beam. Therefore, it can be achieved that the reference beam and the vortex beam are coaxially transmitted throughout the entire transmission process, ensuring that the measured interference intensity is definitely the coaxial interference intensity, solving the problem that the vortex beam and the reference beam are difficult to strictly coaxial in traditional Mach-Zehnder interferometer experimental measurements. At the same time, a small amount of experimental equipment can be used to achieve stable coaxial interference of the vortex beam and accurate measurement of the orbital angular momentum spectrum, greatly reducing the difficulty of building the experimental interference optical path.

[0034] 2. The present invention significantly improves the efficiency of light field intensity acquisition. This method does not require shielding the reference beam path or the vortex beam path; it only requires adjusting the rotation angle of the polarizer to acquire the desired light field intensity. By splitting the beam for measurement, four light intensity patterns can be measured simultaneously, potentially enabling real-time measurement of the angular momentum spectrum of vortex beams. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1 Schematic diagram of the structure of an experimental device for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry according to the present invention;

[0037] Figure 2 A schematic diagram of an experimental setup of an existing Mach-Zehnder interferometer solution in the background art of the present invention;

[0038] Figure 3 This is a light field intensity distribution diagram used to calculate the orbital angular momentum spectrum of a vortex beam carrying a single mode (and orbital angular momentum modes m=+7, m=-7) obtained by experimental measurement in an embodiment of the present invention;

[0039] Figure 4The orbital angular momentum spectrum measurement results of a vortex beam carrying a single mode (orbital angular momentum mode m=+7, m=-7);

[0040] Figure 5 The measurement results of the orbital angular momentum spectrum of the dual-mode (m=-4, m=5) vortex beam are shown;

[0041] Figure 6 The measurement results of the orbital angular momentum spectrum of the vortex beam carrying three modes (m=-3, m=1, m=5) are shown;

[0042] Figure 7 This is the measurement result of orbital angular momentum spectrum of the vortex beam carrying four modes (m=-7, m=-3, m=1, m=5).

[0043] In the figure: 1. Helium-neon laser; 2. First lens; 3. Second lens; 4. Polarization beam splitter; 5. Half-wave plate; 6. Spatial light modulator; 7. Quarter-wave plate; 8. Polarizer; 9. CCD camera. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0045] An embodiment of an experimental device for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry of the present invention is as follows: Figure 1 As shown, it includes: a helium-neon laser 1, a beam expansion and collimation system, a spectroscopic modulation component, a spatial light modulator 6, a phase polarization adjustment component and a CCD camera 9. The spatial light modulator 6 is provided on the optical path of the Gaussian beam output by the helium-neon laser 1, and the CCD camera 9 is provided at the end of the optical path of the beam modulated by the spatial light modulator 6; the beam expansion and collimation system and the spectroscopic modulation component are coaxially arranged in sequence on the optical path between the helium-neon laser 1 and the spatial light modulator 6, and the phase polarization adjustment component is coaxially arranged on the optical path between the spatial light modulator 6 and the CCD camera 9, wherein The beam expansion and collimation system is used to expand and collimate the Gaussian beam, and the spectroscopic modulation component is used to modulate the expanded and collimated beam into a target Gaussian beam with equal light field intensity in the horizontal polarization direction and the vertical polarization direction; the spatial light modulator 6 is used to modulate the horizontal polarization direction of the target Gaussian beam into a horizontally polarized vortex beam; and output an outgoing beam that is a superposition of the horizontally polarized vortex beam and the vertically polarized target Gaussian beam; the phase polarization adjustment component is used to introduce 0 or 0 between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing beam. and adjusting the phase-adjusted beam to a preset beam form, wherein the beam forms include: a vortex beam, a Gaussian beam, and an interference beam corresponding to the phase difference; the CCD camera 9 is used to measure the light field intensity corresponding to different beam forms.

[0046] Specifically, when the introduced phase difference is 0, the phase polarization adjustment component includes: a polarizer 8, which is used to adjust the phase-adjusted light beam into a vortex beam, a Gaussian beam or an interference beam with a phase difference of 0; it is used to introduce a phase difference of 0 between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing light beam; Figure 2 As shown, the phase difference introduced is When the phase polarization adjustment component includes: a quarter wave plate 7 and a polarizer 8. The quarter wave plate 7 is arranged on the optical path between the polarizer 8 and the spatial light modulator 6. The quarter wave plate 7 is used to introduce a phase polarization between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing light beam. Phase difference.

[0047] Specifically, the beam expansion and collimation system includes: a first lens 2 and a second lens 3, the first lens 2 and the second lens 3 are coaxially arranged, and the focal length of the second lens 3 is greater than the focal length of the first lens 2, and the focal length of the second lens 3 is five times the focal length of the first lens 2. In this embodiment, the focal length of the second lens 3 is 25 mm, and the focal length of the first lens 2 is 5 mm.

[0048] Specifically, the spectroscopic modulation component includes: a polarization beam splitter 4 and a half-wave plate 5. The polarization beam splitter 4 is used to split the expanded collimated light beam into a horizontally polarized light beam and a vertically polarized light beam that are perpendicular to each other; the half-wave plate 5 is used to modulate the corresponding light field intensities of the horizontally polarized light beam and the vertically polarized light beam that are perpendicular to each other into a target Gaussian beam with equal light field intensity.

[0049] Specifically, the spatial light modulator 6 is a reflective modulator or a transmissive modulator, such as Figure 1 As shown, in this embodiment, the spatial light modulator 6 is a reflective modulator.

[0050] In summary, if Figure 1As shown, an embodiment of the experimental device for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry of the present invention specifically includes: a helium-neon laser (He-Ne Laser), a beam expansion and collimation system consisting of a first lens (L1) with a focal length of 5 cm and a second lens (L2) with a focal length of 25 cm, a polarizing beam splitter (PBS), a half-wave plate (HWP), a spatial light modulator (SLM), a quarter-wave plate (QWP), a polarizer (P), and a CCD camera (CCD).

[0051] An embodiment of an experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry of the present invention comprises the following specific steps:

[0052] Step 1: Turn on the He-Ne laser 1;

[0053] Step 2: Turn on the spatial light modulator 6 and load the corresponding phase hologram onto the spatial light modulator 6 to generate a vortex beam of a preset orbital angular momentum mode (different orbital angular momentum modes require different phase holograms for vortex beams).

[0054] Step 3: Turn on the CCD camera 9;

[0055] Step 4: Adjust the polarizer 8 so that the angle between the polarization direction and the horizontal direction is 0°, and the CCD camera 9 collects the current first light field intensity. ;

[0056] Step 5: Adjust the polarizer 8 so that the angle between the polarization direction and the horizontal direction is 90°, and the CCD camera collects the current second light field intensity. ;

[0057] Step 6: Adjust the polarizer 8 so that the angle between the polarization direction and the horizontal direction is 45°, and the CCD camera 9 collects the current first interference light field intensity. ;

[0058] Step 7: Add a quarter wave plate 7 and adjust the polarizer 8 so that the angle between the polarization direction and the horizontal direction is 45°. The CCD camera 9 collects the current second interference light field intensity. ;

[0059] Step 8: Obtain an orbital angular momentum spectrum of the vortex beam corresponding to the orbital angular momentum mode m according to the first light field intensity, the second light field intensity, the first interference light field intensity, and the second interference light field intensity. Specifically, the steps of obtaining the orbital angular momentum spectrum of the vortex beam corresponding to the orbital angular momentum mode m are as follows:

[0060] Step 81: According to the spiral harmonic decomposition theory, the complex amplitude of the horizontally polarized vortex beam light field can be expanded to express:

[0061] (1)

[0062] Where, is the complex amplitude of the horizontally polarized vortex beam light field; is the expansion coefficient when the orbital angular momentum mode is m; represents an imaginary unit; Indicates the azimuth in the polar coordinate system.

[0063] in, It can be obtained by Fourier transform of the vortex beam light field, that is:

[0064] (2)

[0065] Where, is the expansion coefficient when the orbital angular momentum mode is m; is the complex amplitude of the horizontally polarized vortex beam light field.

[0066] The orbital angular momentum spectrum of the vortex beam corresponding to the orbital angular momentum mode m is defined as:

[0067] (3)

[0068] Where, is the orbital angular momentum spectrum of the vortex beam corresponding to the orbital angular momentum mode m; is the sum of all orbital angular momentum modal energies contained in the vortex beam (i.e., all the energy of the light field), ; Represents the radius in polar coordinates.

[0069] According to formula (2) and formula (3), to obtain the orbital angular momentum spectrum of the vortex beam, it is necessary to measure the complex amplitude of the light field of the vortex beam. or all expansion coefficients This embodiment uses the interferometry method to measure the orbital angular momentum spectrum of the vortex beam, which requires a total of four light field intensities: 1) the first light field intensity of the horizontally polarized vortex beam, 2) the second light field intensity of the reference beam (vertically polarized target Gaussian beam), 3) the first interference light field intensity with a phase difference of 0 between the vortex beam and the reference beam, and 4) the additional phase difference between the vortex beam and the reference beam. The following is the formula for calculating the orbital angular momentum spectrum of the vortex beam corresponding to different orbital angular momentum modes by using the first light field intensity, the second light field intensity, the first interference light field intensity, and the second interference light field intensity. Suppose the complex amplitude of the light field of the vertically polarized target Gaussian beam of the outgoing light beam passing through the spatial light modulator 6 is ( G represents a Gaussian beam, i.e., the reference beam in the present invention), the complex amplitude of the light field of the horizontally polarized vortex beam is , the angle between the polarizer 8 and the horizontal direction is The complex amplitude of the light field after the coaxial superposition beam passes through the polarizer 8 is:

[0070] (4)

[0071] The CCD camera 9 receives the image when the polarizer 8 is at an angle with the horizontal direction. , and the phase difference introduced between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing beam is The corresponding interference light field intensity is:

[0072] (5)

[0073] Where, Indicates that the angle between the polarizer 8 and the horizontal direction is , and the phase difference introduced between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing beam is The corresponding interference light field intensity when ; represents the intensity of the first light field; represents the intensity of the second light field; Represents the interference term in the interference light field intensity;

[0074] in,

[0075] (6)

[0076] (7)

[0077] (8)

[0078] Where, represents the phase difference introduced between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing beam; * represents conjugation; represents the phase difference term introduced by the quarter-wave plate; represents the real part; represents an imaginary unit;

[0079] It should be noted that when a quarter wave plate 7 with a slow axis parallel to the polarization direction of the reference beam is added between the spatial light modulator 6 and the polarizer 8, , without adding a quarter-wave plate .when hour, ,when hour ; Then using formula (1), It can be expressed as:

[0080] (9)

[0081] Where, Represents the interference term in the interference light field intensity; represents the phase difference between the expansion coefficient of the orbital angular momentum mode m and the complex amplitude of the light field of the vertically polarized target Gaussian beam; arg represents the acquisition angle.

[0082] Using phase difference , And the angle between the polarization direction of the polarizer and the horizontal direction is The first interference light field intensity , the second interference light field intensity And formula (8), we have:

[0083] (10)

[0084] According to formula (10), we can get :

[0085] (11)

[0086] Substituting Equation (11) into Equation (3) can obtain the orbital angular momentum spectrum of the vortex beam. Therefore, a total of four light field intensities are required, namely 、 、 、 In order to maintain the best interference effect, when obtaining the second interference light field intensity and the first interference light field intensity Generally 45° is taken.

[0087] Two specific measurement examples are given below to illustrate the measurement process and practicality of this embodiment:

[0088] Measurement Example 1: Orbital Angular Momentum Spectrum Measurement of a Single-Mode Vortex Beam:

[0089] In this example, the OAM spectrum (orbital angular momentum spectrum) of a vortex beam carrying a single OAM mode is measured. Figure 3The four light field intensities measured when carrying orbital angular momentum modes m=7 and m=-7. It can be seen that the modulation efficiency of the spatial light modulator cannot reach 100%, resulting in incomplete modulation of the horizontal polarized light. The modulated vortex beam contains some horizontally polarized Gaussian light that is not modulated, so the intensity The corresponding OAM spectrum measurement results are as follows: Figure 4 (a) and Figure 4 As shown in (b), the theoretical value is basically consistent with the experimental value, where the energy distribution at m=0 comes from the incomplete modulation part of the spatial light modulator.

[0090] Measurement Example 2: Orbital Angular Momentum Spectrum Measurement of Multimodal Vortex Beams:

[0091] In this example, the OAM spectrum of a vortex beam carrying multiple orbital angular momentum modes is measured. Figure 5 The OAM spectrum measurement results of dual-mode (m=-4, m=5) vortex beams with different energy ratios are shown in Figure 2. Figure 6 The OAM spectrum measurement results of three-mode (m=-3, m=1, m=5) vortex beams with different energy ratios are shown in Figure 2. Figure 7 The OAM spectrum measurement results of four-mode (m=-7, m=-3, m=1, m=5) vortex beams with different energy ratios are shown. Among them, the preset OAM spectrum is the OAM spectrum that the vortex beam generated by the phase hologram theory loaded on the spatial light modulator should have. The experimentally measured OAM spectrum is consistent with the preset OAM spectrum distribution very well. Due to the modulation efficiency limitation of the spatial light modulator, the experimentally measured OAM spectrum energy ratio is lower than the energy ratio corresponding to the preset OAM, but the energy ratio between modes is consistent with the preset one. Since the modulation mode of the spatial light modulator adopted in this embodiment is pure phase modulation, a part of the unnecessary OAM mode energy distribution will be included in the generated multi-modal vortex beam (in the present invention, it is a smaller part of the energy distribution in the preset OAM spectrum). It can be seen from the measurement results of this example that even in the case of multi-modes with different energy ratios, the present invention still has good measurement accuracy and a large measurement range, which proves the effectiveness and accuracy of the present invention in measuring the complex OAM spectrum of multi-modal vortex beams.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry, characterized in that: include: The experimental setup for angular momentum spectrum includes: A spatial light modulator is provided on the optical path of the Gaussian beam output by a helium-neon laser, and a CCD camera is provided at the end of the optical path of the beam modulated by the spatial light modulator; The beam expansion and collimation system and the light splitting and modulation components are coaxially arranged in the optical path between the He-Ne laser and the spatial light modulator. and a phase polarization adjustment component, coaxially disposed on an optical path between the spatial light modulator and the CCD camera; Among them, the beam expansion and collimation system is used to expand and collimate the Gaussian beam, the spectroscopic modulation component is used to modulate the expanded and collimated beam into a target Gaussian beam with equal light field intensity in the horizontal polarization direction and the vertical polarization direction; the spatial light modulator is used to modulate the horizontal polarization direction of the target Gaussian beam into a horizontally polarized vortex beam; and output an outgoing beam that is a superposition of the horizontally polarized vortex beam and the vertically polarized target Gaussian beam; the phase polarization adjustment component is used to introduce 0 or 0 between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing beam. and adjusting the phase-adjusted light beam to a preset light beam form, wherein the light beam form includes: a vortex beam, a Gaussian beam, and an interference beam corresponding to the phase difference; a CCD camera is used to measure the light field intensity corresponding to different light beam forms; Experimental device for testing: Turn on the HeNe laser; turn on the spatial light modulator, and load the corresponding phase hologram onto the spatial light modulator to generate a vortex beam of a preset orbital angular momentum mode; turn on the CCD camera; Adjust the polarizer so that the angle between the polarization direction and the horizontal direction is 0°, and use the CCD camera to collect the current first light field intensity; Adjust the polarizer so that the angle between the polarization direction and the horizontal direction is 90°, and use the CCD camera to collect the current intensity of the second light field; Adjust the polarizer so that the angle between the polarization direction and the horizontal direction is 0°~90°, and the CCD camera collects the current first interference light field intensity; Add a quarter-wave plate and adjust the polarizer so that the angle between the polarization direction and the horizontal direction is 0°~90°. The CCD camera collects the current intensity of the second interference light field. According to the first light field intensity, the second light field intensity, the first interference light field intensity, and the second interference light field intensity, the orbital angular momentum spectrum of the vortex light beam corresponding to different orbital angular momentum modes is obtained; the expression of the orbital angular momentum spectrum is: Where, is the orbital angular momentum spectrum of the vortex beam corresponding to the orbital angular momentum mode m; is the expansion coefficient when the orbital angular momentum mode is m; is the sum of all orbital angular momentum modal energies contained in the vortex beam; An angle between the polarization direction of the polarizer and the horizontal direction when obtaining the first interference light field intensity and the second interference light field intensity; represents the phase difference introduced between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing beam; represents the intensity of the first light field; represents the intensity of the second light field; represents the intensity of the first interference light field; represents the intensity of the second interference light field is the complex amplitude of the horizontally polarized vortex beam light field; is the complex amplitude of the vertically polarized Gaussian beam light field; is the interference light field intensity received by the CCD camera; * indicates conjugation; It represents the phase difference between the expansion coefficient of orbital angular momentum mode m and the complex amplitude of Gaussian beam light field; represents an imaginary unit; Represents the azimuth in the polar coordinate system; represents the radius in polar coordinate system; represents the phase difference term introduced by the quarter-wave plate; represents the real part; Represents the interference term in the interference light field intensity; represents the interference term in the first interference light field intensity; Represents the interference term in the second interference light field intensity.

2. The experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry according to claim 1, characterized in that: Before collecting the first interference light field intensity and the second interference light field intensity, the angle between the polarization direction of the polarizer and the horizontal direction is adjusted to 45°.

3. The experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry according to claim 1, characterized in that: When the introduced phase difference is 0, the phase polarization adjustment component includes: a polarizer, which is used to adjust the phase-adjusted light beam into a vortex beam, a Gaussian beam or an interference beam with a phase difference of 0; it is used to introduce a phase difference of 0 between the horizontally polarized vortex beam and the vertically polarized target Gaussian beam in the outgoing light beam; when the introduced phase difference is The phase polarization adjustment component includes: a quarter wave plate and a polarizer. The quarter wave plate is set in the optical path between the polarizer and the spatial light modulator. The quarter wave plate is used to introduce a phase difference between the horizontally polarized vortex beam in the outgoing beam and the vertically polarized target Gaussian beam. Phase difference.

4. The experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry according to claim 1, characterized in that: The beam expansion and collimation system comprises a first lens and a second lens, wherein the first lens and the second lens are coaxially arranged, and the focal length of the second lens is greater than that of the first lens.

5. The experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry according to claim 4, characterized in that: The focal length of the second lens is five times that of the first lens.

6. The experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry according to claim 1, characterized in that: The optical splitter modulation components include: a polarization beam splitter for splitting the expanded and collimated light beam into a horizontally polarized light beam and a vertically polarized light beam perpendicular to each other, wherein the transmitted horizontally polarized light beam remains in the light path; And a half-wave plate is used to adjust the polarization direction of the horizontally polarized light beam after being split by the polarization beam splitter, so that the outgoing light beam is a target Gaussian beam with equal light field intensity in the horizontal polarization direction and the vertical polarization direction.

7. The experimental method for measuring the orbital angular momentum spectrum of a vortex beam based on coaxial interferometry according to claim 1, characterized in that: The spatial light modulator adopts a reflective modulator or a transmissive modulator.

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