A TGSM light beam regulation method and system based on an active GRIN medium

Abstract

This invention discloses a TGSM beam control method and system based on an active GRIN medium. The method involves acquiring beam and active GRIN medium parameters, constructing the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium, and, based on the desired target beam parameters, inversely calculating and modulating a suitable torsion factor and the complex refractive index distribution of the active GRIN medium. Then, a phase mask is generated based on the inversely calculated torsion factor, and the initial beam is modulated. The modulated beam is then filtered and coupled before being input into the active GRIN medium. The parameters of the output beam are detected at the output end of the active GRIN medium, and the phase mask parameters or active GRIN medium parameters are corrected based on the detection results, achieving stable TGSM beam control. This scheme can simultaneously achieve gain amplification, periodic focusing, OAM mode redistribution, and beam quality control within the same system; it can also compensate for output variations caused by pump fluctuations, device drift, or coupling errors through closed-loop feedback.

Description

Technical Field

[0001] This invention belongs to the field of optics and optoelectronics, specifically relating to a TGSM beam manipulation method and system based on an active GRIN medium. Background Technology

[0002] Random structured light fields combine the statistical tunability of partially coherent light with the spatial mode characteristics of structured light fields. TGSM beams can change the coherent structure and OAM mode distribution by twisting the phase, making them suitable as a control target.

[0003] A distorted Gaussian Scherrer model beam is a typical random structured light field formed by introducing a cross-phase term into a traditional Gaussian Scherrer model beam. Distortion factor. It will change the phase structure of the cross spectral density function, causing the beam to exhibit characteristics such as changes in the transverse coherence region, beam rotation trend, and OAM mode spectrum redistribution during propagation.

[0004] Active GRIN media simultaneously provide gradient refractive index light guiding and gain amplification, enabling periodic focusing, intensity enhancement, and mode redistribution.

[0005] Current technologies still struggle to simultaneously balance light intensity, DOC, OAM spectrum, and The target control of factors, especially the lack of a scheme that unifies input phase distortion, dielectric gain and output feedback. Summary of the Invention

[0006] The purpose of this invention is to provide a TGSM beam modulation method and system based on an active GRIN medium, which matches the beam width, coherence length, and distortion factor of the TGSM beam with the refractive index gradient, propagation length, and gain distribution of the active GRIN medium, thereby achieving optimal output light intensity, DOC, OAM spectrum, and [other parameters]. Joint regulation of factors.

[0007] The specific technical solution for achieving the objective of this invention is as follows:

[0008] A TGSM beam manipulation method based on an active GRIN medium includes the following steps:

[0009] Step 1: Obtain the initial parameters of the beam and determine the active GRIN medium parameters;

[0010] Step 2: Using the cross-spectral density function of the tortuous Gauss-Sherlock model beam as the input model, and combining it with the active GRIN medium parameters, construct the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium.

[0011] Step 3: Based on the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium, and according to the values ​​and images of the required target output intensity, cross-spectral density modulus, orbital angular momentum mode weights, and beam quality factor, inversely deduce and modulate a suitable distortion factor. The imaginary refractive index parameter of the complex refractive index distribution of active GRIN media. ;

[0012] Step 4: The distortion factor based on reverse calculation Generate a phase mask and modulate the initial beam;

[0013] Step 5: After filtering and coupling, the modulated beam is input into the active GRIN medium. The parameters of the output beam are detected at the output end of the active GRIN medium. The phase mask parameters or active GRIN medium parameters are corrected based on the detection results to achieve stable control of the TGSM beam.

[0014] This solution also provides a TGSM beam manipulation system based on an active GRIN medium, including a laser, an attenuation / polarization unit, a TGSM beam generation unit, a 4f filter unit, an active GRIN medium, a detection and acquisition unit, and a processing and feedback unit;

[0015] The laser is used to output an initial beam;

[0016] The attenuation / polarization unit is used to adjust the power and polarization state of the initial beam;

[0017] The TGSM beam generation unit is used to generate a phase mask according to the distortion factor and load the phase mask onto the initial beam to form a TGSM beam.

[0018] The 4f filter unit is used to filter out non-target diffraction orders and improve the quality of the incident beam.

[0019] The active GRIN medium is used for gradient refractive index guiding and gain control of the TGSM beam;

[0020] The detection and acquisition unit is used to detect the intensity distribution, coherence distribution, orbital angular momentum spectrum, and beam quality factor of the output beam.

[0021] The processing and feedback unit is used to correct the phase mask parameters or pump power based on the deviation between the detection result and the target output state.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] This invention determines phase modulation parameters and pump control parameters based on the target optical field state. When the target is to increase the center light intensity and maintain a low... When the target is to control the distortion factor, the system prioritizes controlling the distortion factor and suppressing the diffusion of higher-order modes; when the target is to enhance the OAM mode control capability, the system increases the distortion phase intensity and compensates for propagation loss through the gain distribution of the active GRIN medium; when the target is to maintain a specific DOC distribution, the system corrects the phase mask and pump power through feedback to make the output coherent structure tend to be stable.

[0024] This solution can unify the random structured light field modulation at the input end and the active gain adjustment at the medium end, reducing manual trial and error parameter tuning; it can take into account gain amplification, periodic focusing, OAM mode redistribution and beam quality control in the same system; and it can compensate for output changes caused by pump fluctuations, device drift or coupling errors through closed-loop feedback.

[0025] The present invention will be further described below with reference to specific embodiments. Attached Figure Description

[0026] Figure 1 This is a flowchart of the TGSM beam manipulation method based on active GRIN medium of the present invention.

[0027] Figure 2 This is a beam intensity distribution diagram of TGSM beams with different torsion factors passing through an active GRIN medium in an embodiment of the present invention.

[0028] Figure 3 This is a two-dimensional DOC distribution diagram of the TGSM beam at a fixed propagation distance in an embodiment of the present invention.

[0029] Figure 4 The OAM spectrum distribution of TGSM beams with different torsion factors at different propagation distances is shown in the embodiments of the present invention.

[0030] Figure 5 TGSM beams with different torsion factors in embodiments of the present invention Graph showing the variation of factors with propagation distance. Detailed Implementation

[0031] Example

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0034] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0035] Combination Figure 1 A TGSM beam modulation method based on an active GRIN medium includes the following steps:

[0036] Step 1: Obtain the initial parameters of the beam and determine the active GRIN medium parameters;

[0037] The initial parameters of the beam include beam width, coherence length, center wavelength, and polarization state.

[0038] The active GRIN medium parameters include complex refractive index distribution, effective length, and loss parameters;

[0039] The complex refractive index distribution of the active GRIN medium can be expressed as:

[0040]

[0041] in , and These represent the complex refractive index parameter and the complex gradient parameter along the z-axis, respectively. The real part of the complex refractive index determines the light-guiding behavior of the GRIN medium, while the imaginary part determines the gain or loss effect of the medium. The imaginary gain parameter can be changed by adjusting the pump conditions, thereby affecting the energy distribution and coherence structure of the TGSM beam.

[0042] For an active gradient refractive index medium with gain or loss, the refractive index formation is a complex characterization given by the following equation:

[0043]

[0044] in , , , It is a real constant. According to the above two equations, The real and imaginary parts can be written as:

[0045]

[0046] in , .

[0047] Step 2: Using the cross-spectral density function of the tortuous Gaussian Scherrer model beam as the input model, and combining it with the active GRIN medium parameters, construct the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium:

[0048] Step 2-1, the cross spectral density function of the twisted Gaussian Sher model beam is:

[0049]

[0050] in, and Let be the position vector of any two points in the source plane. For free space wavenumber, and These represent the transverse beam width and transverse coherence length on the source plane, respectively. The distortion factor is represented by , and when the distortion factor = 0, the above equation degenerates into the cross spectral density of a normal GSM beam;

[0051] In the propagation modeling process, the cross spectral density function of the tortuous Gaussian Sher model beam in the source plane of the TGSM beam is transformed into a tensor form, and the correspondence between the input and output surfaces is established using the ray transmission matrix of the active GRIN medium:

[0052]

[0053]

[0054] in, Represents the position vector in the source plane. Represents the generalized partially coherent complex curvature tensor of the source plane;

[0055] Step 2-2: Combining the parameters of the active GRIN medium, construct the cross-spectral density function expression of the TGSM beam at the output surface of the active GRIN medium:

[0056]

[0057]

[0058]

[0059] in, This represents the generalized partially coherent complex curvature tensor of the output plane. , , and These represent the transverse beam width, transverse coherence length, distortion factor, and radius of curvature on the output surface, respectively. This represents the lateral position vector on the output plane. , , , and Indicates active GRIN media Light transmission matrix.

[0060] Step 3: Based on the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium, and according to the values ​​and images of the required target output intensity, cross-spectral density modulus, orbital angular momentum mode weights, and beam quality factor, inversely deduce and modulate a suitable distortion factor. The imaginary refractive index parameter of the complex refractive index distribution of active GRIN media. :

[0061] The complex refractive index distribution of the active GRIN medium is determined based on the target output light intensity distribution;

[0062] The coherence length adjustment direction of the input TGSM beam is determined based on the target cross spectral density modulus;

[0063] The adjustment direction of the distortion factor is determined based on the weight of the target orbital angular momentum mode;

[0064] Determine the higher-order mode suppression or enhancement strategy based on the target beam quality factor;

[0065] By combining the above adjustment directions, the phase mask parameters and the pump power of the active GRIN medium are determined, thereby realizing the adjustment of the imaginary refractive index parameter of the active GRIN medium.

[0066] Step 4: The distortion factor based on reverse calculation A phase mask is generated and the initial beam is modulated to generate a distorted Gaussian Sher model beam;

[0067] Step 5: After filtering and coupling, the modulated beam is input into the active GRIN medium. The parameters of the output beam are detected at the output end of the active GRIN medium. The phase mask parameters or active GRIN medium parameters are corrected based on the detection results to achieve stable control of the TGSM beam.

[0068] The parameters of the output beam, including intensity distribution and coherence, are detected at the output end of the active GRIN medium. The factors and orbital angular momentum spectra are compared with the target state, and the pump power or phase mask parameters are dynamically corrected.

[0069] For beam quality evaluation, this invention employs a method based on the second moment of the Wigner distribution function. Factors. This evaluation relationship can simultaneously reflect spatial width, angular spectral width, and the correlation between position and angle. The factor is:

[0070]

[0071] in:

[0072]

[0073] The orbital angular momentum spectrum is:

[0074]

[0075] in Represents total energy, different corresponding This constitutes the OAM spectrum, where the energy weight of each OAM mode of the TGSM beam is defined as:

[0076]

[0077] The probability density for each OAM mode is:

[0078]

[0079] in: It is ordered In It was obtained at that time. The specific form is given by the following formula:

[0080]

[0081]

[0082] here These are two polar coordinates, and angle brackets represent the ensemble mean. In the formula... Indicates the order of the OAM mode. Indicates the order of the radial mode. This represents a Laguerre polynomial, a mathematical function in the radial part of the mode. In calculations, the focus is on the spectral variation of the OAM mode. The paper focuses on the changes in radial annular structures, rather than analyzing the radial annular structures. Take 0, Take 1. Different This corresponds to different angular phase change rates and different orbital angular momentum modes. When When, it corresponds to the central or fundamental model component; when As the value increases, it corresponds to a higher-order angular pattern. and These reflect the weighting coefficients and radial normalization factors of the corresponding modes, which are determined by the beam width, coherence length, and distortion factor after propagation.

[0083] When the output light intensity is lower than the target light intensity and the beam quality factor meets the target range, increase the pump power of the active GRIN medium.

[0084] When the target order energy weight of the output beam's OAM mode is higher than the target range and the beam quality When the factor increases, reduce the distortion factor or adjust the pump gain distribution;

[0085] When the output coherence distribution deviates from the target coherence distribution, the phase mask parameters and pump power are corrected simultaneously.

[0086] When the output beam reaches the range of target light intensity distribution, target coherence distribution, target orbital angular momentum mode weight, and target beam quality factor, the current control parameters are maintained.

[0087] This scheme determines the phase modulation parameters and pump control parameters inversely based on the target optical field state. When the target is to increase the center light intensity and maintain a low... When the target is to control the distortion factor, the system prioritizes controlling the distortion factor and suppressing the diffusion of higher-order modes; when the target is to enhance the OAM mode control capability, the system increases the distortion phase intensity and compensates for propagation loss through the gain distribution of the active GRIN medium; when the target is to maintain a specific DOC distribution, the system corrects the phase mask and pump power through feedback to make the output coherent structure tend to be stable.

[0088] Combination Figure 2 , representing different distortion factors in this embodiment. The intensity distribution of the TGSM beam passing through the active GRIN medium is determined by the refractive index gradient, gain distribution, and twist phase of the TGSM beam propagation in the active GRIN medium.

[0089] Compare and In both cases, it can be observed that adding a distorted phase results in a relative decrease in peak intensity and a more gradual intensity distribution. This indicates that the distortion factor affects the distribution of beam energy in the lateral space. The distorted phase introduces lateral coordinate cross-coupling, causing the beam energy to no longer be completely concentrated in the central region, but rather to diffuse more easily to the edges and higher-order modes, thus suppressing the central intensity gain.

[0090] Combination Figure 3 The two-dimensional DOC distribution is used to characterize the changes in the spatial coherence structure of the output beam. Figure 3 A fixed propagation distance is given. Two-dimensional DOC distribution under different distortion factors, where the reference point is the center of the optical axis. It can be seen that, in Initially, the coherent region is mainly concentrated near the beam center and exhibits a relatively regular symmetrical distribution. As the distortion factor increases, the effective range of the DOC distribution gradually shrinks, and the lateral coherence weakens. This indicates that phase distortion enhances phase coupling between different lateral positions, making the spatial coherence relationship more complex, thereby reducing the lateral correlation of the optical field. This result further illustrates that when manipulating TGSM beams in active GRIN media, a balance between intensity enhancement and coherence degradation must be considered simultaneously. As the distortion factor increases, the high-coherence region in the two-dimensional DOC diagram narrows, while the low-coherence region expands. This indicates that the lateral coordinate coupling introduced by the distorted phase shortens the effective coherence length, reducing the statistically correlated region of the optical field in the lateral plane.

[0091] Combination Figure 4 OAM spectrum is used to reflect the mode energy redistribution under different distortion factors and propagation distances. Figure 4 The normalized OAM mode energy weight distribution of TGSM beams at different propagation distances under different distortion factors is presented. It can be seen that when the propagation distance is small, the beam energy is mainly concentrated in low-order modes, especially near the center mode; as the propagation distance increases, the energy weight of the center mode gradually decreases, while the energy weight of higher-order OAM modes gradually increases, exhibiting a significant spectral broadening phenomenon.

[0092] Further comparison of different distortion factors reveals that the larger the distortion factor, the more pronounced the expansion of the OAM spectrum towards higher-order modes, indicating that phase distortion can promote energy transfer from lower-order modes to higher-order modes. This is because the cross-spectral density function of the TGSM beam includes a transverse coordinate cross-coupling term, which gives the optical field a statistically significant spiral phase and rotating energy flux, thereby introducing richer OAM mode components.

[0093] Reference Figure 5 , The factor is used to evaluate the degree to which the beam deviates from the ideal Gaussian beam, providing a quantitative basis for feedback control. Figure 5 The propagation time of TGSM beams through active GRIN medium under different distortion factors is given. Factors vary with propagation distance The changes are evident. It can be seen that as the propagation distance increases, all curves show a gradual upward trend, indicating that the beam quality continuously decreases as the beam propagates in the active GRIN medium. Simultaneously, as the distortion factor increases, The value of the factor also increases significantly, meaning that the stronger the phase distortion, the more pronounced the beam quality degradation. This phenomenon is mainly due to the gain effect and refractive index gradient in the active GRIN medium altering the transverse second moment distribution of the beam. Because TGSM beams have a strong intensity distribution at the center and weak intensity at the edges, the central region is more susceptible to gain saturation, leading to a more complex beam mode structure. The factor increases with the distance of propagation.

[0094] Furthermore, phase distortion disrupts the relatively concentrated mode distribution of a typical GSM beam, causing energy to diffuse towards higher-order OAM modes. The larger the distortion factor, the higher the proportion of higher-order modes, and therefore the corresponding... The larger the factor, the better.

[0095] If the goal is high brightness and low divergence output, then control the distortion factor and optimize the gain distribution; if the goal is OAM multi-mode control, then appropriately enhance the distortion phase and limit it through feedback. The factor increases.

[0096] When the goal is to enhance the low-order mode and keep it small When the factor is applied, the processing and feedback unit reduces the distortion factor. And by increasing the appropriate pump power, the output beam can obtain a strong central light intensity at the focusing position.

[0097] When the goal is to increase the proportion of high-order OAM modes, the processing and feedback unit increases the distortion factor. Furthermore, by adjusting the pump distribution, higher-order modes can obtain relatively higher gains, thereby increasing the weight of the mode corresponding to the target topology load number.

[0098] When environmental disturbances cause the output beam When the factor deviates from the target range, the detection and acquisition unit transmits the deviation information to the processing and feedback unit. The processing and feedback unit adjusts the pump power according to the PID control law, so that the imaginary part of the complex refractive index changes and compensates for the output drift.

[0099] This solution achieves faster input-side adjustment by updating the phase mask and more stable dielectric-side adjustment by adjusting the pump power. The combination of these two methods balances response speed and output stability. Therefore, this invention selects and adjusts the input distortion phase or dielectric gain based on the output state, avoiding mode degradation caused by solely pursuing light intensity amplification.

[0100] In addition, this solution also provides a TGSM beam control system based on an active GRIN medium, including a laser, an attenuation / polarization unit, a TGSM beam generation unit, a 4f filter unit, an active GRIN medium, a detection and acquisition unit, and a processing and feedback unit.

[0101] The laser is used to output an initial beam;

[0102] The attenuation / polarization unit is used to adjust the power and polarization state of the initial beam;

[0103] The TGSM beam generation unit is used to generate a phase mask according to the distortion factor and load the phase mask onto the initial beam to form a TGSM beam.

[0104] The 4f filter unit is used to filter out non-target diffraction orders and improve the quality of the incident beam.

[0105] The active GRIN medium is used for gradient refractive index guiding and gain control of the TGSM beam;

[0106] The detection and acquisition unit is used to detect the intensity distribution, coherence distribution, orbital angular momentum spectrum, and beam quality factor of the output beam.

[0107] The processing and feedback unit is used to correct the phase mask parameters or pump power based on the deviation between the detection result and the target output state.

[0108] This solution also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to perform the following steps:

[0109] Step 1: Obtain the initial parameters of the beam and determine the active GRIN medium parameters;

[0110] Step 2: Using the cross-spectral density function of the tortuous Gauss-Sherlock model beam as the input model, and combining it with the active GRIN medium parameters, construct the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium.

[0111] Step 3: Based on the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium, and according to the values ​​and images of the required target output intensity, cross-spectral density modulus, orbital angular momentum mode weights, and beam quality factor, a suitable distortion factor is deduced and modulated. The imaginary refractive index parameter of the complex refractive index distribution of active GRIN media. ;

[0112] Step 4: The distortion factor based on reverse calculation Generate a phase mask and modulate the initial beam;

[0113] Step 5: After filtering and coupling, the modulated beam is input into the active GRIN medium. The parameters of the output beam are detected at the output end of the active GRIN medium. The phase mask parameters or active GRIN medium parameters are corrected based on the detection results to achieve stable control of the TGSM beam.

[0114] This solution also provides a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the following steps:

[0115] Step 1: Obtain the initial parameters of the beam and determine the active GRIN medium parameters;

[0116] Step 2: Using the cross-spectral density function of the tortuous Gauss-Sherlock model beam as the input model, and combining it with the active GRIN medium parameters, construct the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium.

[0117] Step 3: Based on the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium, and according to the values ​​and images of the required target output intensity, cross-spectral density modulus, orbital angular momentum mode weights, and beam quality factor, a suitable distortion factor is deduced and modulated. The imaginary refractive index parameter of the complex refractive index distribution of active GRIN media. ;

[0118] Step 4: The distortion factor based on reverse calculation Generate a phase mask and modulate the initial beam;

[0119] Step 5: After filtering and coupling, the modulated beam is input into the active GRIN medium. The parameters of the output beam are detected at the output end of the active GRIN medium. The phase mask parameters or active GRIN medium parameters are corrected based on the detection results to achieve stable control of the TGSM beam.

[0120] The embodiments described above are merely one implementation method of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A TGSM beam manipulation method based on an active GRIN medium, characterized in that, Includes the following steps: Step 1: Obtain the initial parameters of the beam and determine the active GRIN medium parameters; Step 2: Using the cross-spectral density function of the tortuous Gauss-Sherlock model beam as the input model, and combining it with the active GRIN medium parameters, construct the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium. Step 3: Based on the cross-spectral density function of the TGSM beam at the output surface of the active GRIN medium, and according to the values ​​and images of the required target output intensity, cross-spectral density modulus, orbital angular momentum mode weights, and beam quality factor, inversely deduce and modulate a suitable distortion factor. The imaginary refractive index parameter of the complex refractive index distribution of active GRIN media. ; Step 4: The distortion factor based on reverse calculation Generate a phase mask and modulate the initial beam; Step 5: After filtering and coupling, the modulated beam is input into the active GRIN medium. The parameters of the output beam are detected at the output end of the active GRIN medium. The phase mask parameters or active GRIN medium parameters are corrected based on the detection results to achieve stable control of the TGSM beam.

2. The TGSM beam modulation method based on active GRIN medium according to claim 1, characterized in that, The initial parameters of the beam include beam width, coherence length, center wavelength, and polarization state; The active GRIN medium parameters include complex refractive index distribution, effective length, and loss parameters.

3. The TGSM beam modulation method based on active GRIN medium according to claim 1, characterized in that, The construction of the tensor transport model of the TGSM beam in the active GRIN medium in step 2 is specifically as follows: Step 2-1, the cross spectral density function of the twisted Gaussian Sher model beam is: ； in, and Let be the position vector of any two points in the source plane. For free space wavenumber, and These represent the transverse beam width and transverse coherence length on the source plane, respectively. Indicates the distortion factor; The cross spectral density function of the distorted Gauss-Sherlock model beam is then converted into a tensor form: ； ； in, Represents the position vector in the source plane. Represents the generalized partially coherent complex curvature tensor of the source plane; Step 2-2: Combining the parameters of the active GRIN medium, construct the cross-spectral density function expression of the TGSM beam at the output surface of the active GRIN medium: ； ； ； in, This represents the generalized partially coherent complex curvature tensor of the output plane. , , and These represent the transverse beam width, transverse coherence length, distortion factor, and radius of curvature on the output surface, respectively. This represents the lateral position vector on the output plane. , , , and Indicates active GRIN media Light transmission matrix.

4. The TGSM beam modulation method based on active GRIN medium according to claim 3, characterized in that, The reverse calculation and modulation of a suitable distortion factor in step 3 and the imaginary refractive index parameter of the medium Specifically: The complex refractive index distribution of the active GRIN medium is determined based on the target output light intensity distribution; The coherence length adjustment direction of the input TGSM beam is determined based on the target cross spectral density modulus; The adjustment direction of the distortion factor is determined based on the weight of the target orbital angular momentum mode; Determine the higher-order mode suppression or enhancement strategy based on the target beam quality factor; By combining the above adjustment directions, the phase mask parameters and the pump power of the active GRIN medium are determined, thereby realizing the adjustment of the imaginary refractive index parameter of the active GRIN medium.

5. The TGSM beam modulation method based on active GRIN medium according to claim 3, characterized in that, The inverse-based distortion factor in step 4 A phase mask is generated and the initial beam is modulated to generate a distorted Gaussian Shear model beam.

6. The TGSM beam modulation method based on active GRIN medium according to claim 3, characterized in that, Step 5, which involves correcting the phase mask parameters or active GRIN medium parameters based on the detection results, specifically involves: The parameters of the output beam, including intensity distribution and coherence, are detected at the output end of the active GRIN medium. The factors and orbital angular momentum spectra are compared with the target state, and the pump power or phase mask parameters are dynamically corrected. The The factor is: ； in: ； The orbital angular momentum spectrum is: ； in Represents total energy, different corresponding This constitutes the OAM spectrum, where the energy weight of each OAM mode of the TGSM beam is defined as: ； The probability density for each OAM mode is: ； in: It is ordered In When obtained; The specific form is given by the following formula: ； ； here These are two polar coordinates, and angle brackets represent the ensemble mean. In the formula... Indicates the order of the OAM mode. Indicates the order of the radial mode. This represents a Laguerre polynomial, different For different angular phase change rates and different orbital angular momentum modes, when When, it corresponds to the central or fundamental model component; when As the value increases, it corresponds to a higher-order angular pattern. and These respectively reflect the weighting coefficients and radial normalization factors of the corresponding models.

7. The TGSM beam modulation method based on active GRIN medium according to claim 6, characterized in that, The dynamic correction of pump power or phase mask parameters is specifically as follows: When the output light intensity is lower than the target light intensity and the beam quality factor meets the target range, increase the pump power of the active GRIN medium. When the target order energy weight of the output beam's OAM mode is higher than the target range and the beam quality When the factor increases, reduce the distortion factor or adjust the pump gain distribution; When the output coherence distribution deviates from the target coherence distribution, the phase mask parameters and pump power are corrected simultaneously. When the output beam reaches the range of target light intensity distribution, target coherence distribution, target orbital angular momentum mode weight, and target beam quality factor, the current control parameters are maintained.

8. A TGSM beam control system based on an active GRIN medium, characterized in that, It includes a laser, attenuation / polarization unit, TGSM beam generation unit, 4f filter unit, active GRIN medium, detection and acquisition unit, and processing and feedback unit; The laser is used to output an initial beam; The attenuation / polarization unit is used to adjust the power and polarization state of the initial beam; The TGSM beam generation unit is used to generate a phase mask according to the distortion factor and load the phase mask onto the initial beam to form a TGSM beam. The 4f filter unit is used to filter out non-target diffraction orders and improve the quality of the incident beam. The active GRIN medium is used for gradient refractive index guiding and gain control of the TGSM beam; The detection and acquisition unit is used to detect the intensity distribution, coherence distribution, orbital angular momentum spectrum, and beam quality factor of the output beam. The processing and feedback unit is used to correct the phase mask parameters or pump power based on the deviation between the detection result and the target output state.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-7.

10. A computer-storable medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

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