Method for generating a vector vortex beam applied to a SERF magnetic field measurement device

Abstract

A vector vortex beam generation method applied to the SERF magnetic field measurement device is proposed. Based on the optical field distribution formula of the vortex beam, a computational holographic method and a polarization mode decomposition method are used to generate the vector vortex beam. Then, the phase, amplitude, polarization direction, and other parameters of the beam are iteratively optimized using a combination of global NSGA-II and local SPGD algorithms. The uniformity of the electronic steady-state polarization is then checked to see if it meets expectations. If it does, the optimization ends, and the optimized beam is used as a pump beam to pump alkali metal atoms for subsequent magnetic field measurements. If it does not meet expectations, the parameters are changed and optimization continues until the uniformity of the electronic steady-state polarization meets the requirements. Compared to using a traditional Gaussian beam, the atomic polarization in the gas cell is stabilized at the required value, effectively suppressing the atomic spin gradient field of the device, while enhancing the differential performance of the device, which is beneficial to improving the sensitivity of the SERF magnetic field measurement device.

Description

Technical Field

[0001] This invention relates to the field of SERF atomic magnetic field measurement technology, and specifically to a method for generating a vector vortex beam for use in SERF magnetic field measurement devices. Background Technology

[0002] Ultra-sensitive magnetic field measurement devices based on the spin-free exchange relaxation (SERF) effect of atomic spin are widely used in magnetic field detection and quantum information fields. SERF magnetic field measurement devices typically use scalar optical fields (such as Gaussian beams) as the pump source. The disadvantages of Gaussian beams include non-uniform lateral polarization distribution, as the intensity is strong at the center and weak at the edges, resulting in a Gaussian distribution of polarizability across the alkali metal cell cross-section, forming a lateral polarization gradient. Gaussian beams also cause a decaying trend in longitudinal polarization, as the beam is absorbed as it passes through the high optical depth of the alkali metal cell, gradually attenuating its intensity along the propagation direction, leading to a gradual decrease in longitudinal polarizability from the incident end to the exit end, forming a longitudinal polarization gradient. Furthermore, the optical frequency shift gradient is difficult to suppress; the non-uniformity of the Gaussian beam enhances the virtual magnetic field gradient of the optical frequency shift, which dynamically changes with the pump power and frequency and cannot be completely eliminated by static magnetic compensation. Therefore, the inherent distribution characteristics of Gaussian beam confinement polarization uniformity optimization make it difficult to significantly improve the polarization gradient even if the pump beam parameters are optimized.

[0003] For magnetic field measurement devices, polarization gradients significantly amplify gradient noise in differential measurement systems, reducing the common-mode rejection ratio (CMRR) and thus weakening the ability to suppress common-mode magnetic noise. Polarization inhomogeneity is transformed into a virtual magnetic field gradient through light-atom interaction. This dynamic gradient cannot be fully compensated for by static gradient coils, introducing additional spin relaxation, reducing the transverse relaxation time of the atomic ensemble, and ultimately affecting the theoretical sensitivity of magnetic field measurements. The virtual magnetic field gradient caused by polarization exacerbates atomic spin relaxation through diffusion effects, leading to broadening of the magnetic resonance linewidth and further reducing the signal-to-noise ratio (SNR) of magnetic field measurements. In differential measurements, the polarization gradient manifests as non-common-mode noise, and its amplitude is inversely proportional to the gradient baseline length, directly limiting the improvement of differential sensitivity.

[0004] As a pump beam, vector vortex beams exhibit the following significant advantages in atomic spin polarization compared to traditional Gaussian beams: Vector vortex beams possess a more uniform transverse intensity distribution. By controlling polarization and phase, some vector vortex beams (such as flat-top vortex beams) can achieve a more uniform transverse intensity distribution, reducing the polarization gradient; Spatial polarization control can improve polarization efficiency. The polarization state of some vector vortex beams exhibits regular spatial changes (such as radial or angular polarization), allowing for more efficient coupling with atomic spin states. Furthermore, symmetrical polarization distribution can counteract the spatial non-uniformity of optical frequency shift; Phase vortexes suppress relaxation effects. The vortex phase carrying topological charge can induce orbital angular momentum exchange of atomic spins, suppressing relaxation caused by diffusion.

[0005] Currently, methods for generating vortex beams include direct generation, mode conversion, spiral phase plate generation, fiber generation, and computational holography. Direct generation allows for direct generation within the laser resonant cavity, but it struggles to obtain stable vortex beams and achieve high-order vortex beams. Mode conversion offers high conversion efficiency, but its optical structure is relatively complex, device fabrication is difficult, and controlling the type and parameters of the vortex beam is challenging. Spiral phase plate generation also boasts high conversion efficiency, but controlling the type and parameters of the vortex beam and fabricating high-quality phase plates are difficult. Fiber generation facilitates application in optical communication systems and produces relatively stable vortex beams, but currently only low-order vortex beams can be experimentally achieved, with high-order beams proving difficult to realize. Computational holography allows for controllable position, size, and parameters of the vortex beam, but requires incident light at the center of the hologram and imposes strict optical path requirements. For application in SERF magnetic field measurement devices, computational holography is suitable, as it, combined with a spatial light modulator, allows for flexible beam control outside the resonant cavity by adjusting the optical path structure.

[0006] Currently, the main methods for generating vector beams are intracavity generation and extracavity generation. Intracavity generation has the advantage of efficiently generating vector beams with specific polarization states, but its disadvantage is limited beam modes and poor flexibility. Extracavity generation offers flexible beam mode control, but its efficiency is lower. Therefore, for application in SERF magnetic field measurement devices, extracavity generation is more suitable.

[0007] To be applied to a SERF magnetic field measurement device, this invention utilizes a spatial light modulator, employs computational holography to generate a vortex beam, and polarization mode decomposition to generate a vector beam. The generated vector vortex beam is then optimized using a global NSGA-II algorithm (Non-Dominated Sorting Genetic Algorithm) and a local SPGD algorithm (stochastic parallel gradient descent algorithm) on parameters such as phase, amplitude, and polarization direction. This allows for precise control of the beam's phase, amplitude, and polarization direction, stabilizing the atomic polarizability in the gas chamber at the desired value. This reduces the impact of the polarization gradient on the sensitivity of the SERF magnetic field measurement device, thereby improving the device's sensitivity and stability. Summary of the Invention

[0008] This invention addresses the shortcomings of existing technologies by providing a vector vortex beam generation method for SERF magnetic field measurement devices. Based on a spatial light modulator, a computational holographic method is used to generate a vortex beam, and a polarization mode decomposition method is used to generate a vector beam. Then, the generated vector vortex beam is optimized using a global NSGA-II algorithm and a local SPGD algorithm on parameters such as phase, amplitude, and polarization direction. This allows for precise control of the beam's phase, amplitude, and polarization direction, stabilizing the atomic polarizability in the gas cell at the desired value. This reduces the impact of the polarization gradient on the sensitivity of the SERF magnetic field measurement device, thereby improving the device's sensitivity and stability.

[0009] The technical solution of the present invention is as follows:

[0010] A method for generating a vector vortex beam for use in a SERF magnetic field measurement device is characterized by comprising a combination of a first beam splitter, a spatial light modulator, and a vortex waveplate disposed on the pump optical path before the pump light incident side of the atomic gas cell in the SERF magnetic field measurement device. The exit plane of the spatial light modulator is conjugate to the incident plane of the vortex waveplate. The first beam splitter splits the Gaussian light from the pump laser into a first reflected Gaussian beam and a second transmitted Gaussian beam. The second transmitted Gaussian beam illuminates the spatial light modulator loaded with a computational hologram. The spatial light modulator converts the second transmitted Gaussian beam into a vortex beam and emits the vortex beam back to the first beam splitter through its exit plane. The first beam splitter reflects the vortex beam and the first reflected Gaussian beam back to the vortex waveplate to generate a vector vortex beam.

[0011] Includes the following steps:

[0012] Step 1: Determine the theoretical model of the vortex beam. First, determine the complex amplitude expression, and then obtain the expression for the light field distribution of the vortex beam through Fourier transform.

[0013] Step 2: Based on the expression of the light field distribution of the vortex beam, the intensity map and phase map are obtained by simulation. The interference pattern of the plane wave is superimposed using the computational holography method to generate a fork grating pattern. Then, based on the correspondence between the phase value of each pixel and the gray value of the spatial light modulator, the gray map is generated from the phase map and loaded into the spatial light modulator to generate the required vortex beam.

[0014] Step 3: For vortex waveplates of order 30 or higher, a polarization mode decomposition method is used. An additional phase modulation factor is added to the optical field distribution expression of the vortex beam to decompose the original complex polarization mode of the beam into multiple polarization modes, which are distributed in space. Then, the parameters of the phase modulation factor are adjusted to reduce the energy density of other polarization modes. Finally, only the target polarization mode is retained to extract any polarization mode in the beam and obtain a vector vortex beam of any order.

[0015] Step 4: For the obtained vector vortex beam, iterative optimization is performed on the beam in terms of phase, amplitude, and polarization direction parameters. First, global NSGA-II algorithm optimization is performed to initialize control parameters, which include beam phase, polarization direction, and amplitude parameters. Multiple objective functions are defined, which involve polarization purity and phase error. Then, multi-objective fitness values ​​are calculated, and the population is sorted in a non-dominated manner to obtain Pareto front solutions of different levels. Then, selection, crossover, and mutation are performed and iteratively repeated until the target convergence is reached, and a set of candidate beam generation parameters for Pareto optimal solutions are obtained.

[0016] Step 5: Perform local SPGD algorithm optimization on the candidate beams. Select several candidate solutions that are close to the ideal target from the leading edge solutions generated by NSGA-II as the initial input of SPGD, initialize the control parameters, define the performance index of SPGD, introduce small perturbations, measure the performance index, calculate the performance difference, update the control parameters, perform iterative optimization, and finally select the parameter combination with the best beam quality from the locally optimized solutions as the final parameter combination.

[0017] Step 6: Measure the uniformity of electronic steady-state polarization;

[0018] Step 7: Determine whether the electronic polarization uniformity meets the requirements. If not, return to step 4, modify the topological charge, and continue iterative optimization. If yes, the optimization ends and proceed to step 8.

[0019] Step 8: Use the optimized beam as a pump beam to pump alkali metal atoms for subsequent magnetic field measurements.

[0020] In step 1, the expression for the optical field distribution of the vortex beam is:

[0021] ,

[0022] In the formula This is the light field distribution function of the vortex beam, describing the electric field intensity distribution of the vortex beam at different positions in polar coordinates, where r is the radial coordinate and θ is the angular coordinate. It is the imaginary unit. It is the topological charge number or orbital angular momentum quantum number. It is the waist radius of the Gaussian beam. It is half the width of a ring. These are mode parameters. It is the beam radius. It is a modified Bessel function of the first kind.

[0023] The computational holography method in step 2 includes generating an interference pattern between the target light field and the reference light field through a computer program based on the principles of light interference and diffraction, thereby generating a vortex beam. The computational holography method is implemented by generating a computational hologram and combining it with a spatial light modulator. The computational hologram is realized using a fork-shaped grating. The fork-shaped grating is used as a holographic film. After being irradiated by a Gaussian plane wave, the expected light field distribution is obtained. The fork-shaped grating pattern is loaded onto the spatial light modulator, so that the Gaussian plane wave is directly incident on the surface of the modulator, thereby achieving effective control of the output light field and finally forming the desired vortex beam.

[0024] Step 3 involves extracting a specific polarization mode from the beam by simultaneously satisfying the following two conditions: the first condition is that the entangled polarization modes are separated in space; the second condition is that the separated polarization modes have different characteristics, so as to eliminate other polarization modes and retain only the target polarization mode. The first condition is achieved by breaking the modulation symmetry of the beam. When a phase modulation factor is added, the symmetry is broken, and the higher-order polarization modes are located on the outside, while the lower-order polarization modes are located on the inside. The separated polarization modes propagate independently in space. The second condition is achieved based on the energy density of different polarization modes. The mode with the larger the topological charge has a greater degree of divergence in space and a lower energy density. By adjusting the parameters of the phase modulation factor, the energy density of the target polarization mode is made much greater than the energy density of other polarization modes, so that only the target polarization mode is retained.

[0025] The initialization of control parameters in step 5 involves using the control parameters for controlling the generation of the vector vortex beam as control variables for SPGD, including initializing a parameter vector. , , to These are the first to the Nth control variables, where N is a positive integer.

[0026] In step 5, defining the performance index of SPGD includes defining a performance index J that measures the quality of the vector vortex beam as the optimization target of SPGD. The performance index includes: (1) mode purity: the degree of matching between the polarization and phase distribution of the beam and the target mode; (2) phase and polarization stability: the stability of the phase and polarization distribution of the beam; (3) intensity distribution: the intensity distribution of the beam cross section, ensuring that the intensity characteristics of the vortex at the center of the beam meet the requirements.

[0027] In step 5, introducing a small perturbation involves applying a small random disturbance to the control parameters in each iteration. Two perturbation vectors u+ are generated. and u- And apply it to the device, including adding small perturbations to the phase pattern of the spatial light modulator, or applying tiny rotations to the angle of the waveplate.

[0028] In step 5, the performance indicators are measured by measuring two performance indicators of the output vector vortex beam under two different perturbations. and .

[0029] In step 5, the performance difference is calculated using the results of two perturbation measurements. , ,Will This serves as the basis for optimizing the step size using the following expression:

[0030] ,

[0031] in It is the gain coefficient. It adjusts the step size of the update control parameters.

[0032] The pump laser is connected sequentially to the input side of the first beam splitter via a first isolator, a first half-wave plate, a first polarizing beam splitter, a first concave lens, and a first convex lens. The reflection side of the first polarizing beam splitter is connected to a first wavelength meter via a first reflecting mirror. The reflection side of the first beam splitter is connected to the vortex waveplate sequentially via a second convex lens and a third convex lens. The vortex waveplate is connected to the pump light incident side of the atomic gas cell sequentially via a fourth convex lens, a fifth convex lens, a second half-wave plate, a second polarizing beam splitter, and a first quarter-wave plate. The detection light incident side of the atomic gas chamber is connected to the detection laser in sequence through a second 1 / 4 wave plate, a Glan Taylor prism, a third reflecting mirror, a sixth convex lens, a second concave lens, a third polarizing beam splitter, a third 1 / 2 wave plate, and a second isolator. The reflection side of the third polarizing beam splitter is connected to a second wavelength meter through a second reflecting mirror. The detection light emitting side of the atomic gas chamber is connected to a host computer through a detector. The atomic gas chamber is located inside a magnetic compensation coil, the magnetic compensation coil is located inside an oven, the oven is located inside a vacuum chamber, and the vacuum chamber is located inside a magnetic shielding barrel.

[0033] The technical effects of this invention are as follows: This invention applies to the vector vortex beam generation method of a SERF magnetic field measurement device. Based on the optical field distribution formula of the vortex beam, and combining computational holography and polarization mode decomposition methods, a vector vortex beam is generated. Then, the phase, amplitude, polarization direction, and other parameters in the beam are iteratively optimized using a combination of global NSGA-II and local SPGD algorithms. The uniformity of the electronic steady-state polarizability is then determined. If it meets expectations, the optimization ends, and the optimized beam is used as a pump beam to pump alkali metal atoms for subsequent magnetic field measurements. If it does not meet expectations, the parameters are changed and optimization continues until the uniformity of the electronic steady-state polarizability meets expectations. Using this as a pump beam, compared to using a traditional pump beam (Gaussian beam), stabilizes the atomic polarizability in the gas cell at the required value, reducing the impact of the polarization gradient on the sensitivity of the SERF magnetic field measurement device, effectively suppressing the atomic spin gradient field of the device, and enhancing the differential performance of the device, thus improving the sensitivity of the SERF magnetic field measurement device.

[0034] Compared with existing technologies, the advantages of this technology are: (1) It can effectively suppress the atomic spin gradient field of the device and improve the uniformity of electron polarization in the gas cell by precisely controlling the phase, amplitude and polarization direction of the beam; (2) It introduces a multi-objective optimization mechanism (NSGA-Ⅱ+SPGD) that combines global and local optimization. Compared with traditional single optimization strategies (such as genetic algorithm, particle swarm algorithm, etc.), this invention can further finely adjust the local performance on the basis of ensuring global convergence, which significantly improves the accuracy and efficiency of beam control; (3) Through iterative optimization of the feedback loop between beam structure parameters and atomic response characteristics, a beam generation method guided by "system performance" is realized, which can be closer to the actual performance index requirements, rather than relying solely on the ideal model parameters of the optical field itself, and has stronger engineering practicality. Attached Figure Description

[0035] Figure 1 A schematic diagram of the structure of the SERF magnetic field measuring device involved in implementing the vector vortex beam generation method of the present invention applied to the SERF magnetic field measuring device.

[0036] Figure 2 This is a schematic diagram of the vector vortex beam generation method for implementing the present invention in a SERF magnetic field measurement device. Figure 2 The process includes: Step 1, determining the expression for the optical field distribution of the vortex beam; Step 2, calculating and generating the vortex beam using the holographic method; Step 3, generating the vector beam using the polarization mode decomposition method; Step 4, optimizing the beam using the global NSGA-II algorithm (NSGA, Non-Dominated Sorting Genetic Algorithm); Step 5, optimizing the beam using the local SPGD algorithm (SPGD, stochastic parallel gradient descent algorithm); Step 6, measuring the uniformity of the electronic steady-state polarization; Step 7, determining whether the electronic polarization uniformity meets the requirements. If not, return to Step 4, modify parameters such as the topological charge number, and continue iterative optimization. If yes, the optimization ends, and proceed to Step 8; Step 8, using the optimized beam as a pump beam to pump alkali metal atoms for subsequent magnetic field measurements.

[0037] The reference numerals in the attached figures are explained as follows: 1-Pump laser; 2-First isolator; 3-First half-wave plate; 4-First polarizing beam splitter; 5-First reflecting mirror; 6-First wavelength meter; 7-First concave lens; 8-First convex lens; 9-First beam splitter; 10-Spatial light modulator; 11-Second convex lens; 12-Third convex lens; 13-Vortex waveplate; 14-Fourth convex lens; 15-Fifth convex lens; 16-Second half-wave plate; 17-Second polarizing beam splitter; 18-First quarter-wave plate; 19 - Detector laser; 20 - Second isolator; 21 - Third half-wave plate; 22 - Third polarizing beam splitter; 23 - Second mirror; 24 - Second wavelength meter; 25 - Second concave lens; 26 - Sixth convex lens; 27 - Third mirror; 28 - GlanTeller prism; 29 - Second quarter-wave plate; 30 - Magnetic shielding barrel; 31 - Vacuum cavity; 32 - Oven; 33 - Magnetic compensation coil; 34 - Atomic gas chamber; 35 - Detector; 36 - Host computer; XYZ - Cartesian coordinate system (X-axis, Y-axis, Z-axis). Detailed Implementation

[0038] The following is in conjunction with the attached diagram ( Figures 1-2 The present invention will be described in conjunction with the examples.

[0039] Figure 1 A schematic diagram of the structure of the SERF magnetic field measuring device involved in implementing the vector vortex beam generation method of the present invention applied to the SERF magnetic field measuring device. Figure 2 This is a schematic diagram illustrating the process of generating a vector vortex beam for applying the present invention to a SERF magnetic field measurement device. (Reference) Figures 1 to 2 As shown, a method for generating a vector vortex beam applied to a SERF magnetic field measurement device includes a combination of a first beam splitter 9, a spatial light modulator 10, and a vortex waveplate 13 arranged on the pump light path before the pump light incident side of the atomic gas cell 34 in the SERF magnetic field measurement device. The exit plane of the spatial light modulator 10 is conjugate to the incident plane of the vortex waveplate 13. The first beam splitter 9 splits the Gaussian light from the pump laser 1 into a first reflected Gaussian beam and a second transmitted Gaussian beam. The second transmitted Gaussian beam illuminates the spatial light modulator 10 loaded with a hologram. The spatial light modulator 10 converts the second transmitted Gaussian beam into a vortex beam and emits the vortex beam to the first beam splitter 9 through its exit plane. The first beam splitter 9 reflects the vortex beam and the first reflected Gaussian beam to the vortex waveplate 13 to generate a vector vortex beam.

[0040] The pump laser 1 is connected to the input side of the first beam splitter 9 via a first isolator 2, a first half-wave plate 3, a first polarizing beam splitter 4, a first concave lens 7, and a first convex lens 8. The reflection side of the first polarizing beam splitter 4 is connected to a first wavelength meter 6 via a first reflecting mirror 5. The reflection side of the first beam splitter 9 is connected to the vortex waveplate 13 via a second convex lens 11 and a third convex lens 12. The vortex waveplate 13 is connected to the pump light incident side of the atomic gas cell 34 via a fourth convex lens 14, a fifth convex lens 15, a second half-wave plate 16, a second polarizing beam splitter 17, and a first quarter-wave plate 18. The detection light incident side of the 4 is connected to the detection laser 19 via the second 1 / 4 wave plate 29, Glan Taylor prism 28, third reflecting mirror 27, sixth convex lens 26, second concave lens 25, third polarizing beam splitter 22, third 1 / 2 wave plate 21, and second isolator 20. The reflection side of the third polarizing beam splitter 22 is connected to the second wavelength meter 24 via the second reflecting mirror 23. The detection light emitting side of the atomic gas chamber 34 is connected to the host computer 36 via the detector 35. The atomic gas chamber 34 is located inside the magnetic compensation coil 33. The magnetic compensation coil 33 is located inside the oven 32. The oven 32 is located inside the vacuum chamber 31. The vacuum chamber 31 is located inside the magnetic shielding barrel 30.

[0041] To be applied to a SERF magnetic field measurement device, this invention uses a spatial light modulator and a computational holographic method to generate a vortex beam. A polarization mode decomposition method is then used to generate a vector beam. The generated vector vortex beam is then optimized using a global NSGA-II algorithm and a local SPGD algorithm on parameters such as phase, amplitude, and polarization direction. This allows for precise control of the beam's phase, amplitude, and polarization direction, stabilizing the atomic polarizability in the gas chamber at the desired value. This reduces the impact of the polarization gradient on the sensitivity of the SERF magnetic field measurement device, thereby improving the device's sensitivity and stability.

[0042] A method for generating a vector vortex beam for use in a SERF magnetic field measurement device includes the following steps:

[0043] Step 1: Determine the theoretical model of the vortex beam. First, determine the complex amplitude expression, and then obtain its optical field distribution expression through Fourier transform.

[0044] Step 2: Based on the expression of the light field distribution of the vortex beam, the intensity map and phase map are obtained by simulation. The interference pattern of the plane wave is superimposed using the computational holography method. Finally, the two phase maps are superimposed to generate a fork grating. Then, based on the correspondence between the phase value of each pixel and the gray value of the spatial light modulator, a gray map is generated from the phase map and loaded into the spatial light modulator to generate the required vortex beam.

[0045] Step 3: For vortex waveplates of order 30 or higher, a polarization mode decomposition method is used. An additional phase modulation factor is added to the optical field distribution expression to decompose the original complex polarization mode of the beam into multiple polarization modes, which will be dispersed in space. Then, the parameters of the phase modulation factor are adjusted to reduce the energy density of other polarization modes. Finally, only the target polarization mode is retained, realizing the extraction of arbitrary polarization modes in the beam and obtaining a vector beam of arbitrary order.

[0046] Step 4: For the obtained vector vortex beam, iterative optimization is performed on the beam in terms of phase, amplitude, and polarization direction parameters. First, global NSGA-II algorithm optimization is performed to initialize control parameters (including beam phase, polarization direction, and amplitude parameters), define multiple objective functions such as polarization purity and phase error, and then calculate multi-objective fitness values. The population is sorted in a non-dominated manner to obtain Pareto front solutions of different levels. Then, selection, crossover, and mutation are performed, and the above steps are repeated iteratively until the target convergence is reached, thus obtaining a set of candidate beam generation parameters for Pareto optimal solutions.

[0047] Step 5: Perform local SPGD algorithm optimization on the beam. Select several candidate solutions that are close to the ideal target from the leading edge solution generated by NSGA-II as the initial input of SPGD, initialize the control parameters, define the performance index of SPGD, introduce small perturbations, measure the performance index, calculate the performance difference, update the control parameters, perform iterative optimization, and finally select the parameter combination with the best beam quality from the locally optimized solution as the final parameter combination.

[0048] Step 6: Measure the uniformity of electronic steady-state polarization.

[0049] Step 7: Determine whether the electronic polarization uniformity meets the requirements. If not, return to step 4, modify parameters such as topological charge number, and continue iterative optimization. If yes, the optimization ends, and proceed to step 8.

[0050] Step 8: Use the optimized beam as a pump beam to pump alkali metal atoms for subsequent magnetic field measurements.

[0051] In step 1, the expression for the light field distribution of the vortex beam is:

[0052]

[0053] In the formula, It is the beam radius. It is the waist radius of the Gaussian beam. It is half the width of a ring. This is a modified Bessel function of the first kind. E(r,θ) is the light field distribution function, describing the electric field intensity distribution of the vortex beam at different locations in polar coordinates. r is the radial coordinate in polar coordinates, representing the straight-line distance between a point and the origin (beam center). θ is the angular coordinate in polar coordinates, representing the rotation angle of a point relative to a reference direction (such as the positive x-axis). i is the imaginary unit, used for the complex form of the light field phase description. l is the topological charge number (or orbital angular momentum quantum number). imθ is the imaginary phase factor, representing the overall spiral phase structure. i: imaginary unit, m: mode parameter (radial mode number or angular mode number). The exp(imθ) term is the core characteristic of the vortex beam; its spiral phase causes the beam to carry orbital angular momentum.

[0054] In step 2, the computational holography method employed is based on the principles of light interference and diffraction. A computer program generates an interference pattern between the target light field and the reference light field to produce a vortex beam. Specifically, this can be achieved by generating a computational hologram and combining it with a spatial light modulator. The computational hologram can be implemented using a fork-shaped grating. This fork-shaped grating serves as the holographic substrate, and after being illuminated by a Gaussian plane wave, the desired light field distribution can be obtained. Further, the fork-shaped grating pattern is loaded onto the spatial light modulator, allowing the Gaussian plane wave to directly incident on the modulator surface, thereby achieving effective control of the output light field and ultimately forming the desired vortex beam.

[0055] In step 3, to extract a specific polarization mode from the beam, the following two conditions must be met simultaneously: First, the entangled polarization modes must be separated in space; second, the separated polarization modes must possess different characteristics to eliminate other polarization modes and retain only the target polarization mode. The first condition can be achieved by disrupting the beam's modulation symmetry. When a phase modulation factor is added, the symmetry is broken, with higher-order polarization modes located on the outer side and lower-order polarization modes on the inner side. The separated polarization modes will then propagate independently in space. The second condition can be achieved based on the energy density of different polarization modes. Modes with higher topological charges exhibit greater divergence in space and lower energy densities. By adjusting the phase modulation factor parameters, the energy density of the target polarization mode can be made significantly higher than that of other polarization modes, thus retaining only the target polarization mode.

[0056] In step 5, the initialization control parameters for SPGD algorithm correction are the parameters used to control the generation of the vector vortex beam, which are then used as control variables for SPGD. For example, the phase distribution of the spatial light modulator and the adjustment angle of the waveplate are initialized into a parameter vector. The parameter vector u contains all the control variables used to optimize the vector vortex beam. By adjusting these parameters, the phase distribution, polarization state, and amplitude distribution of the beam can be precisely controlled. u1 represents the first independent variable controlling the generation of the vector vortex beam during the optimization process, representing the grayscale value of a certain phase modulation region of the spatial light modulator. N : Represents the last independent variable in the parameter vector.

[0057] In step 5, the performance index set for SPGD algorithm correction is to define a performance index J that measures the quality of the vector vortex beam, as the optimization target of SPGD. The proposed performance indexes include: (1) mode purity: the degree of matching between the polarization and phase distribution of the beam and the target mode; (2) phase and polarization stability: the stability of the phase and polarization distribution of the beam; (3) intensity distribution: the intensity distribution of the beam cross section, ensuring that the intensity characteristics of the vortex at the center of the beam meet the requirements.

[0058] In step 5, the perturbation introduced for SPGD algorithm correction is to apply a small random perturbation to the control parameters in each iteration. Two perturbation vectors u+ are generated. and u- And apply it to the device. For example, a small perturbation can be added to the phase pattern of a spatial light modulator, or a tiny rotation can be applied to the angle of the waveplate.

[0059] In step 5, the performance index of the SPGD algorithm correction is measured by measuring the performance index of the output vector vortex beam under two different perturbations. and .

[0060] In step 5, the computational performance difference corrected by the SPGD algorithm is calculated using the results of two perturbation measurements. This serves as the basis for optimizing the step size.

[0061] Update control parameters: Adjust control parameters using the following update rules:

[0062] ,

[0063] in It is the gain coefficient, which adjusts the update step size.

[0064] In step 8, the pump optical path in the magnetic field measurement optical path consists of a 795nm pump laser from pump laser 1, polarized by the first isolator 2; the first half-wave plate 3 and the first polarizing beam splitter 4 are used to adjust the power ratio; one beam of light passes through the first reflector 5 and enters the first wavelength meter 6 to collect the wavelength of the pump beam, while the other beam is expanded by a beam-expanding system composed of the first concave lens 7 and the first convex lens 8; then, it passes through a first beam splitter 9, splitting the beam into two beams, one of which goes to the spatial light modulator 10. The reflected light passes through a 4f system composed of the second convex lens 11 and the third convex lens 12 to reach the vortex waveplate 13, and the exit plane of the spatial light modulator 10 is conjugate to the incident plane of the vortex waveplate 13. Then, the light passes through a second 4f system consisting of a fourth convex lens 14 and a fifth convex lens 15; then it passes through a system consisting of a second half-wave plate 16 and a second polarizing beam splitter 17 to adjust the power; finally, it passes through a first quarter-wave plate 18 to convert the linearly polarized light into circularly polarized light, which then enters the magnetically shielded barrel to pump the Rb atoms in the gas chamber.

[0065] In step 8, the detection optical path in the magnetic field measurement optical path consists of a detection laser generated by the detection laser 19, which passes through the second isolator 20, then through a system composed of the third half-wave plate 21 and the third polarizing beam splitter 22 to adjust the power, then through a beam expanding system composed of the second concave lens 25 and the sixth convex lens 26 to expand the beam, then through the third reflecting mirror 27, then through the Glan Taylor prism 28, and finally through the second quarter-wave plate 29 to enter the atomic gas chamber. At the other end of the device, a lens is used to focus the beam, and finally a detector 35 is used to detect the magnetic field signal.

[0066] refer to Figures 1 to 2A vector vortex beam generation device and method for use in SERF magnetic field measurement devices includes a beam expanding system composed of a first concave lens 7 and a first convex lens 8, a first beam splitter 9 that splits the beam to a spatial light modulator, a spatial light modulator 10 for loading a phase pattern, two 4f systems composed of a second convex lens 11, a third convex lens 12, a fourth convex lens 14, and a fifth convex lens 15, a vortex waveplate 13 for generating a higher-order vector beam, a pump optical system, a detection optical system, and an active / passive magnetic field control system. The beam expanding system composed of the first concave lens 7 and the first convex lens 8 is used to increase the beam spot radius. The first beam splitter 9 is used to split the expanded beam into two beams, one of which is transmitted to the spatial light modulator, and the light reflected by the spatial light modulator is reflected again by the beam splitter prism. The spatial light modulator 10 is used to load a phase pattern to generate a vortex beam, and simultaneously combines with the vortex waveplate 13 to generate a vector beam. The two 4f systems are used to filter the beam, and the vortex waveplate 13 is used to generate a vector beam with arbitrary polarization modes. The pumping optical system pumps alkali metal atoms, with a planned low density of potassium atoms, and the detection optical system detects the optical rotation angle of the dichroism of rubidium atoms to obtain the magnitude of the magnetic field to be measured.

[0067] A method for generating a vector vortex beam for use in a SERF magnetic field measuring device, utilizing the aforementioned vector vortex beam generating device for use in a SERF magnetic field measuring device.

[0068] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A method for generating a vector vortex beam for use in a SERF magnetic field measurement device, characterized in that, The device includes a combination of a first beam splitter, a spatial light modulator, and a vortex plate arranged on the pump light path before the pump light incident side of the atomic gas cell in the SERF magnetic field measurement device. The exit plane of the spatial light modulator is conjugate to the incident plane of the vortex plate. The first beam splitter splits the Gaussian light from the pump laser into a first reflected Gaussian beam and a second transmitted Gaussian beam. The second transmitted Gaussian beam illuminates the spatial light modulator loaded with a hologram. The spatial light modulator converts the second transmitted Gaussian beam into a vortex beam and emits the vortex beam to the first beam splitter through its exit plane. The first beam splitter reflects the vortex beam and the first reflected Gaussian beam to the vortex plate to generate a vector vortex beam. Includes the following steps: Step 1: Determine the theoretical model of the vortex beam. First, determine the complex amplitude expression, and then obtain the expression for the light field distribution of the vortex beam through Fourier transform. Step 2: Based on the expression of the light field distribution of the vortex beam, the intensity map and phase map are obtained by simulation. The interference pattern of the plane wave is superimposed using the computational holography method to generate a fork grating pattern. Then, based on the correspondence between the phase value of each pixel and the gray value of the spatial light modulator, the gray map is generated from the phase map and loaded into the spatial light modulator to generate the required vortex beam. Step 3: For vortex waveplates of order 30 or higher, a polarization mode decomposition method is used. An additional phase modulation factor is added to the optical field distribution expression of the vortex beam to decompose the original complex polarization mode of the beam into multiple polarization modes, which are distributed in space. Then, the parameters of the phase modulation factor are adjusted to reduce the energy density of other polarization modes. Finally, only the target polarization mode is retained to extract any polarization mode in the beam and obtain a vector vortex beam of any order. Step 4: For the obtained vector vortex beam, iterative optimization is performed on the beam in terms of phase, amplitude, and polarization direction parameters. First, global NSGA-II algorithm optimization is performed to initialize control parameters, which include beam phase, polarization direction, and amplitude parameters. Multiple objective functions are defined, which involve polarization purity and phase error. Then, multi-objective fitness values ​​are calculated, and the population is sorted in a non-dominated manner to obtain Pareto front solutions of different levels. Then, selection, crossover, and mutation are performed and iteratively repeated until the target convergence is reached, and a set of candidate beam generation parameters for Pareto optimal solutions are obtained. Step 5: Perform local SPGD algorithm optimization on the candidate beams. Select several candidate solutions that are close to the ideal target from the leading edge solutions generated by NSGA-II as the initial input of SPGD, initialize the control parameters, define the performance index of SPGD, introduce small perturbations, measure the performance index, calculate the performance difference, update the control parameters, perform iterative optimization, and finally select the parameter combination with the best beam quality from the locally optimized solutions as the final parameter combination. Step 6: Measure the uniformity of electronic steady-state polarization; Step 7: Determine whether the electronic polarization uniformity meets the requirements. If not, return to step 4, modify the topological charge, and continue iterative optimization. If yes, the optimization ends and proceed to step 8. Step 8: Use the optimized beam as a pump beam to pump alkali metal atoms for subsequent magnetic field measurements.

2. The vector vortex beam generation method for a SERF magnetic field measurement device according to claim 1, characterized in that, In step 1, the expression for the optical field distribution of the vortex beam is: ， In the formula This is the light field distribution function of the vortex beam, describing the electric field intensity distribution of the vortex beam at different positions in polar coordinates, where r is the radial coordinate and θ is the angular coordinate. It is the imaginary unit. It is the topological charge number or orbital angular momentum quantum number. It is the waist radius of the Gaussian beam. It is half the width of a ring. These are mode parameters. It is the beam radius. It is a modified Bessel function of the first kind.

3. The vector vortex beam generation method for a SERF magnetic field measurement device according to claim 1, characterized in that, The computational holography method in step 2 includes generating an interference pattern between the target light field and the reference light field through a computer program based on the principles of light interference and diffraction, thereby generating a vortex beam. The computational holography method is implemented by generating a computational hologram and combining it with a spatial light modulator. The computational hologram is realized using a fork-shaped grating. The fork-shaped grating is used as a holographic film. After being irradiated by a Gaussian plane wave, the expected light field distribution is obtained. The fork-shaped grating pattern is loaded onto the spatial light modulator, so that the Gaussian plane wave is directly incident on the surface of the modulator, thereby achieving effective control of the output light field and finally forming the desired vortex beam.

4. The vector vortex beam generation method for a SERF magnetic field measurement device according to claim 1, characterized in that, Step 3 involves extracting a specific polarization mode from the beam by simultaneously satisfying the following two conditions: the first condition is that the entangled polarization modes are separated in space; the second condition is that the separated polarization modes have different characteristics, so as to eliminate other polarization modes and retain only the target polarization mode. The first condition is achieved by breaking the modulation symmetry of the beam. When a phase modulation factor is added, the symmetry is broken, and the higher-order polarization modes are located on the outside, while the lower-order polarization modes are located on the inside. The separated polarization modes propagate independently in space. The second condition is achieved based on the energy density of different polarization modes. The mode with the larger the topological charge has a greater degree of divergence in space and a lower energy density. By adjusting the parameters of the phase modulation factor, the energy density of the target polarization mode is made much greater than the energy density of other polarization modes, so that only the target polarization mode is retained.

5. The vector vortex beam generation method for a SERF magnetic field measurement device according to claim 1, characterized in that, The initialization of control parameters in step 5 involves using the control parameters for controlling the generation of the vector vortex beam as control variables for SPGD, including initializing a parameter vector. , , to These are the first to the Nth control variables, where N is a positive integer.

6. The vector vortex beam generation method for a SERF magnetic field measurement device according to claim 1, characterized in that, In step 5, defining the performance index of SPGD includes defining a performance index J that measures the quality of the vector vortex beam as the optimization target of SPGD. The performance index includes: (1) mode purity: the degree of matching between the polarization and phase distribution of the beam and the target mode; (2) phase and polarization stability: the stability of the phase and polarization distribution of the beam; (3) intensity distribution: the intensity distribution of the beam cross section, ensuring that the intensity characteristics of the vortex at the center of the beam meet the requirements.

7. The vector vortex beam generation method for a SERF magnetic field measurement device according to claim 1, characterized in that, In step 5, introducing a small perturbation involves applying a small random disturbance to the control parameters in each iteration. Two perturbation vectors u+ are generated. and u- And apply it to the device, including adding small perturbations to the phase pattern of the spatial light modulator, or applying tiny rotations to the angle of the waveplate.

8. The vector vortex beam generation method for a SERF magnetic field measurement device according to claim 1, characterized in that, In step 5, the performance indicators are measured by measuring two performance indicators of the output vector vortex beam under two different perturbations. and ; In step 5, the performance difference is calculated using the results of two perturbation measurements. , ,Will This serves as the basis for optimizing the step size using the following expression: ， in It is the gain coefficient. It is to adjust and update control parameters The step size.

9. The vector vortex beam generation method for a SERF magnetic field measurement device according to claim 1, characterized in that, The pump laser is connected sequentially to the input side of the first beam splitter via a first isolator, a first half-wave plate, a first polarizing beam splitter, a first concave lens, and a first convex lens. The reflection side of the first polarizing beam splitter is connected to a first wavelength meter via a first reflecting mirror. The reflection side of the first beam splitter is connected to the vortex waveplate sequentially via a second convex lens and a third convex lens. The vortex waveplate is connected to the pump light incident side of the atomic gas cell sequentially via a fourth convex lens, a fifth convex lens, a second half-wave plate, a second polarizing beam splitter, and a first quarter-wave plate. The detection light incident side of the atomic gas chamber is connected to the detection laser in sequence through a second 1 / 4 wave plate, a Glan Taylor prism, a third reflecting mirror, a sixth convex lens, a second concave lens, a third polarizing beam splitter, a third 1 / 2 wave plate, and a second isolator. The reflection side of the third polarizing beam splitter is connected to a second wavelength meter through a second reflecting mirror. The detection light emitting side of the atomic gas chamber is connected to a host computer through a detector. The atomic gas chamber is located inside a magnetic compensation coil, the magnetic compensation coil is located inside an oven, the oven is located inside a vacuum chamber, and the vacuum chamber is located inside a magnetic shielding barrel.

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