Light field reverse design method and system based on double coherent arrays

Abstract

The invention provides a light field reverse design method and system based on a bicoherent array, and the method comprises the steps: determining a target structure light field, initializing the array parameters of a bicoherent laser array in staggered distribution, and building a physical forward model of the bicoherent laser array from an emission surface near-field light field to a far-field light field; constructing a first-stage loss function by taking the generated target structure light field as a guide, optimizing amplitude, phase and tilt parameters of all sub-beams through back propagation iteration until convergence, and outputting array parameters after first-stage optimization; and introducing a light beam position penalty term on the basis of the first-stage loss function to update the loss function so as to continuously iteratively optimize the array parameters until no light beams are overlapped, and driving the dual-coherent laser array to perform coherent combination by using the finally optimized array parameters to generate a target structure light field. According to the invention, multiple typical and specific attribute structured light fields can be accurately customized, far-field side lobes are effectively inhibited, and the mode quality and the energy utilization rate are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of structured light generation and laser array control technology, and particularly relates to a light field reverse design method and system based on a dual-coherent array. BACKGROUND

[0002] Structured light, with its unique spatial intensity and phase distribution, has shown great potential in modern advanced applications such as optical communication, super-resolution imaging, quantum sensing, and particle manipulation. Current methods for generating structured light rely on optical devices such as spatial light modulators, phase plates, gratings, metasurfaces, micromirrors, and photonic crystals, or by designing internal components of a resonant cavity to extract the target structured light field in a specific mode.

[0003] However, the above-mentioned traditional methods have significant limitations: due to the limitations of the power threshold and response speed of optical devices, it is difficult to achieve high-power output of structured light while ensuring fast and flexible dynamic control; and traditional optical materials are prone to thermal effects and nonlinear distortion under high-power conditions, further restricting the performance of structured light.

[0004] To overcome the shortcomings of traditional methods, coherent laser arrays have gradually become a research hotspot for flexible generation and editing of structured light. Coherent laser arrays use Gaussian beams as the basic unit, and by arranging a specific number of beams with specified intensity and phase distribution on the emission surface, the desired structured light can be generated in the far field. This method is free from the dependence on additional optical devices, effectively breaks through the output power limit of traditional methods, and supports flexible and fast dynamic control through independent manipulation of sub-beams. It can also be implemented through various modern platforms such as integrated photonics, phased arrays, multi-core optical fibers, and nanometer laser arrays, with high design flexibility.

[0005] However, there are still key technical bottlenecks when using existing coherent laser arrays for structured light generation: there is a lack of a general design method, and current array structure design relies on heuristic principles and is mostly tailored for specific types of structured light, lacking flexibility and being difficult to adapt to the generation needs of various structured light fields; at the same time, the structured light generated by existing array design methods often has significant sidelobes in the far field, not only causing energy waste but also severely affecting the quality of the target mode. Therefore, developing a coherent laser array design method that is highly versatile, can suppress far-field sidelobes, and can accurately customize various structured light fields has become a key to promoting the development of structured light technology. SUMMARY

[0006] The present application aims to overcome the problems of power limitation, insufficient dynamic control, poor universality of coherent laser array design, obvious sidelobes of generated structured light far field, and low mode quality in existing structured light generation technology, and provides an optical field reverse design method and system based on a double coherent array, which realizes adaptive optimization of array parameters through a physical model gradient descent algorithm, accurately customizes various types and specific properties of structured light fields without additional optical device assistance, effectively suppresses far field sidelobes, and improves mode quality and energy utilization.

[0007] To achieve the above technical purposes, the technical solutions adopted by the present application are as follows:

[0008] In one aspect, the present application provides an optical field reverse design method based on a double coherent array, comprising the following steps: determining a target structured light field to be generated; configuring initial array parameters of a double coherent laser array, two coherent laser arrays in the double coherent laser array fill the emission plane in an interleaved distribution manner, and the light field of each sub-beam in the array is defined by amplitude, phase, array surface position, and tilt parameters in x and y directions; establishing a physical forward model of the double coherent laser array from the near-field light field of the emission surface to the far-field light field based on the Gaussian beam array model and the Kirchhoff diffraction integral theory; constructing a first-stage loss function guided by generating the target structured light field, iteratively optimizing the amplitude, phase, and tilt parameters of all sub-beams through back propagation until convergence, and outputting the first-stage optimized array parameters; introducing a beam position penalty term to construct a second-stage loss function based on the first-stage loss function, continuing to iteratively optimize the array parameters based on the second-stage loss function until there is no beam overlap in the double coherent array, and outputting the second-stage optimized array parameters; driving the double coherent laser array to perform coherent synthesis according to the second-stage optimized array parameters, and generating the target structured light field.

[0009] On the other hand, an optical field reverse design system based on a double coherent array is provided, which is used to implement the above-mentioned optical field reverse design method based on a double coherent array, and comprises: A configuration unit is configured to determine a target structured light field to be generated, and configure initial array parameters of a double coherent laser array; A modeling unit is configured to establish a physical forward model of the double coherent laser array from the near-field light field of the emission surface to the far-field light field based on the Gaussian beam array model and the Kirchhoff diffraction integral theory; The optimization unit is used to perform two-stage optimization, including: constructing a first-stage loss function guided by the generation of the target structured light field, iteratively optimizing the amplitude, phase, and tilt parameters of all sub-beams through backpropagation until convergence, and outputting the array parameters after the first-stage optimization; constructing a second-stage loss function by introducing a beam position penalty term based on the first-stage loss function, and continuing to iteratively optimize the array parameters based on the second-stage loss function until there is no beam overlap in the dual coherent array, and outputting the array parameters after the second-stage optimization. The dual coherent laser array comprises two coherent laser arrays that fill the emission plane in an alternating manner. The dual coherent laser array receives the array parameters optimized in the second stage and drives each sub-beam to coherently combine them to generate the target structured light field in the far field.

[0010] The present invention has the following technical effects: This invention provides a method for inverse optical field design based on a dual-coherent array. It automatically performs complex parameter optimization and beam arrangement calculations based on the target structured light field to be generated. Adaptive optimization of array parameters is achieved through a physical model gradient descent algorithm. This method can accurately customize various types and specific properties of structured light fields without the need for additional optical components, while effectively suppressing far-field sidelobes and improving mode quality and energy utilization. The proposed method is highly versatile and adaptable to the generation of various structured light fields, including Hermitian-Gaussian beams, Laguerre-Gaussian beams, and Bessel beams.

[0011] Furthermore, this invention adopts a goal-oriented reverse design approach, and through a customized loss function, it can adapt to the generation requirements of typical structured light and image-type light fields, thus solving the problem of poor versatility of traditional array design methods.

[0012] The proposed solution of this invention has significant far-field sidelobe suppression, high mode quality and energy utilization. Specifically, the two coherent laser arrays in the dual coherent laser array of this invention fill the emission plane in an alternating manner, and the parameters of the dual coherent laser array are optimized in a coordinated manner, which can effectively suppress the far-field periodic sidelobes when generating structured light with a traditional single array, and greatly improve the mode quality and energy utilization.

[0013] This invention does not rely on additional optical devices such as spatial light modulators and phase plates. It can generate structured light fields simply by optimizing the parameters of a dual coherent laser array. The optimization process is based on the gradient descent algorithm of the physical model and combined with the automatic differentiation and backpropagation capabilities of machine learning libraries such as PyTorch to achieve adaptive joint optimization of array parameters. It can converge quickly on the NVIDIA GeForce RTX 3090 GPU platform.

[0014] In the first-stage optimization process, this invention constructs a first-stage loss function guided by the generation of the target structured light field. Iterative optimization of the amplitude, phase, and tilt parameters of all sub-beams is performed through backpropagation until convergence, outputting the optimized array parameters for the first stage. Based on the optimization results of the first stage, a beam position penalty term is introduced into the first-stage loss function to construct a second-stage loss function. The array parameters are then iteratively optimized based on the second-stage loss function until there is no beam overlap within the dual-coherent array, outputting the optimized array parameters for the second stage. This two-stage optimization, coupled with the introduction of a beam position penalty term into the loss function of the second-stage optimization process, ensures that the optimized array parameters meet physical implementation constraints, avoiding beam overlap issues. The array structure used in this invention can be implemented using various mature platforms such as integrated photonic chips, multi-core optical fibers, and laser phased arrays, catering to the application needs of both large-scale equipment and micro-devices, demonstrating high engineering practicality.

[0015] In addition to controlling the beam position, amplitude, phase, and tilt parameters, this invention can also incorporate more adjustable parameters such as polarization, size, and wavelength, further enriching the modulation dimension of the structured light field and providing the possibility for the generation of higher-dimensional structured light. At the same time, the idea of ​​multi-array collaborative optimization can be extended to a larger number of array combinations to generate more complex structured light fields. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of the reverse design and generation process of structured light field based on a dual coherent laser array provided in one embodiment; Figure 2 The images show a comparison of the generation effects of different types of structured light. Figure 2 (a) is the light field of the Hermetic-Gaussian mode. Figure 2 (b) is the light field of the zeroth-order Laguerre-Gaussian mode. Figure 2 (c) represents the light field of a higher-order Laguerre-Gaussian mode and Figure 2 (d) is the light field in the Modiogaussian mode. Figure 2 (e) Figure 2 (f) Figure 2 (g) and Figure 2 (h) are respectively obtained based on the optical field inverse design method based on dual coherent arrays provided by this invention. Figure 2 (a) Figure 2 (b) Figure 2(c) and Figure 2 (d) Corresponding customization results; Figure 2 (i) Figure 2 (j) Figure 2 (k) and Figure 2 ( l These represent the light fields of four different target images. Figure 2 (m) Figure 2 (n) Figure 2 (o) and Figure 2 (p) are respectively obtained based on the optical field inverse design method based on dual coherent arrays provided by this invention. Figure 2 (i) Figure 2 (j) Figure 2 (k) and Figure 2 ( l The corresponding customized results. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] Reference Figure 1 One embodiment provides a method for reverse design of optical fields based on a dual coherent array, comprising: Determine the target structured light field to be generated; Configure the initial array parameters of the dual coherent laser array. The two coherent laser arrays in the dual coherent laser array fill the emission plane in an alternating manner. The optical field of each sub-beam in the array is defined by the amplitude, phase, array plane position and tilt parameters in the x and y directions. Based on the Gaussian beam array model and Kirchhoff diffraction integral theory, a physical forward model of a dual coherent laser array from the near-field optical field to the far-field optical field of the emitting surface is established. The first-stage loss function is constructed with the generation of the target structured light field as the guide. The amplitude, phase and tilt parameters of all sub-beams are iteratively optimized through backpropagation until convergence, and the array parameters after the first-stage optimization are output. A beam position penalty term is introduced on the basis of the first-stage loss function to construct the second-stage loss function. The array parameters are iteratively optimized based on the second-stage loss function until there is no beam overlap in the dual coherent array. The optimized array parameters of the second stage are then output. The dual coherent laser array is driven to coherently synthesize the target structured light field based on the array parameters optimized in the second stage.

[0020] The sub-beams in both the first and second coherent laser arrays of the dual coherent laser array are arranged in a square array, i.e., both are square coherent laser arrays. The two arrays are staggered to cover the entire emitting surface, ensuring that the beams from both arrays jointly fill the emitting plane. Each coherent laser array consists of multiple fundamental mode Gaussian beams of the same frequency and polarization. In one embodiment, the initial array parameters are set as follows: the first coherent laser array is arranged in a 9×9 beam pattern, the second coherent laser array is arranged in an 8×8 beam pattern, the amplitude of all sub-beams in both arrays is initialized to 1, the phase is initialized to a co-phase state, and the tilt parameters in the x and y directions are initialized to 0. In practical applications, the arrangement of the first and second coherent laser arrays and the initial array parameter settings can be adjusted as needed and are not limited.

[0021] For a dual-coherent laser array, let the total number of sub-beams in the dual-coherent laser array be n, and let the nth sub-beam in the dual-coherent laser array be n. j The light field of the sub-beam at the emitting surface, i.e., z=0 for:

[0022] in j Number the sub-beams. j =1,2,......,n, where n is the total number of subbeams in the dual-coherent laser array; x , y () represents any coordinate position on the launch surface, x j , y j ) is the first j The coordinates of the sub-beam on the emitting surface. A j For the first j The amplitude of the individual beams, ω 0 represents the beam waist width. d For sub-beam aperture, circ It is a circular domain function.

[0023] Near-field optical field of a dual coherent laser array at the emitting surface, i.e., z=0 for:

[0024] in j For the first j Phase of individual beams k For wave vector, θ jx and θ jy For the first j The tilt angle of the sub-beam in the x and y directions.i The imaginary unit is exp, which represents the exponentiation of e.

[0025] Based on the Gaussian beam array model and Kirchhoff diffraction integral theory, a physical forward model of a dual-coherent laser array from the near field to the far field is constructed to describe the mapping relationship between array parameters and the far-field optical field. This physical forward model calculates the optical field from the near field of the emitting surface to the far field behind the focusing lens using Fourier transform. Under the paraxial approximation, the dual-coherent laser array... z = L The far-field light field at that location is:

[0026] in( u , v )for z = L The far-field coordinates of the point, where λ is the laser wavelength. f For the focal length of the focusing lens, L For the propagation distance, F(·) represents the Fourier transform.

[0027] This invention employs a two-stage gradient descent optimization of the physical model. In the first stage of optimization, a targeted loss function is constructed based on the target structured light field requirements. When the target structured light field is the target mode light field, the inverse of the mode purity between the far-field light field output by the physical forward model and the target mode is used as the first-stage loss function. The mode purity is calculated by the square of the overlap integral of the far-field light field output by the normalized physical forward model and the target mode.

[0028] When the target structured light field is the target image light field, the mean square error between the reconstruction intensity and the target image intensity distribution is used as the first-stage loss function. The reconstruction intensity refers to the light intensity distribution on the far-field observation surface calculated after the current array parameters are input into the physical forward model.

[0029] In the first stage of optimization, the Adam optimizer is used to calculate the gradient of the first-stage loss function with respect to each array parameter through backpropagation algorithm, and the array parameters are iteratively optimized until the loss function converges. Furthermore, after the first-stage optimization converges, the process includes filtering beams that significantly contribute to the target light field based on a preset beam intensity threshold, and removing beams with minimal contributions below the beam intensity threshold.

[0030] To address the potential beam position overlap issue within the same array that may occur during the first-stage optimization, this invention designs a second-stage optimization process. A physical penalty term for beam position is introduced into the first-stage loss function to construct the second-stage loss function: Loss2 = Loss1 + σΣPenalty, where Loss1 and Loss2 are the first-stage and second-stage loss functions, respectively. σ is a penalty factor that increases progressively with iteration, and Penalty is the beam position penalty term, calculated using a distance-based ReLU function. The penalty term is applied when the distance between the centers of any two sub-beams is less than the aperture diameter of the sub-beam. d When the condition is met, the ReLU function produces a positive penalty value; otherwise, the ReLU function outputs 0. Iterative optimization continues based on the second-stage loss function to ensure that the array parameters satisfy physical constraints while maintaining the generation quality of the target structured light field.

[0031] The following example demonstrates the generation of a Laguerre-Gaussian beam (LG). 22 Taking an example, the specific implementation process of an embodiment of the present invention is described as follows: (1) The target structured light field is a Laguerre-Gaussian beam LG 22 Laguerre-Gaussian beam (LG) 22 Requirements Definition: The target is clearly defined as LG. 22 The Laguerre-Gaussian beam is used to obtain its standard complex amplitude distribution as the target optical field E, and mode purity is defined as the core evaluation index.

[0032] (2) Initialize the parameters of the dual coherent laser array: the first coherent laser array is arranged in a 9×9 square, the second coherent laser array is arranged in an 8×8 square, and the two arrays are staggered to cover the emission surface; the amplitude of all sub-beams is initialized to 1, the phase is initialized to coherent state, and the tilt parameters in the x and y directions are initialized to 0.

[0033] (3) Physical forward model construction: Based on the Gaussian beam array model and Kirchhoff diffraction integral theory, a physical forward model from near field to far field is constructed. The input is the array parameters and the output is the far field optical field distribution. The far field optical field calculation under the paraxial approximation is realized through Fourier transform.

[0034] (3) Two-stage optimized execution: The first stage of optimization involves calling the first-stage loss function, namely the mode purity loss function Loss1 = -Purity(H(P,A,Φ,Θ),E), where Purity is the mode purity, H(·) is the forward physical model, P, A, Φ, and Θ are the array beam position, amplitude, phase, and tilt parameters, respectively, and E is the complex amplitude of the target structured light field. The Adam optimizer is started, and the gradient of the loss function with respect to each array parameter is calculated through backpropagation, iteratively updating the beam position, amplitude, phase, and tilt parameters. When the loss function converges, the first-stage iteration stops. Based on a preset beam intensity threshold (set to 10% of the maximum intensity in this embodiment), beams with intensities below the beam intensity threshold are removed, while beams with significant contributions and intensities greater than or equal to the beam intensity threshold are retained.

[0035] Second-stage optimization: Based on the first-stage loss function, a beam position penalty term is introduced to construct the second-stage loss function. The penalty factor σ is set to gradually increase with iteration (initial value is 0.1, increasing by 0.05 every 5 iterations). Iterative optimization is continued based on the second-stage loss function until there is no beam overlap in the array and the loss function converges and stabilizes. Then, the iteration is stopped, and the final optimized array parameters are recorded.

[0036] 5) Structured Light Field Generation and Verification: The final optimized array parameters are sent to the dual coherent laser array to drive the corresponding devices to adjust the sub-beam parameters. After propagating in free space, the emitted beam from the dual coherent laser array forms an LG field in the far field. 22 Structured light field.

[0037] like Figure 2 As shown, Figure 2 The images show a comparison of the generation effects of different types of structured light. Figure 2 (a) is the light field of the Hermetic-Gaussian mode. Figure 2 (b) is the light field of the zeroth-order Laguerre-Gaussian mode. Figure 2 (c) represents the light field of a higher-order Laguerre-Gaussian mode and Figure 2 (d) is the light field in the Modiogaussian mode. Figure 2 (e) Figure 2 (f) Figure 2 (g) and Figure 2 (h) are respectively obtained based on the optical field inverse design method based on dual coherent arrays provided by this invention. Figure 2 (a) Figure 2 (b) Figure 2 (c) and Figure 2 (d) Corresponding customization results; Figure 2 (i) Figure 2 (j) Figure 2 (k) and Figure 2 ( l These represent the light fields of four different target images. Figure 2 (m)Figure 2 (n) Figure 2 (o) and Figure 2 (p) are respectively obtained based on the optical field inverse design method based on dual coherent arrays provided by this invention. Figure 2 (i) Figure 2 (j) Figure 2 (k) and ​ ( l The corresponding customized results. This invention is adaptable to the generation of various structured light fields. The target structured light field can be a target mode light field or a target image light field. The target mode light field includes various classical structured light fields, including Hermitian-Gaussian beams, Laguerre-Gaussian beams, Bessel beams, and their superposition states. The target image of the target image light field is not limited at all and can be a custom image of various shapes.

[0038] In another embodiment, a system for reverse optical field design based on a dual coherent array is provided to implement the method for reverse optical field design based on a dual coherent array described in any of the above embodiments, comprising: The configuration unit is used to determine the target structured light field to be generated and to configure the initial array parameters of the dual coherent laser array; The modeling unit is used to establish a physical forward model of a dual coherent laser array from the near-field optical field to the far-field optical field of the emitting surface, based on the Gaussian beam array model and Kirchhoff diffraction integral theory. The optimization unit is used to perform two-stage optimization, including: constructing a first-stage loss function guided by the generation of the target structured light field, iteratively optimizing the amplitude, phase, and tilt parameters of all sub-beams through backpropagation until convergence, and outputting the array parameters after the first-stage optimization; constructing a second-stage loss function by introducing a beam position penalty term based on the first-stage loss function, and continuing to iteratively optimize the array parameters based on the second-stage loss function until there is no beam overlap in the dual coherent array, and outputting the array parameters after the second-stage optimization. The dual coherent laser array comprises two coherent laser arrays that fill the emission plane in an alternating manner. The dual coherent laser array receives the array parameters optimized in the second stage and drives each sub-beam to coherently combine them to generate the target structured light field in the far field.

[0039] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for reverse design of optical fields based on dual coherent arrays, characterized in that, include: Determine the target structured light field to be generated; Configure the initial array parameters of the dual coherent laser array. The two coherent laser arrays in the dual coherent laser array fill the emission plane in an alternating manner. The optical field of each sub-beam in the array is defined by the amplitude, phase, array plane position and tilt parameters in the x and y directions. Based on the Gaussian beam array model and Kirchhoff diffraction integral theory, a physical forward model of a dual coherent laser array from the near-field optical field to the far-field optical field of the emitting surface is established. The first-stage loss function is constructed with the generation of the target structured light field as the guide. The amplitude, phase and tilt parameters of all sub-beams are iteratively optimized through backpropagation until convergence, and the array parameters after the first-stage optimization are output. A beam position penalty term is introduced on the basis of the first-stage loss function to construct the second-stage loss function. The array parameters are iteratively optimized based on the second-stage loss function until there is no beam overlap in the dual coherent array. The optimized array parameters of the second stage are then output. The dual coherent laser array is driven to coherently synthesize the target structured light field based on the array parameters optimized in the second stage.

2. The optical field inverse design method based on a dual coherent array according to claim 1, characterized in that, The sub-beams in the first coherent laser array and the second coherent laser array of the dual coherent laser array are arranged in a square array.

3. The optical field inverse design method based on a dual coherent array according to claim 1, characterized in that, The first in the dual coherent laser array j The light field of the sub-beam at the emitting surface, i.e., z=0 for: in j Number the sub-beams. j =1,2,......,n, where n is the total number of sub-beams in the dual coherent laser array; ( x , y () represents any coordinate position on the launch surface, x j , y j ) is the first j The coordinates of the sub-beam on the emitting surface. A j For the first j The amplitude of the individual beam ω 0 represents the beam waist width. d For sub-beam aperture, circ It is a circular domain function.

4. The optical field inverse design method based on a dual coherent array according to claim 3, characterized in that, The near-field optical field of the dual coherent laser array at the emitting surface, i.e., z=0. for: in j For the first j Phase of individual beams k For wave vector, θ jx and θ jy For the first j The tilt angle of the sub-beam in the x and y directions. i The imaginary unit is exp, which represents the exponentiation of e.

5. The optical field inverse design method based on a dual coherent array according to claim 4, characterized in that, The physical forward model calculates the optical field from the near field of the emitting surface to the far field behind the focusing lens using Fourier transform. Under the paraxial approximation, the dual coherent laser array... z = L The far-field light field at that location is: in( u , v )for z = L The far-field coordinates of the point, where λ is the laser wavelength. f For the focal length of the focusing lens, L For the propagation distance, F(·) represents the Fourier transform.

6. The optical field reverse design method based on a dual coherent array according to claim 1, 2, 3, 4, or 5, characterized in that, The target structured light field is a target mode light field or a target image light field, wherein the target mode light field includes Hermite-Gaussian beams and Laguerre-Gaussian beams.

7. The optical field inverse design method based on a dual coherent array according to claim 6, characterized in that, When the target structured light field is the target mode light field, the negative of the mode purity between the far-field light field output by the physical forward model and the target mode is used as the first-stage loss function.

8. The optical field inverse design method based on a dual coherent array according to claim 6, characterized in that, When the target structured light field is the target image light field, the mean square error between the reconstructed intensity and the intensity distribution of the target image is used as the loss function. The reconstructed intensity refers to the light intensity distribution on the far-field observation surface calculated after the current array parameters are input into the physical forward model.

9. The optical field reverse design method based on a dual coherent array according to claim 1, 2, 3, 4, 5, 7, or 8, characterized in that, The beam position penalty term in the second-stage loss function is calculated using a distance-based ReLU function, which applies when the distance between any two sub-beam centers is less than the sub-beam aperture diameter. d When the value is positive, the ReLU function produces a positive penalty value; otherwise, the ReLU function outputs 0.

10. A system for reverse optical field design based on a dual-coherent array, characterized in that, The method for implementing the optical field inverse design method based on a dual coherent array as described in claim 1, 2, 3, 4, 5, 7, or 8 includes: The configuration unit is used to determine the target structured light field to be generated and to configure the initial array parameters of the dual coherent laser array; The modeling unit is used to establish a physical forward model of a dual coherent laser array from the near-field optical field to the far-field optical field of the emitting surface, based on the Gaussian beam array model and Kirchhoff diffraction integral theory. The optimization unit is used to perform two-stage optimization, including: constructing a first-stage loss function guided by the generation of the target structured light field, iteratively optimizing the amplitude, phase, and tilt parameters of all sub-beams through backpropagation until convergence, and outputting the array parameters after the first-stage optimization; constructing a second-stage loss function by introducing a beam position penalty term based on the first-stage loss function, and continuing to iteratively optimize the array parameters based on the second-stage loss function until there is no beam overlap in the dual coherent array, and outputting the array parameters after the second-stage optimization. The dual coherent laser array comprises two coherent laser arrays that fill the emission plane in an alternating manner. The dual coherent laser array receives the array parameters optimized in the second stage and drives each sub-beam to coherently combine them to generate the target structured light field in the far field.

Images