Method for manufacturing two-dimensional beam-splitting diffraction grating of specific dot matrix pattern

Abstract

This invention discloses a method for fabricating a two-dimensional beam-splitting diffraction grating with a specific dot matrix pattern. The method involves constructing a first cost function `cost_x` and a second cost function `cost_y` based on the actual required diffraction order of the spot array in the x and y directions, combined with diffraction efficiency and diffraction order uniformity error. The optimized spatial modulation coordinates of the phase change points in the x and y directions are obtained by minimizing the first and second cost functions `cost_x` and `cost_y`, respectively. The optimized spatial modulation coordinates of the phase change points in the x and y directions are then orthogonally multiplied to obtain orthogonal two-dimensional diffraction grating structure parameters. The orthogonal two-dimensional grating structure is processed using at least one pattern transformation method to obtain the final two-dimensional diffraction grating structure parameters and etching depth, and a photomask is generated. Finally, a substrate is micro- or nano-fabricated using the photomask to obtain a two-dimensional beam-splitting diffraction grating element.

Description

Technical Field

[0001] This invention belongs to the field of optical technology, specifically relating to a method for fabricating a two-dimensional beam-splitting diffraction grating that realizes a specific dot matrix pattern. Background Technology

[0002] An optical array generator is a device that can split an incident laser beam into an array of outgoing beams with a specific power distribution. Among various optical array generators, the Damman grating achieves a laser far-field multi-level spectral point equal intensity beam array by modulating the spatial coordinate position of the binary optical phase change point.

[0003] As early as the 1970s, Dammann et al., in their research on multiple image replication, proposed the concept of the Dammann grating and introduced large-scale integrated circuit technology into the field of optics for the first time. This laid the foundation for the development of micro-nano optics. The Dammann grating can efficiently convert incident monochromatic light into a lattice with equal intensity distribution at the far field, exhibiting advantages such as simple design structure, mature fabrication process, and no need for precise registration. In recent years, it has attracted widespread attention due to its enormous potential in fields such as facial recognition, 3D imaging, structured light projection, optical communication and optical computing, and VR (virtual reality) / AR (augmented reality).

[0004] Traditional damman gratings are designed by optimizing the spatial modulation coordinates of phase change points to determine a one-dimensional grating structure. Then, they are unfolded in the orthogonal direction of the one-dimensional grating to obtain a two-dimensional grating structure. In the far field, they can only realize axisymmetric diffraction lattice patterns, such as square lattices and circular lattices, but cannot realize other specific forms of lattice patterns, such as non-axisymmetric diffraction lattice patterns, unequally spaced diffraction lattice patterns, bar diffraction lattice patterns, and non-square lattice patterns. This greatly limits the application of damman gratings in specific fields such as non-centrosymmetric lattices and realizing the maximum diffraction lattice pattern features of specific diffraction orders, such as three-dimensional measurement, laser cutting, and laser scanning.

[0005] Another method for generating specific patterned dot matrix features is mainly based on the principle of diffraction optics. According to the desired target dot matrix pattern, the phase information required by the diffraction optical element is optimized through iterative algorithms (such as the Gerchberg-Saxton algorithm, gradient descent algorithm, etc.), and then the etching information of the diffraction optical element is obtained. However, this method will generate stray light interference in the far field, the background noise is relatively serious, and the diffraction efficiency is low. The diffraction efficiency can only be improved by increasing the etching order of the diffraction optical element or using electron beam lithography to design metasurface structures. This will greatly increase the processing difficulty, process uncertainty and processing cost, and is not conducive to the industrial replication and large-scale mass production of diffraction optical elements. Summary of the Invention

[0006] In view of this, the main objective of the present invention is to provide a method for fabricating a two-dimensional beam-splitting diffraction grating that realizes a specific dot pattern.

[0007] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0008] This invention provides a method for fabricating a two-dimensional beam-splitting diffraction grating with a specific dot matrix pattern, the method comprising:

[0009] Based on the actual required diffraction orders of the spot array in the x and y directions, and combined with the diffraction efficiency and diffraction order uniformity error, a first cost function cost_x and a second cost function cost_y are constructed respectively.

[0010] The optimized spatial modulation coordinates of the phase change points in the x and y directions are obtained by minimizing the first cost function cost_x and the second cost function cost_y, respectively.

[0011] The spatial modulation coordinates of the phase change points optimized in the x and y directions are orthogonally multiplied and expanded to obtain the orthogonal two-dimensional diffraction grating structure parameters;

[0012] The orthogonal two-dimensional grating structure is processed by at least one pattern transformation method to obtain the final two-dimensional diffraction grating structure parameters and etching depth, and a photomask is generated.

[0013] The substrate is micro- and nano-fabricated using the photolithography mask to obtain a two-dimensional beam-splitting diffraction grating element.

[0014] In the above scheme, obtaining the optimized spatial modulation coordinates of the phase change points in the x and y directions by minimizing the first cost function cost_x and the second cost function cost_y respectively specifically involves: using a computer iterative optimization algorithm to minimize the first cost function cost_x and the second cost function cost_y to obtain the optimized spatial modulation coordinates of the phase change points in the x and y directions; the computer iterative optimization algorithm includes simulated annealing iterative optimization algorithm and gradient descent iterative optimization algorithm.

[0015] In the above scheme, the simulated annealing iterative optimization algorithm minimizes the first cost function cost_x to obtain the optimized spatial modulation coordinates of the phase change point in the x-direction, specifically as follows:

[0016] Set the initial temperature T = T0, randomly generate the initial solution x of the normalized phase change point spatial modulation coordinates, with a range of 0 < x < 1, and obtain the first cost function cost_x(x);

[0017] Set the number of iterations L for each T value, and let T = kT, where 0 < k < 1, and k represents the rate of temperature decrease;

[0018] Apply a random perturbation to the current solution x to generate a new solution in its neighborhood: x_new = x + Δx;

[0019] Determine the cost function value cost_x(x_new) for the new solution and the increment of the objective function value Δcost_x = cost_x(x_new) - cost_x(x);

[0020] If the increment of the objective function value Δcost_x < 0, then x_new is accepted as the new current solution; otherwise, the probability exp(-Δcost_x / kT) is used to determine whether to accept x_new as the new current solution.

[0021] At temperature T, repeat the perturbation and acceptance process L times, that is, perform the above steps;

[0022] Determine if the temperature T has reached the termination temperature level. If so, terminate the algorithm and obtain the spatial modulation coordinates of the optimized phase change point in the x direction; otherwise, return to apply a random perturbation to the current solution x and repeat the iterative process.

[0023] In the above scheme, the simulated annealing iterative optimization algorithm minimizes the second cost function cost_y to obtain the optimized spatial modulation coordinates of the phase change point in the y-direction, specifically as follows:

[0024] Set the initial temperature T = T0, randomly generate the initial solution y of the normalized phase change point spatial modulation coordinates, with a range of 0 < y < 1, and obtain the first cost function cost_y(y);

[0025] Set the number of iterations L for each T value, and let T = kT, where 0 < k < 1, and k represents the rate of temperature decrease;

[0026] Apply a random perturbation to the current solution y to generate a new solution in its neighborhood: y_new = y + Δy;

[0027] Determine the cost function value cost_y(y_new) for the new solution and the increment of the objective function value Δcost_y = cost_y(y_new) - cost_y(y);

[0028] If the increment of the objective function value Δcost_y < 0, then y_new is accepted as the new current solution; otherwise, the probability exp(-Δcost_y / kT) is used to determine whether to accept y_new as the new current solution.

[0029] At temperature T, repeat the perturbation and acceptance process L times, that is, perform the above steps;

[0030] Determine if the temperature T has reached the termination temperature level. If so, terminate the algorithm and obtain the spatial modulation coordinates of the optimized phase change point in the y direction; otherwise, return to apply a random perturbation to the current solution y and repeat the iterative process.

[0031] In the above scheme, the orthogonal multiplication and expansion of the optimized phase change point spatial modulation coordinates in the x and y directions to obtain orthogonal two-dimensional diffraction grating structure parameters is specifically as follows: the one-dimensional grating structure in the x and y directions is determined by the optimized phase change point spatial modulation coordinates in the x and y directions, and then the orthogonal expansion of the one-dimensional grating in the x and y directions is performed to obtain the orthogonal two-dimensional grating structure.

[0032] In the above scheme, the graphic transformation methods include shear transformation, rotation transformation, and graphic splicing.

[0033] In the above scheme, the orthogonal two-dimensional grating structure is processed by the shear transformation method to obtain the final two-dimensional diffraction grating structure parameters and etching depth. Specifically, in the horizontal direction, the directed distance from each point of the orthogonal two-dimensional grating structure to a line parallel to that direction is sheared by 30° according to the proportion to obtain the final two-dimensional diffraction grating structure. The final two-dimensional diffraction grating structure parameters and etching depth are determined based on the final two-dimensional diffraction grating structure.

[0034] In the above scheme, the orthogonal two-dimensional grating structure is processed by the rotation transformation method and the image stitching method to obtain the final two-dimensional diffraction grating structure parameters and etching depth. Specifically, the orthogonal two-dimensional diffraction grating is maximized with the target in the x-direction to achieve a far-field light intensity of 0 to ±2 diffraction orders, and then rotated clockwise by 0° and 90° respectively. Finally, the final two-dimensional diffraction grating structure is obtained by image stitching. The final two-dimensional diffraction grating structure parameters and etching depth are determined based on the final two-dimensional diffraction grating structure.

[0035] In the above scheme, the orthogonal two-dimensional grating structure is processed by the rotation transformation method and the image stitching method to obtain the final two-dimensional diffraction grating structure parameters and etching depth. Specifically, the orthogonal two-dimensional diffraction grating is maximized with the target in the x-direction to achieve a far-field light intensity of 0 to ±2 diffraction orders, and then rotated clockwise by 0°, 45°, -45°, and 90° respectively. Finally, the final two-dimensional diffraction grating structure is obtained by image stitching. The final two-dimensional diffraction grating structure parameters and etching depth are determined based on the final two-dimensional diffraction grating structure.

[0036] Compared with existing technologies, the two-dimensional grating structure obtained by this invention can realize non-axisymmetric diffraction lattice patterns, unequal interval diffraction lattice patterns, bar diffraction lattice patterns, non-square lattice patterns, etc., according to actual application needs. Compared with traditional methods, it produces more diverse pattern types, has a simple design structure, mature manufacturing process, and is easy to mass-produce in industrial applications, which can further expand its application in multiple fields. Attached Figure Description

[0037] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and, together with their descriptions, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0038] Figure 1 A flowchart is provided for an embodiment of the present invention to provide a method for fabricating a two-dimensional beam-splitting diffraction grating that realizes a specific dot matrix pattern;

[0039] Figure 2 This is a diagram of an orthogonal two-dimensional diffraction grating structure provided in Embodiment 1 of the present invention;

[0040] Figure 3 This is a diagram of an orthogonal two-dimensional diffraction grating structure provided in Embodiment 2 of the present invention;

[0041] Figure 4 This is a diagram of a two-dimensional diffraction grating structure obtained by the shear transformation provided in Embodiment 1 of the present invention;

[0042] Figure 5 This is a diagram of a two-dimensional diffraction grating structure obtained by the shear transformation provided in Embodiment 2 of the present invention;

[0043] Figure 6 This is a diagram of a two-dimensional diffraction grating structure obtained by rotational transformation according to Embodiment 1 of the present invention;

[0044] Figure 7 This is a diagram of a two-dimensional diffraction grating structure obtained by rotational transformation according to Embodiment 2 of the present invention;

[0045] Figure 8 This is a diagram of a two-dimensional diffraction grating structure obtained by stitching together graphics according to Embodiment 3 of the present invention;

[0046] Figure 9 This is a diagram of a two-dimensional diffraction grating structure obtained by graphic splicing according to Embodiment 4 of the present invention;

[0047] Figure 10 This is a schematic diagram of far-field light spot array imaging of an orthogonal two-dimensional diffraction grating provided in Embodiment 1 of the present invention;

[0048] Figure 11 This is a schematic diagram of far-field light spot array imaging of an orthogonal two-dimensional diffraction grating provided in Embodiment 2 of the present invention;

[0049] Figure 12 The two-dimensional diffraction grating structure obtained by the shear transformation provided in Embodiment 1 of the present invention;

[0050] Figure 13 The two-dimensional diffraction grating structure obtained by the shear transformation provided in Embodiment 2 of the present invention;

[0051] Figure 14 The two-dimensional diffraction grating structure obtained by rotational transformation provided in Embodiment 1 of the present invention;

[0052] Figure 15 The two-dimensional diffraction grating structure obtained by rotational transformation provided in Embodiment 2 of the present invention;

[0053] Figure 16 The two-dimensional diffraction grating structure diagram obtained by graphic splicing provided in Embodiment 3 of the present invention;

[0054] Figure 17 The two-dimensional diffraction grating structure diagram obtained by graphic splicing provided in Embodiment 4 of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0056] In the accompanying drawings of this embodiment, the same or similar reference numerals correspond to the same or similar components. In the description of this invention, it should be understood that the terms "upper," "lower," "left," "right," "inner," "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the accompanying drawings are only for illustrative purposes and should not be construed as limiting this patent. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0057] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, article, or apparatus that includes that element.

[0058] This invention provides a method for fabricating a two-dimensional beam-splitting diffraction grating that realizes a specific dot matrix pattern, such as... Figure 1 As shown, the method includes:

[0059] Step 1: Based on the actual required diffraction order of the light spot array in the x and y directions, and combined with the diffraction efficiency and diffraction order uniformity error, construct the first cost function cost_x and the second cost function cost_y.

[0060] Specifically, taking the target to minimize the diffraction order as ±p and ±q as an example, the cost function is expressed as: Where I k’ To minimize the far-field intensity distribution of the diffraction order ±p and ±q orders, I k Let N be the far-field light intensity distribution of the k-th diffraction order excluding the target minimization diffraction order, ranging from -n to n, excluding ±p and ±q, where N is the sum of diffraction orders excluding the target minimization diffraction order, and η is the total target diffraction efficiency.

[0061] According to the fundamental theory of Fourier optics, the intensity distribution of each diffraction order of a periodic binary phase grating can be obtained by performing a Fourier transform operation on the transmission function of the grating. The expression for this distribution is:

[0062]

[0063]

[0064] Where I0 is the zeroth order diffraction order intensity, I k Let x be the intensity of the kth diffraction order. i Let p be the normalized spatial modulation coordinates of the phase change point, where x is the x-axis. i The total number of items.

[0065] Step 2: Obtain the optimized spatial modulation coordinates of the phase change points in the x and y directions by minimizing the first cost function cost_x and the second cost function cost_y, respectively;

[0066] Specifically, a computer iterative optimization algorithm is used to minimize the first cost function cost_x and the second cost function cost_y to obtain the spatial modulation coordinates of the phase change points in the x and y directions after optimization; the computer iterative optimization algorithm includes simulated annealing iterative optimization algorithm and gradient descent iterative optimization algorithm.

[0067] Taking the simulated annealing iterative optimization algorithm as an example, the specific optimization process of the first cost function cost_x is as follows:

[0068] Step 201: Set the initial temperature T = T0, randomly generate the initial solution x of the normalized phase change point spatial modulation coordinates, with a range of 0 < x < 1, and obtain the first cost function cost_x(x);

[0069] Step 202: Set the number of iterations L for each T value, let T = kT, where 0 < k < 1, and k represents the rate of temperature decrease;

[0070] Step 203: Apply a random perturbation to the current solution x to generate a new solution in its neighborhood: x_new = x + Δx;

[0071] Step 204: Determine the cost function value cost_x(x_new) for the new solution and the increment of the objective function value Δcost_x = cost_x(x_new) - cost_x(x);

[0072] Step 205: If the increment of the objective function value Δcost_x < 0, then accept x_new as the new current solution; otherwise, use the probability exp(-Δcost_x / kT) to determine whether to accept x_new as the new current solution.

[0073] Step 206: At temperature T, repeat the perturbation and acceptance process L times, that is, perform the above steps;

[0074] Step 207: Determine whether the temperature T has reached the termination temperature level. If so, terminate the algorithm and obtain the spatial modulation coordinates of the optimized phase change point in the x direction; otherwise, return to step 203 and repeat the iteration process.

[0075] Taking the simulated annealing iterative optimization algorithm as an example, the specific optimization process of the second cost function cost_y is as follows:

[0076] Step 2001: Set the initial temperature T = T0, randomly generate the initial solution y of the normalized phase change point spatial modulation coordinates, with a range of 0 < y < 1, and obtain the first cost function cost_y(y);

[0077] Step 2002: Set the number of iterations L for each T value, let T = kT, where 0 < k < 1, and k represents the rate of temperature decrease;

[0078] Step 2003: Apply a random perturbation to the current solution y to generate a new solution in its neighborhood: y_new = y + Δy;

[0079] Step 2004: Determine the new solution cost function value cost_y(y_new) and the objective function value increment Δcost_y = cost_y(y_new) - cost_y(y);

[0080] Step 2005: If the increment of the objective function value Δcost_y < 0, then accept y_new as the new current solution; otherwise, use the probability exp(-Δcost_y / kT) to determine whether to accept y_new as the new current solution.

[0081] Step 2006: At temperature T, repeat the perturbation and acceptance process L times, i.e., perform the above steps;

[0082] Step 2007: Determine whether the temperature T has reached the termination temperature level. If so, terminate the algorithm and obtain the spatial modulation coordinates of the optimized phase change point in the y direction; otherwise, return to step 2003 and repeat the iteration process.

[0083] In some embodiments, Example 1 is to maximize the far-field light intensity of the target in the x-direction by 0 to ±7 diffraction order and the target in the y-direction by ±1 diffraction order. The normalized phase change point spatial modulation coordinate values ​​of the two-dimensional beam splitting diffraction grating with non-uniform width strip dot matrix feature pattern are calculated by the simulated annealing algorithm.

[0084] Table 1 shows the normalized phase change point spatial modulation coordinates provided in Embodiment 1 of the present invention.

[0085]

[0086] Example 2 uses the scenario of maximizing the far-field light intensity of the target in the x-direction to the diffraction order of 0 to ±15 and the target in the y-direction to the diffraction order of ±1 / ±2 / ±4 / ±5 as an example. Through simulated annealing algorithm, the normalized phase change point spatial modulation coordinate values ​​of two types of two-dimensional beam-splitting diffraction gratings with non-uniform width stripe dot matrix feature patterns are calculated.

[0087] Table 2 shows the normalized phase change point spatial modulation coordinates provided in Embodiment 2 of the present invention.

[0088]

[0089] Step 3: Perform orthogonal multiplication expansion on the spatial modulation coordinates of the optimized phase change points in the x and y directions to obtain the orthogonal two-dimensional diffraction grating structure parameters;

[0090] Specifically, the one-dimensional grating structure in the x and y directions is determined by the optimized spatial modulation coordinates of the phase change points in the x and y directions. Then, the one-dimensional gratings in the x and y directions are unfolded orthogonally to obtain an orthogonal two-dimensional grating structure.

[0091] In some embodiments, such as Figure 2 , 3The figures shown are orthogonal two-dimensional diffraction grating structures provided in Examples 1 and 2, respectively. Black represents the etched area and white represents the non-etched area. The number of two-dimensional grating periods can be determined based on the minimum linewidth of the actual photolithography process and the required far-field angle.

[0092] Step 4: Process the orthogonal two-dimensional grating structure using at least one pattern transformation method to obtain the final two-dimensional diffraction grating structure parameters and etching depth, and generate a photomask.

[0093] Specifically, the graphic transformation methods include shearing transformation, rotation transformation, and graphic splicing.

[0094] The shear transformation refers to scaling the directed distance from each point of the original two-dimensional grating structure to a straight line parallel to that direction by a certain angle in a certain direction, thereby obtaining a new two-dimensional grating structure.

[0095] Rotation transformation refers to rotating all points on the original two-dimensional grating structure in the same direction and by the same angle around a fixed point to obtain a new two-dimensional grating structure.

[0096] Pattern splicing refers to combining multiple different two-dimensional grating structures to obtain a new two-dimensional grating structure.

[0097] Taking the shear transformation method as an example, in the horizontal direction, the directed distance from each point of the orthogonal two-dimensional grating structure to a line parallel to that direction is sheared by 30° according to the proportion, to obtain the final two-dimensional diffraction grating structure. Based on the final two-dimensional diffraction grating structure, the final two-dimensional diffraction grating structure parameters and etching depth are determined.

[0098] like Figure 4 , Figure 5 The images shown are two-dimensional diffraction grating structures obtained by a 30° horizontal shear transformation provided in Examples 1 and 2, respectively, where black represents the etched area and white represents the non-etched area.

[0099] Taking rotation transformation and image stitching as examples, the far-field light intensity of the orthogonal two-dimensional diffraction grating is maximized in the x-direction by 0 to ±2 diffraction orders. Then, it is rotated clockwise by 0° and 90° respectively. Finally, the final two-dimensional diffraction grating structure is obtained by image stitching. The final two-dimensional diffraction grating structure parameters and etching depth are determined based on the final two-dimensional diffraction grating structure.

[0100] like Figure 6 , Figure 7 The images shown are two-dimensional diffraction grating structures obtained by rotating the gratings clockwise by 30° as provided in Examples 1 and 2, respectively. Black represents the etched area, and white represents the non-etched area.

[0101] Taking rotation transformation and image stitching as examples, the far-field light intensity of the orthogonal two-dimensional diffraction grating is maximized in the x-direction by 0 to ±2 diffraction orders. Then, it is rotated clockwise by 0°, 45°, -45°, and 90° respectively. Finally, the final two-dimensional diffraction grating structure is obtained by image stitching. The final two-dimensional diffraction grating structure parameters and etching depth are determined based on the final two-dimensional diffraction grating structure.

[0102] Example 3 is an orthogonal two-dimensional diffraction grating structure obtained by maximizing the far-field light intensity of 0 to ±2 diffraction orders (5x1 lattice) in the x-direction. The orthogonal two-dimensional diffraction grating is rotated clockwise by 0° and 90° respectively, and a new two-dimensional grating structure is formed by stitching the patterns together. Example 4 is an orthogonal two-dimensional diffraction grating structure obtained by maximizing the far-field light intensity of 0 to ±2 diffraction orders (5x5 lattice) in the x-direction and y-direction respectively. The orthogonal two-dimensional diffraction grating is rotated clockwise by 0°, 45°, -45°, and 90° respectively, and a new two-dimensional grating structure is formed by stitching the patterns together.

[0103] like Figure 8 , Figure 9 The images shown are two-dimensional diffraction grating structures obtained by stitching together the graphics provided in Examples 3 and 4, respectively, where black represents the etched area and white represents the non-etched area.

[0104] The etching depth s is expressed as: Where λ is the incident light wavelength and n1 is the refractive index of the substrate material.

[0105] The two-dimensional grating structure can realize non-axisymmetric diffraction lattice patterns, unequal interval diffraction lattice patterns, bar diffraction lattice patterns, non-square lattice patterns, etc., according to actual application needs. The design structure is simple, the manufacturing process is mature, and it is easy to carry out large-scale industrial production, which can further expand its application in multiple fields.

[0106] Step 5: Perform micro-nano fabrication on the substrate based on the photolithography mask to obtain a two-dimensional beam splitting diffraction grating element.

[0107] The schematic diagram of far-field light spot array imaging of the two-dimensional diffraction grating provided in Examples 1-4 is shown below. Figure 9-16 As shown, a two-dimensional beam splitting diffraction grating element is obtained by micro-nano fabrication of the substrate.

[0108] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention.

Claims

1. A method for fabricating a two-dimensional beam-splitting diffraction grating to realize a specific dot matrix pattern, characterized in that, The method includes: According to respectively The first cost function is constructed by determining the actual required diffraction order of the beam array in the desired direction, combined with diffraction efficiency and diffraction order uniformity error. Second cost function ; By minimizing the first cost function respectively Second cost function get , y Spatial modulation coordinates of the phase change point after direction optimization; Regarding the , The spatial modulation coordinates of the phase change points after direction optimization are orthogonally multiplied and expanded to obtain the orthogonal two-dimensional diffraction grating structure parameters; The orthogonal two-dimensional grating structure is processed by at least one pattern transformation method to obtain the final two-dimensional diffraction grating structure parameters and etching depth, and a photomask is generated. The substrate is micro- and nano-fabricated according to the photolithography mask to obtain a two-dimensional beam-splitting diffraction grating element. The first cost function is minimized respectively. Second cost function get , y The spatial modulation coordinates of the phase change point after direction optimization are specifically determined by minimizing the first cost function using a computer iterative optimization algorithm. Second cost function get , y The spatial modulation coordinates of the phase change point after direction optimization; the computer iterative optimization algorithm includes simulated annealing iterative optimization algorithm and gradient descent iterative optimization algorithm; The above , The spatial modulation coordinates of the phase change points after direction optimization are orthogonally multiplied and expanded to obtain the orthogonal two-dimensional diffraction grating structure parameters, specifically: obtained through optimization. direction and Determination of spatial modulation coordinates of phase change points after direction optimization , A one-dimensional grating structure in the direction, then, the... direction and The one-dimensional grating is unfolded in an orthogonal direction to obtain an orthogonal two-dimensional grating structure; The graphic transformation methods include shearing transformation, rotation transformation, and graphic splicing.

2. The method for fabricating a two-dimensional beam-splitting diffraction grating with a specific dot matrix pattern according to claim 1, characterized in that, The simulated annealing iterative optimization algorithm minimizes the first cost function. get The spatial modulation coordinates of the phase change point after direction optimization are as follows: Set initial temperature Randomly generate the initial solution of the normalized phase change point spatial modulation coordinates. , range Obtain the first cost function ; Set each Number of iterations of the value ,make ,in , Indicates the rate of temperature decrease; For the current solution Applying a random perturbation produces a new solution in its neighborhood: ; Determine the cost function value of the new solution Increment of objective function value ; If the increment of the objective function value Then accept As the new current solution, otherwise with probability Determine whether to accept As the new current solution; At temperature Next, repeat The process of perturbation and acceptance involves performing the above steps. Determine temperature Has the termination temperature level been reached? If so, terminate the algorithm and obtain the result. The spatial modulation coordinates of the phase change point in the direction are optimized; otherwise, return the current solution. Apply random perturbations and repeat the iterative process.

3. The method for fabricating a two-dimensional beam-splitting diffraction grating with a specific dot matrix pattern according to claim 2, characterized in that, The simulated annealing iterative optimization algorithm minimizes the second cost function. get The spatial modulation coordinates of the phase change point after direction optimization are as follows: Set initial temperature Randomly generate the initial solution of the normalized phase change point spatial modulation coordinates. , range Obtain the first cost function ; Set each Number of iterations of the value ,make ,in , Indicates the rate of temperature decrease; For the current solution Applying a random perturbation produces a new solution in its neighborhood: ; Determine the cost function value of the new solution Increment of objective function value ; If the increment of the objective function value Then accept As the new current solution, otherwise with probability Determine whether to accept As the new current solution; At temperature Next, repeat The process of perturbation and acceptance involves performing the above steps. Determine temperature Has the termination temperature level been reached? If so, terminate the algorithm and obtain the result. The spatial modulation coordinates of the phase change point in the direction are optimized; otherwise, return the current solution. Apply random perturbations and repeat the iterative process.

4. The method for fabricating a two-dimensional beam-splitting diffraction grating with a specific dot matrix pattern according to claim 3, characterized in that, The orthogonal two-dimensional grating structure is processed by the aforementioned shear transformation method to obtain the final two-dimensional diffraction grating structure parameters and etching depth. Specifically, in the horizontal direction, the directed distance from each point of the orthogonal two-dimensional grating structure to a line parallel to that direction is sheared by 30° according to the proportion to obtain the final two-dimensional diffraction grating structure. The final two-dimensional diffraction grating structure parameters and etching depth are determined based on the final two-dimensional diffraction grating structure.

5. The method for fabricating a two-dimensional beam-splitting diffraction grating with a specific dot matrix pattern according to claim 4, characterized in that, The orthogonal two-dimensional grating structure is processed by the rotation transformation method and image stitching method to obtain the final two-dimensional diffraction grating structure parameters and etching depth. Specifically, the orthogonal two-dimensional diffraction grating is maximized with the target in the x-direction to achieve a far-field light intensity of 0~±2 diffraction order, and then rotated clockwise by 0° and 90° respectively. Finally, the final two-dimensional diffraction grating structure is obtained by image stitching. The final two-dimensional diffraction grating structure parameters and etching depth are determined based on the final two-dimensional diffraction grating structure.

6. The method for fabricating a two-dimensional beam-splitting diffraction grating with a specific dot matrix pattern according to claim 5, characterized in that, The orthogonal two-dimensional grating structure is processed by the rotation transformation method and image stitching method to obtain the final two-dimensional diffraction grating structure parameters and etching depth. Specifically, the orthogonal two-dimensional diffraction grating is maximized with the target in the x-direction to achieve a far-field light intensity of 0~±2 diffraction order, and then rotated clockwise by 0°, 45°, -45°, and 90° respectively. Finally, the final two-dimensional diffraction grating structure is obtained by image stitching. The final two-dimensional diffraction grating structure parameters and etching depth are determined based on the final two-dimensional diffraction grating structure.

Images