A design method of diffraction periodic structure and application of diffraction periodic structure

Abstract

The present invention relates to the technical field of optical element design, and specifically provides a design method of a diffraction periodic structure and an application of the diffraction periodic structure. According to the target function of the diffraction periodic structure, the period of the diffraction periodic structure is calculated, and the number of discrete structural units, constraints and objective functions within a single diffraction period are determined. A variable set is set, and an optimization algorithm is used to obtain an optimal solution variable set of the objective function to solve the vertex coordinates of the discrete structural unit, further obtain the diffraction periodic structure of a single diffraction period, and then the obtained diffraction periodic structure is spliced ​​to construct different diffraction devices. The present invention transforms the diffraction periodic structure design into an optimal solution for solving the vertex coordinates of the discrete structural unit, simplifies the design, and thus improves the design efficiency and the degree of freedom of the optimization design.

Description

Technical Field

[0001] The invention relates to the technical field of optical element design, and specifically provides a design method of a diffraction periodic structure and an application of the diffraction periodic structure. Background Art

[0002] Optical systems play an important role in aerospace, industrial inspection and other fields. Controlling the direction of light beam propagation is the core function of many optical devices. Most of the relevant functional unit devices in optics rely on the principles of refraction or diffraction, such as lenses and Fresnel lenses for imaging. In traditional optics, refractive devices are widely used and have achieved good results. However, refractive devices have certain limitations in terms of rapidly changing wavefront control, device thickness and versatility. Thin and light diffractive devices can make up for these shortcomings of refractive devices, especially the birth of thin and light metasurfaces has brought revolutionary changes to this field.

[0003] Metasurface is a two-dimensional planar structure composed of artificial structural units of subwavelength size, which can precisely control the phase, amplitude and polarization of light. Metasurfaces show significant advantages in light field control. They can not only achieve precise modulation of complex wavefronts, amplitude and phase, but also complete most of the functions required by traditional optical devices with extremely thin thickness. Metasurfaces show great application potential in device integration, miniaturization and lightweight. Due to its two-dimensional structure and subwavelength scale design, metasurfaces can achieve complex optical functions in a very small volume, allowing optical systems to integrate more functional modules while greatly reducing the overall size and weight. For example, metasurface lenses can achieve high-quality imaging while greatly reducing the thickness and weight of optical systems, which is particularly critical in portable devices, micro sensors and integrated photonic chips. By integrating metasurfaces into optical devices, more compact, lightweight and powerful optical systems can be achieved, providing new solutions for the miniaturization and high integration of modern optical technology.

[0004] The realization of the function of the metasurface comes from the "macro" interference superposition of each single structure after the light scattering at the "micro" scale. The metasurface can be regarded as a collection of multiple diffraction units. Therefore, the design of the diffraction unit is the core of the metasurface. At present, many metasurface diffraction units or phase libraries are constructed by scanning the structural parameters. Although this method can find better units, it is inefficient. Moreover, since this method involves a large number of parameter combinations, each possible design scheme requires complex electromagnetic simulation calculations. Untargeted parameter scanning is time-consuming and consumes huge computing resources. In addition, in terms of the coverage of the design space, this method also relies on the parameter range and resolution set a priori, resulting in the missing of some design parameters with excellent performance, which limits the diversity and innovation of the design. Although scanning parameter design has certain application value in metasurface design, its various limitations restrict its wide application in complex design tasks. Summary of the invention

[0005] In order to solve the above problems, the present invention provides a design method of a diffraction periodic structure and an application of the diffraction periodic structure. By solving the vertex coordinates of discrete structural units, the design of the diffraction periodic structure is realized, the design difficulty is reduced, and the design efficiency is improved. The designed diffraction periodic structure is then spliced ​​to construct different diffraction devices to obtain a high-precision, customizable diffraction device.

[0006] The design method of the diffraction periodic structure provided by the present invention comprises:

[0007] S1: According to the target function of the diffraction periodic structure, set the period of the diffraction periodic structure and the number of discrete structural units in each period. , the constraints that the discrete structural unit needs to satisfy and the objective function for evaluating the effect of the diffraction periodic structure;

[0008] S2: Set variable set:

[0009] ;

[0010] in, represents the horizontal coordinate of the vertex below the discrete structural unit, represents the height of the discrete structural unit, Represents the inclination angle of the line connecting the upper vertex and the lower vertex of the discrete structural unit;

[0011] Find the optimal solution variable set of the objective function among all the variable sets that satisfy the constraints;

[0012] S3: Solve the horizontal coordinates of the upper vertices of the discrete structural unit based on the optimal solution variable set;

[0013] S4: Determine the diffraction periodic structure based on the horizontal coordinates of the lower vertex and the upper vertex in the optimal solution variable set.

[0014] Preferably, the optimal solution variable set is solved based on the parameter optimization function combined with the rigorous coupled wave theory.

[0015] Preferably, the upper vertex abscissa of the discrete structural unit The solution is:

[0016] ;

[0017] in, Represents the inclination angle of the line connecting the upper vertex and the lower vertex of the discrete structural unit, Represents the serial number of the horizontal coordinate of the upper vertex or the lower vertex of any discrete structural unit, .

[0018] Preferably, the method further includes solving the ordinates of the upper and lower vertices of the discrete structural unit:

[0019] If the vertical coordinate of the vertex below the discrete structure unit is set to 0, the vertical coordinate of the vertex above the discrete structure unit is .

[0020] Preferably, the discrete structure unit comprises an incident substrate end, a discrete structure and an exit end, and the discrete structure is located between the incident substrate end and the exit end.

[0021] An application of a diffraction periodic structure, using the diffraction periodic structure obtained by the design method of the diffraction periodic structure to design a diffraction device.

[0022] Preferably, the diffraction device is a beam deflector, a beam splitter or a concave lens.

[0023] Preferably, the target function includes the diffraction angle or the output phase of the diffraction device.

[0024] Preferably, the objective functions of the beam deflector and the concave lens are:

[0025] ;

[0026] in, represents the first-order diffraction efficiency;

[0027] The constraints for both the beam deflector and the concave lens are:

[0028] ;

[0029] in, , , , , , , , , Indicates the minimum processable line width. Indicates the aspect ratio of the processed structure, Represents the difference between the abscissa of the vertex below the discrete structural unit and the abscissa of the adjacent upper vertex.

[0030] Preferably, the objective function of the beam splitter is:

[0031] ;

[0032] in, and Respectively and The diffraction efficiency of the two diffraction orders, represents the splitting ratio of the beam splitter and satisfies and are between 0 and 1, and , All represent weight coefficients;

[0033] The constraints of the beam splitter are:

[0034] ;

[0035] in, , .

[0036] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0037] The embodiment of the present invention transforms the diffraction periodic structure design into the discrete structure unit vertex coordinate optimization based on the target function. Compared with the existing design scheme of determining the structure for parameter scanning, the diffraction periodic structure design method of the present invention improves the design accuracy, reduces the design difficulty, makes the design process more flexible, and thus improves the design efficiency. The designed diffraction periodic structure is easy to process and realize. At the same time, when optimizing the vertex coordinates of the discrete structure unit, it can be compatible with many parameter optimization algorithms, and the degree of freedom of the optimization design is carried out and improved, and the optimization difficulty is reduced.

[0038] When constructing a diffraction device, the diffraction angle or output phase of the diffraction device is used as the target function, and a specific diffraction periodic structure is accurately set and spliced. The optical performance of the diffraction device can be customized according to specific application requirements, and the diffraction device can be highly customized, and the diffraction device can be accurately constructed. During the construction process, the objective function is optimized under constraints to maximize key performance indicators such as diffraction efficiency and resolution. Through optimization, the energy loss of the target diffraction order caused by high-order diffraction spots can also be reduced, thereby improving the actual application effect of the diffraction device. The diffraction periodic structure is constructed according to the diffraction angle or output phase of the diffraction device, so that the diffraction device can flexibly adapt to different application scenarios and requirements, broadening the application range of the diffraction device. The parameterization of the diffraction device construction process shortens the design cycle and improves the design efficiency of the diffraction device. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of a diffraction periodic structure design provided according to an embodiment of the present invention;

[0040] Figure 2 is a schematic diagram of a diffraction period structure provided according to an embodiment of the present invention;

[0041] Figure 3 is a schematic diagram of the distribution of discrete structures within a period provided by an embodiment of the present invention;

[0042] Figure 4 is a schematic diagram of a discrete structural unit provided according to an embodiment of the present invention;

[0043] Figure 5 is a diagram of a process of processing a diffraction periodic structure provided according to an embodiment of the present invention;

[0044] Figure 6 is a design flow chart of a beam deflector according to an embodiment of the present invention;

[0045] Figure 7 is a cross-sectional view of a small-angle beam deflector structure provided according to an embodiment of the present invention;

[0046] Figure 8 is an optical performance diagram of a large-angle beam deflector provided according to an embodiment of the present invention;

[0047] Fig. 9 is an optical performance diagram of a small-angle beam deflector provided according to an embodiment of the present invention;

[0048] Fig.10 is a schematic diagram of objective function values ​​corresponding to different numbers of iterations provided by an embodiment of the present invention;

[0049] Fig.11is a schematic diagram of optical performance of a beam splitter provided according to an embodiment of the present invention;

[0050] Fig.12 is a schematic diagram of a method for constructing a concave lens provided in an embodiment of the present invention;

[0051] Fig.13 is a flowchart for solving the period and diffraction angle of the concave lens diffraction periodic structure provided by an embodiment of the present invention;

[0052] Fig.14 is a schematic diagram of the diffraction periodic structure parameters of a concave lens provided according to an embodiment of the present invention;

[0053] Fig.15 is a schematic diagram of the optical performance of a concave lens provided according to an embodiment of the present invention;

[0054] Fig.16 It is a schematic diagram of the optimization design result of the diffraction periodic structure with phase as the objective function provided according to an embodiment of the present invention.

[0055] Reference numerals include:

[0056] Incident substrate end 1, discrete structure 2, exit end 3 DETAILED DESCRIPTION

[0057] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0058] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0059] like Figure 1 As shown, the embodiment of the present invention provides a design method of a diffraction periodic structure and an application of the diffraction periodic structure, and various diffraction devices are constructed by the designed diffraction periodic structure. The design method of the diffraction periodic structure is as follows:

[0060] S1: A diffraction periodic structure is a structure with periodic characteristics. When electromagnetic radiation such as light waves passes through or encounters such a structure, diffraction occurs. In view of its periodic characteristics, the embodiment of the present invention is designed for a one-dimensional diffraction periodic structure. When designing a diffraction periodic structure, only a diffraction periodic structure within a single diffraction period is designed, and a complete diffraction periodic structure can be obtained by splicing according to requirements.

[0061] like Figure 2As shown, it is a single diffraction period (0 to period ), the horizontal and vertical directions are the x-axis and z-axis respectively, and the y-axis is perpendicular to the x-axis and z-axis (paper surface) and extends infinitely. The three-layer structure in the figure is the incident substrate end 1, the discrete structure 2 and the output end 3 from bottom to top. The discrete structure 2 is composed of multiple discrete structural units. represents the exit angle, that is, the diffraction angle of a certain order, represents the target order emission phase, represents the incident angle, represents the refractive index of the output end 3, represents the refractive index of the incident substrate end 1, 0, That is, the starting and ending coordinates of the diffraction periodic structure.

[0062] like Figure 3 As shown, Figure 2 Schematic diagram of the discrete structure 2, in which 201 and 202 represent the first material region and the second material region within the discrete structure 2, respectively. represents the refractive index of the first material region 201, represents the refractive index of the second material region 202, represents the horizontal coordinate of the vertex below the discrete structural unit, represents the horizontal coordinate of the vertex above the discrete structural unit, represents the height of the discrete structural unit, represents the inclination angle of the line connecting the upper and lower vertices of the discrete structural unit, represents any vertex above the discrete structure 2, Represents any vertex in the vertices below the discrete structure 2.

[0063] Before designing a diffraction periodic structure, it is necessary to first clarify the target function to be achieved by the designed diffraction periodic structure, that is, the working conditions of the diffraction periodic structure, including the incident wavelength. , angle of incidence , the diffraction angle achieved by the diffraction unit And suitable diffraction periodic structure materials, etc. Among them, the incident wavelength is the wavelength of the light wave or electromagnetic wave before it enters the diffraction periodic structure, and the incident angle The incident angle of the light wave or electromagnetic wave relative to the normal line of the diffraction periodic structure. The diffraction angle is the diffraction angle of the light wave or electromagnetic wave that the diffraction unit hopes to achieve. After obtaining the target function of the diffraction periodic structure, the period of the diffraction periodic structure needs to be calculated based on these parameters. The period of a diffraction periodic structure is a physical quantity that describes the spatial distance between repeating units or features in the structure and can be calculated using the grating equation.

[0064] After determining the period of the diffraction periodic structure, it is necessary to determine the number of discrete structural units contained in each period. . These discrete structural units can be simple geometric shapes, such as rectangles, circles, etc., or more complex structures. At the same time, constraints and objective functions need to be set, such as the minimum spacing between discrete structural units, the shape and size of discrete structural units, etc., to ensure the stability and diffraction performance of the diffraction periodic structure. The objective function is used to describe the desired effect of the diffraction periodic structure, that is, its diffraction effect or performance. The physical parameters of the diffraction periodic structure, such as the phase and diffraction efficiency, can be solved using algorithms such as FEM, RCWA, and FDTD. Each diffraction periodic structure is composed of multiple discrete structural units. A single discrete structural unit is a closed area of ​​a certain material with a specific refractive index. Each discrete structural unit has four vertices. By obtaining the coordinates of the four vertices, a discrete structural unit within the diffraction period can be determined. By obtaining the vertex coordinates of all discrete structural units, the discrete structural units within the diffraction period can be obtained, and then the diffraction periodic structure can be determined.

[0065] S2: Set variable set:

[0066] ;

[0067] in, represents the horizontal coordinate of the vertex below the discrete structural unit, represents the height of the discrete structural unit, Indicates the inclination of the line connecting the upper and lower vertices of the discrete structural unit. This variable set contains various data about the discrete structural unit.

[0068] Determining the operating wavelength , the number of discrete structural units in a period Finally, according to the physical goal to be achieved by the diffraction periodic structure, for example, to achieve a specific diffraction angle or output phase , the coordinates of discrete points are continuously updated through the optimization algorithm to find the optimal solution variable set of the coordinates of discrete points that approximate the objective function. The embodiment of the present invention adopts a parameter optimization function combined with a rigorous coupled wave theory to solve the optimal solution variable set, wherein the parameter optimization function is the fmincon function in matlab.

[0069] There can be multiple sets of values ​​for the variable set here, all of which can meet the requirements of satisfying the constraints. However, among these variable sets that meet the constraints, as the optimization algorithm iterates, a set of variable sets will be found that can make the functional effect of the diffraction periodic structure most consistent with the target function that is hoped to be possessed when designing the diffraction periodic structure. This set of variable sets is the optimal solution variable set of the objective function.

[0070] S3: Optimal solution of the variable set The variable set includes the horizontal coordinates, heights, and inclinations of the lines connecting the upper and lower vertices of the lower vertex of the discrete structural unit. Based on these data, the horizontal coordinates of the upper vertex of the discrete structural unit can be calculated. The specific solution equation is as follows:

[0071] ;

[0072] in, Represents the serial number of the horizontal coordinate of the upper vertex or the lower vertex of any discrete structural unit, .

[0073] It is also necessary to solve the vertical coordinates of the vertices of the discrete structural unit. In the embodiment of the present invention, the vertical coordinates of the vertices below the discrete structural unit are set to 0, and the vertical coordinates of the vertices above the discrete structural unit are , and further obtain the coordinates of the four vertices of the discrete structural unit, namely:

[0074] ;

[0075] in, represents the horizontal coordinate of any vertex below the discrete structural unit, and Respectively represent and The horizontal coordinate of the vertex above the corresponding discrete structural unit, .

[0076] S4: The discrete structural units are arranged according to the vertex coordinates of all discrete structural units obtained by calculation, so as to obtain a diffraction periodic structure with a single diffraction period.

[0077] The embodiment of the present invention transforms the diffraction periodic structure design into the discrete structure unit vertex coordinate parameter optimization, and is compatible with many parameter optimization algorithms. The design scheme proposed in the embodiment of the present invention improves the design efficiency and the degree of freedom of the optimization design compared with the previous design scheme of determining the structure for parameter scanning.

[0078] Corresponding to the diffraction periodic structure obtained by the design method of the diffraction periodic structure, the embodiment of the present invention provides a processing method of the diffraction periodic structure. The processing process is as follows: Figure 5 As shown, the details are as follows:

[0079] J1: A material film layer 1-1 corresponding to the selected processed diffraction periodic structure is grown on the surface of the incident substrate end 1.

[0080] J2: Prepare a photoresist layer 1-2 on the material film layer 1-1.

[0081] J3: Patterning the photoresist to form a photoresist structure 1-3 by using an electron beam exposure process or a stepper lithography process including but not limited to the above.

[0082] J4: Using a tilted etching process including but not limited to, etching the material film layer 1-1 from top to bottom according to the photolithography structure 1-3 to the tilted incident substrate end 1 to form a diffraction periodic structure 1-4.

[0083] J5: Remove the photoresist structure 1-3 to obtain a diffraction periodic structure.

[0084] The diffraction periodic structure designed by the above method and the diffraction periodic structure obtained by splicing optimization can be used to construct a grating of any diffraction order, a beam deflector of any angle, a beam splitter, a diffraction lens device, etc. The embodiment of the present invention provides a method for constructing three devices, namely, a beam deflector of any angle, a beam splitter of any splitting ratio, and a concave lens based on a diffraction periodic structure, based on the above diffraction periodic structure.

[0085] Embodiment 1, as Figure 6 As shown, a diffraction periodic structure is designed according to the above diffraction periodic structure design method, and a beam deflector of any angle is constructed by the diffraction periodic structure. The specific method is as follows:

[0086] Before constructing a beam deflector, it is necessary to first clarify the target function of the beam deflector, that is, its working conditions, such as the diffraction angle or output phase performance that the beam deflector is to achieve. In Example 1 of the present invention, the inclination angle of the line corresponding to the upper and lower vertices of the discrete structural unit of the beam deflector is set to a fixed inclination angle, and the inclination angles of the lines corresponding to the upper and lower vertices of all discrete structural units are consistent, and the value is ,Right now All equal to 85°.

[0087] Diffraction angle of the beam deflector designed in Example 1 of the present invention It is set to two, that is, there are two emission angles, a large angle of 80° and a small angle of 5°, and the working wavelength is 0.64 microns, that is There are many choices of materials. In the first embodiment of the present invention, the material of the incident substrate end 1 is selected as titanium dioxide TiO 2 The material of the first material region 201 of the discrete structure 2 is titanium dioxide TiO 2 , the material of the second material region 202 is air, and the material of the output end 3 is air, correspondingly, , which is the refractive index of titanium dioxide, , which is the refractive index of air.

[0088] According to the target function of the above beam deflector, the period of the diffraction periodic structure is determined , the number of discrete structural units , objective function and constraints.

[0089] Specifically, the period of the diffraction periodic structure can be determined by the diffraction grating equation, and the period of the diffraction periodic structure obtained by calculation is:

[0090] ;

[0091] in, represents the selected order, and its sign depends on the relative direction of the horizontal components of the incident wave vector and the diffracted wave vector. The value is 1.

[0092] For the number of discrete structural units in a period , whose value is limited by the minimum processing line width At the same time, a small number of discrete structural units will lead to a low sampling rate, which will further affect the optical performance. Therefore, in Example 1 of the present invention, the number of discrete structural units is The value is , and then consider the constraints on processing capacity.

[0093] The main purpose of the beam deflector is to achieve a specific angle deflection of the light beam, wherein the light beam with the deflection angle is a high-order light beam of a diffraction periodic structure. The value is 1, so the objective function In order to maximize the diffraction order, Example 1 of the present invention applies the parameter optimization function combined with the rigorous coupled wave theory to solve the objective function The optimal solution variable set, where the parameter optimization function is the fmincon function in Matlab, and the objective function target value can be expressed as ,in, Represents the first-order diffraction efficiency.

[0094] The design optimization process of the first embodiment of the present invention takes into account the practical application of the beam deflector. The rationality of the diffraction periodic structure and the possibility of processing the diffraction periodic structure are considered in the design stage. For the processing technology, there are two relatively important parameters, namely, the minimum line width of the process Aspect ratio of the processed structure To design a reasonable diffraction periodic structure, it is necessary to set the constraints reasonably:

[0095] For the minimum processable line width , constraints need to be considered ,

[0096] For the aspect ratio of the processed structure , constraints need to be considered ,

[0097] When the inclination angle of the discrete structure 2 is too large, a visual "overlap" phenomenon will occur when looking down at the discrete structure 2. To avoid the "overlap" phenomenon of the discrete structure 2, it is necessary to ensure that the vertices below The horizontal coordinate is greater than the upper vertex The horizontal coordinate of ,Right now , Represents the vertex below the discrete structural unit The horizontal coordinate of the adjacent upper vertex At the same time, this difference is also restricted by the processing technology. Usually It can be greater than twice the processing line width accuracy of the processing equipment.

[0098] At the same time, considering the rationality of discrete structure 2, it is necessary to consider the constraints .

[0099] Embodiment 1 of the present invention applies parameter optimization function combined with strict coupled wave theory to perform optimization design, wherein the parameter optimization function is the fmincon function in MATLAB, and the constraint condition adopts linear constraint. Then the above constraint condition can be converted into a matrix form for expression, that is, , as follows:

[0100] For the minimum processable line width , the corresponding matrix is ​​expressed as and ,but:

[0101] ;

[0102] ;

[0103] Among them, the matrix The dimensions are: ,matrix The dimensions are: .

[0104] For the aspect ratio of the processed structure , the corresponding matrix is ​​expressed as and ,but:

[0105] ;

[0106] ;

[0107] Among them, the matrix The dimensions are: ,matrix The dimensions are: .

[0108] For the rationality of the discrete structure 2, the corresponding matrix is ​​expressed as and ,but:

[0109] ;

[0110] ;

[0111] Among them, the matrix The dimensions are: ,matrix The dimensions are: .

[0112] In summary, the matrix ,matrix , the final constraints are:

[0113] .

[0114] Embodiment 1 of the present invention uses parameter optimization function combined with rigorous coupled wave theory to optimize the objective function under the above constraints. The optimization design is performed to solve the optimal solution variable set, where the parameter optimization function is the fmincon function in MATLAB. By judging whether the number of iterations executed is greater than the maximum number of iterations and whether the calculated result is less than the maximum tolerance err, the solution is updated or the optimization is stopped.

[0115] Under the above constraints, the objective function is optimized by combining the optimization function with the rigorous coupled wave theory to obtain the optimal solution variable set corresponding to the beam deflector. , that is, the horizontal coordinate of the vertex below the discrete structural unit, the height of the discrete structural unit, and the optimal value of the inclination of the corresponding connecting line between the upper and lower vertices of the discrete structural unit are obtained.

[0116] The coordinates of all the upper vertices of the discrete structural unit are calculated by obtaining the horizontal coordinates of the vertices below the discrete structural unit, the height of the discrete structural unit, and the merit of the inclination of the corresponding connecting line between the upper and lower vertices of the discrete structural unit. In Example 1 of the present invention, the two horizontal coordinates of the discrete structural unit are grouped together, that is, the obtained horizontal coordinates are:

[0117] ;

[0118] Each group represents the horizontal coordinates of the two vertices below a discrete structural unit. Two upper vertices and two lower vertices can determine a discrete structural unit. The cross-section of a discrete structural unit can be obtained by simply inserting the two upper vertices into the above grouping.

[0119] The solution method for the ordinate of the discrete structural unit is as follows:

[0120] The vertical coordinate of the vertex below the discrete structure unit is set to 0, and the two vertical coordinates of the vertex above are , then the coordinates of the four vertices of the single discrete structural unit are:

[0121] .

[0122] According to the above vertex coordinates, we can obtain Figure 7 The cross section of the diffraction periodic structure shown in FIG. 1 is used to construct a beam deflector according to the diffraction angle or the output phase of the beam deflector, thus obtaining a large-angle or small-angle beam deflection device. The beam deflection performance is shown in FIG. Figure 8 and Fig. 9 In the first embodiment of the present invention, it is only necessary to form a one-dimensional array of the obtained diffraction periodic structure.

[0123] Embodiment 2: A beam splitter with an arbitrary splitting ratio is constructed based on the above diffraction periodic structure, and the construction method is as follows:

[0124] Before constructing a beam splitter, it is necessary to first clarify the target function of the beam splitter, that is, its working conditions, such as the diffraction angle or output phase performance to be achieved by the beam splitter. In embodiment 2 of the present invention, the discrete structure 2 of the beam splitter is set to have no tilt angle. ,Right now are all equal to 90°, and the working wavelength is 0.64 microns, that is, The material is the same as that in Example 1 of the present invention, that is, the material of the incident substrate end 1 is selected to be titanium dioxide TiO 2 The material of the first material region 201 of the discrete structure 2 is titanium dioxide TiO 2 , the material of the second material region 202 is air, and the material of the output end 3 is air, correspondingly, , which is the refractive index of titanium dioxide, , which is the refractive index of air.

[0125] The beam splitter of embodiment 2 of the present invention aims to achieve a 1:1 splitting of two beams with a half angle of 55° and determine the diffraction angle of the positive first order. .because , then the minus first order diffraction angle is , meeting the requirement of beam splitting with a half angle of 55°.

[0126] According to the target function of the above beam splitter, the period of the diffraction periodic structure is determined , the number of discrete structural units , objective function and constraints.

[0127] Embodiment 2 of the present invention changes the objective function of the beam splitter to Defined as:

[0128] ;

[0129] in, and Respectively and The diffraction efficiency of the two diffraction orders, represents the splitting ratio of the beam splitter and satisfies and are between 0 and 1, and , Both represent weight coefficients, which are used to ensure that the final splitting ratio of the two beams is close to the target value and the diffraction efficiency of each beam is large enough. In Example 2 of the present invention, the objective function The parameter values ​​are: , , , .exist Under the condition of When , the "asymmetric" beam splitting of the beam splitter can be achieved.

[0130] In Embodiment 2 of the present invention, for the period of the diffraction periodic structure The solution method is the same as that of the diffraction periodic structure period in the beam deflector in Example 1 of the present invention. The solution method is the same as that of , when determining the period of the diffraction periodic structure through the diffraction grating equation, the diffraction order is used and and its corresponding diffraction angle and After calculating the period, the larger period is selected as the period of the final diffraction periodic structure of the beam splitter. It should be noted that and and its corresponding diffraction angle and These four parameters are not completely independent, but are mutually determined.

[0131] In Embodiment 2 of the present invention, the number of discrete structural units of the diffraction periodic structure is , its value and restrictions are the same as those in Example 1 of the present invention, that is, its value is limited by the minimum processing line width At the same time, a small number of discrete structural units will lead to a low sampling rate, which will further affect the optical performance. Therefore, in Example 2 of the present invention, the number of discrete structural units is also The value is , and then consider the constraints on processing capacity.

[0132] Regarding the constraint conditions, the constraint conditions in the second embodiment of the present invention are the same as those in the first embodiment of the present invention. However, in the second embodiment of the present invention, the discrete structure 2 of the beam splitter is set to have no inclination angle. ,Right now are all equal to 90°, so the final linear constraint matrix ,matrix .

[0133] In the second embodiment of the present invention, under the above constraints, the objective function of the second embodiment is optimized by combining the parameter optimization function with the rigorous coupled wave theory algorithm. Perform optimization design, where the parameter optimization function is the fmincon function in matlab. By judging whether the number of iterations executed is greater than the maximum number of iterations and whether the calculated result is less than the maximum tolerance err, update the solution or stop the optimization. During the iteration process, the objective function The target value changes as Fig.10 shown.

[0134] Under the above constraints, the objective function is optimized by combining the optimization function with the rigorous coupled wave theory to obtain the optimal solution variable set corresponding to the beam splitter. , that is, the horizontal coordinate of the vertex below the discrete structural unit, the height of the discrete structural unit, and the optimal value of the inclination of the corresponding connecting line between the upper and lower vertices of the discrete structural unit are obtained.

[0135] The method for solving the vertex coordinates of the discrete structural unit in Example 2 of the present invention is the same as that in Example 1 of the present invention, but it should be noted that in Example 2 of the present invention, the discrete structural unit has no inclination angle, so the horizontal coordinate of the upper vertex is , as follows:

[0136] By obtaining the horizontal coordinate of the vertex below the discrete structural unit, the height of the discrete structural unit, and the figure of merit of the inclination of the corresponding line connecting the upper and lower vertices of the discrete structural unit, the coordinates of all the upper vertices of the discrete structural unit are calculated, and the vertex coordinates of all the discrete structural units are further obtained. Embodiment 2 of the present invention divides the two horizontal coordinates of the discrete structural unit into one group, that is, the horizontal coordinate obtained is:

[0137] ;

[0138] Each group represents the horizontal coordinates of the two vertices below a discrete structural unit. Two upper vertices and two lower vertices can determine a discrete structural unit. The cross-section of a discrete structural unit can be obtained by simply inserting the two upper vertices into the above grouping.

[0139] The solution method for the ordinate of the discrete structural unit is as follows:

[0140] The vertical coordinate of the vertex below the discrete structure unit is set to 0, and the two vertical coordinates of the vertex above are , then the coordinates of the four vertices of the single discrete structural unit are:

[0141] .

[0142] The above-mentioned solution process is performed on each discrete structural unit to obtain a diffraction periodic structure profile, and a diffraction periodic structure is obtained, and a beam splitter is constructed according to the diffraction angle or output phase required in a specific space. Example 2 of the present invention only needs to form a one-dimensional array of the obtained diffraction periodic structure.

[0143] Through the above optimization process, a beam splitter with a splitting ratio of 1:1 and a beam half angle of 55° is obtained. Its optical performance is as follows: Fig.11 shown.

[0144] Example 3: A concave lens is constructed based on the above diffraction periodic structure. The construction method is as follows:

[0145] Before constructing the beam splitter, it is necessary to first clarify the target function of the concave lens, that is, its working conditions, such as the diffraction angle or output phase performance to be achieved by the concave lens. In Example 3 of the present invention, the working wavelength of the concave lens is set to 0.64 microns, that is, The material is the same as that in Example 1 of the present invention, that is, the material of the incident substrate end 1 is selected to be titanium dioxide TiO 2 The material of the first material region 201 of the discrete structure 2 is titanium dioxide TiO 2 , the material of the second material region 202 is air, and the material of the output end 3 is air, correspondingly, , which is the refractive index of titanium dioxide, , which is the refractive index of air.

[0146] like Fig.12 As shown, unlike beam deflectors and beam splitters, building a concave lens requires a combination of diffraction periodic structures with different diffraction angles. First, determine the focal length of the concave lens to be built. ,diameter Considering that the on-axis points have a large transmittance, we define , and define , defining the diameter of the concave lens According to the target function of the above concave lens, the diffraction angle of the light beam for each diffraction periodic structure of the concave lens is determined. , and cycle Then, the number of discrete structural units of each diffraction periodic structure is , objective function , and constraints are determined one by one.

[0147] According to the above prerequisites, each period and diffraction angle of the diffraction periodic structure is calculated by the following loop, and the loop calculation method is as follows Fig.13 As shown, the details are as follows:

[0148] Define a sequence number K , represents the serial number of the diffraction periodic structure required to construct the concave lens, let , diffraction angle array ,cycle ,judge Is it established:

[0149] If not, the calculated diffraction angle and period results are output, and the process ends;

[0150] If established, then ,calculate , , re-judge Whether it is established, the process loops until the calculated diffraction angle and period results are output, and the process ends.

[0151] The parameters of each diffraction periodic structure required to construct the concave lens are obtained through the above calculations. The diffraction periodic structure parameters required to construct the concave lens obtained in Example 3 of the present invention are as follows: Fig.14 As shown, 2 is a discrete structure, To construct the period of different diffraction periodic structures required for concave lenses, Represents the number of diffraction periodic structures required to construct a concave lens.

[0152] For the number of discrete structural units in a period , the number of discrete structural units in Example 3 of the present invention and in Example 1 and Example 2 The same value is taken as the number of discrete structural units The value is limited by the minimum processing line width At the same time, a small number of discrete structural units will lead to a low sampling rate, which will further affect the optical performance. Therefore, in Example 3 of the present invention, the number of discrete structural units is also The value is , and then consider the constraints on processing capacity.

[0153] In Embodiment 3 of the present invention, the constraint conditions and the objective function Constraints and objective functions corresponding to the first embodiment of the present invention same.

[0154] In the third embodiment of the present invention, under the above constraints, the objective function of the third embodiment is optimized by combining the parameter optimization function with the rigorous coupled wave theory algorithm. The optimization design is performed, in which the parameter optimization function is the fmincon function in Matlab. The solution is updated or the optimization is stopped by judging whether the number of iterations executed is greater than the maximum number of iterations and whether the calculated result is less than the maximum tolerance err.

[0155] Under the above constraints, the objective function is optimized by combining the optimization function with the rigorous coupled wave theory to obtain the optimal solution variable set corresponding to the concave lens. , that is, the horizontal coordinate of the vertex below the discrete structural unit, the height of the discrete structural unit, and the optimal value of the inclination of the corresponding connecting line between the upper and lower vertices of the discrete structural unit are obtained.

[0156] By obtaining the horizontal coordinate of the vertex below the discrete structural unit, the height of the discrete structural unit and the figure of merit of the inclination of the corresponding connecting line between the upper and lower vertices of the discrete structural unit, the coordinates of all the upper vertices of the discrete structural unit are calculated. The calculation method of the horizontal coordinate of the upper vertex is the same as that in Example 1 of the present invention.

[0157] The solution method for the ordinate of the discrete structural unit is as follows:

[0158] The vertical coordinate of the vertex below the discrete structure unit is set to 0, and the two vertical coordinates of the vertex above are , and finally obtain all vertex coordinates of the discrete structural unit, and further obtain the diffraction periodic structure of multiple specific diffraction angles for constructing the concave lens.

[0159] According to the diffraction angle or output phase of the concave lens, multiple diffraction periodic structures with specific diffraction angles are constructed into a concave lens. When constructing, it is necessary to consider the periodic parameters of the previous periodic structure to avoid overlap, that is, The target diffractive concave lens can be obtained by rotating the obtained structure 360°.

[0160] The optical properties of the constructed concave lens are as follows Fig.15 As shown, based on the solution of constructing a concave lens by splicing diffraction periodic structures proposed in Example 3 of the present invention, Fig.15 The divergence performance of the concave lens on the light beam is shown. It can be seen that the diffraction periodic structure of the "near-axis position" (small-angle beam deflection area) needs to be carefully designed to ensure the smoothness of the wavefront. For the construction of the diffraction concave lens, the following can be used: Fig.16 The phase shown is the design of the optimization function, and then the target diffraction lens is constructed based on the distribution of the spatial position phase.

[0161] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

[0162] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for designing a diffraction periodic structure, characterized in that: include: S1: According to the target function of the diffraction periodic structure, set the period of the diffraction periodic structure and the number of discrete structural units in each period. , constraints that the discrete structural unit needs to satisfy and an objective function for evaluating the effect of the diffraction periodic structure; S2: Set variable set: ； in, represents the horizontal coordinate of the vertex below the discrete structural unit, represents the height of the discrete structural unit, Represents the inclination angle of the line connecting the upper vertex and the lower vertex of the discrete structural unit; Solve the optimal solution variable set of the objective function in all the variable sets that satisfy the constraint conditions, and solve the optimal solution variable set according to the parameter optimization function combined with the strict coupled wave theory; S3: solving the abscissa of the upper vertex of the discrete structural unit according to the optimal solution variable set; the abscissa of the upper vertex of the discrete structural unit The solution is: ； in, Represents the inclination angle of the line connecting the upper vertex and the lower vertex of the discrete structural unit, Represents the serial number of the horizontal coordinate of the upper vertex or the lower vertex of any discrete structural unit, , The horizontal coordinate of any vertex below the discrete structural unit; S4: Arrange the lower vertex horizontal coordinate and the upper vertex horizontal coordinate in the optimal solution variable set to determine the diffraction periodic structure.

2. The design method of the diffraction periodic structure according to claim 1, characterized in that: It also includes solving the ordinates of the vertices above and below the discrete structural unit: The ordinate of the vertex below the discrete structural unit is set to 0, and the ordinate of the vertex above the discrete structural unit is .

3. The design method of the diffraction periodic structure according to claim 1, characterized in that: The discrete structure unit comprises an incident substrate end, a discrete structure and an exit end, and the discrete structure is located between the incident substrate end and the exit end.

4. An application of a diffraction periodic structure, using the diffraction periodic structure obtained by the design method of a diffraction periodic structure as described in any one of claims 1 to 3 to design a diffraction device.

5. The use of the diffraction periodic structure as claimed in claim 4, characterized in that: The diffraction device is a beam deflector, a beam splitter or a concave lens.

6. The use of the diffraction periodic structure as claimed in claim 5, characterized in that: The target function includes the diffraction angle or the output phase of the diffraction device.

7. The use of the diffraction periodic structure as claimed in claim 5, characterized in that: The objective functions of the beam deflector and the concave lens are: ； in, represents the first-order diffraction efficiency; The constraints of the beam deflector and the concave lens are: ； in, , , , , , , , , Indicates the minimum processable line width. Indicates the aspect ratio of the processed structure, Represents the difference between the abscissa of the vertex below the discrete structural unit and the abscissa of the adjacent upper vertex.

8. The use of the diffraction periodic structure as claimed in claim 5, characterized in that: Place The objective function of the beam splitter is: ； in, and Respectively and The diffraction efficiency of the two diffraction orders, represents the splitting ratio of the beam splitter and satisfies and are between 0 and 1, and , All represent weight coefficients; The constraints of the beam splitter are: ； in, , .

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