Angle filter design method, device and filter of non-periodic multilayer film structure

Abstract

The present invention discloses an angle filter design method, device and filter of a non-periodic multilayer film structure. The design method includes: constructing a fitness function, whose input is transmittance and whose output is a fitness value characterizing the performance of the angle filter; determining the initial thickness of each layer of dielectric film as the current thickness within a preset thickness range; importing the current thickness into a transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure; inputting the transmittance into the fitness function to determine whether the fitness value outputted by the fitness function reaches a preset threshold value, if the preset threshold value is not reached, optimizing the current thickness of each layer of dielectric film, and recalculating the corresponding transmittance according to the optimized thickness, iteratively calculating the fitness function, until the fitness value outputted by the fitness function reaches the preset threshold value, and then taking the current thickness of each layer of dielectric film as the design result. The filter designed by the present invention can achieve good bandwidth and thickness robustness.

Description

Technical Field

[0001] The present invention relates to the field of micro-nano optical light field regulation, and in particular to an angle filter design method, device and filter of a non-periodic multilayer film structure. Background Art

[0002] Angle filters are devices that can control the transmission or reflection of waves at specific frequencies and different incident directions, and can select light waves from different incident directions. To achieve the above purpose, the angle filter is required to achieve high transmittance within a certain angle range and low transmittance within other angle ranges. Among them, collimating filters that achieve high transmittance at normal incidence and suppress other angles are the most widely used, and have a broad market in the fields of projection display, mobile devices, and augmented / virtual reality.

[0003] Common methods for achieving angle filtering include one-dimensional gratings, metasurfaces, and photonic crystals. Although the production of one-dimensional gratings is relatively mature, there are multiple diffraction directions, so there is still a part of light emitting at a large angle; and the metasurface solution requires a lot of time and cost from design to production, which is not conducive to actual industrial production. Periodic multilayer film structures, also known as one-dimensional photonic crystals, are often used as distributed Bragg reflectors to achieve high reflectivity for a certain wavelength bandwidth; general one-dimensional photonic crystals are often designed as periodic equal-thickness structures as angle filters, that is, different dielectric film layers are arranged periodically, and the same dielectric film layers have the same thickness. Once the design accuracy cannot be achieved due to the existence of preparation errors, the periodic structure will be destroyed, and the error from the design value is often large.

[0004] In summary, existing angular filter design methods cannot achieve good bandwidth and thickness robustness.

[0005] The disclosure of the above background technology content is only used to assist in understanding the inventive concept and technical solution of the present invention. It does not necessarily belong to the prior art of this patent application, nor does it necessarily provide technical guidance. In the absence of clear evidence that the above content has been disclosed before the filing date of this patent application, the above background technology should not be used to evaluate the novelty and creativity of the present application. Summary of the invention

[0006] The object of the present invention is to provide an angular filter capable of achieving good bandwidth and thickness robustness and a design method thereof.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A method for designing an angle filter based on a non-periodic multilayer film structure, wherein the angle filter comprises a non-periodic multilayer film structure, wherein the non-periodic multilayer film structure comprises a plurality of dielectric films sequentially stacked along a thickness direction of the non-periodic multilayer film structure, and at least two layers of the dielectric films have different thicknesses. The method comprises the following steps:

[0009] S1: constructing a fitness function, wherein the input parameter of the fitness function includes the transmittance of the non-periodic multilayer film structure, and the output parameter of the fitness function is a fitness value characterizing the performance of the angle filter;

[0010] S2: determining the initial thickness of each dielectric film within a preset thickness range, and using the initial thickness as the current thickness;

[0011] S3: importing the current thickness of each dielectric film layer into the transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure;

[0012] S4: inputting the transmittance into the fitness function, and determining whether the fitness value output by the fitness function reaches a preset threshold;

[0013] S5: If the fitness value output by the fitness function does not reach the preset threshold, the current thickness of each dielectric film is optimized, the optimized thickness is used as the current thickness, and the process returns to S3 until the fitness value output by the fitness function reaches the preset threshold;

[0014] S6: The current thickness of each dielectric film layer is used as a design result.

[0015] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the fitness function is used to perform weighted calculation on the transmittance of different wavelengths, angles and thicknesses to obtain the fitness value;

[0016] The fitness value is obtained by weighted calculation of the transmittances of different wavelengths, angles and thicknesses, including:

[0017] Obtaining a preset wavelength range and a preset angle range; wherein the preset angle range includes a high transmission angle range and a low transmission angle range, the preset wavelength range includes multiple wavelengths, and the high transmission angle range and the low transmission angle range both include multiple incident angles;

[0018] Performing a weighted summation on the current transmittances corresponding to all wavelengths within the preset wavelength range to obtain the fitness value;

[0019] The current transmittance is related to the average transmittance within the high transmission angle range and the average transmittance within the low transmission angle range.

[0020] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the weighted sum of the current transmittances corresponding to all wavelengths within the preset wavelength range to obtain the fitness value includes:

[0021] Inputting the current wavelength, the current thickness and each incident angle in the high transmission angle range into the transmission matrix to obtain a plurality of transmittances; averaging all the transmittances to obtain an average high transmittance;

[0022] Input the current wavelength, the current thickness and each incident angle in the low transmission angle range into the transmission matrix to obtain a plurality of transmittances; average all the transmittances to obtain an average low transmittance;

[0023] The average high transmittance and the average low transmittance are weightedly summed to obtain the current transmittance.

[0024] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the input parameter of the fitness function also includes the thickness of each dielectric film of the multilayer film structure;

[0025] The fitness function is:

[0026]

[0027] in, W (λ)= exp (-0.5((λ-λ center ) / σ) 2 );

[0028] in, fitness is the fitness value, W (λ) is the wavelength weight, λ center is the central wavelength of the preset wavelength range, σ is the standard deviation of the Gaussian distribution, T(λ,θ,d) is the wavelength λ, angle i ,thickness d Corresponding transmittance; ω1 is the high transmission angle range i t The corresponding transmittance weight, ω2 is the low transmission angle range i 0 The corresponding transmittance weight; | i t | is the number of angles in the high transmission angle range, | i 0 | is the number of angles in the low transmission angle range; l max is the maximum incident wavelength in the preset wavelength range, lmin is the minimum incident wavelength in the preset wavelength range.

[0029] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the current thickness of each dielectric film layer is introduced into the transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure, including:

[0030] Calculating a value of a transmission matrix based on each wavelength in a preset wavelength range, the current thickness, and each incident angle in a preset angle range;

[0031] Based on the value of the transmission matrix, a transmission coefficient is calculated;

[0032] The transmittance is calculated based on the transmission coefficient.

[0033] Further, based on any one of the above technical solutions or a combination of multiple technical solutions, the multilayer film structure j The transmission matrix M of the dielectric film j for

[0034]

[0035] Among them, δ j =(2π / l j )× n j × d j ×cos i j , i j For the j The incident angle of the dielectric film is l j For the j The incident wavelength of the dielectric film, δ j For the j The phase difference of the dielectric film, or j For the j The optical admittance of the dielectric film, n j For the j The refractive index of the dielectric film, d j For the j The thickness of the dielectric film, .

[0036] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the transmission matrix of the multilayer film structure is expressed as:

[0037]

[0038] in, N is the number of dielectric films, A、B、C、D for N The four matrix elements of the transmission matrix of the dielectric film.

[0039] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the calculation formula of the transmission coefficient t is as follows:

[0040]

[0041] Among them, η in =n in ×cos i in , η out =n out ×cos i out ;

[0042] The calculation formula of transmittance T is as follows: T = t × t *, where η in for N The optical admittance of the incident medium of the dielectric film structure, n in is the refractive index of the incident medium, i in for N The light incident angle of the dielectric film structure; η out for N The optical admittance of the output medium of the multi-layer dielectric film structure, n out is the refractive index of the output medium, i out for N Light emission angle of the dielectric film structure; t *for t The transpose of .

[0043] Further, based on any one of the above technical solutions or a combination of multiple technical solutions, after S5 and before S6, the method further includes:

[0044] Based on the thickness random error and the current thickness, the fitness value output by the corresponding fitness function is calculated;

[0045] If the fitness value reaches the preset threshold, S6 is executed; otherwise, the current thickness of each dielectric film is optimized, the optimized thickness is used as the current thickness, and the process returns to S3.

[0046] Further, based on any one of the above-mentioned technical solutions or a combination of multiple technical solutions, the step of calculating the fitness value based on the thickness random error and the current thickness includes:

[0047] Assume i The current thickness value of the layer is h nm, i The random error of the thickness of the layer is ±anm. i The thickness range of the layer is ( h -a)~( h +a)nm;

[0048] Calculate the i The transmittances corresponding to multiple thicknesses within the thickness range of the layer are averaged to obtain an average transmittance;

[0049] The average transmittance is input into the fitness function to obtain the fitness value output by the fitness function.

[0050] According to another aspect of the present invention, there is provided an angular filter design device based on a non-periodic multilayer film structure, which is used to design an angular filter including a non-periodic multilayer film structure, wherein the non-periodic multilayer film structure includes a plurality of dielectric films stacked in sequence along the thickness direction of the non-periodic multilayer film structure, and at least two layers of the dielectric films have different thicknesses, and the design device includes the following modules:

[0051] A fitness function construction module is used to construct a fitness function, wherein the input parameter of the fitness function includes the transmittance of the non-periodic multilayer film structure, and the output parameter of the fitness function is a fitness value characterizing the performance of the angle filter;

[0052] An initial parameter generation module is used to determine the initial thickness of each dielectric film layer within a preset thickness range and use the initial thickness as the current thickness;

[0053] A transmittance calculation module is used to import the current thickness of each dielectric film layer into the transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure;

[0054] The optimization module inputs the transmittance into the fitness function, determines whether the fitness value output by the fitness function reaches a preset threshold value, and if the fitness value output by the fitness function does not reach the preset threshold value, optimizes the current thickness of each layer of the dielectric film, and imports the optimized thickness into the transmittance calculation module to obtain the transmittance of each dielectric film of the corresponding multi-layer film structure; and iteratively calculates the fitness function according to the transmittance until the fitness value output by the fitness function reaches the preset threshold value, and then takes the current thickness of each layer of the dielectric film as the design result.

[0055] According to another aspect of the present invention, a filter with a non-periodic multilayer film structure is provided, comprising a non-periodic multilayer film structure, wherein the non-periodic multilayer film structure comprises a plurality of dielectric films stacked in sequence along a thickness direction of the non-periodic multilayer film structure, and at least two layers of the dielectric films have different thicknesses;

[0056] The thickness of each dielectric film layer of the angle filter is determined by using the angle filter design method based on the non-periodic multilayer film structure as described above.

[0057] The beneficial effects brought by the technical solution provided by the present invention are as follows:

[0058] a. The multilayer film structure designed in the present invention has different thicknesses for each layer of the medium, which changes the thickness periodicity of the photonic crystal. The thickness of each layer is optimized, thereby improving the bandwidth and thickness robustness of the angle filter.

[0059] b. The present invention calculates the reflectivity and transmittance of the multilayer film system through the transfer matrix algorithm, which greatly improves the overall calculation speed and ensures the accuracy of the design results.

[0060] c. The transfer matrix algorithm is combined with the particle swarm algorithm to optimize the fitness function composed of multiple parameters, so that the multilayer film structure can realize the function of angle filtering. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0062] Figure 1 A schematic flow chart of a method for designing an angle filter based on a non-periodic multilayer film structure according to the present invention;

[0063] Figure 2 A schematic flow chart of an angular filter design method for setting a thickness random error to characterize the robustness effect of the filter provided by an exemplary embodiment of the present invention;

[0064] Figure 3 A schematic diagram of a multilayer film system structure provided for an exemplary embodiment of the present invention;

[0065] Figure 4 A schematic diagram showing how the transmittance of a multilayer film system varies with the incident angle provided for an exemplary embodiment of the present invention;

[0066] Figure 5A schematic diagram showing how the transmittance of a multilayer film system after adding random errors varies with the incident angle provided by an exemplary embodiment of the present invention;

[0067] Figure 6 A schematic block diagram of an angular filter design device based on a non-periodic multilayer film structure provided for an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0069] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, device, product or equipment that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or equipment.

[0070] The present invention provides a design method applicable to filters based on periodic multilayer film structures, and also applicable to filters based on non-periodic multilayer film structures. In particular, after the stacking sequence of the non-periodic multilayer film structure is designed, the design method provided by the present invention can be used to determine the optimized thickness of each dielectric film layer that can meet the filter performance; the design method provided by the present invention is not limited to a specific multilayer film structure.

[0071] In one embodiment of the present invention, a method for designing an angle filter based on a non-periodic multilayer film structure is provided. Figure 1 As shown, the angle filter includes a non-periodic multilayer film structure, the non-periodic multilayer film structure includes multiple dielectric films stacked in sequence along the thickness direction of the non-periodic multilayer film structure, at least two dielectric films have different thicknesses, and the design method includes the following steps:

[0072] S1: construct a fitness function, the input parameters of the fitness function include the transmittance of the non-periodic multilayer film structure, and the output parameters of the fitness function are the fitness values ​​that characterize the performance of the angle filter.

[0073] By optimizing the fitness function composed of multiple parameters, the multilayer film structure can achieve the function of angle filtering. The fitness function is used to perform weighted calculations on the transmittances of different wavelengths and angles, maximize the transmittance of the target angle range, minimize the transmittance of the remaining angle ranges, and obtain the weighted sum of the transmittances at all wavelengths and angles as the output parameter of the fitness function, i.e., the fitness value. The higher the fitness value, the better the filtering effect.

[0074] S2: Determine the initial thickness of each dielectric film within a preset thickness range, and use the initial thickness as the current thickness.

[0075] In one embodiment, a random algorithm is used to randomly generate an initial value of the thickness of the dielectric film from a preset dielectric film thickness range, which can reduce the amount of calculation; in addition, considering that the actual thickness range of the multilayer film will not be very large, it is practical to randomly generate a thickness value as the initial thickness within a certain preset thickness range.

[0076] S3: Import the current thickness of each dielectric film layer into the transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure.

[0077] Based on each wavelength in a preset wavelength range, the current thickness, and each incident angle in a preset angle range, the value of the transmission matrix is ​​calculated; then, based on the value of the transmission matrix, the transmission coefficient is calculated; and based on the transmission coefficient, the transmittance is calculated.

[0078] S4: Input the transmittance into the fitness function, and determine whether the fitness value output by the fitness function reaches a preset threshold.

[0079] The specific threshold setting value depends on the design accuracy requirement of the angle filter. If the accuracy requirement is higher, the fitness threshold is higher. For example, the preset threshold is 0.88, 0.9 or 0.92, or even 0.99, which represents that the overall transmittance performance of the optimized design within the target wavelength and angle range reaches an ideal 88%, 90% or 92%, or even 99%; if the accuracy requirement is general, the preset threshold can be appropriately lowered, such as the preset threshold is 0.85, 0.86 or 0.87; if the accuracy requirement is lower, the preset threshold is lower, such as the preset threshold is 0.80, 0.82 or 0.84.

[0080] S5: If the fitness value output by the fitness function does not reach the preset threshold, the current thickness of each layer of the dielectric film is optimized, and the optimized thickness is used as the current thickness.

[0081] After the optimized thickness is used as the current thickness, the process returns to S3 until the fitness value output by the fitness function reaches a preset threshold.

[0082] S6: If the fitness value output by the fitness function reaches a preset threshold, the current thickness of each dielectric film layer is used as a design result.

[0083] The present invention provides an angular filter design method capable of achieving good bandwidth. The present invention calculates the reflectivity and transmittance of a multilayer film system through a transfer matrix algorithm, which greatly improves the overall calculation speed and ensures the accuracy of the design results.

[0084] The specific implementation method of importing the thickness into the transmission matrix to calculate the transmittance of the non-periodic multilayer film structure in step S3 is described in detail below:

[0085] S31: Import the thickness into the calculation formula of the transmission matrix to obtain the matrix elements of the transmission matrix.

[0086] Multilayer film structure j The transmission matrix M of the dielectric film j for:

[0087]

[0088] Among them, δ j =(2π / l j )× n j × d j ×cos i j , i j For the j The incident angle of the dielectric film is l j For the j The incident wavelength of the dielectric film, δ j For the j The phase difference of the dielectric film, or j For the j The optical admittance of the dielectric film, n j For the j The refractive index of the dielectric film, d j For the j The thickness of the dielectric film, .

[0089] The transmission matrix of the multilayer film structure is expressed as:

[0090]

[0091] in, N is the number of dielectric films, A、B、C、D for N The four matrix elements of the dielectric film transmission matrix.

[0092] S32: Calculate the transmission coefficient using the matrix elements of the transmission matrix.

[0093] In getting the matrix elements A、B、C、D After that, the transmission coefficient t The calculation formula is as follows:

[0094]

[0095] Among them, η in =n in ×cos i in , η out =n out ×cos i out ; η in for N The optical admittance of the incident medium of the dielectric film structure, n in is the refractive index of the incident medium, i in for N The light incident angle of the dielectric film structure; η out for N The optical admittance of the output medium of the multi-layer dielectric film structure, n out is the refractive index of the output medium, i out for N The light emission angle of the multi-layer dielectric film structure.

[0096] S33: Calculate the transmittance using the transmission coefficient.

[0097] The calculation formula of transmittance T is as follows: T = t × t *,in, t *for t The transpose of .

[0098] The specific implementation method of calculating the fitness value by the fitness function in step S4 is described in detail below: the fitness function is used to perform weighted calculation on the transmittances of different wavelengths, angles and thicknesses to obtain the fitness value; wherein the fitness value is obtained by weighted calculation on the transmittances of different wavelengths, angles and thicknesses, including:

[0099] S41: Obtain a preset wavelength range and a preset angle range.

[0100] The preset angle range includes a high transmission angle range and a low transmission angle range, the preset wavelength range includes multiple wavelengths, and the high transmission angle range and the low transmission angle range both include multiple incident angles.

[0101] S42: Perform weighted summation on the current transmittances corresponding to all wavelengths within the preset wavelength range to obtain a fitness value.

[0102] The current transmittance is related to the average transmittance in the high transmission angle range and the average transmittance in the low transmission angle range. Specifically, the current wavelength, the current thickness, and each incident angle in the high transmission angle range are input into the transmission matrix to obtain multiple transmittances; all transmittances are averaged to obtain an average high transmittance; the current wavelength, the current thickness, and each incident angle in the low transmission angle range are input into the transmission matrix to obtain multiple transmittances; all transmittances are averaged to obtain an average low transmittance; and the average high transmittance and the average low transmittance are weighted summed to obtain the current transmittance.

[0103] In one embodiment of the present invention, the input parameter of the fitness function also includes the thickness of each dielectric film of the multilayer film structure, and its expression can be as follows:

[0104]

[0105] in, fitness is the fitness value, W (λ) is the wavelength weight, λ center is the central wavelength of the preset wavelength range, σ is the standard deviation of the Gaussian distribution, T(λ,θ,d) is the wavelength λ, angle i ,thickness d Corresponding transmittance; ω1 is the high transmission angle range i t The corresponding transmittance weight, ω2 is the low transmission angle range i 0 The corresponding transmittance weight; | i t | is the number of angles in the high transmission angle range, | i 0 | is the number of angles in the low transmission angle range; l max is the maximum incident wavelength in the preset wavelength range, l min is the minimum incident wavelength in the preset wavelength range.

[0106] Specifically, by using a wavelength weight with Gaussian distribution, the wavelength near the central wavelength contributes the most to the fitness value, that is, the calculation formula of the weight is as follows: W (λ)= exp(-0.5((λ-λ center ) / σ) 2 ),

[0107] Among them, λ center is the central wavelength of the preset wavelength range, and σ is the standard deviation of the Gaussian distribution.

[0108] In one embodiment of the present invention, a thickness random error is further set to characterize the robustness effect of the filter. Specifically, after S5 and before S6, the following is performed: Figure 2 Steps shown:

[0109] S71: Based on the thickness random error and the current thickness, calculate the fitness value output by the corresponding fitness function.

[0110] Assume i The current thickness value of the layer is h nm, i The random error of the thickness of the layer is ±anm, then i The thickness range of the layer is ( h -a)~( h +a)nm, calculate the i Multiple thicknesses within the thickness range of the layer, such as in ( h -a)~( h +a)nm, take 1000 thicknesses, import the transmission matrix into each thickness to calculate the corresponding transmittance, and find the average value of the 1000 transmittance calculation results to get the average transmittance, and input the average transmittance into the fitness function to get the fitness value output by the fitness function.

[0111] S72: Determine whether the fitness value calculated based on the thickness random error and the current thickness reaches a preset threshold.

[0112] If the fitness value calculated based on the random thickness error and the current thickness reaches the preset threshold, S6 is executed; otherwise, the current thickness of each dielectric film is optimized, the optimized thickness is used as the current thickness, and the process returns to S3.

[0113] It can be understood that the preset thresholds of step S72 and step S4 may be the same or different, and may be set according to specific application requirements.

[0114] The optimization of the current thickness mentioned here and the optimization of the current thickness of each layer of dielectric film in the above step S5 can be optimized by using the particle swarm optimization (PSO) algorithm, which finds the global optimal solution through the collaborative search of multiple particles to maximize the fitness function and thus achieve the best angle filtering performance. The particle swarm algorithm includes:

[0115] (1) Initialize particle swarm

[0116] It mainly includes particle initialization, where the position of each particle corresponds to the thickness of each layer of the membrane; velocity initialization: assigning an initial velocity to each particle; and population initialization: generating a population containing multiple particles to form a diverse initial solution.

[0117] (2) Calculate the fitness value

[0118] Fitness evaluation: For each particle in the population, the corresponding transmittance data is calculated according to the transmission matrix algorithm, and the angle filtering performance of the current thickness combination is evaluated using the fitness function to obtain the fitness value.

[0119] (3) Update the particle's velocity and position

[0120] (4) Iterate the optimization until the fitness function value converges.

[0121] The specific process of the particle swarm algorithm is the same as that in the related art, and the present invention will not go into details therein.

[0122] The embodiment of the present invention introduces the PSO algorithm into the field of micro-nano optics, bringing the following beneficial effects: first, in the PSO algorithm, individuals in the "population" tend to operate in an independent and collaborative manner, thereby enhancing the search efficiency; second, the iteration steps of the PSO algorithm are designed to be more concise, making it easier to optimize the current thickness of each layer of dielectric film. Based on this, the PSO algorithm is combined with the transfer matrix algorithm to optimize the fitness function composed of multiple parameters, thereby achieving the best angle filtering performance.

[0123] In a specific numerical embodiment of the present invention, Figure 3 As shown, a 20-layer non-periodic multilayer film structure is designed, for example, a SiO2 film 21 and a TiO2 film 22 are grown alternately on a GaN substrate 20. The total thickness of each dielectric film is 3.3 μm, the central wavelength is 436 nm, and the goal is to achieve ±10° angle filtering, where the cut-off angle can be defined as the transmittance T=1 / e 2 The angle of time.

[0124] Before algorithm optimization, the optimization variable is first set to the dielectric film thickness, the thickness range of the dielectric film is set to 1-500nm, 20 thickness values ​​are randomly generated within the thickness range of the dielectric film, the number of iterative optimization times is 1000 times, and the preset wavelength range is the wavelength within a certain range centered on the central wavelength. In this embodiment, the preset wavelength range is {431nm, 432nm, 433nm, 434nm, 435nm, 436nm, 437nm, 438nm, 439nm, 440nm, 441nm}.

[0125] Input the above initialization parameters into the transmission matrix algorithm to obtain the transmittance corresponding to different wavelengths and different incident angles. Figure 4 ; Input the obtained transmittance and thickness initialization parameters into the fitness function as shown below:

[0126]

[0127] Then, it is determined whether the calculated fitness value reaches the set threshold, and the thickness of each dielectric film after reaching the threshold is taken as the final design result.

[0128] Among them, ω1 and ω2 are used to balance the importance of the two parts. ω1 and ω2 are dynamically adjusted according to the optimized structure. According to the target characteristics, if high transmittance performance is prioritized, ω1 is dynamically increased.

[0129] In this embodiment, ω1 and ω2 are 0.7 and 0.3 respectively. W (λ) is the wavelength weight, which is described by Gaussian distribution and is used to emphasize the weight distribution near the central wavelength. This ensures that the wavelength weight is the largest near the target central wavelength of the design.

[0130] The width of the Gaussian distribution is controlled by the standard deviation σ so that the distribution range of the weight near the central wavelength meets the design requirements. σ determines the bandwidth size. In this embodiment, σ is 0.05.

[0131] Furthermore, the robustness analysis of the structure was carried out by adding a random error of ±5nm to the thickness of each film layer, and each error was randomized 1000 times to take the average transmittance. Figure 5 The graph of average transmittance versus incident angle for each layer of film thickness with a random error of ±5nm is provided. It can be found that the angular filtering characteristics of the structure still exist, maintaining a filtering effect of ±10°.

[0132] In one embodiment of the present invention, the present invention provides an angle filter design device based on a non-periodic multilayer film structure, which is used to design an angle filter including a non-periodic multilayer film structure, wherein the non-periodic multilayer film structure includes a plurality of dielectric films stacked in sequence along the thickness direction of the non-periodic multilayer film structure, and at least two dielectric films have different thicknesses, such as Figure 6 As shown, the design device includes a fitness function building module, a transmittance calculation module and an optimization module.

[0133] The fitness function construction module is used to construct the fitness function. The input parameters of the fitness function include the transmittance of the non-periodic multilayer film structure, and the output parameters of the fitness function are the fitness values ​​that characterize the performance of the angle filter; the initial parameter generation module is used to determine the initial thickness of each layer of the dielectric film within a preset thickness range, and use the initial thickness as the current thickness.

[0134] The transmittance calculation module is used to import the current thickness of each dielectric film layer into the transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure.

[0135] The optimization module is used to input the transmittance into the fitness function and determine whether the fitness value output by the fitness function reaches a preset threshold. If the fitness value output by the fitness function does not reach the preset threshold, the current thickness of each layer of the dielectric film is optimized, and the optimized thickness is imported into the transmittance calculation module to obtain the transmittance of each dielectric film of the corresponding multi-layer film structure; and the fitness function is iteratively calculated according to the transmittance until the fitness value output by the fitness function reaches the preset threshold, and the current thickness of each layer of the dielectric film is used as the design result.

[0136] The angle filter design device based on the non-periodic multilayer film structure provided in this embodiment and the angle filter design method based on the non-periodic multilayer film structure provided in the above embodiment belong to the same inventive concept. The entire contents of the angle filter design method based on the non-periodic multilayer film structure are incorporated into the embodiment of the angle filter design device based on the non-periodic multilayer film structure by reference and will not be repeated here.

[0137] In one embodiment of the present invention, an angle filter of a non-periodic multilayer film structure is provided, including a non-periodic multilayer film structure, wherein the non-periodic multilayer film structure includes multiple dielectric films stacked in sequence along the thickness direction of the non-periodic multilayer film structure, and the thickness of at least two dielectric films is different.

[0138] The thickness of each dielectric film layer of the angle filter is determined using the above angle filter design method based on a non-periodic multilayer film structure.

[0139] In one embodiment of the present invention, the filter further includes: a robustness detection module, which is used to characterize the robustness effect of the filter by setting a thickness random error and calculating whether the fitness value reaches a preset threshold.

[0140] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0141] The above is only a specific implementation of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for designing an angle filter based on a non-periodic multilayer film structure, characterized in that: The angle filter comprises a non-periodic multilayer film structure, wherein the non-periodic multilayer film structure comprises a plurality of dielectric films stacked in sequence along the thickness direction of the non-periodic multilayer film structure, and at least two layers of the dielectric films have different thicknesses. The method comprises the following steps: S1: constructing a fitness function, wherein the input parameter of the fitness function includes the transmittance of the non-periodic multilayer film structure, and the output parameter of the fitness function is a fitness value characterizing the performance of the angle filter; the fitness function is used to perform weighted calculation on the transmittance of different wavelengths, angles and thicknesses to obtain the fitness value, including: obtaining a preset wavelength range and a preset angle range; wherein the preset angle range includes a high transmission angle range and a low transmission angle range, the preset wavelength range includes multiple wavelengths, and the high transmission angle range and the low transmission angle range both include multiple incident angles; The fitness value is obtained by weighted summing the current transmittances corresponding to all wavelengths within the preset wavelength range using the following fitness function: ； in, fitness is the fitness value, W (λ)= exp (-0.5((λ-λ center ) / σ) 2 ); W (λ) is the wavelength weight, λ center is the central wavelength of the preset wavelength range, σ is the standard deviation of the Gaussian distribution, T(λ,θ,d) is the wavelength λ, angle θ ,thickness d Corresponding transmittance; ω1 is the high transmission angle range θ t The corresponding transmittance weight, ω2 is the low transmission angle range θ 0 The corresponding transmittance weight; | θ t | is the number of angles in the high transmission angle range, | θ 0 | is the number of angles in the low transmission angle range; λ max is the maximum incident wavelength in the preset wavelength range, λ min is the minimum incident wavelength in the preset wavelength range; wherein the current transmittance is related to the average transmittance in the high transmission angle range and the average transmittance in the low transmission angle range; S2: determining the initial thickness of each dielectric film within a preset thickness range, and using the initial thickness as the current thickness; S3: importing the current thickness of each dielectric film layer into the transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure; S4: inputting the transmittance into the fitness function, and determining whether the fitness value output by the fitness function reaches a preset threshold; S5: If the fitness value output by the fitness function does not reach the preset threshold, the current thickness of each dielectric film is optimized, the optimized thickness is used as the current thickness, and the process returns to S3 until the fitness value output by the fitness function reaches the preset threshold; S6: The current thickness of each dielectric film layer is used as a design result.

2. The method for designing an angle filter based on a non-periodic multilayer film structure according to claim 1, characterized in that: The step of performing weighted summation on the current transmittances corresponding to all wavelengths within the preset wavelength range to obtain the fitness value includes: Inputting the current wavelength, the current thickness and each incident angle in the high transmission angle range into the transmission matrix to obtain a plurality of transmittances; averaging all the transmittances to obtain an average high transmittance; Input the current wavelength, the current thickness and each incident angle in the low transmission angle range into the transmission matrix to obtain a plurality of transmittances; average all the transmittances to obtain an average low transmittance; The average high transmittance and the average low transmittance are weightedly summed to obtain the current transmittance.

3. The method for designing an angle filter based on a non-periodic multilayer film structure according to claim 1, characterized in that: The method of importing the current thickness of each dielectric film layer into the transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure includes: Calculating a value of a transmission matrix based on each wavelength in a preset wavelength range, the current thickness, and each incident angle in a preset angle range; Based on the value of the transmission matrix, a transmission coefficient is calculated; The transmittance is calculated based on the transmission coefficient.

4. The method for designing an angle filter based on a non-periodic multilayer film structure according to claim 3, characterized in that: The multilayer film structure j The transmission matrix M of the dielectric film j for ； Among them, δ j =(2π / λ j )× n j × d j ×cos θ j , θ j For the j The incident angle of the dielectric film is λ j For the j The incident wavelength of the dielectric film, δ j For the j The phase difference of the dielectric film, η j For the j The optical admittance of the dielectric film, n j For the j The refractive index of the dielectric film, d j For the j The thickness of the dielectric film, ; The transmission matrix of the multilayer film structure is expressed as: ； in, N is the number of dielectric films, A, B, C, D for N The four matrix elements of the transmission matrix of the dielectric film; The calculation formula of the transmission coefficient t is as follows: ； Among them, h in =n in ×cos θ in ,or out =n out ×cos θ out ; The calculation formula of the emissivity T is as follows: T = t × t *, where η in for N The optical admittance of the incident medium of the layer dielectric film structure, n in is the refractive index of the incident medium, θ in for N The light incident angle of the dielectric film structure; η out for N The optical admittance of the output medium of the multi-layer dielectric film structure, n out is the refractive index of the output medium, θ out for N Light emission angle of the dielectric film structure; t *for t The transpose of .

5. The method for designing an angle filter based on a non-periodic multilayer film structure according to claim 1, characterized in that: After S5 and before S6, the following further includes: Based on the thickness random error and the current thickness, the fitness value output by the corresponding fitness function is calculated; If the fitness value reaches the preset threshold, S6 is executed; otherwise, the current thickness of each dielectric film is optimized, the optimized thickness is used as the current thickness, and the process returns to S3.

6. The method for designing an angle filter based on a non-periodic multilayer film structure according to claim 5, characterized in that: The step of calculating the fitness value based on the thickness random error and the current thickness includes: Assume i The current thickness value of the layer is h nm, i The random error of the thickness of the layer is ±anm. i The thickness range of the layer is ( h -a)~( h +a)nm; Calculate the i The transmittances corresponding to multiple thicknesses within the thickness range of the layer are averaged to obtain an average transmittance; The average transmittance is input into the fitness function to obtain the fitness value output by the fitness function.

7. An angular filter design device based on a non-periodic multilayer film structure, characterized in that: The angle filter design device is used for designing an angle filter including a non-periodic multilayer film structure, wherein the non-periodic multilayer film structure includes a plurality of dielectric films stacked in sequence along the thickness direction of the non-periodic multilayer film structure, and at least two layers of the dielectric films have different thicknesses. The angle filter design device includes the following modules: A fitness function construction module is used to construct a fitness function, wherein the input parameter of the fitness function includes the transmittance of the non-periodic multilayer film structure, and the output parameter of the fitness function is a fitness value characterizing the performance of the angle filter; The fitness function is used to perform weighted calculation on the transmittances of different wavelengths, angles and thicknesses to obtain the fitness value, including: obtaining a preset wavelength range and a preset angle range; wherein the preset angle range includes a high transmission angle range and a low transmission angle range, the preset wavelength range includes multiple wavelengths, and the high transmission angle range and the low transmission angle range both include multiple incident angles; and performing weighted summation of the current transmittances corresponding to all wavelengths within the preset wavelength range by the following fitness function to obtain the fitness value: ； in, fitness is the fitness value, W (λ)= exp (-0.5((λ-λ center ) / σ) 2 ); W (λ) is the wavelength weight, λ center is the central wavelength of the preset wavelength range, σ is the standard deviation of the Gaussian distribution, T(λ,θ,d) is the wavelength λ, angle θ ,thickness d Corresponding transmittance; ω1 is the high transmission angle range θ t The corresponding transmittance weight, ω2 is the low transmission angle range θ 0 The corresponding transmittance weight; | θ t | is the number of angles in the high transmission angle range, | θ 0 | is the number of angles in the low transmission angle range; λ max is the maximum incident wavelength in the preset wavelength range, λ min is the minimum incident wavelength in the preset wavelength range; wherein the current transmittance is related to the average transmittance in the high transmission angle range and the average transmittance in the low transmission angle range; An initial parameter generation module is used to determine the initial thickness of each dielectric film layer within a preset thickness range and use the initial thickness as the current thickness; A transmittance calculation module is used to import the current thickness of each dielectric film layer into the transmission matrix to calculate the transmittance of the corresponding non-periodic multilayer film structure; The optimization module inputs the transmittance into the fitness function, determines whether the fitness value output by the fitness function reaches a preset threshold value, and if the fitness value output by the fitness function does not reach the preset threshold value, optimizes the current thickness of each layer of the dielectric film, and imports the optimized thickness into the transmittance calculation module to obtain the transmittance of each dielectric film of the corresponding multi-layer film structure; and iteratively calculates the fitness function according to the transmittance until the fitness value output by the fitness function reaches the preset threshold value, and then takes the current thickness of each layer of the dielectric film as the design result.

8. An angle filter with a non-periodic multilayer film structure, characterized in that: The thickness of each dielectric film layer of the angle filter is determined by using the angle filter design method based on a non-periodic multilayer film structure as described in any one of claims 1 to 6.

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