Information processing device, design system, design method and program

Abstract

To provide an apparatus, a design method, a system, and a program for designing a meta-surface that can reduce a calculation amount.SOLUTION: An information processing apparatus for designing a meta-surface includes: a unit structure generation unit that generates data representing a unit structure of the meta-surface based on data representing a complex refractive index distribution; a reflectance calculation unit that calculates a reflectance of the generated unit structure by electromagnetic field analysis using quasi-static approximation; and a distribution determination unit that determines an optimum complex refractive index distribution based on the calculated reflectance.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to an information processing device, a design system, a design method, and a program. [Background technology]

[0002] A metasurface is a type of artificially designed metamaterial with properties not found in nature. Metasurfaces are created, for example, by regularly arranging nanoparticles into a thin film, and have the property of exhibiting high reflectivity.

[0003] Metasurfaces with high reflectivity in the near-infrared region can be used for transparent reflective films that transmit visible light and reflect near-infrared light. For example, Non-Patent Document 1 discloses a transparent reflective film with high near-infrared reflectivity, which is produced by arranging tin-doped indium oxide nanoparticles in a hexagonal close-packed pattern.

[0004] Recently, attempts have been made to design metamaterials using computer simulations. Metamaterials are composed of unit structures repeated in three dimensions, and these unit structures are made of materials with predetermined optical properties such as refractive index and absorption coefficient. In conventional metamaterial design simulations, unit structures are created from specific materials prepared as materials, and electromagnetic field analyses such as the finite element method, the finite difference time domain (FDTD) method, and the rigorous coupled wave analysis (RCWA) method are used from these unit structures.

[0005] For example, Patent Document 1 discloses a design method that uses computer simulation to design metamaterials from a wide range of materials. In the design method disclosed in Patent Document 1, in order to obtain a metamaterial with a desired refractive index, the complex refractive index distribution of materials that make up unit structures that are sufficiently smaller than the wavelength of the electromagnetic wave to be applied is optimized. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Patent No. 6199586 [Non-patent literature]

[0007] [Non-Patent Document 1] Hiroaki Matsui, Takayuki Hasebe, Noriyuki Hasuike, and Hitoshi Tabata, ACS Applied Nano Materials 2018, 1, 1853-1862. Summary of the Invention [Problem to be solved by the invention]

[0008] However, as described in Non-Patent Document 1, it is difficult to regularly arrange unit structures that are sufficiently smaller than the wavelength of the electromagnetic waves to be applied, and metasurfaces are obtained by coating the surface of nanoparticles with organic molecules. Therefore, actual metasurfaces are composed of unit structures that are approximately the same size as or larger than the wavelength of the electromagnetic waves to be applied. Therefore, even if the technology described in Patent Document 1 is applied to the design of actual metasurfaces, the enormous amount of calculation required makes it difficult to realistically design them.

[0009] In view of the problems associated with the above-mentioned conventional technologies, one aspect of the present invention aims to provide an apparatus, design method, system, and program for designing metasurfaces that can reduce the amount of calculations required. [Means for solving the problem]

[0010] In order to achieve the above object, an information processing device according to one aspect of the present invention comprises: An information processing device for designing a metasurface, a unit structure generating unit that generates data representing a unit structure of a metasurface based on data representing a complex refractive index distribution; a reflectance calculation unit that calculates the reflectance of the generated unit structure by electromagnetic field analysis using quasi-static approximation; and a distribution determining section that determines an optimum complex refractive index distribution based on the calculated reflectance. [Effects of the Invention]

[0011] According to one aspect of the present invention, it is possible to provide an apparatus, a design method, a system, and a program for designing a metasurface that can reduce the amount of calculation. [Brief explanation of the drawings]

[0012] [Figure 1] System configuration diagram of the design system. [Figure 2] FIG. 1 is a functional configuration diagram of an information processing apparatus according to a first embodiment. [Figure 3] 10 is a flowchart showing an example of the flow of a design process. [Figure 4] Schematic diagram of the metasurface. [Figure 5] Schematic diagram of the unit structure of a metasurface. [Figure 6] Schematic of unit cell distribution within the unit structure of the metasurface. [Figure 7] FIG. 10 is a diagram showing a state in which the unit structure is divided into a mesh. [Figure 8] Schematic diagram of a calculation model using the FDTD method. [Figure 9] FIG. 10 is a diagram showing boundary surfaces perpendicular to the X and Y directions and the Z direction of the calculation model. [Figure 10] FIG. 10 is a diagram showing a state in which a pulse wave is generated in the calculation model. [Figure 11] Schematic of a computational model for calculating reflectance using the quasi-static approximation. [Figure 12] FIG. 10 is an explanatory diagram showing steps for searching for a material that realizes an optimized complex refractive index distribution from materials whose complex refractive indexes are known. [Figure 13] FIG. 1 is an explanatory diagram showing a step of predicting the complex refractive index of an existing substance whose complex refractive index is unknown from first-principles calculations, and a step of searching for a substance that realizes the optimized complex refractive index distribution from the existing substances whose complex refractive indexes have been predicted. [Figure 14]FIG. 1 is an explanatory diagram showing a step of predicting the complex refractive index of a new substance from first-principles calculations, and a step of searching for a substance that realizes the optimized complex refractive index distribution from the new substance whose complex refractive index has been predicted. [Figure 15] FIG. 10 is a functional configuration diagram of an information processing apparatus according to a second embodiment. [Figure 16] 10 is a flowchart showing an example of the flow of a design process according to the second embodiment. [Figure 17] FIG. 1 is an explanatory diagram showing a step of predicting the complex refractive index of an existing substance whose complex refractive index is unknown by machine learning, and a step of searching for a substance that realizes the optimized complex refractive index distribution from the existing substances whose complex refractive indexes have been predicted. [Figure 18] FIG. 1 is an explanatory diagram showing a step of predicting the complex refractive index of a new substance using machine learning, and a step of searching for a substance that realizes the optimized complex refractive index distribution from the new substance whose complex refractive index has been predicted. DETAILED DESCRIPTION OF THE INVENTION

[0013] Hereinafter, embodiments for carrying out the present invention will be described, but the present invention is not limited to the following embodiments, and various modifications and substitutions can be made to the following embodiments without departing from the scope of the present invention.

[0014] (First embodiment) The design system according to this embodiment is a system for designing metasurfaces. Metasurfaces are a type of artificially designed metamaterial with properties that do not exist in nature. Metasurfaces are created, for example, by regularly arranging nanoparticles in a planar shape, and have the property of exhibiting high reflectivity.

[0015] Figure 1 is a system configuration diagram of the design system.

[0016] The design system includes an information processing device 1 and a server 2. The information processing device 1 and the server 2 are connected to each other so that they can communicate with each other via a network such as the Internet. The information processing device 1 is, for example, a computer, and includes a CPU 101, a storage device 102, an input device 103, a display device 104, an output device 105, and the like.

[0017] The CPU 101 executes the processing defined in the program for realizing the metasurface design method.

[0018] The memory device 102 is a storage means such as a hard disk or an optical disk, and stores, for example, a program for realizing a method for designing a metasurface, a database of materials with known complex refractive indices, various conditions for designing a metasurface, and various other data.

[0019] The input device 103 consists of a keyboard, a mouse, and other pointing devices, and accepts input of data necessary for designing the metasurface. The display device 104 displays the data necessary for designing the metasurface, the design results of the metasurface, etc. The output device 105 outputs the data necessary for design, the design results of the metasurface, etc. to other devices, etc., in response to requests from other devices, etc.

[0020] The server 2 is a device that stores a substance database 201. In response to a request from the information processing device 1, the server 2 transmits data contained in the substance database 201 to the information processing device 1. The substance database 201 contains data on substances whose complex refractive indices are known. Note that the substance database 201 may also contain data on substances whose complex refractive indices are unknown.

[0021] Next, a description will be given of the functions of the information processing device 1. Fig. 2 is a functional configuration diagram of the information processing device according to the first embodiment.

[0022] The information processing device 1 includes a storage unit 11, a unit structure generation unit 12, a reflectance calculation unit 13, a distribution determination unit 14, and a material search unit 15. Each of these units is realized by a CPU 101 reading out a program stored in a storage device 102 and executing processing defined in the program.

[0023] The storage unit 11 stores various information. Specifically, it stores parameters, calculation formulas, etc. necessary for designing a metasurface. It may also store data on substances received by the information processing device 1 from the server 2.

[0024] The unit structure generating unit 12 receives an input of a complex refractive index distribution and generates data representing a unit structure having the received complex refractive index.

[0025] The reflectance calculation unit 13 calculates the reflectance of the metasurface composed of the unit structures indicated in the generated data.

[0026] The distribution determination unit 14 determines a complex refractive index distribution whose reflectance satisfies a predetermined condition. Specifically, the unit structure generation unit 12 and the reflectance calculation unit 13 repeat the process until the calculated reflectance satisfies the predetermined condition, and when the calculated reflectance satisfies the predetermined condition, the distribution determination unit 14 determines the input complex refractive index distribution.

[0027] The substance searching unit 15 searches for a substance having the determined complex refractive index distribution from the substance database 201 of the server 2. Note that the substance searching unit 15 may search from the storage unit 11 if the storage unit 11 stores data on the substance in advance.

[0028] Next, a description will be given of a metasurface design method executed by the design system, which includes the steps of generating data representing unit structures of a metasurface based on data representing a complex refractive index distribution, calculating the reflectance of the generated unit structures by electromagnetic field analysis using quasi-static approximation, and determining an optimal complex refractive index distribution based on the calculated reflectance.

[0029] The design process for a metasurface will be specifically described below. Fig. 3 is a flowchart showing an example of the flow of the design process. In the following design process, the information processing device 1 receives a reference value δ of reflectance as a parameter and designs a metasurface that satisfies the condition that the reflectance is greater than the reference value δ.

[0030] The unit structure generating unit 12 receives an input of a complex refractive index distribution and generates data indicating a unit structure of a metasurface having the received complex refractive index distribution (step S1).

[0031] Next, the reflectance calculation unit 13 calculates the reflectance of the entire unit structure of the metasurface by electromagnetic field analysis (step S2). The reflectance of the entire unit structure does not mean the reflectance of each individual substance contained in the unit structure, but the reflectance of the entire unit structure calculated according to the position, proportion, size, etc. of each substance contained in the unit structure.

[0032] Next, the distribution determination unit 14 determines whether the calculated reflectance is greater than the reference value δ (step S3). If the distribution determination unit 14 determines that the reflectance is not greater than the reference value δ (step S3: No), the unit structure generation unit 12 returns to the process of step S1, accepts a new input of a complex refractive index distribution, and generates data indicating a unit structure of a metasurface having the accepted complex refractive index distribution.

[0033] If the distribution determining unit 14 determines that the calculated reflectance is greater than the reference value δ (step S3: Yes), it determines the input complex refractive index distribution as the optimum complex refractive index distribution (step S4).

[0034] The material searching unit 15 searches for a material that realizes the determined complex refractive index distribution (step S5).

[0035] Next, the details of the processing of each of the above steps will be described. First, the details of the processing of step S1 in Fig. 3 will be described. Fig. 4 is a schematic diagram of a metasurface. As shown in Fig. 4, the metasurface 50 to be designed is constructed by repeatedly arranging unit structures 51 in two-dimensional directions. Furthermore, the unit structures 51 to be generated may be of a size equal to or larger than the wavelength of the electromagnetic wave to be applied.

[0036] Figure 5 is a schematic diagram of a unit structure of a metasurface. Figure 6 is a schematic diagram of the unit cell distribution within the unit structure of a metasurface. A unit structure 51 is further composed of multiple unit cells 52. As shown in Figures 5 and 6, the unit structure generator 12 constructs a rectangular parallelepiped unit structure 51 on Cartesian coordinates (x, y, z). In this case, the input values input to construct the unit structure 51 are (i) the width a of the unit structure, (ii) the depth b of the unit structure, (iii) the height h of the unit structure, (iv) each position of the unit cell (Cartesian coordinates (x, y, z)), and (v) the complex refractive index n(x, y, z) (complex refractive index distribution) at each position (Cartesian coordinates (x, y, z)) within the unit structure. The complex refractive index n can be separated into a real part n' and an imaginary part k as shown in the following equation (1):

[0037] n=n′-ik (1)

[0038] FIG. 7 is a diagram showing a state in which unit structures are divided into meshes. The unit structure generation unit 12 calculates the complex refractive index (complex refractive index distribution) at each position in the unit structure 51. Specifically, as shown in FIG. 7, the unit structure generation unit 12 divides each unit structure 51 into an appropriate mesh 60, such as a tetrahedral mesh or a hexahedral mesh, using commercially available meshing software such as HyperMesh or Cubit, and assigns a complex refractive index n to each node 61 of the mesh 60. Alternatively, the unit structure generation unit 12 may use a GUI integrated with electromagnetic field analysis software. This makes it possible to divide the unit structure 51 into the mesh 60 and assign a complex refractive index n to each node 61.

[0039] Next, the details of the process of step S2 in Fig. 3 will be described. First, a conventional method will be described. In the process of step S2, the conventional reflectance calculation unit 13 calculates the reflectance of the entire unit structure of the metasurface 50 by performing electromagnetic field analysis on the constructed unit structure 51 using a finite element method, a finite-difference time-domain method (FDTD method), a rigorous coupled-wave analysis (RCWA) method, or the like.

[0040] Here, an example will be described in which the FDTD method is used to calculate the reflectance of the entire unit structure of the metasurface 50. Examples of software using the FDTD method include SALMON, Fullwave, and Poything.

[0041] Fig. 8 is a schematic diagram of a calculation model using the FDTD method. Using the FDTD method, the reflectance calculation unit 13 assumes a rectangular parallelepiped calculation model 73 including a slab 70 with a length d in the Z direction, which includes one unit feature 51 in the X, Y, and Z directions, and vacuum layers 71 and 72 that sandwich the slab 70 in the Z+ and Z- directions and are sufficiently thicker than the wavelength of the electromagnetic wave, as shown in Fig. 8.

[0042] The reflectance calculation unit 13 uses the FDTD method to calculate the time evolution of the electric field E and the magnetic field H based on the following Maxwell's equations (2) and (3).

[0043]

number

[0044]

number

[0045] Here, the electric field E and the magnetic field H are vector values consisting of x, y, and z components. μ0 is the magnetic permeability in a vacuum, 4π×10 -7 (H / m), μ ris the relative permeability, ε0 is the permittivity in a vacuum 8.854187817620×10 -12 F / m, ε r is the relative permittivity and t is time.

[0046] The magnetic permeability μ and permittivity ε in a material are expressed by the following equations (4) and (5).

[0047]

number

[0048] The complex refractive index n is expressed as the following equation (6) using the magnetic permeability μ and the dielectric constant ε.

[0049]

number

[0050] In the visible light region, the relative permeability μ r can be considered to be 1.0, so the complex refractive index n is r This is expressed by the following equation (7).

[0051]

number

[0052] Therefore, the reflectance calculation unit 13 calculates the relative dielectric constant ε r is determined from the value of the complex refractive index n, which is an input condition, as shown in the following equation (8).

[0053]

number

[0054] Therefore, the reflectance calculation unit 13 adds the relative dielectric constant ε r and relative permeability μ r is entered.

[0055]

number

[0056] Next, specific calculations in the FDTD method will be further explained. First, as boundary conditions, a periodic boundary condition is applied to a boundary surface 80 perpendicular to the X and Y directions of the calculation model 73, and an absorbing boundary condition is applied to a boundary surface 81 perpendicular to the Z direction, as shown in Fig. 9. One method for applying the absorbing boundary condition is the Perfectly Matched Layer (PML).

[0057] The reflectance calculation unit 13 calculates the time evolution of the electromagnetic field by simulating the generation of a pulse wave 82 having an arbitrary polarization state and a propagation direction in the Z+ direction as an incident wave from the air layer 83 of the slab 70, as shown in Figure 10, at time t = 0.

[0058] The reflectivity calculation unit 13 performs time evolution calculations using the FDTD method until the amplitudes of the electric field and magnetic field at all points in the calculation model 73 reach the values at t = 0, i.e., 0. As a result, the time evolution of the amplitude and phase of the electric field and magnetic field at each point in the calculation model 73 is obtained.

[0059] The reflectance calculation unit 13 performs a Fourier transform on the electric field and magnetic field at each point as follows: This calculates the frequency ω dependency.

[0060]

number

[0061] Using equation (11), the reflected electric field E r , transmitted electric field E t can be expressed as the following equations (13) and (14).

[0062]

number

[0063] Here, z0 is the z coordinate of a point in the Z-direction sufficiently far from the metasurface, and z1 is the z coordinate of a point in the Z+direction sufficiently far from the metasurface, as shown in Figure 10. Also, E' is the Fourier transform of the time evolution of the electric field in a vacuum, i.e., when no metasurface exists.

[0064] The reflectance calculation unit 13 calculates the reflectance R and transmittance T of the entire metasurface from the transmitted electric field and reflected electric field using the following equations (15) and (16).

[0065]

number

[0066] The conventional reflectance calculation method described above has the problem that the amount of calculation required is enormous, making it difficult to design in a practical manner. Therefore, as a technique to solve this problem, we will explain a method for calculating the reflectance of the entire metasurface using quasi-static approximation.

[0067] 11 is a schematic diagram of a calculation model for calculating the reflectance using quasi-static approximation. As shown in FIG. 11, the reflectance calculation unit 13 calculates the reflectance by a=L x r0, b=L y The unit package constituting the unit structure 51 of the metasurface of r0 is assumed to be a spheroid, and each spheroid is expressed by the following formula (22).

[0068]

number

[0069] where n represents each spheroid and a n r0, b n r0 represents the radius of each spheroid. n ′,y n ′,z n ′) is a coordinate system rotated by θn around the x-axis and φn around the z-axis from the original coordinates (x, y, z), and is expressed by the following equations (23), (24), and (25).

[0070]

number

[0071] In order to apply the quasi-static approximation, we assume that each spheroid is sufficiently smaller than the wavelength of light and is distributed within the unit structure of the metasurface so that they do not interact with each other.

[0072] At the original coordinates (x, y, z), the incident electric field E i is expressed by the following equation (26).

[0073]

number

[0074] Also, the coordinate system (x n ′,y n ′,z n The incident electric field E at i '(ω) is given by equation (27).

[0075]

number

[0076] This E i Using ', the total electric field E in the nth spheroid τ,n '(ω) is calculated as shown in equation (28).

[0077]

number

[0078] where A n is the depolarization coefficient, and in the case of a spheroid, it is calculated by the following equations (29), (30), (31), (32) and (33).

[0079]

number

[0080]

number

[0081] A a,n +2A b,n =1→A b,n =(1-A a,n ) / 2···(33)

[0082] Equation (28) can be calculated as follows using equation (27):

[0083]

number

[0084] This E τ,n ′ is expressed in the coordinate system (x, y, z) τ,n is calculated as in the following equation (35).

[0085]

number

[0086] Therefore, the current density j flowing within the nth spheroid in the coordinate system (x, y, z) is n is calculated as follows:

[0087]

number

[0088] Next, the reflectance calculation unit 13 performs calculations assuming a uniform thin film with a thickness of 0 that has reflectance and transmittance equivalent to those of the metasurface. The current density J of this thin film is calculated as shown in the following equation (37).

[0089]

number

[0090] where: ~ J is the dimension [A / m 2 ] is a two-dimensional current density. At this time, the electric field in the thin film is calculated by the following equation (38).

[0091]

number

[0092] Here, E t , E r represent the transmitted electric field and the reflected electric field, respectively. c is the speed of light in a vacuum. In order for this thin film to have reflectance and transmittance equivalent to those of the metasurface, the following equation (39) must be satisfied.

[0093]

number

[0094] Here, N is the total number of unit cells contained in the unit structure. The z component of the electric field exists only within the thin film and does not contribute to the reflected or transmitted electric field, so it is ignored. From equations (38) and (39), the reflected electric field E r is calculated by the following equation (40):

[0095]

number

[0096] Transmitted electric field E t is calculated from the boundary conditions as follows:

[0097]

number

[0098] Then, the reflectance calculation unit 13 calculates the reflectance R and transmittance T of the metasurface using the incident electric field E i , the reflected electric field E in Eq. (40) r , the transmitted electric field E in Eq. (41) tThe calculation is performed using the following equations (42) and (43).

[0099]

number

[0100] In this way, the reflectance calculation unit 13 calculates the reflectance of the metasurface by using equation (42).

[0101] According to the calculation based on the quasi-static approximation described above, the unit package constituting the unit structure 51 of the metasurface is an ellipsoid, which requires less calculation effort than the calculation using the FDTD method described above, and makes it possible to calculate the reflectance with a realistic amount of calculation effort.

[0102] Next, the details of the process of step S5 in Fig. 3 will be described. Specifically, as shown in Fig. 12, the substance searching unit 15 searches a database 100 of substances with known complex refractive indices, such as substances having the complex refractive index values n1 and n2 of the optimal complex refractive index distribution. The substance searching unit 15 searches for substances having complex refractive indices that match or are close to the complex refractive index values of the optimal complex refractive index distribution. Note that the database 100 may be included in the storage device 102 of the information processing device 1, or may be part of the substance database 201 of the server 2.

[0103] The material searching unit 15 ends the search when it finds data of a material that satisfies the search conditions in the database 100 or when it has searched the data of all materials in the database 100. When the information processing device 1 finds data of a material that satisfies the search conditions, it designs the metasurface 50 using the data of that material.

[0104] According to this embodiment, unit structures 51 are determined that have an optimal complex refractive index distribution so that the reflectance of the entire unit structures of metasurface 50 is equal to or greater than a reference value, and a material that realizes this optimal complex refractive index distribution is searched for from materials with known complex refractive indices. In this case, even for unit structures that are approximately the same size as the wavelength of the electromagnetic wave to be applied or larger, it is possible to calculate the reflectance with a realistic amount of calculation using calculations based on quasi-static approximation. Therefore, metasurfaces can be designed with a realistic amount of calculation.

[0105] The unit structure generation unit 12, the reflectance calculation unit 13, and the distribution determination unit 14 are an example of an optimization means that optimizes the complex refractive index distribution of a metasurface composed of unit structures whose size is approximately equal to or larger than the wavelength of the electromagnetic wave to which an arbitrary complex refractive index distribution is applied, so that the reflectance of the entire unit structure of the metasurface, calculated by electromagnetic field analysis from unit structures whose size is approximately equal to or larger than the wavelength of the electromagnetic wave to which the complex refractive index distribution is applied, is equal to or larger than a reference value.

[0106] In the processing of step S5 in FIG. 3, the material searching unit 15 may predict the complex refractive index of an existing material whose complex refractive index is unknown from first-principles calculations, and search for a material that realizes an optimized complex refractive index distribution from among the existing materials whose complex refractive indexes have been predicted.

[0107] 13, the molecular structure of a substance is extracted from the material structure database 110, and the complex refractive index of an existing substance is predicted by performing first-principles calculations. The material structure database 110 is a collection of data indicating the molecular structure of a substance. The material structure database 110 may be included in the storage device 102 of the information processing device 1, or may be part of the material database 201 of the server 2.

[0108] Commercially available programs for first-principles calculations that can predict complex refractive index include VASP, CASTEP, and WIEN2K. To perform first-principles calculations, the molecular structure of an existing substance is input using Cartesian coordinates or a Z-Matrix. To do this, commercially available modeling software such as Material Studio or MedeA can be used to easily input the coordinates of each atom.

[0109] By inputting the molecular structure of an existing substance into the above-mentioned first-principles calculation program and executing it, the information processing device 1 calculates a value indicating the ground state electronic state based on the density functional theory, and further calculates and predicts the complex refractive index based on the obtained value indicating the electronic state and the linear response theory. The storage unit 11 of the information processing device 1 stores information indicating the prediction results.

[0110] The material search unit 15 searches for a material that realizes each of the complex refractive index values n1 and n2 of the optimal complex refractive index distribution of the unit structure 51 determined by the processes from step S1 to step S4 in Fig. 3 from among existing materials whose complex refractive indexes have been predicted. At this time, the material search unit 15 searches for an existing material having a complex refractive index value that matches or is close to each of the complex refractive index values of the optimal complex refractive index distribution.

[0111] Furthermore, in the processing of step S5 in FIG. 3, the material searching unit 15 may predict the complex refractive index of a new material from first-principles calculations, and search for a material that realizes an optimized complex refractive index distribution from among the new materials whose complex refractive indexes have been predicted.

[0112] 14, the user designs a new substance, and the information processing device 1 predicts the complex refractive index of the new substance from first-principles calculations and searches for a new substance whose predicted value satisfies the search conditions. Any new substance can be designed without any particular restrictions as long as the electronic state converges in the first-principles calculations.

[0113] Furthermore, the material search unit 15 may sequentially execute the above-described processes in the process of step S5 in Fig. 3. Specifically, the material search unit 15 first searches for a material that realizes an optimal complex refractive index distribution from materials whose complex refractive indices are known. Then, if the material search unit 15 cannot find a material that realizes an optimal complex refractive index distribution, it predicts the complex refractive index of an existing material whose complex refractive index is unknown from first-principles calculations, and searches for a material that realizes an optimal complex refractive index distribution from existing materials whose complex refractive indices are predicted. Furthermore, if the material search unit 15 cannot find a material that realizes an optimal complex refractive index distribution from existing materials, it predicts the complex refractive index of a new material from first-principles calculations, and searches for a material that realizes an optimal complex refractive index distribution from new materials whose complex refractive indices are predicted.

[0114] (Second embodiment) A second embodiment will be described below with reference to the drawings. The second embodiment differs from the first embodiment in that, when searching for a substance that realizes an optimal complex refractive index distribution, the complex refractive index of an existing substance whose complex refractive index is unknown is predicted based on a prediction model obtained by machine learning. Therefore, the following description of the second embodiment will focus on the differences from the first embodiment, and components having the same functional configuration as those in the first embodiment will be assigned the same reference numerals as those used in the description of the first embodiment, and their description will be omitted.

[0115] 15 is a functional configuration diagram of an information processing device according to the second embodiment. The information processing device 1 according to this embodiment has a configuration in which a prediction unit 16 is added to the information processing device 1 according to the first embodiment.

[0116] The prediction unit 16 constructs a prediction model by machine learning and stores the constructed prediction model in the storage unit 11. Furthermore, when searching for a substance that will achieve an optimal complex refractive index distribution, the prediction unit 16 predicts the complex refractive index of an existing substance whose complex refractive index is unknown based on the prediction model and stores the predicted data in the storage unit 11. The prediction unit 16 is realized by the CPU 101 reading out a program stored in the storage device 102 and executing processing defined in the program.

[0117] Furthermore, in the process of step S5 in FIG. 3, when searching for a material that realizes an optimal complex refractive index distribution, the material searching unit 15 searches for the complex refractive index of an existing material whose complex refractive index is unknown from the prediction result by the prediction unit 16.

[0118] 16 is a flowchart showing an example of the flow of prediction processing according to the second embodiment. The information processing device 1 executes prediction processing as pre-processing before design processing. First, the prediction unit 16 constructs a prediction model (step S11).

[0119] Specifically, the prediction unit 16 extracts the complex refractive index of a substance from a database 100 of substances with known complex refractive indices, and constructs a prediction model that predicts the complex refractive index based on this information. Prediction model creation methods include, for example, multiple regression, LASSO regression, Ridge regression, Elastic-Net regression, Kernel regression, decision tree regression, random forest regression, gradient boosting, and neural networks. To construct a prediction model, the prediction unit 16 creates descriptors that characterize existing substances. Descriptors include, for example, the weighted average, weighted variance, weighted sum, maximum value, and minimum value of the physical property values of each element contained in the substance. For example, for a binary substance A wA B wB In this case, the physical property value f is the physical property value f of elements A and B. A ,f B Using these, the following equations (17), (18), (19), (20), and (21) are obtained.

[0120] Weighted average: f ave =(wAf A +wBf B ) / (wA+wB) (17) Weighted variance:f var =[wA(f A -f ave ) 2 +wB(f B -f ave ) 2 ] / (wA+wB)···(18) Weighted sum:f sum =wAf A+wBf B ···(19) Maximum value: f max =max(f A ,f B )···(20) Minimum: f min =min(f A ,f B )···(twenty one)

[0121] The physical property value f is the period, number of protons, atomic number, atomic radius, atomic radius according to Rahm, atomic volume, atomic mass, atomic volume according to the Inorganic Crystal Structure Database, lattice constant, van der Waals (vdW) radius, vdW radius according to Alvarez, vdW radius according to Batsanov, vdW radius according to Bondi, vdW radius according to DREIDING FF, MM3 FF vdW radius, Rowland and Taylor vdW radius, Truhlar vdW radius, UFF vdW radius, Bragg covalent radius, Cerdero covalent radius, Pyykko single bond distance, Pyykko double bond distance, Pyykko triple bond distance, Slater covalent radius, vdW coefficient C6, Gould and Bucko vdW coefficient C6, Density at 295K, Proton affinity, Dipole polarizability, Electron affinity, Electronegativity, Allen scale electronegativity, Ghosh scale electronegativity, Mulliken scale electronegativity, These include the DFT band gap, DFT energy, DFT lattice constant of BCC, DFT lattice constant of FCC, DFT magnetic moment, DFT volume, HHI coefficient, specific heat at 20°C, gas-phase basicity, first ionization energy, heat of fusion, heat of formation, molar specific heat capacity, specific heat capacity, heat of vaporization, thermal expansion coefficient, boiling point, Brinell hardness, compressibility, melting point, single bond distance of metallic bond radius, distance of nearest neighbor of metallic bond radius, thermal conductivity at 25°C, speed of sound, Vickers hardness, polarizability, Young's modulus, Poisson's ratio, molar volume, total number of unoccupied electrons, total number of valence electrons, number of unoccupied d electrons, number of d valence electrons, number of unoccupied f electrons, number of f valence electrons, number of unoccupied p electrons, number of p electrons, number of unoccupied s electrons, and number of s valence electrons. Other examples include the radial distribution function, Voronoi diagram, and Crystal-Graph-Convolutional-Neural-Network. These descriptors are input and the complex refractive index of existing materials is output, and a prediction model is constructed using the above-mentioned methods.

[0122] Next, the prediction unit 16 receives input of data indicating the molecular structure of an existing substance whose complex refractive index is unknown (step S12). Then, the prediction unit 16 inputs a descriptor of the existing substance whose complex refractive index is unknown into the constructed prediction model, and predicts the complex refractive index (step S13). Then, the storage unit 11 stores the data predicted by the prediction unit 16.

[0123] 17, in step S13 of Fig. 16, prediction unit 16 extracts the molecular structure of a substance from material structure database 110 and predicts the complex refractive index of an existing substance based on a prediction model. Then, material search unit 15 searches for a substance with a complex refractive index that satisfies the search conditions from data indicating the complex refractive index predicted based on the prediction model constructed by machine learning.

[0124] Furthermore, the prediction unit 16 may predict the complex refractive index of the new substance by machine learning in step S13 of FIG.

[0125] Specifically, in step S13 of Fig. 16, the prediction unit 16 acquires data on the design of a new substance as shown in Fig. 18, and predicts the complex refractive index of the new substance based on a prediction model. Then, the substance search unit 15 searches for a new substance with a complex refractive index that satisfies the search conditions from the data indicating the complex refractive index predicted based on the prediction model constructed by machine learning.

[0126] Furthermore, the material searching unit 15 may sequentially execute the above-described processes in the process of step S5 in Fig. 3. Specifically, the material searching unit 15 first searches for a material that realizes an optimal complex refractive index distribution from materials whose complex refractive indices are known. Then, if the material searching unit 15 cannot find a material that realizes an optimal complex refractive index distribution, it searches for a material that realizes an optimal complex refractive index distribution from existing materials whose complex refractive indices have been predicted by the prediction unit 16. Furthermore, if the material searching unit 15 cannot find a material that realizes an optimal complex refractive index distribution from existing materials, it searches for a material that realizes an optimal complex refractive index distribution from new materials whose complex refractive indices have been predicted by the prediction unit 16.

[0127] In step S5 of FIG. 3, the material searching unit 15 may search for a material that realizes an optimal complex refractive index distribution by searching from materials whose complex refractive indexes are known, from existing materials whose complex refractive indexes are unknown, or from new materials, in any order and in any combination.

[0128] According to the information processing device 1 of this embodiment, not only substances whose complex refractive indexes are known, but also existing substances or newly designed substances whose complex refractive indexes are unknown can be searched for by predicting the complex refractive index based on a prediction model constructed by machine learning. [Industrial Applicability]

[0129] The present invention can be used in the design of window glass, car windshields, etc. [Explanation of symbols]

[0130] 1 Information processing device 1 2 Server 11 Storage section 12 Unit structure generation section 13 Reflectance calculation section 14 Distribution determining part 15 Material Exploration Department 16 Prediction Department 101 CPU 102 Storage device 103 Input Device 104 Display device 105 Output Device 201 Substance Database

Claims

1. An information processing device for designing a metasurface, a unit structure generation unit that uses a mesh obtained by dividing a unit structure of a metasurface into a plurality of meshes based on data indicating a complex refractive index distribution, and assigns complex refractive indices to nodes of the mesh; a reflectance calculation unit that calculates the reflectance of the entire unit structure generated by electromagnetic field analysis using quasi-static approximation with Maxwell's equations; a distribution determination unit that determines an optimum complex refractive index distribution based on the calculated reflectance, the reflectance calculation unit approximates a unit package included in the unit structure to a spheroid and calculates the reflectance of the entire unit structure. Information processing device.

2. a material searching unit that searches for a material having the determined complex refractive index distribution; the material searching unit predicts the complex refractive index of an existing material whose complex refractive index is unknown from first-principles calculations, and searches for the existing material whose complex refractive index has been predicted; The information processing device according to claim 1 .

3. a material searching unit that searches for a material having the determined complex refractive index distribution; the substance searching unit predicts the complex refractive index of a new substance from first-principles calculations and searches for a new substance from existing substances whose complex refractive indexes have been predicted; The information processing device according to claim 1 .

4. a material search unit that searches for a material having the determined complex refractive index distribution; a prediction unit that predicts the complex refractive index of an existing substance or the complex refractive index of a new substance, the complex refractive index of which is unknown, based on a prediction model by machine learning; the material searching unit searches for a material having a complex refractive index distribution based on the predicted complex refractive index. The information processing device according to claim 1 .

5. A metasurface design system, comprising: an optimization means for optimizing the complex refractive index distribution of a metasurface composed of unit structures having a size equal to or larger than the wavelength of an electromagnetic wave to which an arbitrary complex refractive index distribution is applied, the unit structures having a size equal to or larger than the wavelength of the electromagnetic wave to which the complex refractive index distribution is applied, the unit structures having a complex refractive index assigned to the nodes of the mesh, the unit structures having a size equal to or larger than the wavelength of the electromagnetic wave to which the complex refractive index distribution is applied ... a material search unit that searches for a material that realizes the optimized complex refractive index distribution from materials whose complex refractive indexes are known, The reflectance of the entire unit structure is calculated by approximating a unit package included in the unit structure to a spheroid. Design system.

6. 1. A computer-implemented method for designing metasurfaces, comprising: a step of assigning complex refractive indices to nodes of a mesh obtained by dividing a unit structure of the metasurface into a plurality of meshes based on data indicating a complex refractive index distribution; calculating the reflectance of the entire unit structure generated by electromagnetic field analysis using quasi-static approximation with Maxwell's equations; determining an optimum complex refractive index profile based on the calculated reflectance; the calculating step approximates a unit package included in the unit structure to a spheroid, and calculates the reflectance of the entire unit structure; Design method.

7. On the computer, a step of assigning complex refractive indices to nodes of a mesh obtained by dividing a unit structure of the metasurface into a plurality of meshes based on data indicating a complex refractive index distribution; calculating the reflectance of the entire unit structure generated by electromagnetic field analysis using quasi-static approximation with Maxwell's equations; determining an optimal complex refractive index profile based on the calculated reflectance; Execute the calculating step approximates a unit package included in the unit structure to a spheroid, and calculates the reflectance of the entire unit structure; program.

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