Photonic crystal second harmonic generation method based on deep learning
Through deep learning-based methods, the nonlinear relationship between photonic crystal structure parameters and energy band data is learned, and the optimal photonic crystal structure parameters are designed, which solves the time-consuming problem of photonic crystal design process and realizes efficient second harmonic generation.
Patent Information
- Application Number
- CN202510230107.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-28
- Publication Date
- 2025-06-06
AI Technical Summary
The high-dimensional nonlinearity of the parameter space of photonic crystals leads to a time-consuming design process and relies on a large number of numerical calculations. Traditional design methods are inefficient and difficult to meet the design needs of complex photonic crystal structures.
Using a deep learning-based method, through forward prediction network and reverse network model, the nonlinear relationship between photonic crystal structure parameters and energy band data is learned, and the optimal photonic crystal structure parameters are designed to achieve efficient second harmonic generation.
It reduces manual trial and error costs, improves the design efficiency of complex photonic crystal structures, realizes efficient second harmonic generation, and improves the prediction accuracy and generalization ability of the model for energy band structures.
Smart Images
Figure CN120105066A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of micro-nano optics, and specifically is a photonic crystal second harmonic generation method based on deep learning. Background Art
[0002] Photonic crystal (PC) is an artificial material with a periodic structure. Through the periodic distribution of dielectric constants, a photonic band structure similar to the electronic band in semiconductors can be formed. Photonic crystals can regulate the propagation behavior of photons within a specific frequency range, especially by limiting or allowing the propagation of light of a specific wavelength through photonic band gaps, thereby achieving precise control of light waves. This characteristic gives photonic crystals a wide range of applications in optical communications, sensors, lasers, and quantum computing. For example, in optical communications, photonic crystals can be used for high-efficiency filters or low-loss waveguides; in sensors, photonic crystal structures can respond to environmental changes (such as refractive index, temperature, stress, etc.) with high sensitivity; and in lasers, photonic crystals can achieve high-quality factor resonant cavity design, thereby improving the efficiency and stability of the laser.
[0003] Second harmonic generation (SHG) is a second-order nonlinear optical effect. Its physical essence is the nonlinear polarization of the material under the action of a strong light field, which can convert the fundamental frequency light with a frequency of ω into the second harmonic light with a frequency of 2ω. Among them, the second-order nonlinear effect is caused by the second-order nonlinear polarization rate χ (2) It is caused by the energy conversion between the fundamental frequency light and the second harmonic light.
[0004] However, the parameter space of photonic crystals is usually high-dimensional and nonlinear, and the relationship between the target function (such as band gap size, transmission efficiency, mode coupling, etc.) and the structural parameters is difficult to express intuitively, resulting in a time-consuming design process that relies on a large number of numerical calculations. This complexity makes traditional design methods inefficient and difficult to meet the design requirements of complex photonic crystal structures. Summary of the invention
[0005] The present invention aims to address the deficiencies of the above-mentioned prior art and proposes a photonic crystal second harmonic generation method based on deep learning, in order to reduce the cost of manual trial and error and improve the design efficiency of complex photonic crystal structures, thereby achieving efficient generation of second harmonics.
[0006] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:
[0007] The method for generating second harmonics of photonic crystals based on deep learning is characterized in that it is performed according to the following steps:
[0008] Step 1: Use the parametric scanning method to scan along the high symmetry point of the first Brillouin zone , perform wave vector scanning on the energy band of the photonic crystal, obtain the photonic crystal energy band data set and perform preprocessing to obtain the preprocessed photonic crystal energy band data set ,in, represents the structural parameters of the i-th group, Represents S i The jth structural parameter in represents the energy band data of the i-th group, W i The frequency of the j-th energy band data in , m represents the total frequency of the energy band data, and m=n×k, n represents the number of energy bands in the parametric scanning unit cell, k represents the number of wave vectors required to scan each energy band, and N represents the number of groups;
[0009] Step 2: Construct a pre-training model F, including: M-layer network structure, each layer of which is composed of a fully connected layer, a batch normalization layer and a RELU activation function, and perform S i Processing is performed to obtain the predicted energy band data of group i ,in, Represents the i-th group of predicted energy band data The frequency number of the j-th energy band data in ;
[0010] Step 3: Use formula (1) to construct the average error loss function Loss of the energy band data F , and train the pre-trained model F to obtain the forward prediction network model :
[0011] (1)
[0012] Step 4: Construct the reverse network model G, including: K-layer network structure, each layer of network structure is composed of a fully connected layer, a batch normalization layer and a RELU activation function, and connect the reverse network model G with the forward prediction network model After the series connection, the series network model T is constructed, and W is sequentially i Processing is performed to obtain the predicted energy band data of group i ,in, Represents the i-th group of predicted energy band data The frequency of the j-th energy band data in ;
[0013] Step 5: Construct the loss function Loss of the series network T T , and used for training the series network T to obtain the series network model :
[0014] Step 6: and Composition of the dataset , and calculate The frequency width of the fundamental frequency gap and the frequency width of the octave gap The cumulative sum between them is calculated, and the structural parameter corresponding to the maximum value among the N cumulative sums is selected as the target structural parameter , Represents the target structure parameters The jth structural parameter in ;
[0015] Step 7: According to the target structure parameters , using the second-order nonlinear effect to generate the second harmonic:
[0016] The method for generating second harmonics of photonic crystals based on deep learning described in the present invention is also characterized in that step 4 is performed as follows:
[0017] Step 4.1: The inverse network model G is used for the i-th group of energy band data W i Processing is performed to obtain the predicted structural parameters of the i-th group ,in, represents the predicted structural parameters of the i-th group The jth structural parameter in ;
[0018] Step 4.2: Input forward prediction network model The predicted energy band data of group i is obtained by processing .
[0019] Furthermore, the loss function Loss in step 5.1 T It is constructed in the following steps:
[0020] Step 5.1: Use formula (2) to construct the loss function of the reverse network G :
[0021] (2)
[0022] Step 5.2: Use formula (3) to construct the loss function Loss of the series network T T :
[0023] (3).
[0024] Further, step 7 is performed as follows:
[0025] Step 7.1: The corresponding photonic crystal PC 1 Conduct characteristic modeling and construct photonic crystal PC 1 The geometric structure and the high symmetry point along the first Brillouin zone , perform parameterized scanning on the wave vector k and obtain the photonic crystal PC 1 The band structure of the photonic crystal PC 1 The baseband gap center frequency f 0 and the center frequency of the double band gap f 1 ;
[0026] Step 7.2: Break the Photonic Crystal PC 1 After the rotational symmetry of the photonic crystal PC is obtained 2 , and processed according to the process of step 7.1 to obtain the photonic crystal PC 2 The band structure of
[0027] Step 7.3, build by PC 1 and PC 2 The dimension of the supercell system is N×1, and the fundamental frequency band gap frequency is f 0 and the double bandgap frequency band f 1 The wave vector k is parametrically scanned on the upper and lower planes to obtain the band structure of the supercell system, thereby determining the fundamental frequency boundary state FW and the double frequency boundary state SHG of the supercell system, where N represents the PC in the y direction of the supercell system. 1 and PC 2 The total number of PCs in the y direction of the supercell system 1 The number of PCs in the y direction is N / 2. 2 The number of is N / 2;
[0028] Step 7.4: Based on the fundamental frequency boundary state FW and the double frequency boundary state SHG, use the wave vector matching relationship , get the fundamental frequency of the wave vector matching intersection point and frequency multiplication ;
[0029] Step 7.5: Build from PC 1 and PC 2 The dimension of the boundary state system is M×R, and the excitation source I is placed at port 1 of the boundary state system. 0 , place detector P at port 2 0 , where I 0 For sine wave , E 0 represents the intensity of the sine wave, is the fundamental frequency of the wave vector matching intersection point; where M represents the PC in the y direction in the boundary state system 1 and PC 2 The total number of PC in the y direction in the boundary state system 1 The number of PCs in the y direction is M / 2. 2 The number of is M / 2, R represents the PC in the x direction in the boundary state system1 The number of PCs in the x direction 2 The number of PCs in the x direction 1 With PC 2 The number of is equal and all are R;
[0030] Step 7.6: Using Excitation Source I 0 Exciting the fundamental frequency boundary state FW to generate the second harmonic , and the detector P 0 After discrete Fourier transform of the generated spectrum, the amplitude of the second harmonic excited by the fundamental frequency boundary state FW is obtained;
[0031] Step 7.7, build by PC 1 and PC 2 The dimensions of the composition are The corner state system and determine the fundamental frequency of the corner state system and frequency multiplication ;
[0032] Step 7.8: Set the fundamental frequency of the sine wave to Then, return to step 7.6 to obtain the amplitude of the second harmonic excited by the corner state system.
[0033] An electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the photonic crystal second harmonic generation method, and the processor is configured to execute the program stored in the memory.
[0034] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the photonic crystal second harmonic generation method when the computer program is executed by a processor.
[0035] Compared with the prior art, the present invention has the following beneficial effects:
[0036] 1. The present invention introduces a forward prediction network model. This method learns the nonlinear relationship between the photonic crystal structure parameters and the energy band data by inputting the structure parameters of the photonic crystal. This solves the problem of high trial and error cost caused by the difficult-to-express correspondence between the target function and the structural parameters, and improves the prediction accuracy and generalization ability of the model for the energy band structure.
[0037] 2. The present invention introduces a series network model. This method connects the forward prediction model in series, inputs the energy band data of the photonic crystal, and designs the structural parameters, thereby solving the one-to-many problem caused by using only the reverse network and improving the accuracy of the model in designing the structural parameters.
[0038] 3. The present invention takes second harmonic generation as its goal. The method designs the optimal photonic crystal structure parameters through network training and utilizes the strong localization of boundary states and corner states to achieve efficient second harmonic generation. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 It is a schematic diagram of the process of the present invention;
[0040] Figure 2 Schematic diagram of the model structure of the method of the present invention. DETAILED DESCRIPTION
[0041] In this embodiment, a photonic crystal second harmonic generation method based on deep learning is provided. Figure 1 As shown, the steps are as follows:
[0042] Step 1: Use the parametric scanning method to scan along the high symmetry point of the first Brillouin zone , perform wave vector scanning on the energy band of the photonic crystal, obtain the photonic crystal energy band data set and perform preprocessing to obtain the preprocessed photonic crystal energy band data set ,in, represents the structural parameters of the i-th group, Represents S i The jth structural parameter in represents the energy band data of the i-th group, W i The frequency of the j-th energy band data in the lattice, m represents the total frequency of the energy band data, and m=n×k, n represents the number of energy bands of the parametric scanning unit cell, k represents the number of wave vectors required to scan each energy band, and N represents the number of groups; in this embodiment, based on the two-dimensional diamond lattice, the air contains two radii of r a and r b The refractive index of the dielectric column material is , the lattice constant of the photonic crystal is a, and the structural parameters are ,in, Represents the radius of the medium column r a , Represents the radius of the medium column r b , represents the lattice constant a of the photonic crystal, Represents the refractive index of the dielectric column material , parametrically scan the first 6 energy bands of the unit cell, each energy band contains 48 wave vector numbers, the total frequency number of the energy band data is 288, and a total of 8000 sets of data are collected, so n=6, k=48, m=288, N=8000.
[0043] Step 2: Figure 2As shown in the figure, a pre-training model F is constructed, including: M-layer network structure, each layer of the network structure is composed of a fully connected layer, a batch normalization layer and a RELU activation function, and S i Processing is performed to obtain the predicted energy band data of group i ,in, Represents the i-th group of predicted energy band data The frequency of the j-th energy band data in the present embodiment, in order to verify the forward prediction model In order to improve the prediction ability of the network, the data set was divided into training set and test set according to the ratio of 4:1. The pre-trained model F was trained with the training set. After the training, the model ability was verified on the test set. Three samples were randomly selected from the test set to draw comparison charts of the real energy band data and the energy band data trained by the forward network model for comparison.
[0044] Step 3: Use formula (1) to construct the average error loss function Loss of the energy band data F , and train the pre-trained model F to obtain the forward prediction network model :
[0045] (1)
[0046] Step 4: Figure 2 As shown in the figure, the reverse network model G is constructed, including: K-layer network structure, each layer of the network structure is composed of a fully connected layer, a batch normalization layer and a RELU activation function, and the reverse network model G is connected with the forward prediction network model After the series connection, the series network model T is constructed, and W is sequentially i Processing is performed to obtain the predicted energy band data of group i ,in, Represents the i-th group of predicted energy band data The frequency of the j-th energy band data in ;
[0047] In this embodiment, the pre-trained model F and the reverse network model G are both 7-layer network structures, and the series network model T is a 14-layer network structure. In order to determine the prediction ability of the network, the data set was divided into training set and test set at a ratio of 4:1. The series network model T was trained using the training set. After the training, the model capability was verified on the test set. Three samples were randomly selected from the test set to draw comparison charts of the real energy band data and the energy band data trained by the series network.
[0048] Step 4.1: The inverse network model G is used for the i-th group of energy band data W i Processing is performed to obtain the predicted structural parameters of the i-th group ,in, represents the predicted structural parameters of the i-th group The jth structural parameter in ;
[0049] Step 4.2: Input forward prediction network model The predicted energy band data of group i is obtained by processing .
[0050] Step 5: Construct the loss function Loss of the series network T T , and used for training the series network T to obtain the series network model :
[0051] Step 5.1: Use formula (2) to construct the loss function of the reverse network G :
[0052] (2)
[0053] Step 5.2: Use formula (3) to construct the loss function Loss of the series network T T :
[0054] (3)
[0055] Step 6: and Composition of the dataset , and calculate The frequency width of the fundamental frequency gap and the frequency width of the octave gap The cumulative sum between them is calculated, and the structural parameter corresponding to the maximum value among the N cumulative sums is selected as the target structural parameter , Represents the target structure parameters In this embodiment, considering the feasibility of the material, the nonlinear material AlGaAs is selected, and the refractive index About 3.2772, the target structure parameters are .
[0056] Step 7: According to the target structure parameters , using the second-order nonlinear effect to generate the second harmonic:
[0057] Step 7.1: The corresponding photonic crystal PC 1 Conduct characteristic modeling and construct photonic crystal PC 1 The geometric structure and the high symmetry point along the first Brillouin zone , perform parameterized scanning on the wave vector k and obtain the photonic crystal PC 1The band structure of the photonic crystal PC 1 The baseband gap center frequency f 0 and the center frequency of the double band gap f 1 In this embodiment, the photonic crystal PC 1 The baseband gap center frequency f 0 is 75 Thz, and the center frequency of the double frequency band gap is f 1 It is 150Thz.
[0058] Step 7.2: Break the Photonic Crystal PC 1 After the rotational symmetry of the photonic crystal PC is obtained 2 , and processed according to the process of step 7.1 to obtain the photonic crystal PC 2 The band structure of
[0059] Step 7.3, build by PC 1 and PC 2 The dimension of the supercell system is N×1, and the fundamental frequency band gap frequency is f 0 and the double bandgap frequency band f 1 The wave vector k is parametrically scanned on the upper and lower planes to obtain the band structure of the supercell system, thereby determining the fundamental frequency boundary state FW and the double frequency boundary state SHG of the supercell system, where N represents the PC 1 and PC 2 Total number of PC 1 The number of PC is N / 2, 2 The number of is N / 2.
[0060] Step 7.4: Based on the fundamental frequency boundary state FW and the double frequency boundary state SHG, use the wave vector matching relationship , get the fundamental frequency of the wave vector matching intersection point and frequency multiplication , and then according to the frequency and momentum relationship expression , the relationship between wavelength and frequency , and the fundamental frequency is obtained The corresponding wavelength In this embodiment, the fundamental frequency of the wave vector matching intersection is is 78.06 Thz, wavelength λ 0 It is 3840.5nm.
[0061] Step 7.5: Build from PC 1 and PC 2 The dimension of the boundary state system is M×R, and the excitation source I is placed at port 1 of the boundary state system. 0 , place detector P at port 2 0 , where I 0 For sine wave , E 0 represents the intensity of the sine wave, is the fundamental frequency of the wave vector matching intersection point; where M represents the PC 1 and PC 2 Total number of PC 1 The number of PC is M / 2, 2 The number is M / 2, R represents the PC in the x direction 1 and PC 2 The number of PC 1 With PC 2 The number of is equal to R.
[0062] Step 7.6: Using Excitation Source I 0 Exciting the fundamental frequency boundary state FW to generate the second harmonic , and the detector P 0 After discrete Fourier transform of the generated spectrum, the amplitude of the second harmonic excited by the fundamental frequency boundary state FW is obtained;
[0063] Step 7.7, build by PC 1 and PC 2 The dimensions of the composition are The angular state system and determine the fundamental frequency of the angular state system and frequency multiplication , thereby determining the fundamental frequency Corresponding wavelength In this embodiment, the fundamental frequency of the angular state system is The wavelength is 84.888 Thz. It is 3531.6nm.
[0064] Step 7.8: Set the fundamental frequency of the sine wave to Then, return to step 7.6 to obtain the amplitude of the second harmonic excited by the corner state system.
[0065] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.
[0066] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.
Claims
1. A method for generating second harmonics in photonic crystals based on deep learning, characterized in that: The steps are as follows: Step 1: Use the parametric scanning method to scan along the high symmetry point of the first Brillouin zone , perform wave vector scanning on the energy band of the photonic crystal, obtain the photonic crystal energy band data set and perform preprocessing to obtain the preprocessed photonic crystal energy band data set ,in, represents the structural parameters of the i-th group, Represents S i The jth structural parameter in represents the energy band data of the i-th group, W i The frequency of the j-th energy band data in , m represents the total frequency of the energy band data, and m=n×k, n represents the number of energy bands in the parametric scanning unit cell, k represents the number of wave vectors required to scan each energy band, and N represents the number of groups; Step 2: Construct a pre-training model F, including: M-layer network structure, each layer of which is composed of a fully connected layer, a batch normalization layer and a RELU activation function, and perform S i Processing is performed to obtain the predicted energy band data of group i ,in, Represents the i-th group of predicted energy band data The frequency number of the j-th energy band data in ; Step 3: Use formula (1) to construct the average error loss function Loss of the energy band data F , and train the pre-trained model F to obtain the forward prediction network model : (1) Step 4: Construct the reverse network model G, including: K-layer network structure, each layer of network structure is composed of a fully connected layer, a batch normalization layer and a RELU activation function, and connect the reverse network model G with the forward prediction network model After the series connection, the series network model T is constructed, and W is sequentially i Processing is performed to obtain the predicted energy band data of group i ,in, Represents the i-th group of predicted energy band data The frequency of the j-th energy band data in ; Step 5: Construct the loss function Loss of the series network T T , and used for training the series network T to obtain the series network model : Step 6: and Composition of the dataset , and calculate The frequency width of the fundamental frequency gap and the frequency width of the octave gap The cumulative sum between them is calculated, and the structural parameter corresponding to the maximum value among the N cumulative sums is selected as the target structural parameter , Represents the target structure parameters The jth structural parameter in ; Step 7: According to the target structure parameters , using the second-order nonlinear effect to generate second harmonics.
2. The method for generating second harmonics in photonic crystals based on deep learning according to claim 1, characterized in that: Step 4 is performed as follows: Step 4.1: The inverse network model G is used for the i-th group of energy band data W i Processing is performed to obtain the predicted structural parameters of the i-th group ,in, represents the predicted structural parameters of the i-th group The jth structural parameter in ; Step 4.2: Input forward prediction network model The predicted energy band data of group i is obtained by processing .
3. The method for generating second harmonics in photonic crystals based on deep learning according to claim 2, characterized in that: Loss function in step 5.1 T It is constructed as follows: Step 5.1: Use formula (2) to construct the loss function of the reverse network G : (2) Step 5.2: Use formula (3) to construct the loss function Loss of the series network T T : (3)。 4. The method for generating second harmonics in photonic crystals based on deep learning according to claim 3, characterized in that: Step 7 is performed as follows: Step 7.1: The corresponding photonic crystal PC1 is characteristically modeled, the geometric structure of the photonic crystal PC1 is constructed, and the high symmetry point along the first Brillouin zone is , perform parameterized scanning on the wave vector k to obtain the band structure of the photonic crystal PC1, thereby determining the fundamental band gap center frequency f0 and the double frequency band gap center frequency f1 of the photonic crystal PC1; Step 7.2, after breaking the rotational symmetry of the photonic crystal PC1, the photonic crystal PC2 is obtained, and the process of step 7.1 is performed to obtain the band structure of the photonic crystal PC2; Step 7.3, construct a supercell system of dimension N×1 composed of PC1 and PC2, and perform parameterized scanning of the wave vector k in the fundamental band gap frequency segment f0 and the double-frequency band gap frequency segment f1, respectively, to obtain the band structure of the supercell system, thereby determining the fundamental frequency boundary state FW and the double-frequency boundary state SHG of the supercell system, where N represents the total number of PC1 and PC2 in the y direction in the supercell system, and the number of PC1 in the y direction in the supercell system is N / 2, and the number of PC2 in the y direction is N / 2; Step 7.4: Based on the fundamental frequency boundary state FW and the double frequency boundary state SHG, use the wave vector matching relationship , get the fundamental frequency of the wave vector matching intersection point and frequency multiplication ; Step 7.5: Construct a boundary state system of dimension M×R consisting of PC1 and PC2, and place the excitation source I0 at port 1 of the boundary state system and the detector P0 at port 2, where I0 is a sine wave. , E0 represents the intensity of the sine wave, is the fundamental frequency of the wave vector matching intersection point; where M represents the total number of PC1 and PC2 in the y direction in the boundary state system, and the number of PC1 in the y direction in the boundary state system is M / 2, and the number of PC2 in the y direction is M / 2; R represents the number of PC1 in the x direction or the number of PC2 in the x direction in the boundary state system, and the number of PC1 and PC2 in the x direction is equal and both are R; Step 7.6: Use the excitation source I0 to excite the fundamental frequency boundary state FW to generate the second harmonic , and after performing discrete Fourier transform on the spectrum generated by detector P0, the amplitude of the second harmonic excited by the fundamental frequency boundary state FW is obtained; Step 7.7: Construct the dimension composed of PC1 and PC2 as The corner state system and determine the fundamental frequency of the corner state system and frequency multiplication ; Step 7.8: Set the fundamental frequency of the sine wave to Then, return to step 7.6 to obtain the amplitude of the second harmonic excited by the corner state system.
5. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the photonic crystal second harmonic generation method according to any one of claims 1 to 4, and the processor is configured to execute the program stored in the memory.
6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the photonic crystal second harmonic generation method according to any one of claims 1 to 4 are executed.