Q value optimization method of photonic crystal microcavity, storage medium and equipment

Abstract

The invention discloses a Q value optimization method of a photonic crystal microcavity, a storage medium and equipment, and relates to the technical field of photonic crystal microcavities, the photonic crystal microcavity comprises a one-dimensional photonic crystal, the center of the one-dimensional photonic crystal is a gradual change area with 12 hole radiuses and lattice constants gradually changing, and the two sides of the one-dimensional photonic crystal are reflection areas with fixed lattice constants and hole radiuses. The optimization method comprises the following steps: taking the cavity length of the photonic crystal microcavity and six lattice constants of the gradual change region as parameters to be optimized; obtaining a first data sample set and a second data sample set of to-be-optimized parameters, dividing the first data sample set into a training set and a test set to train and test the LSSVM model, and outputting log10Q; and taking the second data sample set as an initial population of a genetic algorithm, taking log10Q as a fitness function, and obtaining an optimized Q value until the fitness function tends to be stable. According to the invention, the Q value of the one-dimensional photonic crystal microcavity can be greatly increased in a short time.

Description

Technical Field

[0001] The present invention relates to the technical field of photonic crystal microcavity, and in particular to a Q value optimization method, storage medium and equipment of a photonic crystal microcavity. Background Art

[0002] In current biological tissues, the size of viruses is relatively small, about 100nm. The radius of some chemical product particles, such as polystyrene particles, is even smaller, about 40nm. In order to achieve small radius particle detection, the pursuit of high-performance and high-sensitivity optical particle sensors has become a hot topic in research. Photonic crystals can confine light to a very small area, especially one-dimensional photonic crystals, which have high freedom of design, easy to achieve high Q value and small mode volume, and can create high-intensity evanescent fields on the surface of their devices to interact with extremely small radius particles, thereby realizing small nano-radius particle detection. As an important branch of the field of artificial intelligence, the development of machine learning has promoted the integration of interdisciplinary fields and is conducive to solving major problems in the fields of medicine and nanophotonics. By utilizing the powerful data analysis capabilities and high mobility of the algorithm, a high-Q value one-dimensional photonic crystal microcavity was obtained in a relatively short time and applied to particle sensing simulation.

[0003] In the simulation of photonic crystal microcavities, the optimization of Q value is an important issue. The Q value represents the energy loss and light storage efficiency of the photonic crystal microcavity, and is an important parameter for evaluating the performance of the microcavity. The Q value of the microcavity can be improved by adjusting the structural parameters of the microcavity and optimizing the refractive index of the material in the FDTD (Finite-Difference Time-Domain) simulation. By establishing a sensing model, constructing a model of the photonic crystal microcavity, and performing Q value optimization and electric field diagram simulation and other analyses, the performance and characteristics of the photonic crystal microcavity can be deeply studied. When using FDTD to optimize the Q value of the photonic crystal microcavity, in order to obtain more accurate results, a high-precision model and mesh division will be established, which requires a large number of iterative calculations, which may lead to a significant increase in calculation time. Summary of the invention

[0004] The purpose of the present invention is to solve the problem of long time for optimizing the Q value of a photonic crystal microcavity in the prior art, and to provide a Q value optimization method for a photonic crystal microcavity, wherein the photonic crystal microcavity comprises: a one-dimensional photonic crystal, the central part of the one-dimensional photonic crystal is a gradual change zone with 12 hole radii and a lattice constant gradually changing, and both sides are reflection zones with fixed lattice constants and hole radii, and the method comprises the following steps:

[0005] S1, taking the cavity length L of the photonic crystal microcavity and six lattice constants (a1, a2, a3, a4, a5, a6) of the gradient zone as parameters to be optimized;

[0006] S2, obtaining a first data sample set of the cavity length L and six lattice constants of the gradient zone, and dividing the first data sample set into a training set and a test set;

[0007] S3. Use the training set and test set to train and test the LSSVM model, and output log 10 Q;

[0008] S4, obtaining a second data sample set of the cavity length L and the six lattice constants of the gradient zone, taking the second data sample set as the initial population, and converting the logarithm output by the LSSVM model into 10 Q is used as the fitness function, and crossover and mutation operations are performed through the genetic algorithm until the fitness function tends to be stable. The iteration ends and the optimized Q value of the photonic crystal microcavity is obtained.

[0009] Furthermore, the numerical range of the cavity length L and the six lattice constants of the gradual change region in the first data sample set and the second data sample set is [-1 nm, 1 nm].

[0010] Furthermore, the loss function of the LSSVM model is:

[0011]

[0012] Among them, L loss represents the loss function of the LSSVM model, N represents the number of test sets, T r is the predicted value of the LSSVM model, T p is the actual value of the test set.

[0013] Furthermore, the optimization problem of the LSSVM model is:

[0014]

[0015] Among them, J represents the loss function, w represents the weight coefficient vector, C represents the penalty factor, l represents the number of input samples, ξ i represents the error vector of the i-th sample, y i represents the output of the i-th input sample of the LSSVM model, φ() represents a nonlinear function, and x i represents the i-th input, the input is n-dimensional, n=7, and b represents the bias term.

[0016] Furthermore, the optimization problem is solved according to the Lagrange function:

[0017]

[0018] Where L represents the Lagrange function, α i Represents the Lagrange multiplier.

[0019] Further,

[0020] The decision function of the LSSVM model is:

[0021]

[0022] Among them, f(x) represents the decision function of the LSSVM model, K(x i ,x j ) represents the kernel function in Mercer's condition, x j represents the jth input.

[0023] Furthermore, the Gaussian kernel function expression that satisfies the Mercer condition is:

[0024]

[0025] Among them, K(x i ,x j ) G represents the Gaussian kernel function that satisfies the Mercer condition, x i represents the i-th input, x j represents, and σ represents the width parameter.

[0026] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the Q value optimization method of the photonic crystal microcavity is implemented.

[0027] The present invention also proposes an electronic device, comprising a processor and a memory, wherein the processor and the memory are interconnected, wherein the memory is used to store a computer program, the computer program comprises computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the above-mentioned Q value optimization method of the photonic crystal microcavity.

[0028] The beneficial effects brought by the technical solution provided by the present invention are:

[0029] The present invention uses LSSVM algorithm model prediction to replace the FDTD simulation process. After the introduction of the genetic algorithm, thanks to its cross-mutation high-efficiency optimization characteristics, the optimization speed is significantly accelerated. In order to achieve more accurate Q value prediction, the LSSVM algorithm model with a small loss function is selected. Compared with the traditional FDTD simulation optimization, the optimization method based on the LSSVM algorithm combined with the genetic algorithm greatly improves the Q value of the one-dimensional photonic crystal microcavity in a short time. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a structural diagram of a photonic crystal microcavity according to an embodiment of the present invention;

[0031] Figure 2 is a flow chart of a Q value optimization method of a photonic crystal microcavity according to an embodiment of the present invention;

[0032] Figure 3 1 is a bar graph of the data set of Q value and log10Q in the embodiment of the present invention, wherein (a) is a bar graph of Q value, and (b) is a bar graph of log10Q;

[0033] Figure 4 This is a forward identification structure diagram of the LSSVM algorithm according to an embodiment of the present invention;

[0034] Figure 5 is a block diagram of an electronic device in an exemplary embodiment of the present invention;

[0035] Figure 6 is the correlation coefficient between the training set and the test set of the LSSVM algorithm model in the embodiment of the present invention, Figure 6 (a) is the correlation coefficient of the LSSVM algorithm model training set. Figure 6 (b) is the correlation coefficient of the LSSVM algorithm model test set;

[0036] Figure 7 is the optimization of the genetic algorithm under the LSSVM algorithm model with different loss functions in the embodiment of the present invention, Figure 7 The loss function values ​​of (a), (b), (c), and (d) are 16.622%, 15.407%, 10.732%, and 11.441%, respectively;

[0037] Figure 8 Schematic diagram of particle placement in FDTD simulation in an embodiment of the present invention;

[0038] Fig. 9 The transmission spectrum of the gold particles with a radius of 10 nm before and after being placed in the embodiment of the present invention is changed. DETAILED DESCRIPTION

[0039] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0040] The Q value optimization method of the photonic crystal microcavity of the embodiment of the present invention is optimized on the basis of the following photonic crystal microcavity, the photonic crystal microcavity comprises: a one-dimensional photonic crystal, the central part of the one-dimensional photonic crystal is a gradual change zone with 12 hole radii and lattice constants gradually changing, and the two sides are reflection zones with fixed lattice constants and hole radii. The structural diagram of the photonic crystal microcavity of the embodiment of the present invention is referred to Figure 1 The overall thickness of the device is 220nm and the width is 500nm.

[0041] The flowchart of the Q value optimization method of the photonic crystal microcavity according to the embodiment of the present invention is shown in FIG. Figure 2, specifically including:

[0042] S1. The cavity length L of the photonic crystal microcavity and the six lattice constants (a1, a2, a3, a4, a5, a6) of the gradient zone are taken as parameters to be optimized. x =0.28a x ,x=1,2,...,6.

[0043] S2. Obtain a first data sample set of the cavity length L and the six lattice constants of the gradient zone, and divide the first data sample set into a training set and a test set. In the embodiment of the present invention, the values ​​of the cavity length L and the six lattice constants of the gradient zone are randomly changed within [-1nm, 1nm] to obtain 1084 sets of data sample sets, and the FDTD method is used to calculate the Q value corresponding to each set of data sample sets. Most of the Q value distributions corresponding to these 1084 sets of microcavity structures are concentrated in the 106-107 region.

[0044] S3. Use the training set to train the LSSVM model, deduce the relationship between the Q value of the one-dimensional photonic crystal microcavity and the structural parameters to be optimized, and use the test set to test the LSSVM model to verify whether its Q value prediction for the existing structure is accurate. By comparing the error between the Q value predicted by the LSSVM algorithm model and the Q value calculated by FDTD simulation, the prediction performance of the LSSVM algorithm model can be judged. The LSSVM model outputs log 10 Q. Figure 3 1 is a bar graph of the data set of Q value and log10Q in the embodiment of the present invention, wherein (a) is a bar graph of Q value, and (b) is a bar graph of log10Q.

[0045] LSSVM (Least Squares Support Vector Machines) is a variant of support vector machine (SVM). Its training process uses the least squares method to solve the optimization problem. The LSSVM algorithm uses nonlinear functions The samples are mapped to a high-dimensional feature space, thereby converting the nonlinear function estimation problem in the sample space into a linear function estimation problem in Hibert, and its regression expression is:

[0046]

[0047] Where w is the weight coefficient vector, represents a nonlinear function, b∈R is a bias term. The error ξ is selected during the optimization process i The square of is used as the loss function, and the optimization problem is:

[0048]

[0049] Among them, J represents the loss function, w represents the weight coefficient vector, C represents the penalty factor, l represents the number of input samples, ξ i represents the error vector of the i-th sample, y i represents the output of the i-th input sample of the LSSVM model, x i represents the i-th input, the input is n-dimensional, n=7, and b represents the bias term.

[0050] To solve the above optimization problem, simplify the Lagrange function:

[0051]

[0052] Where L represents the Lagrange function, α i Represents the Lagrange multiplier.

[0053] Finally, the decision function of LSSVM is obtained as:

[0054]

[0055] Among them, f(x) represents the decision function of the LSSVM model, K(x i ,x j ) represents the kernel function in Mercer's condition, x j represents the jth input.

[0056] The kernel functions of the common LSSVM algorithm model mainly include polynomial kernel function, Gaussian kernel function and Sigmoid kernel function. All three have very good nonlinear mapping capabilities, but when processing large-scale data and requiring accurate prediction, the Gaussian kernel function has stronger robustness and excellent computational efficiency than the first two. This paper selects the LSSVM algorithm model with the Gaussian kernel function as the kernel function, and the Gaussian kernel function expression that meets the Mercer condition is:

[0057]

[0058] Among them, K(x i ,x j ) G represents the Gaussian kernel function that satisfies the Mercer condition, x i represents the i-th input, x j represents, and σ represents the width parameter.

[0059] The LSSVM algorithm model has seven inputs (L, a1, a2, a3, a4, a5, a6) and outputs log 10Q. For the above 1084 data sets, 70% are used as training sets to train the LSSVM algorithm model, and 30% are used as test sets to test the accuracy of the LSSVM algorithm model in predicting the Q value. The way to measure whether the LSSVM algorithm model predicts the Q value accurately is to calculate the size of the loss function. The loss function is defined as:

[0060]

[0061] Among them, L loss represents the loss function of the LSSVM model, N represents the number of test sets, T r is the predicted value of the LSSVM model, T p is the actual value of the test set.

[0062] The smaller the loss function, the higher the prediction accuracy of the model. In the embodiment of the present invention, the minimum loss function that the LSSVM algorithm model can achieve is 0.095, which has the best prediction accuracy.

[0063] The forward identification structure diagram based on the LSSVM algorithm model is as follows Figure 4 As shown, the identified system P refers to any system or process that needs to be modeled, predicted or analyzed by the LSSVM algorithm, such as the Q value optimization problem of the photonic crystal microcavity in the embodiment of the present invention. The difference between the output of the LSSVM algorithm model and the system output is used as the training signal of the model, and the model output is approached to the system output by continuously optimizing the model parameters. The input-output relationship of this process can be described as:

[0064] y(k)=f[u(k),u(k-1),...u(km);y(k-1),....y(kn)]

[0065] Among them, u is the system input, y is the system output, m is the order of the system input, n is the order of the system output, and f(.) is a nonlinear function. In this section, the order of the system input is 7 (the 7 parameters to be optimized (L, a1, a2, a3, a4, a5, a6)), and the order of the system output is 1.

[0066] S4, randomly select values ​​in [-1nm, 1nm] to obtain the second data sample set of the cavity length L and the six lattice constants of the gradient zone, use the second data sample set as the initial population, and log the output of the LSSVM model 10 Q is used as the fitness function, and crossover and mutation operations are performed through the genetic algorithm until the fitness function tends to be stable. The iteration ends and the optimized Q value of the photonic crystal microcavity is obtained.

[0067] In an exemplary embodiment, a computer-readable storage medium is included, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the Q value optimization method of the photonic crystal microcavity is implemented.

[0068] See also Figure 5 In an exemplary embodiment, an electronic device is also included, including at least one processor, at least one memory, and at least one communication bus.

[0069] The memory stores a computer program, which includes computer-readable instructions. The processor calls the computer-readable instructions stored in the memory through a communication bus to execute the Q value optimization method of the photonic crystal microcavity.

[0070] In order to verify the fitting degree of the LSSVM algorithm model to the data set, the input real Q value and the output predicted Q value distribution are normalized here to obtain the correlation coefficient R of the model. The maximum value of R is 1, which means that the fitting of the LSSVM algorithm model to the data set is completely positively correlated. However, for the nonlinear situation of high Q value one-dimensional photonic crystal microcavity structure parameters and Q value optimization, its R value can only be infinitely close to 1. It is believed that the larger the R value, the better the model fits the data set. Figure 6 As shown in the figure, the black dotted line represents that the real Q value is equal to the predicted Q value, and the blue solid line is the data fitting curve. It is not difficult to find that the data points are evenly distributed on both sides of the fitting curve, and the R values ​​of the training set and the test set are 0.95492 and 0.95297 respectively, which means that the data fitting degree of the model is high. Therefore, the trained LSSVM algorithm model can fully and accurately predict the Q value of the one-dimensional photonic crystal microcavity.

[0071] The initial stage of the genetic algorithm is to randomly change the population information encoding (lattice constant and cavity length of the central gradient zone) within [-1nm, 1nm]; then, the predicted log10Q of the LSSVM algorithm model is used as its fitness function, and the crossover and mutation operations of the genetic algorithm are repeatedly iterated. When the fitness function tends to be stable, the optimization ends.

[0072] The optimization of genetic algorithm under LSSVM algorithm model with different loss functions is as follows: Figure 7 shown. Figure 7The loss function values ​​of (a), (b), (c) and (d) are 16.622%, 15.407%, 10.732% and 11.441% respectively. After 400 consecutive iterations, the fitness function gradually stabilizes at around 8.0. The red curve in the figure represents the best individual in each generation during the iteration process, and the black curve represents the average situation of each generation. Individuals above the average level are cross-bred, and individuals below the average level are self-mutated. In this way, the average fitness and the best individual are steadily improved. The FDTD method is used for simulation verification. Figure 7 The Q values ​​of the one-dimensional photonic crystal microcavity corresponding to the structures (a), (b), (c) and (d) are 5.37×107, 8.08×107, 1.31×108 and 1.03×10^8 respectively. It can be found that the LSSVM algorithm model with a small loss function has a positive effect on the optimization of the genetic algorithm, and it is easier to obtain a high Q value structure.

[0073] The high-Q photonic crystal microcavity structure obtained in the embodiment of the present invention is applied to particle sensing. Currently, common particle sizes include virus particles with a diameter of about 100 nm and protein molecules with a diameter of more than 300 nm. Common polystyrene particles have a diameter of 40 nm or more.

[0074] In order to verify that the designed high-Q one-dimensional photonic crystal microcavity has a low particle radius detection limit, a single 10nm radius gold particle is first placed at the position where the device light field is strongest, such as Figure 8 shown.

[0075] The transmission spectrum of a 10nm radius gold particle changes before and after placement. Fig. 9 As shown in the figure, it can be seen that the transmittance decreases before and after the particles are placed. This is due to the increase in device scattering loss caused by the presence of particles. After FDTD simulation verification, the wavelength shift caused by the presence of 10nm radius gold particles on the device surface is 1.47nm.

[0076] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing the Q value of a photonic crystal microcavity, the photonic crystal microcavity comprising: A one-dimensional photonic crystal, wherein the central part of the one-dimensional photonic crystal is a gradient zone with 12 aperture radii and a lattice constant gradient, and both sides are reflection zones with fixed lattice constants and aperture radii, characterized in that the method comprises the following steps: S1, taking the cavity length of the photonic crystal microcavity and six lattice constants of the gradient zone as parameters to be optimized; S2, obtaining a first data sample set of the cavity length L and six lattice constants of the gradient zone, and dividing the first data sample set into a training set and a test set; S3. Use the training set and test set to train and test the LSSVM model, and output log 10 Q; S4, obtaining a second data sample set of the cavity length L and the six lattice constants of the gradient zone, taking the second data sample set as the initial population, and converting the logarithm output by the LSSVM model into 10 Q is used as the fitness function, and crossover and mutation operations are performed through the genetic algorithm until the fitness function tends to be stable. The iteration ends and the optimized Q value of the photonic crystal microcavity is obtained.

2. The Q value optimization method of a photonic crystal microcavity according to claim 1, characterized in that: The numerical range of the cavity length L and the six lattice constants of the gradient region in the first data sample set and the second data sample set is [-1nm, 1nm].

3. The Q value optimization method of a photonic crystal microcavity according to claim 1, characterized in that: The loss function of the LSSVM model is: Among them, L loss represents the loss function of the LSSVM model, N represents the number of test sets, T r is the predicted value of the LSSVM model, T p is the actual value of the test set.

4. The Q value optimization method of a photonic crystal microcavity according to claim 1, characterized in that: The optimization problem of the LSSVM model is: Among them, J represents the loss function, w represents the weight coefficient vector, C represents the penalty factor, l represents the number of input samples, ξ i represents the error vector of the i-th sample, y i represents the output of the i-th input sample of the LSSVM model, represents a nonlinear function, x i represents the i-th input, the input is n-dimensional, n=7, and b represents the bias term.

5. The Q value optimization method of a photonic crystal microcavity according to claim 4, characterized in that: Solve the optimization problem according to the Lagrange function: Where L represents the Lagrange function, α i Represents the Lagrange multiplier.

6. The Q value optimization method of a photonic crystal microcavity according to claim 5, characterized in that: The decision function of the LSSVM model is: Among them, f(x) represents the decision function of the LSSVM model, K(x i ,x j ) represents the kernel function in Mercer's condition, x j represents the jth input.

7. The Q value optimization method of a photonic crystal microcavity according to claim 6, characterized in that: The Gaussian kernel function expression that satisfies the Mercer condition is: Among them, K(x i ,x j ) G represents the Gaussian kernel function that satisfies the Mercer condition, x i represents the i-th input, x j represents, σ ​​represents the width parameter.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the processor and the memory are interconnected, wherein the memory is used to store a computer program, the computer program comprises computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the method according to any one of claims 1 to 7.

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