A method of designing or optimizing a polarization-modulated nanophotonic device

Abstract

The application discloses a kind of polarization modulation nanophotonics device design or optimization method, according to polarization conversion needs, utilize deep neural network and bayesian optimization algorithm such as recommendation generation nanophotonics device (such as wave plate) structure parameter, complete the design of required polarization modulation device.This method utilizes the efficient parallel computing capacity of deep neural network and bayesian optimization, under the limited computing resources, recommend to generate a large number of wave plates with efficient polarization conversion capability, and construct structure database, can further support the development of various polarization-dependent optical devices.Compared with the traditional design strategy based on preset physical rules or prior design experience, the present application has higher design optimization efficiency and design freedom, reduces the consumption of computing resources, and provides a new paradigm for the design and optimization of nanophotonics devices.

Description

TECHNICAL FIELD

[0001] The present application relates to a design or optimization method for a nano-photonic device for polarization modulation, in particular to a method for designing a nano-photonic device with high polarization conversion efficiency by using an optimization algorithm such as Bayesian optimization and a deep neural network to optimize device structure parameters. BACKGROUND

[0002] Polarization is a basic property of light, which is of great significance in both basic scientific fields including the study of light-matter interaction, optical nonlinearity, and practical application fields such as sensing, imaging, optical display, quantum information processing. Polarization state modulation can be achieved by optical waveplates. Traditional waveplates are usually composed of bulk materials such as birefringent wafer with precise thickness. Due to the different propagation speeds of the two orthogonal polarized lights perpendicular and parallel to the optical axis in the wafer, the phase difference is accumulated by the propagation distance, and the modulation of the polarization state of light is achieved. However, due to the disadvantages of traditional waveplate devices such as large volume, difficult processing and poor compatibility of preparation process, it is difficult to apply to miniaturization and high integration of optical systems. In recent years, with the continuous development of nanomaterial preparation technology, artificial photonic structures including photonic crystals, metamaterials are widely used to regulate light-matter interaction. These artificial photonic structures can modulate the polarization state of light at the subwavelength scale, providing rich design options for integrated optical devices. Through reasonable structure design, effective modulation of light polarization state can be achieved on compact planar optical devices, which has great application potential in polarization imaging, sensing, communication and other application fields.

[0003] Reverse design, a classic design strategy, its core is to find an effective algorithm from the requirement to the physical implementation system under the premise of determining the target requirement. In optical design, we can use the strategy of reverse design to find the structure that meets the requirements in the design space from the required optical performance. For a specific design problem, the device structure can be parameterized based on the prior physical model or existing experience to generate the design space. Then, through numerical simulation or verification experiment, the optical response of the structure point in the design space is obtained, and the structure database is constructed to provide data support for subsequent device optimization. There are two challenges in the classic reverse design process. First, without prior physical model or experience to guide, it is difficult to complete the device structure design or optimization. Second, the resources consumed in generating the structure database increase exponentially with the dimension of the design space, so it is difficult to open the structure freedom to construct high-dimensional design space to complete the design of more efficient devices.

[0004] Artificial intelligence algorithms such as deep neural networks (DNNs) are composed of a large number of logic computing nodes of biological-like neurons, and by adjusting the weights and biases of the computing nodes, the error between the deep neural network and the given target output data is minimized. Compared with traditional design methods based on prior physical rules, artificial intelligence algorithms can spontaneously learn the inherent rules and relationships from the structure database and establish the mapping relationship between the input data and the output data. Therefore, through a reasonable parameterization strategy, artificial intelligence algorithms can be migrated to the research of nanophotonics. With strong generalization ability in a given design space, artificial intelligence algorithms bring development opportunities to many photonic research fields such as spectrum prediction, ultrafast pulse reconstruction, structure inverse design, photonic band structure analysis, etc. Bayesian optimization is a design strategy for global optimization of functions, which has the advantages of parallel computing and gradient insensitivity, and has important applications in many design problems in scientific frontiers and engineering applications. SUMMARY

[0005] The purpose of the present application is to provide a general design or optimization method for polarization modulation nanophotonic devices. The method of the present application can recommend the structure parameters of nanophotonic devices (such as wave plates) according to the polarization conversion requirements, using algorithms such as deep neural networks and Bayesian optimization, to complete the design of the required polarization modulation device.

[0006] The method of the present application can recommend a large number of nanostructures with efficient polarization conversion capability and construct a structure database using the efficient parallel computing capability of deep neural networks and Bayesian optimization under limited computing resources. Then, considering the device preparation accuracy and process tolerance, the best structure parameters are found from the database. Moreover, the constructed structure database can further support the development of various polarization-dependent optical devices. Compared with traditional design strategies based on pre-set physical rules or prior design experience, the method of the present application has higher design optimization efficiency and design freedom, and can complete the design and optimization of polarization modulation wave plates and other devices, and can further support the development of multifunctional polarization-dependent devices.

[0007] The technical solutions of the present application are as follows:

[0008] A design or optimization method for polarization modulation nanophotonic devices, comprising the following steps:

[0009] 1) Randomly generate nanostructures for polarization modulation and obtain their corresponding optical response data to construct an initial data set;

[0010] 2) Train a deep neural network using the initial data set so that it can predict the optical response data of the nanostructure according to the structure data of the nanostructure;

[0011] 3) Select a certain proportion of samples from the initial data set, usually about 10%, as the initial input data for subsequent optimization, and then use Bayesian optimization, genetic algorithm, topology optimization and other optimization algorithms to recommend and generate a number of nanostructures according to the design target;

[0012] 4) Use a deep neural network to predict the optical response data of the nanostructures generated in step 3) to evaluate their performance;

[0013] 5) Repeat steps 3) and 4) until the optimization algorithm model converges, and obtain the required nanostructure for the polarization modulation nano-optical device.

[0014] During the optimization process of repeating steps 3) and 4), store the nanostructures with higher expected functions and their optical response data to develop a structure database, which can support the design and optimization of subsequent polarization modulation waveplate devices or other polarization modulation nano-optical devices.

[0015] The above step 1) randomly generates nanostructures according to the target optical properties and working bandwidth to determine the material type, structure composition and parameterization scheme of the nanostructure. The optical response data corresponding to the nanostructure can be obtained by simulation using software such as finite difference time domain (FDTD) or multi-physical field simulation (COMSOL).

[0016] The above step 2) uses the initial data set to train the deep neural network, which means that the structure data of the nanostructure is input into the deep neural network, and the network node weight is adjusted using the gradient descent method, so that the output data of the deep neural network approximates the optical response data of the nanostructure in the data set.

[0017] In the above step 3), taking the Bayesian optimization algorithm as an example, the independent variables of the Bayesian optimization should be set as the structure parameters of the nanostructure, and the dependent variables can be set as the device performance indicators derived from the optical response data. Through the Gaussian process, Bayesian optimization can automatically analyze the black box function between the independent variables and the dependent variables based on the input data, and generate a sampling function combined with the confidence interval. According to the maximum value of the sampling function, Bayesian optimization can recommend the structure parameters of the next generation of nanostructures.

[0018] In the above step 4), the deep neural network can predict the optical response data of the generated nanostructure, thereby evaluating the performance indicators of the device.

[0019] Further, the data type in the initial data set in step 1) should be tensor data to meet the training requirements of the deep neural network. To open the degree of freedom of design, the geometric configuration of the nanostructure can be parameterized as a two-dimensional 0-1 structure matrix during the construction of the initial data set, where 1 represents the presence of a nanostructure, and 0 represents air. To further enhance the flexibility of the design, the optical response data stored in the initial data set is a wide-spectrum Jones matrix, rather than spectral data or the polarization conversion rate of a wave plate. When designing a device, the polarization conversion efficiency (PCE, the intensity of the required polarized light divided by the total intensity of the incident light) or the polarization conversion ratio (PCR, the intensity of the required polarized light divided by the total intensity of the total reflected or transmitted light) and other performance indicators can be extracted from the wide-spectrum Jones matrix according to the following formulas (1) to (3) as optimization objectives to perform device design according to the performance requirements of the device.

[0020]

[0021]

[0022]

[0023] In the above formulas (1), (2) and (3), represents the Jones vector of the incident light, and represents the Jones matrix corresponding to the nanostructure, where R ij represents the complex amplitude of the j-polarized light in the reflected or transmitted light under i-polarized light incidence; represents the Jones vector of the target polarization state, represents the Jones vector of the reflected light, and * represents the transpose operation on the Jones vector.

[0024] Further, the training effect of the deep neural network in step 2) is related to the number of samples in the initial data set. Generally, the larger the data set, the better the training effect of the deep neural network, but more computing resources are required to construct the data set. Therefore, an appropriate number of randomized samples should be selected as training data for specific design examples. The data set can be divided into three groups according to the function, for example, 80% of the data can be selected as the training set, 10% of the data can be selected as the validation set, and 10% of the data can be selected as the test set. The training set is used to train the deep neural network to construct the mapping relationship between the structure morphology and the optical response, the validation set is used to select the best neural network parameters, and the test set is used to evaluate the generalization ability of the deep neural network. The deep neural network is composed of convolutional layers and fully connected layers, where the convolutional layers are mainly used to extract geometric features from the two-dimensional 0-1 structure matrix, and the fully connected layers can construct the mapping relationship from the geometric features to the optical response. The training algebra and learning rate of the deep neural network can be adjusted according to the size of the training set, and regularization and dropout can be reasonably used to balance overfitting and underfitting.

[0025] Further, the Bayesian optimization in step 3) should be applied to the parameter dimension of optimization should be below 20, thus the 0-1 structure matrix should not be directly used as input data to execute the Bayesian optimization process. For example, taking the nanostructure composed of multiple nanorods as an example, the left lower coordinate and the right upper coordinate of each nanorod can be used as structure parameters to execute the Bayesian optimization. During the execution of the Bayesian optimization, the distribution function is constructed based on the current input data to predict the real distribution function of the input data. The confidence interval can be reasonably adjusted according to the optimization requirements, and generally can be set to 95%. The sampling function can be extracted from the upper limit of the confidence interval, and the maximum value of the function is the output data of the current Bayesian optimization. Compared with the original data set, these output structure data have a certain probability of having better device performance, but still need to be verified.

[0026] Further, in step 4), the deep neural network is used to predict the optical response data and calculate the working performance index of the device. The Bayesian optimization and the deep neural network in the method of the present application are two relatively independent functional modules, which are responsible for executing the optimization function and the verification function, respectively. The Bayesian optimization is responsible for recommending the generation of the next generation structure, and the deep neural network predicts the structure data generated by the new recommendation to evaluate the working performance index. The nanostructure generated in the optimization process and the optical response data predicted by the deep neural network will be used as new observed data points, which are merged with the input data of the previous generation of Bayesian optimization to complete the data set update. The updated data set can be used as the input data of the next generation of Bayesian optimization to execute the next generation of Bayesian optimization process. During the optimization process, the threshold of the device performance index can be set, and the structure higher than the set threshold can be stored separately and a structure database is constructed, which provides support for the design and optimization of subsequent polarization modulation wave plate devices, or is further used for the development of other polarization modulation devices.

[0027] In the method of the present application, the deep neural network and the Bayesian optimization do not use the same data set to perform the design or optimization process of the device. The deep neural network can be trained using a high degree of freedom 0-1 structure matrix and its optical response data set, while the Bayesian optimization performs the optimization process based on fewer structure parameters. The deep neural network trained based on the 0-1 matrix data set can predict different geometrical nanostructures, such as multi-nanorods, V-shaped antennas, hole-like structures, etc., and has strong generalization ability. In the method of the present application, the main role of the deep neural network is to replace the numerical simulation software such as FDTD or COMSOL to accelerate the optimization process. Although the prediction accuracy of the deep neural network is less than that of the numerical simulation, the calculation speed is improved by more than 4 orders of magnitude. Therefore, on the basis of ensuring the calculation accuracy of the deep neural network, using it to replace the numerical simulation software can greatly reduce the consumption of computing resources. The main reason for choosing Bayesian optimization is that it is not sensitive to gradient, fast iteration speed and parallel computing. In the actual device design process, if the Bayesian optimization cannot obtain a high-performance structure recommendation, it can also try to replace it with genetic algorithms, topology optimization and other optimization algorithms.

[0028] The design or optimization method of the polarization modulation nano-photonic device proposed in the present application can effectively combine deep neural network and Bayesian optimization to complete the design of any polarization modulation device approaching the theoretical limit. With the advantages of Bayesian optimization such as gradient insensitivity, fast iteration speed and parallel computing, iterative optimization can be performed based on the initially randomly generated data set to develop polarization modulation wave plates and other devices. In the optimization process, the deep neural network can quickly predict the structure generated by each generation of Bayesian optimization recommendation, effectively avoiding the huge consumption of computing resources caused by solving Maxwell's equations, and greatly improving the optimization efficiency. In addition, in the optimization process, a structure database composed of nanostructures with high polarization conversion capability can be constructed, and important support can be provided for the development of various photonic devices based on phase modulation or dispersion modulation, such as achromatic superlenses. In addition, the method of the present application also broadens the working paradigm of using artificial intelligence algorithms for nano-photonic research, and provides a broad platform for exploring the interaction between light and matter. The combined optimization method involving neural network and Bayesian optimization involved in the present application can be used as a standard tool to improve the performance of devices in future research, and has very broad application prospects.

[0029] Compared with the prior art, the present application has the following advantages:

[0030] Compared with the traditional neural network optimization problem, the method of the application combines the core advantages of neural networks and Bayesian optimization in a functionally complementary and framework-independent manner, providing a new paradigm for the design and optimization of nanophotonic devices.

[0031] Compared with traditional design methods such as parameter scanning and traditional optimization algorithms, the method of the application bypasses the numerical solution process of the Maxwell equation set with the help of the powerful parallel computing capability of neural networks, greatly reducing the consumption of computing resources. And in the architecture combining convolutional neural networks and fully connected neural networks, the optical response of the super-high degree of freedom two-dimensional 0-1 structure matrix can be predicted, greatly opening up the design freedom of the structure. Compared with traditional design methods, the method of the application shows higher design efficiency, and can complete the design and optimization process of the polarization modulation device under limited computing resources.

[0032] Compared with the structure parameters of a single optimization wave plate device, the method of the application stores a large number of nanostructures with excellent working performance but different structural appearances in the optimization process with the help of the exploration mechanism of Bayesian optimization. These structures can be used to support the development of various polarization modulation or multiplexing devices. And in constructing the data set, the device performance indicators and the original Jones matrix data are distinguished, so that the phase, amplitude and other information corresponding to the structure can be quickly obtained according to the original Jones matrix data, which can be used for the development of various functional superstructures. At the same time, the wave plate device designed by the method of the application can complete broadband polarization state modulation under a larger bandwidth, and can be further applied to the design of achromatic diffraction focusing imaging devices, multifunctional orbital angular momentum generators and other broadband nanophotonic devices. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 Figure 1 is a design flowchart of a polarization modulation wave plate in the specific embodiment of the application, wherein (a) shows the MIM structure of the wave plate and its parameterized 0-1 structure matrix; (b) shows the architecture of the deep neural network; (c) shows the process of performing Bayesian optimization with the reflection spectrum data predicted by the deep neural network and the 4x4 parameter matrix as input data; (d) shows the finally constructed structure database.

[0034] Figure 2 Figure 2 is a graph of the change of polarization conversion efficiency in the Bayesian optimization process of the half-wave plate design in the specific embodiment of the application, wherein (a) is a comparison graph of the spectrum predicted by the deep neural network (solid line) and the spectrum calculated by FDTD in the initial data set (dotted line); (b) is the value of the best PCE possessed by each generation of nanostructure generated in the iterative optimization process; (c) is the spectrum data corresponding to the representative nanostructure of the first nine generations.

[0035] Figure 3The statistical analysis of the spectral measurement data of the half-wave plate and the quarter-wave plate prepared in the embodiment of the present application and the development database, wherein: (a) the representative nanostructure and its spectral measurement data of the first five generations in the optimization design process of the half-wave plate; (b) the nanostructure and its spectral measurement data obtained from the structure database after the optimization design of the half-wave plate; (c) the nanostructure and its spectral measurement data obtained in the optimization design of the quarter-wave plate; (d) the statistical analysis of the phase data in the structure database stored in the optimization design process of the half-wave plate; (e) the statistical analysis of the group velocity in the structure database stored in the optimization design process of the half-wave plate.

[0036] Figure 4 The structure and function schematic diagram of the achromatic superlens in the embodiment of the present application, wherein: (a) the schematic diagram of the achromatic superlens with the center wavelength of 800 nm and the bandwidth of 200 nm; (b) the enlarged structure diagram of the local superlens; (c) the group velocity (solid line) required to be met by the nanostructure at different radii of the achromatic superlens and the actually realized group velocity (scattered points); (d) the phase profile (solid line) required by the superlens to complete focusing at the wavelengths of 700 nm, 800 nm and 900 nm and the actually realized phase profile (scattered points); (e) the light intensity distribution diagram of the reflected light in the xz plane of the superlens under the incidence of different wavelengths, and the white dotted line is the position of the center wavelength focal plane; (f) the profile diagram of the focusing focal spot of each wavelength light at the position of the focal plane represented by the white dotted line in (e).

[0037] Figure 5 The simulation result diagram of the spectrum of six nanostructures in the half-wave plate database in the embodiment of the present application.

[0038] Figure 6 The nanostructure example diagram of the developed half-wave plate database in the embodiment of the present application. EMBODIMENT

[0039] The present application will be further described in detail below with reference to the design cases of several half-wave plates and quarter-wave plates in the wavelength range of 650 nm-950 nm, so that those skilled in the art can more clearly understand the present application.

[0040] The designed polarization modulation wave plate device is composed of a metal-insulator-metal (MIM) structure. The structure schematic diagram is as follows Figure 1As shown in (a), the gold nanostructure is located on top of the silica spacer layer and the Au substrate. The thicknesses of the gold nanostructure layer and the silica spacer layer are 40 nm and 100 nm, respectively. The gold nanostructure layer consists of square unit structures arranged with a period of 400 nm. Furthermore, this unit structure can be parameterized as a 40×40 0-1 matrix, where 1 represents a square Au nanopillar with dimensions of 10 nm (length) × 10 nm (width) × 40 nm (height), and 0 represents air.

[0041] As a data-driven optimization design strategy, the initial dataset mainly includes 4000 randomly generated nanostructure parameters of unit structures and their corresponding Jones matrix data. To balance the diversity of structural morphology and the accuracy of nanofabrication processes, four rectangular Au nanorods are randomly placed in each unit structure, and overlap between nanorods is allowed. Each nanorod can be uniquely determined by the coordinates of its diagonal vertex (x min, y min, x max, y max), and the minimum size of the nanorod is set to 30 nm. Therefore, the unit structure can be parameterized as a 4×4 parameter matrix. Then, we used FDTD to perform numerical simulation of the nanostructure and obtained its corresponding Jones matrix data. Then, the polarization conversion efficiency (PCE) of the left-hand incident light to the right-hand reflected light of the half-wave plate was obtained through the above equations (1) and (2).

[0042] In this example, the structure matrix (a 40×40 0-1 matrix) and PCE data form the initial dataset, which is then used to train the deep neural network. The entire dataset is split into 80%, 10%, and 10% portions, serving as training, validation, and test samples, respectively. The deep neural network is trained using the training samples, the optimal neural network parameters are selected using the validation samples, and finally, the neural network performance is tested using the test samples. The architecture of the deep neural network is as follows: Figure 1 As shown in (b), it consists of convolutional layers and fully connected layers. The convolutional layers extract the geometric features of the structure, while the fully connected layers construct the mapping between these geometric features and the reflectance spectrum. The Adam optimizer (learning rate set to 5e-4) was used to adjust the neural network weights to minimize the loss function. The loss function is defined as the root mean square error (MSE) between the neural network output and the reflectance spectrum in the dataset. After 500 training iterations, the loss function decreased to 8.89 × 10⁻⁶ on the training set. -4 The value was reduced to 2.53 × 10 on the validation / test set. -3 Compared with traditional numerical simulation methods, deep neural networks can predict the reflection spectrum of a structure through parallel tensor computation without solving Maxwell's equations, thus greatly shortening the computation time and reducing the consumption of computing resources.

[0043] like Figure 1As shown in (c), the reflectance spectrum data predicted by the deep neural network, along with a 4×4 parameter matrix, is used as input data to perform a Bayesian optimization process. Bayesian optimization generates a predicted distribution using a Gaussian process, fitting and estimating the data distribution of the input data. The shaded area represents the confidence interval, quantifying the reliability of the predicted distribution. The upper bound of the confidence interval can be extracted to construct a sampling function, and its maximum point is output as the next generation of recommended structures. These recommended structures and their optical response data can be used to update the dataset and serve as sample data for the next optimization iteration. They can also be used to build a structure database, supporting the development and design of photonic devices such as metalenses. This iterative process improves the overall polarization conversion efficiency (PCE) of the entire dataset. Finally, after the optimization process converges, Bayesian optimization can recommend and generate nanostructures with extremely high polarization conversion efficiency based on the final sampling function, completing the waveplate design.

[0044] Deep neural networks are used to evaluate the device performance metrics of structures generated by Bayesian optimization recommendations; therefore, their accuracy is crucial to the entire optimization design process. In this embodiment, the result output by the deep neural network ( Figure 2 The solid line in figure (a) is compared with the spectrum obtained by FDTD calculation in the initial dataset. Figure 2 The dashed lines in Figure (a) show good consistency. Therefore, deep neural networks can be used to replace FDTD for predicting the spectral data of nanostructures to accelerate the optimization process.

[0045] Figure 2 Figure (b) shows the optimal PCE value in each generation of data during the half-wave plate design optimization process. Within 10 generations, the polarization conversion efficiency of the half-wave plate reaches 80%. Figure 2 Box plot (b) shows the distribution of polarization conversion efficiency (PCE) of the recommended generated nanostructures during the first five iterations. As expected, the PCE of each generation of nanostructures gradually increases with the optimization process. The spectral data for representative structures from the first nine generations are shown below. Figure 2 As shown in (c), the first-generation structure exhibits relatively low polarization conversion efficiency. Bayesian optimization then seeks structures with higher polarization conversion efficiency by adjusting the geometry. As optimization progresses, some common geometric features of the nanostructure gradually exhibit certain regularities, such as the aspect ratio of the nanorods and the fill factor of the structure (the proportion of 1s in a 0-1 structure matrix). Essentially, this trend indicates that the optimization method proposed in this invention can automatically extract valuable information from the initial data to execute the optimization process.

[0046] Furthermore, in this embodiment, the first five generations of nanostructures in the optimization process were prepared using standard electron beam lithography (EBL). Figure 3 (a) and the final optimized nanostructure ( Figure 3 (b)). The reflectance spectra of each sample under left-handed normal incidence were measured using dark-field microscopy. The measurement results showed good agreement with the design expectations, with the polarization conversion efficiency gradually increasing in the first five generations. The final optimized simulation results for the six nanostructures are shown in Figure (b). Figure 5 As shown, the polarization conversion ratio (PCR) of the nanostructures all approach the theoretical limit of 100%. The experimentally measured PCR remains around 90%. To demonstrate the good design flexibility of our method, we changed the optimization objective to a quarter-wave plate, and then extracted the reflection data of right-handed light under x-polarized incident light from the Jones matrix to complete the dataset construction. Then, following the above optimization steps, we completed the design of the quarter-wave plate and obtained good spectral measurement data, such as... Figure 3 As shown in (c).

[0047] Furthermore, this embodiment performs statistical analysis on the structural database stored during the half-wave plate optimization design process and extracts its phase data. Figure 3 (d) and group velocity ( Figure 3 (e)). The structure database developed in this embodiment achieves 2π phase coverage within a 300nm bandwidth while maintaining high polarization conversion efficiency. Figure 6 This study showcases device structures with different phase modulation capabilities at various operating wavelengths. The phase modulation mechanism introduced in this embodiment is resonant phase, which can be further combined with geometric phase to achieve independent modulation of the polarization state and phase of reflected light, applicable to the design of multifunctional metasurfaces. Furthermore, from... Figure 3 In (e), it can be seen that under the premise of ensuring a polarization conversion efficiency of more than 40%, the group velocity corresponding to the nanostructure can be modulated from 0 to 10 fs. This shows that the structure database constructed in this embodiment can support the development of broadband achromatic devices.

[0048] To further verify that the developed structure database can be used for achromatic devices, this embodiment completes the design of an achromatic metalens with a working center wavelength of 800nm ​​and a bandwidth of 200nm based on the aforementioned database. The diameter of the achromatic metalens is 24μm, and the focal length is set to 100μm. In addition to maintaining high polarization conversion efficiency, the unit structure of the achromatic metalens must satisfy the equation described by equation (3) for its group velocity.

[0049]

[0050] where ω, c, r and F represent the angular frequency, the speed of light, the radial coordinate and the focal length, respectively, represents the phase at the center r of the superlens. The group delay at the center r = 0 of the superlens is set to 3.14 fs. Then, the nanostructures with the polarization conversion efficiency higher than 50% and satisfying the condition of the above group velocity are selected from the database, and the achromatic superlens design is completed. The group velocity versus radius of the unit structure of the ideal achromatic superlens is shown as a solid line in (c) of FIG. 6, while the actual structure is shown as a dotted line composed of circles in (c) of FIG. 6, and the two curves exhibit good consistency. Figure 4 Figure 4 Figure 4 The focal length under different wavelengths can be obtained by obtaining the intensity distribution of the reflected light along the z-axis propagation direction, as shown in (e) of FIG. 6. The white dotted line represents the focal plane at the center wavelength of 800 nm. Figure 4 The focal spot profile under illumination of different wavelengths at the focal plane is shown in (f) of FIG. 6. The light field data shows that the profile is clear within the entire working wavelength of 700 nm to 900 nm, proving that the good achromatic imaging function is completed. The design of the achromatic superlens demonstrates that the database developed in the embodiment can support the development of broadband achromatic devices.

[0051] The present application is based on two frontier scientific fields of micro-nano photonics and artificial intelligence, and uses deep learning and Bayesian optimization to design and optimize arbitrary polarization state modulation devices. Through the deep combination of Bayesian optimization and deep neural network, the optimization design of the reflective half-wave plate and quarter-wave plate approaching the theoretical limit is completed. And further development of a structure database composed of nanostructures with high efficient polarization conversion capability can support the design of various polarization devices and achromatic devices. The method has the advantages of high degree of freedom, strong flexibility, high optimization efficiency, etc., and provides a new solution for broadband manipulation of polarization state, and has important guiding significance for the optimization design of broadband nanophotonic devices such as achromatic diffraction focusing imaging devices and multifunctional orbital angular momentum generators.

[0052] Finally, it should be noted that the purpose of publishing the embodiments is to help further understand the present application, and those skilled in the art should understand that various substitutions and modifications are possible without departing from the spirit and scope of the present application and the appended claims. Therefore, the present application should not be limited to the disclosed content of the embodiments, and the scope of protection claimed by the present application is subject to the scope defined by the claims.​​

Claims

1. A method for optimizing a polarization modulation nanophotonic device, comprising the following steps: 1) randomly generate nanostructures for polarization modulation and obtain their corresponding optical response data, construct an initial dataset; the data type in the initial dataset is tensor data, and the stored spectral response data is a wide-spectrum Jones matrix; in the design of polarization modulation nano-photonic devices, the polarization conversion efficiency PCE or the polarization conversion ratio PCR is extracted from the wide-spectrum Jones matrix as the optimization target according to formula (1) to formula (3): wherein represents the Jones vector of the incident light, and represents the Jones matrix corresponding to the nanostructure, wherein represents the complex amplitude of the j-polarized light in the reflected or transmitted light for i-polarized light incidence; represents the Jones vector of the target polarization state, represents the Jones vector of the reflected light, and * represents the transpose operation on the Jones vector; 2) training a deep neural network with an initial dataset so that it can predict optical response data of a nanostructure according to its structural data; 3) selecting a certain proportion of samples from the initial dataset as the initial input data for subsequent optimization, and then using a Bayesian optimization algorithm to recommend generating a number of nanostructures according to a design target, wherein the independent variables of the Bayesian optimization are set as the structural parameters of the nanostructures, and the dependent variables are set as device performance indicators derived from the optical response data; the Bayesian optimization automatically analyzes the black-box function between the independent variables and the dependent variables based on the input data through a Gaussian process, and generates a sampling function in combination with a confidence interval; the maximum value of the sampling function is used to recommend the structural parameters of the next generation of nanostructures; 4) predicting the optical response data of the nanostructures recommended in step 3) by using the deep neural network, and evaluating their performance; 5) iteratively performing steps 3) and 4), and using the nanostructures generated in the optimization process and the optical response data predicted by the deep neural network as new observed data points, which are merged with the previous generation of optimization input data to update the dataset; the updated dataset is used as the input data for the next generation of optimization, and the next generation of optimization process is performed until the optimization algorithm model converges, and the required nanostructure of the polarization modulation nanophotonic device is obtained.

2. The method of claim 1, wherein, In step 1), the optical response data corresponding to the nanostructure is obtained by simulation through finite difference time domain or multi-physics field simulation software.

3. The method of claim 1, wherein, In step 2), the structural data of the nanostructure is input into the deep neural network, and the network node weight is adjusted by using the gradient descent method so that the output data of the deep neural network approximates the optical response data corresponding to the nanostructure in the dataset.

4. The method of claim 1, wherein, The optimization algorithm in step 3) is Bayesian optimization, genetic algorithm or topology optimization.

5. The method of claim 1, wherein, In step 1), when constructing the initial dataset, the geometric configuration of the nanostructure is parameterized as a two-dimensional 0-1 structure matrix, where 1 represents the existence of a nanostructure, and 0 represents air; in step 2), the deep neural network is trained using the dataset composed of the 0-1 structure matrix and its optical response.

6. A polarization modulation nanophotonic device obtained by the optimization method according to any one of claims 1-5.

7. The polarization-modulating nanophotonic device of claim 6, wherein, The polarization modulation nanophotonic device is a polarization modulation wave plate or an achromatic superlens. The polarization modulation nanophotonic device is a polarization modulation wave plate or an achromatic superlens.

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