Nanophotonics demands complex on-chip components to manipulate light waves. Designing these components, such as optical metasurfaces using sub-wavelength meta-atoms, often involves high-dimensional design spaces, making conventional optimization methods inefficient. This research addresses this challenge by proposing a machine learning-based inverse design method for meta-optical structures, specifically focusing on photonic beam engineering. On-chip planar photonic waveguide-based beam engineering offers significant advantages for lab-on-chip applications like infrared, Raman, and fluorescence spectroscopic analysis. The ability to efficiently manipulate photons to generate various beam profiles (Gaussian, focused, collimated) improves the performance of these analytical techniques. Inverse modeling is key; predicting meta-surface design parameters from a desired electromagnetic field outcome. This study leverages deep learning architectures to achieve this, significantly reducing design time compared to traditional methods.

Optimizing metasurface design is a significant area of research in photonics. Several studies have used DNN-based approaches to model the relationship between device geometry and optical response in forward models. Zhang et al. demonstrated the use of artificial neural networks for RF and microwave designs. Gilliard et al. used a multilayer perceptron model to study the dispersion relation of 2D photonic crystal designs. Ferreira et al. employed a hybrid EM optimization method enhanced with an AL algorithm to predict the permittivity of metamaterials. Jiang et al. used generative neural networks (GNNs) for the inverse design of metasurfaces. Yao et al. explored the use of DNNs to efficiently navigate the vast parameter space of nanophotonic structures. Kudyshev et al. utilized GANs for optimizing the topology of metasurface-based thermal emitters. Liu et al. developed DNN-based equivalent EM solvers for designing 1-D, 2-D, and 3-D dielectric metasurfaces. Other relevant works include metasurface designs to enhance waveguide couplers, out-of-plane waveguide-based holography, and chip-integrated geometric metasurfaces for directional couplers.

This research employs a machine learning approach to develop an inverse model for metasurface design. The study focuses on a planar metasurface composed of 5x5 meta-scatterers on a photonic waveguide, designed to diffract engineered light beams into free space. The waveguide is fabricated from SiN on a SiO2-on-Si wafer, supporting fundamental TE and TM modes at C and L bands. The design parameters considered include grating period (λx), gap factor (g), height (h), and scatterer size (C). The diffraction of light is modeled using the Huygens-Fresnel principle, considering constructive and destructive interference. The equations governing diffraction angle, energy leakage, and the relationship between design parameters and diffraction are presented. A cascade mirror model is used to understand light propagation through the meta-grating structure. Two neural network architectures, a feedforward DNN and a CNN, are trained to estimate the inverse model (mapping diffraction profile to design parameters). The DNN utilizes multiple hidden layers with ReLU activation functions, while the CNN incorporates a convolutional layer followed by fully connected layers. The training dataset is generated using FDTD simulations in Lumerical software, varying the design parameters to create a diverse range of diffraction profiles. The models are trained using the mean squared error (MSE) loss function and stochastic gradient descent (SGD) optimization. The performance of different DNN architectures (3, 4, and 5 layers) is evaluated. A DNN validator network, combining the trained inverse model with an FDTD forward model, is used to qualitatively assess the performance of the DNN in predicting different beam profiles (Gaussian, focused, collimated, random). The 3dB bandwidth and power efficiency are analyzed for various beam profiles.

The 4-layer DNN architecture demonstrated the best performance in estimating design parameters, achieving a low test error (0.012/sample). The DNN significantly outperformed the CNN in terms of accuracy. The error in predicting λx, d, and h was significantly lower than that of Ci, suggesting that the former are the primary design parameters controlling the diffraction profile. The DNN validator network showed high correlation coefficients between predicted and ground truth diffraction profiles for Gaussian (0.986), collimated (0.890), and random (0.996) beams. However, the prediction of the focused beam was less accurate (0.925). The bandwidth varied among the different beam profiles (30 nm, 24 nm, 65 nm, and 70 nm for collimated, focused, Gaussian, and random, respectively), suggesting that beam profiles with extreme spatial distribution have smaller operating bandwidths.

The results demonstrate the effectiveness of using deep learning for the inverse design of metasurfaces. The developed DNN-based model offers a significant speed advantage over conventional optimization methods, enabling rapid estimation of design parameters. The finding that λx, d, and h are the primary design parameters provides valuable insights into the design process. The lower accuracy in predicting the focused beam profile suggests potential areas for improvement, such as increasing the number of scatterers or incorporating additional design parameters. The variation in bandwidth across different beam profiles highlights a trade-off between beam shaping and operational bandwidth. This research establishes a powerful paradigm for designing complex nanophotonic structures where conventional methods are less effective.

This paper presents a successful application of deep learning for the inverse design of optical dielectric metasurfaces. The developed DNN model efficiently predicts design parameters for generating various beam profiles. The method offers a significant improvement over conventional time-consuming optimization techniques. Future research could focus on expanding the design space, improving accuracy for complex beam profiles, and exploring applications in apodized meta-grating structures to enhance grating coupler efficiency.

The accuracy of the model is dependent on the quality and quantity of the training data. The current model is trained on a specific type of metasurface structure and may not be directly applicable to other designs. The generalization capability of the model to unseen data requires further investigation. The limited number of scatterers in the current design might restrict the achievable beam shaping capabilities. The observed variation in bandwidth across beam profiles needs further analysis to explore strategies for bandwidth enhancement.