Metamaterial design and fiber beam control are two important topics in the study of optical field manipulation. Metamaterials are artificial materials with periodic structures and physical properties that do not exist naturally in the world. Suitable structural designs are crucial for achieving the potential of metamaterials. Numerical calculations and parameter optimization methods such as finite difference time domain (FDTD), finite element method (FEM), rigorous coupled wave analysis (RCWA), and genetic algorithms are commonly used in metamaterials design. However, these methods suffer from high computational costs and strong dependence on expert experience. Specifically, the high computational cost is due to the complexity of solving partial differential equations, while the reliance on expert experience stems from the fact that these numerical calculation methods depend on physical modeling. Additionally, parameter optimization algorithms also suffer from high computational costs due to the explosion of parameter combinations and repeated calls to numerical computation methods. Therefore, many researchers have turned to deep learning methods, attempting to use a data-driven approach to allow neural network models to learn the mapping relationship between metamaterial structure and optical response during the feature learning process, thus achieving accurate and efficient metamaterial design while shielding underlying physical details.

Fiber beam control refers to adjusting parameters such as amplitude, phase, and polarization of a fiber optic beam to obtain novel features or stable states. Traditional methods mainly include genetic algorithms, stochastic parallel gradient descent (SPGD) algorithm, PID, and other search methods, which are limited by their inability to effectively solve system control problems in complex environments, i.e., speed and accuracy issues. These optimization methods have simple strategies that are unable to generate good behavioral paths, resulting in too many steps to reach the target state. Moreover, they mechanically respond to environmental states, making them vulnerable to system noise interference and limiting the accuracy of system output. Deep reinforcement learning overcomes these limitations by introducing a learning mechanism that can actively respond to environmental stimuli, making up for the shortcomings of traditional methods. Fiber beam control is a dynamic process that can be abstracted into a state machine, which is naturally suitable for control methods based on deep reinforcement learning. Therefore, for such or even more complex systems, deep reinforcement learning-based methods have considerable application prospects.

Multi-layer perceptron (MLP) is a simple and basic neural network model widely used in various metamaterial design works. Peurifoy et al. used MLP to complete the inverse design of an 8-layer spherical shell nanostructure [Fig. 7(a)]. Liu et al. proposed a method that combines forward prediction networks for spectra and inverse design networks for devices [Fig. 7(b)]. Du et al. developed a scalable multi-task learning (SMTL) model for designing low-dimensional nanostructures [Fig. 7(c)]. Zhao et al. released a data-enhanced iterative few-sample (DEIFS) algorithm based on data augmentation [Fig. 7(d)]. In addition to MLP, convolutional neural network (CNN) and generative adversarial network (GAN) are also commonly used network models. Zhu et al. proposed a transfer learning-based method for predicting metamaterials accurately and quickly using the pre-trained Inception V3 model on image data, achieving good results for binary metamaterial prediction [Fig. 8(a)]. Jiang et al. used GAN for the topology design of complex nano-devices, effectively solving the problem of time-consuming iterative optimization methods for designing complex devices, reducing design time by about 80% [Fig. 8(b)]. Sajedian et al. efficiently determined the optimal parameters for three-layer metamaterial devices among 23 different material types and geometry parameters using the double deep Q network (DDQN), greatly improving the computational transmittance efficiency of metamaterials [Fig. 8(c)]. Zhao et al. integrated the idea of reinforcement learning into the model and designed a data-enhanced deep greedy optimization (DEDGO) algorithm [Fig. 8(d)]. Sajedian et al. combined CNN with recurrent neural network (RNN) to predict the absorption spectra of nano-devices, which played an auxiliary role in device design [Fig. 8(e)].

In fiber beam control, the J. N. Kutz team at the University of Washington proposed using deep reinforcement learning algorithms to achieve automatic mode locking control of lasers from a simulation perspective in 2020 [Fig. 11(a)]. In 2021, the team led by researcher Jiang Tian at the National University of Defense Technology designed an automatic mode locking control laser system based on the DDPG strategy and the DELAY reinforcement learning algorithm [Fig. 11(b)]. In mid-2022, Li Zhan et al. from the Chinese Academy of Sciences designed a feedback control algorithm based on deep reinforcement learning and long short-term memory (LSTM) network models to stabilize the state of mode-locked lasers [Fig. 11(c)]. In the latter half of 2022, Luo Saiyu et al. from Nanjing University of Science and Technology applied the TD3 algorithm from deep reinforcement learning to an ultrafast green Ho:ZBLAN laser [Fig. 11(d)]. In 2023, the research team led by Jiang Tian at the National University of Defense Technology once again designed DRCON using reinforcement learning to control the stability of coherent optical neuron systems (Fig. 13).

This article focuses on recent research on deep learning in metamaterial design and fiber beam control. The introduction of deep learning has greatly promoted the development of both fields. Traditional methods face the following problems when dealing with increasingly complex optical systems: (1) inability to effectively transfer expert experience; (2) inability to avoid numerical calculations; and (3) a limited solvable problem space. Compared with traditional methods, deep learning methods can help isolate the underlying physical details to some extent, reducing the difficulty of design and control.