A review of the latest design and cutting-edge application progress of metasurface materials

1. Introduction

As two-dimensional planar materials with low depth profiles, metasurfaces can generate specific phase distributions at their interfaces for transmitted and reflected electromagnetic waves. Therefore, it provides greater flexibility to control the wavefront. The traditional metasurface design process mainly adopts forward algorithms such as finite difference in the time domain and combines manual parameter optimization. However, these methods are time-consuming, and it is difficult to align the designed spectrum with the ideal spectrum. In addition, due to the use of periodic boundary conditions in the element design process and aperiodic conditions in array simulations, coupling between adjacent elements leads to unavoidable errors.

Researchers from Delft University of Technology in the Netherlands recently presented a report on “Recent Advances in Metasurface Design and Quantum Optics Applications with Machine Learning, Physics-Informed Neural Networks, and Topology Optimization Methods.” A review article published in Light: Science & Applications summarizes and prospects the progress of metasurface intelligent design methods.

In this review, the authors introduce and discuss representative metasurface intelligent design methods, including machine learning, physical information neural networks, and topology optimization methods, while elaborating the principles of each method, dissecting their advantages and limitations, and discussing their potential applications. This paper highlights the advantages of intelligent metasurface design and provides the latest references for researchers in the field of metasurfaces and metamaterials, including:

2.1 Fundamentals of machine learning to design metasurfaces

A flowchart of the basic rationale of the machine learning method for metasurface design is shown in Figure 1. The general design process is as follows: For simple cylindrical structures, a dataset of electromagnetic responses can be obtained using a forward solver algorithm with multiple parameter combinations. These datasets can then be used to train a deep neural network that can compute an electromagnetic response when provided with input, which is known as a forward network. Through the same training process, a reverse network is also obtained. Reverse networks differ in that the input is the expected response and the output is the geometric parameter of the structure. Finally, the optimized solution is evaluated using the forward solver algorithm to determine whether the response meets expectations.

Figure 1 Flowchart of the basic principles of machine learning for metasurface design: define the problem, collect the dataset, preprocess the data, train the model, verify the model, train the inverse network, input the expected response, iterative optimization, and achieve the desired performance.

2.2 Basic principles of designing metasurfaces in physical information neural networks

The method is to add information about the laws of physics to the neural network, such as Maxwell’s equations or some other partial differential equation. This can be achieved by incorporating the partial differential equation control dataset into the framework’s loss function. We illustrate in Figure 2 a flowchart of a physical information neural network for metasurface design. The multi-column element structure has a complex design and multiple parameters, and has a greater degree of freedom compared to the previous method. The dataset is obtained by simulating the structure by a forward solver, but as physical laws such as Maxwell’s equations and electromagnetic boundary conditions are embedded in the neural network, the required dataset size is reduced and the computation time is significantly reduced. The rest of the design process aligns with machine learning methods.

Figure 2 Flowchart steps of designing metasurfaces in physical information neural networks: defining problems, creating training data, defining physical principles and loss functions, defining network architecture, verifying networks, training backpropagation networks, entering the expected electromagnetic response, iterating the design process, and obtaining the required metasurface design parameters.

2.3 Topology optimization design metasurface basic principles

Figure 3 illustrates a flowchart of the topology optimization process for metasurface design. The process starts with the initial structure and related parameters, and then calculates the electromagnetic response of the structure using optical theories such as rigorous coupled wave analysis methods. The loss function is then determined by comparing the current electromagnetic response with the desired response. A gradient algorithm such as automatic differentiation is then used to determine the gradient of the loss function of the input parameters. This gradient information is used to update the parameters of the structure in the direction that minimizes the loss function. The process is repeated until the loss function reaches its minimum. The final output is an optimized set of parameters for the desired structure.

Figure 3 Topology optimization metasurface design basic principle flowchart steps: define the problem, input parameters, determine the required electromagnetic response, calculate the loss function, calculate the gradient of the loss function, update and output parameters, iterate the design process, and obtain the required parameters.

3. Summary and outlook

This review elaborates several important methods for metasurface intelligent design. These methods will become the hot spot and frontier of metasurface and metamaterial design in the future, and have obvious advantages in physical accuracy and calculation time. In addition, the above methods can be extended to the design of other optical devices, such as photonic crystals, optical cavities, and integrated optical paths. Intelligent metasurface is a rapidly developing direction with important application prospects in several new revolutionary fields, especially in the field of quantum optics, which has recently developed rapidly.

In addition, metasurface technology has many potential applications in industry. Metamaterials exhibit extraordinary properties such as anomalous reflection, wavefront manipulation, and polarization control, which enable metasurfaces to revolutionize traditional optics and provide innovative solutions for a wide range of industrial applications. In the near future, metasurfaces will be used for sensors, antennas, and solar cells, improving optical efficiency and sensitivity. They can also be used for imaging and holography, providing high imaging resolution and 3D display capabilities. In addition, metasurfaces can be integrated into various devices and systems to improve their functionality. Therefore, the potential to transform metasurfaces into industrial applications is enormous, and further research in this field is expected to open up new possibilities for its practical applications.

4. Introduction of the main author

Ji Wenye, PhD student, School of Applied Sciences, Delft University of Technology, specializes in terahertz regulation, optical imaging, metamaterials and photonic crystal devices.

Chang Jin, a postdoctoral researcher (Quantum Nanoscience department) at the School of Applied Sciences, Delft University of Technology, specializes in superconducting single-photon detection, photomechanics, photo/phonon crystals and their quantum sensing applications.

Other co-authors include Professor Xu Hexiu (Communications) of the Air Force Engineering University, Jian Rong Gao, Paul Urbach (Communications), Professor Aurèle J.L. Adam of the Imphys Department of Delft University of Technology, and Professor Simon Gröblacher of the Department of Quantum Nanoscience of Delft University of Technology. (Source: LightScience Applications WeChat public account)

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