Photonic crystal topological design for polarized and polarization-independent band gaps by gradient-free topology optimization

Recent advances in metasurface design and quantum optics applications with machine learning, physics-informed neural networks, and topology optimization methods

As a two-dimensional planar material with low depth profile, a metasurface can generate non-classical phase distributions for the transmitted and reflected electromagnetic waves at its interface. Thus, it offers more flexibility to control the wave front. A traditional metasurface design process mainly adopts the forward prediction algorithm, such as Finite Difference Time Domain, combined with manual parameter optimization. However, such methods are time-consuming, and it is difficult to keep the practical meta-atom spectrum being consistent with the ideal one. In addition, since the periodic boundary condition is used in the meta-atom design process, while the aperiodic condition is used in the array simulation, the coupling between neighboring meta-atoms leads to inevitable inaccuracy. In this review, representative intelligent methods for metasurface design are introduced and discussed, including machine learning, physics-information neural network, and topology optimization method. We elaborate on the principle of each approach, analyze their advantages and limitations, and discuss their potential applications. We also summarize recent advances in enabled metasurfaces for quantum optics applications. In short, this paper highlights a promising direction for intelligent metasurface designs and applications for future quantum optics research and serves as an up-to-date reference for researchers in the metasurface and metamaterial fields.

Topologically optimized concentric-nanoring metalens with 1 mm diameter, 0.8 NA and 600 nm imaging resolution in the visible

Metalenses can achieve diffraction-limited focusing via localized phase modification of the incoming light beam. However, the current metalenses face to the restrictions on simultaneously achieving large diameter, large numerical aperture, broad working bandwidth and the structure manufacturability. Herein, we present a kind of metalenses composed of concentric nanorings that can address these restrictions using topology optimization approach. Compared to existing inverse design approaches, the computational cost of our optimization method is greatly reduced for large-size metalenses. With its design flexibility, the achieved metalens can work in the whole visible range with millimeter size and a numerical aperture of 0.8 without involving high-aspect ratio structures and large refractive index materials. Electron-beam resist PMMA with a low refractive index is directly used as the material of the metalens, enabling a much more simplified manufacturing process. Experimental results show that the imaging performance of the fabricated metalens has a resolution better than 600 nm corresponding to the measured FWHM of 745 nm.

A Gradient-Free Topology Optimization Strategy for Continuum Structures with Design-Dependent Boundary Loads

In this paper, the topology optimization of continuum structures with design-dependent loads is studied with a gradient-free topology optimization method in combination with adaptive body-fitted finite element mesh. The material-field series-expansion (MFSE) model represents the structural topology using a bounded material field with specified spatial correlation and provides a crisp structural boundary description. This feature makes it convenient to identify the loading surface for the application of the design-dependent boundary loads and to generate a body-fitted mesh for structural analysis. Using the dimension reduction technique, the number of design variables is significantly decreased, which enables the use of an efficient Kriging-based algorithm to solve the topology optimization problem. The effectiveness of the proposed method is demonstrated using several numerical examples, among which a design problem with geometry and contact nonlinearity is included.