Topology optimization of 3D photonic crystals with complete bandgaps

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.

Anisotropic material-field series expansion for the topological design of optical metalens

To determine an effective optimization strategy and facilitate the manufacture of optical metalenses, this paper extends the material-field series-expansion (MFSE) method for the topology design of metalenses. A new anisotropic material-field function with a spatially anisotropic correlation is introduced to describe the structural topology in a narrow design domain. The topological features can be implicitly controlled by material-field correlation lengths in different directions. Then, a generalized sigmoid projection is introduced to construct an interpolation relationship between the unbounded material-field value and the relative permittivity. Based on the series expansion technique, the number of design variables is greatly reduced in this topology optimization process without requiring additional material-field bounded constraints. The MFSE-based metalens design problem is efficiently solved by using a gradient-based algorithm incorporating design sensitivity analysis. Numerical examples demonstrate that the proposed optimization algorithm can successfully obtain an optimized and easy-to-manufacture design in optics inverse design problems.

3-D Metamaterials: Trends on Applied Designs, Computational Methods and Fabrication Techniques

Metamaterials are artificially engineered devices that go beyond the properties of conventional materials in nature. Metamaterials allow for the creation of negative refractive indexes; light trapping with epsilon-near-zero compounds; bandgap selection; superconductivity phenomena; non-Hermitian responses; and more generally, manipulation of the propagation of electromagnetic and acoustic waves. In the past, low computational resources and the lack of proper manufacturing techniques have limited attention towards 1-D and 2-D metamaterials. However, the true potential of metamaterials is ultimately reached in 3-D configurations, when the degrees of freedom associated with the propagating direction are fully exploited in design. This is expected to lead to a new era in the field of metamaterials, from which future high-speed and low-latency communication networks can benefit. Here, a comprehensive overview of the past, present, and future trends related to 3-D metamaterial devices is presented, focusing on efficient computational methods, innovative designs, and functional manufacturing techniques.