Fast approximate solvers for metamaterials design in electromagnetism
arXiv:2503.20065 · doi:10.1109/MAP.2025.3588058
Abstract
In electromagnetism, the model of Maxwell's equations yields accurate and trustworthy predictions. Numerical solvers can reach electromagnetic solutions far beyond the set of analytical closed-form solutions; this is crucial in metamaterials design where the goal is to find the geometry that generates an optimal electromagnetic solution for a desired property. Then why do we still need to create computational methodologies in metamaterials research? And why should we care about analytical models? The simulation and optimization bottlenecks limit the range of applications of the state of the art. Hence, there is room for opportunities to create new computational methodologies. Semi-analytical methods that are customized for classes of applications enable simulation and optimization. We detail the state of the research in customized methodologies using the illustrative example of optical metasurfaces and suggest best practices. We also discuss how machine learning may enhance these methodologies.
References in corpus (37)
- A review of metasurfaces: physics and applications
- Outlook for inverse design in nanophotonics
- Physics-informed neural networks for inverse problems in nano-optics and metamaterials
- Deep neural networks for the evaluation and design of photonic devices
- Metalenses at visible wavelengths: past, present, perspectives
- Deep learning in nano-photonics: inverse design and beyond
- General Metasurface Synthesis Based on Susceptibility Tensors
- High-NA Achromatic Metalenses by Inverse Design
- Inverse design enables large-scale high-performance meta-optics reshaping virtual reality
- Inverse design of large-area metasurfaces
- Inverse design in photonics by topology optimization: tutorial
- Multifunctional Nonlocal Metasurfaces
- Nonlocal Flat Optics
- On the use of Artificial Neural Networks in Topology Optimisation
- Topology optimization of freeform large-area metasurfaces
- Steady-state Ab Initio Laser Theory: Generalizations and Analytic Results
- Leaky-wave metasurfaces for integrated photonics
- Inverse designed metalenses with extended depth of focus
- Why optics needs thickness
- Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations
- Active learning of deep surrogates for PDEs: Application to metasurface design
- Overlapping domains for topology optimization of large-area metasurfaces
- Inverse-designed low-index-contrast structures on silicon photonics platform for vector-matrix multiplication
- 3D-Patterned Inverse-Designed Mid-Infrared Metaoptics
- A newcomer's guide to deep learning for inverse design in nano-photonics
- Fullwave Maxwell inverse design of axisymmetric, tunable, and multi-scale multi-wavelength metalenses
- Computational inverse design for ultra-compact single-piece metalenses free of chromatic and angular aberration
- Inverse Designed Extended Depth of Focus Meta-Optics for Broadband Imaging in the Visible
- Towards 3D-Printed Inverse-Designed Metaoptics
- Manifold Learning for Knowledge Discovery and Intelligent Inverse Design of Photonic Nanostructures: Breaking the Geometric Complexity
- Physics-enhanced deep surrogates for partial differential equations
- Efficient approximation of high-dimensional functions with neural networks
- Sideways adiabaticity: Beyond ray optics for slowly varying metasurfaces
- Trace formulation for photonic inverse design with incoherent sources
- Neural Networks for Generating Better Local Optima in Topology Optimization
- Scalable freeform optimization of wide-aperture 3D metalenses by zoned discrete axisymmetry
- Efficient inverse design of large-area metasurfaces for incoherent light