A T-matrix database to promote information-driven research in nanophotonics

Information-driven methods from machine learning and artificial intelligence for exploring the optical response of metasurfaces and, more generally, photonic systems rely on well-annotated datasets for training. For metasurfaces made from a periodic or aperiodic arrangement of scatterers, the primary information encoding their response is the optical properties of these individual scatterers. In the linear regime, that response is entirely contained in the transition or T-matrix of the individual scatterer. However, despite the widespread use of these T-matrices in exploring advanced photonic materials within the larger community, there is no common infrastructure for distributing them with consistent metadata and a standard representation. That would be important to avoid the repetitive, resource-intensive computation of these T-matrices by researchers worldwide and to enable data-driven research. To overcome this limitation, we introduce the Daphona T-matrix portal at https://tmatrix.scc.kit.edu/, a web-based platform for interactive searching, filtering, and exporting standardized data containing structure-property relations for a wide range of scatterers, as expressed by their T-matrices. Besides introducing this infrastructure, we demonstrate how the available data enables addressing scientific questions in the broader context of information-driven research. The multiple illustrative examples in our contribution cover both surrogate forward models and inverse design models, and operate either directly on the T-matrix or alternatively on optical observables of metasurfaces made from these scatterers.

💡 Research Summary

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The paper addresses a critical bottleneck in nanophotonics and metasurface research: the lack of a common, well‑structured repository for transition (T‑) matrices, which fully describe the linear optical response of individual scatterers. While T‑matrices are widely used to model scattering from nanoparticles, molecules, and more complex assemblies, each research group traditionally computes and stores them in proprietary formats, leading to duplicated effort, poor reproducibility, and barriers to data‑driven methods such as machine learning.

To solve this, the authors introduce the Daphona T‑matrix portal (https://tmatrix.scc.kit.edu/), a web‑based platform that stores T‑matrices in a standardized HDF5 format accompanied by rich metadata. The metadata schema captures geometry (size, shape, orientation), material properties (complex permittivity, dispersion), spectral range, numerical method details, and the exact normalization convention for vector spherical wave (VSW) modes. A fixed ordering of VSW modes, following Jackson’s convention, ensures that matrices from different codes are directly comparable.

The portal’s workflow consists of (i) upload (single files, ZIP archives, or whole directories), (ii) automated validation (structural integrity, completeness of metadata, compliance with the published standard, duplicate detection), (iii) storage in a relational database, and (iv) interactive exploration. The front‑end displays each dataset as a card summarizing key physical and computational attributes, with dynamic filters for geometry type, material, wavelength range, embedding medium, and solver type. Users can visualize selected T‑matrices (e.g., mode amplitudes, phase maps) and download them in the canonical HDF5 representation.

Beyond the graphical interface, an OpenAPI enables programmatic access for batch queries, automated ingestion, and integration into external simulation pipelines or machine‑learning workflows. This API makes it possible to retrieve thousands of T‑matrices on demand, facilitating large‑scale studies that would otherwise be prohibitive.

The authors demonstrate the scientific impact of the database through several illustrative examples. In forward‑problem applications, they train physics‑informed neural networks that take a T‑matrix as input and predict metasurface reflectance, transmittance, and absorption spectra across a broad wavelength range, achieving inference speeds orders of magnitude faster than conventional full‑wave solvers (FEM, BEM). In inverse‑design scenarios, they employ variational autoencoders and conditional GANs to map desired spectral responses back to scatterer geometries and material parameters, using the T‑matrix dataset as the training ground truth. The paper also shows how multi‑scatterer systems—periodic metasurfaces, disordered assemblies, or hybrid structures—can be efficiently modeled by assembling block‑diagonal T‑matrix matrices and translation operators (the (I – TC)⁻¹ formalism). By pulling the required individual T‑matrices directly from the portal, they compute the collective response without re‑solving Maxwell’s equations for each configuration.

A forward‑looking vision is articulated: the community should converge on a shared, ever‑growing repository of T‑matrices, eventually providing the massive, diverse dataset needed to train a universal neural Maxwell solver capable of handling arbitrary geometries, materials, and frequencies. While the current release focuses on linear, single‑frequency scattering, the authors outline pathways to incorporate nonlinear effects, multi‑frequency coupling, temperature or field‑dependent material models, and more complex multilayered structures.

In summary, the Daphona T‑matrix portal delivers three major benefits: (1) it eliminates redundant, energy‑intensive computations by reusing existing high‑quality T‑matrices; (2) it implements FAIR data principles, making scattering data findable, accessible, interoperable, and reusable; and (3) it unlocks the full potential of AI/ML for rapid forward prediction and inverse design in nanophotonics. By providing a robust, standardized infrastructure, the work is poised to accelerate research productivity, foster reproducibility, and catalyze the next generation of metasurface and photonic material innovations.