The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays produce new materials as 3D lattices of scattering unit cells. Computing the response of objects of arbitrary shape made from such materials is typically computationally prohibitive unless an effective homogeneous medium approximates the discrete material. In here, a homogenization method based on the effective transition (T‐)matrix, is introduced. Such a matrix captures the exact response of the discrete material, is determined by the T‐matrix of the isolated unit cell and the material lattice vectors, and is free of spatial dispersion. The truncation of to dipolar order determines the common bi‐anisotropic constitutive relations. When combined with quantum‐chemical and Maxwell solvers, the method allows one to compute the response of arbitrarily‐shaped volumetric patchworks of structured molecular materials and metamaterials.

We propose using deep neural networks for the fast retrieval of effective properties of metamaterials based on their angular-dependent reflection and transmission spectra from thin slabs. While we noticed that non-uniqueness is an issue for a successful application, we propose as a solution an automatic algorithm to subdivide the entire parameter space. Then, in each sub-space, the mapping between the optical response (complex reflection and transmission coefficients) and the corresponding material parameters (dielectric permittivity and permeability) is unique. We show that we can easily train one neural network per sub-space. For the final parameter retrieval, predictions from the different sub-networks are compared, and the one with the smallest error expresses the desired effective properties. Our approach allows a significant reduction in run-time, compared to more traditional least-squares fitting. Using deep neural networks to retrieve effective properties of metamaterials is a significant showcase for the application of AI technology to nanophotonic problems. Once trained, the nets can be applied to retrieve properties of a larger number of different metamaterials.

To characterize electromagnetic metamaterials at the level of an effective medium, nonlocal constitutive relations are required. In the most general sense, this is feasible using a response function that is convolved with the electric field to express the electric displacement field. Even though this is a neat concept, it bears little practical use. Therefore, frequently the response function is approximated using a polynomial function. While in the past explicit constitutive relations were derived that considered only some lowest order terms, we develop here a general framework that considers an arbitrary higher number of terms. It constitutes, therefore, the best possible approximation to the initially considered response function. The reason for the previously self-imposed restriction to only a few lowest order terms in the expansion has been the unavailability of the necessary interface conditions with which these nonlocal constitutive relations have to be equipped. Otherwise one could not make practical use of them. Therefore, besides the introduction of such higher order nonlocal constitutive relations, it is at the heart of contribution to derive the necessary interface conditions to pave the way for the practical use of these advanced material laws.

Nonlocal constitutive relations promise to homogenize metamaterials even though the ratio of period over operational wavelength is not much smaller than unity. However, this ability has not yet been verified, as frequently only discrete structures were considered. This denies a systematic variation of the relevant ratio. Here, we explore, using the example of an electric dipolar lattice, the superiority of the nonlocal over local constitutive relation to homogenize metamaterials when the period tends to be comparable to the wavelength. Moreover, we observe a breakdown of the ability to homogenize the metamaterial at shorter lattice constants. This surprising failure occurs when energy is transported across the lattice thanks to a well-pronounced near-field interaction among the particles forming the lattice. Contrary to common wisdom, this suggests that the period should not just be much smaller than the operational wavelength to homogenize a metamaterial, but, for a given size of the inclusion, there is an optimal period.

The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays produce new materials as three-dimensional lattices of scattering unit cells. Computing the response of objects of arbitrary shape made from such materials is typically computationally prohibitive unless an effective homogeneous medium approximates the discrete material. In here, we introduce a homogenization method based on the effective T-matrix, T eff . Such a matrix captures the exact response of the discrete material, is determined by the T-matrix of the isolated unit cell and the material lattice vectors, and is free of spatial dispersion. The truncation of T eff to dipolar order determines the common bi-anisotropic constitutive relations. When combined with quantum-chemical and Maxwell solvers, the method allows one to compute the response of arbitrarily-shaped volumetric patchworks of structured molecular materials and metamaterials.