Predicting Observable Quantities of Self-Assembled Metamaterials from the T-Matrix of Its Constituting Meta-Atom

Abstract

Self-assembled metamaterials attract considerable interest as they promise to make isotropic bulk metamaterials available at low costs. The optical response of self-assembled metamaterials is derived predominantly from the response of its individual constituents, i.e., the meta-atoms. Beyond effective properties, primary experimentally observable quantities, such as specific cross-sections, are at the focus of interest as they are frequently considered when exploiting metamaterials in specific applications. This posses the challenge of predicting these observable quantities for a diluted ensemble of randomly oriented meta-atoms. Thus far, this has been achieved by either averaging the optical response of the meta-atom across all possible incident fields or by restricting the consideration to only an electric and magnetic dipolar response. This, however, is either time-consuming or imposes an unnecessary limitation. Here, we solve this problem by deriving and presenting explicit expressions for experimentally observable quantities of metamaterials made from randomly arranged and oriented meta-atoms characterized by their T-matrix.

Quantifying Fano properties in self-assembled metamaterials

“…To discuss the features of the response of self-assembled metamaterials, experimentally observable parameters need to be extracted directly from the T matrix of a meta-atom. It has recently been shown [45] that for a sufficiently diluted selfassembled metamaterial, the rotationally averaged properties of an individual meta-atom can be used to describe the properties of bulk self-assembled metamaterials. Here, we focus on the rotationally averaged extinction (σ aver ext ), scattering (σ aver sca ), and absorption (σ aver abs ) cross sections of the meta-atom.…”

“…Under the assumption of a sufficient strong dilution, the optical response from the 3D material can be derived from the ensemble-averaged properties of the isolated meta-atom. The ensemble average takes place over all possible orientations of the meta-atom relative to the illumination [44,45]. In such a situation, due to the fact that meta-atoms are randomly oriented, the definition of mode coupling becomes blurry and the concept of a Fano resonance is therefore hard to discuss.…”

“…This serves as the spectral signature for the Fano resonance. The quantity can be derived directly from the T matrix of the corresponding meta-atom [45]. This parameter expresses how much the coupling between the eigenmodes of the structure contributes to its total scattering cross section.…”

Orientation-averaged light scattering by nanoparticle clusters: far-field and near-field benchmarks of numerical cubature methods

“…incident and scattered fields yield analytical formulas for orientation-averaged optical properties. This powerful formalism enables benchmark calculations for various quantities of interest, which include orientation-averaged extinction, scattering and absorption 19,20 , circular dichroism 21 , but also near-field intensity 22 and local degree of optical chirality 23,24 . Although analytical, these orientationaveraged expressions can become quite involved in the case of near-field quantities, requiring the costly evaluation of translation matrices for each evaluation point.…”

High-resolution interference microscopy with spectral resolution for the characterization of individual particles and self-assembled meta-atoms

“…Such methods can be used to fabricate real three dimensional, isotropic materials with the trade-off of limited control over the macroscopic arrangement of the final structure [7]. In a strongly diluted scenario, the response of the bulk self-assembled metamaterials can be derived directly from the response of its constituent meta-atoms [8,9]. This means that, by understanding the response of a single meta-atom, the response of the whole three-dimensional metamaterials can be understood.…”