Periodic metastructures (including those with a macroperiodicity) have found numerous applications within the microwave to the optical regime. The analysis and synthesis of these structures generally requires the retrieval of equivalent material parameters (EMPs). To achieve this, the well-known approach is the locally periodic approximation (LPA), which is not always valid, e.g., when the angular dependence of the scattering behavior is pronounced. Here, through semianalytical closed-form expressions, we present an alternative approach to nonlocally model metastructures supporting multiple propagating Floquet-Bloch (FB) modes. This approach can be utilized to extract spatially dispersive (nonlocal) and/or position-dependent EMPs from the scattering parameters (S-parameters). The proposed framework can determine heterogeneous angle-dependent EMPs, replicating the scattering behavior of multichannel metastructures, and it provides an intermediary tool for the design of metastructures with macroperiodicity.

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• Optical & microwave phenomena
• Metamaterials
• Metasurfaces
• Effective medium approach
• Materials modeling