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Genuinely homogeneous metamaterials, which may be characterized by local effective constitutive relations, are required for many spectacular metamaterial applications. Such metamaterials have to be made of meta-atoms, i.e., subwavelength resonators, which exhibit only electric and or magnetic dipole and negligible higher-order multipolar polarizabilities in the spectral range of interest. Here, we show that these desired meta-atoms can be designed by exploiting the extreme coupling regime. Appropriate meta-atoms are identified by performing a multipole analysis of the field scattered from the respective meta-atom. To design those particular meta-atoms it is important to disclose the frequency and angular-dependent polarizability of both dipole moments. We demonstrate the applicability of a purely analytical model to accurately calculate for a normally incident plane wave reflection and transmission from meta-surfaces made of periodically arranged meta-atoms. With our work we identify a possible route towards the engineering of artificial materials while only considering the response from its constituents. Our approach is generally applicable to all spectral domains and can be used to evaluate and design metamaterials made from different constituting materials, e.g., metals, dielectrics, or semiconductors

Extreme coupling: A route towards local magnetic metamaterials