Retrieval of coupling coefficients for dense metamaterials

Electromagnetic properties of metamaterials are strongly affected by inter-element coupling between meta-atoms. Our recently proposed method enabling a retrieval of coupling coefficients in metamaterials is based on a transformation of the frequency dependence of complex current amplitudes in interacting meta-atoms, enabling separate deduction of the magnetic and electric coupling coefficients. This method relies on our ability to measure separately currents on two interacting elements. However, in case of dense metamaterials fields from the surroundings mask the required signals severely. In this paper we present a novel technique of coupling retrieval for dense metamaterials, in which spurious fields from environment are accounted for by correction factors. The method is verified on a number of examples using both experimental and simulation data in a wide frequency range from MHz to THz. Our method will serve as a basis for design of densely packed metamaterials with strong inter-element coupling.