Magnetic metasurfaces properties in the near field regions

In this paper, we present a general equivalent-circuit interpretation of finite magnetic metasurfaces interacting with an arbitrary arrangement of RF coils operating in near-field regime. The developed model allows to derive a physical interpretation of the interactions between the metasurface and the surrounding RF coils, both transmitting and receiving. Indeed, especially for near-field applications, the metasurface presence modifies the behavior of each RF coil differently, due to the specific reciprocal interactions. Hence, the proposed approach introduces a source-related complex magnetic permeability matrix, overcoming the traditional bulk definition. To prove the model validity against full-wave simulations, we present two significant test cases, commonly used in practical applications. The former is represented by the simple metasurface-coil arrangement from which important and fundamental considerations can be drawn. The latter system is composed by a transmitting and a receiving coil with a metasurface in between; detailed explanations on the metasurface interactions with both the RF coils are developed. Finally, we also achieved an excellent agreement between the numerical results and the measurements obtained through fabricated prototypes. In summary, the circuit interpretation herein presented, in addition to the rigorous electromagnetic theoretical approaches already appeared in the open literature, reveals useful in providing quantitative, practical, and easy-to-handle guidelines for the design and physical understanding of finite magnetic metasurfaces interacting with arbitrary RF coils arrangements in the near-field regime.