Customizing the Response of Conformal and Low-frequency Magnetic Metasurfaces

In the last decades, metamaterials and metasurfaces has dramatically emerged as a fundamental research topic in electromagnetism due to the wide range of possible applications [1]. They have been proved useful for absorbing the undesired impinging e.m. energy and, thus, reducing an object radar cross section. Moreover, they can achieve exotic behavior, as negative refractive index, negative permeability and permittivity, and perfect lensing property. In the relatively low frequency regime (1-100 MHz), magnetic metasurfaces have become a powerful tool to enhance the performance of wireless power transfer devices as well as to increase the signal-to-noise ratio in MRI radiofrequency coils. As a natural technological development, by starting from planar slabs to be interposed between a particular arrangement of antennas, the actual need is to progressively extend the dimension of the adopted metasurface and achieving conformal characteristic. In this way, the potential applications span can be hugely increased, potentially unveiling a number of new and disruptive practical accomplishments. Nevertheless, while the planar and infinite metasurface case has been deeply studied, a lack of practical modelling is still missing for arbitrarily large and conformal structures. Moreover, the adoption of full-wave electromagnetic software is also unfeasible, since the computational effort is rapidly becoming unmanageable with the array dimension. Therefore, in this work, we try to address this challenge by adopting a novel approach, partially based on already appeared circuital models [2]. In particular, our method consists on a two-stage procedure. First, once the basic unit-cell element is adopted, we preliminary estimate the smallest 2-D array dimension in order to apply an almost ideal infinite periodic condition on the central element. Later, we evaluated the reactive load to be adopted for each element of the metasurface by adopting the circuital analysis already appeared in the literature. Thanks to this approach, not only arbitrarily conformal, but also very large structure can be analyzed since the problem dimension is limited at the first stage, independently from the specific structure under analysis. We prove that a full control on the behavior of magnetic metasurfaces can be achieved when they are excited with an impinging plane wave excitation, both in terms of phase and amplitude of the current circulating in each array element. Further developments will be directed to apply such methodology in practical applications, as for instance, Wireless Power Transfer and Magnetic Resonance Imaging. We also envision an extension of the method to a higher frequency range, also considering near-field excitations.