Fast Optimization Procedure for the Synthesis of Arbitrarily Conformable Magnetic Metasurfaces

In recent times, important research has been carried out within the wireless power transfer (WPT), due to the ever increasing demand for contactless charging systems [1]. The inductive WPT is characterized by the rapid decay of near-field components. The magnetic field decays from the active coil proportionally to the cube of the distance from the passive receiver coil. This is why research in this sector has been oriented towards solutions that improve efficiency and working distance. Many solutions to enhance the performance of an inductive link have been presented in the literature. The three-coil system is probably one of the most common solutions, but at the same time efficient and compact. Instead of using just a driver circuit inductively coupled to a receiver (both resonating at the same frequency), an additional intermediate resonant passive coil is introduced. This transmit coil is strongly coupled to both the driver coil and the receiver. In this way, very small currents in the driver are enough to induce a large amount of current flowing into the transmitter. Our approach is applied to a similar three-coil system, but the intermediate passive coil is substituted by a three-dimensional distribution of small size loops. The system consists of two parallel coils, a transmitter and a receiver, and a planar metasurface placed orthogonally to the plane of the main coils. In particular, the surface is constituted by a planar distribution of unit cells of circular shape, and the size of the unit cell is very small w.r.t the operative wavelength (less than 10 MHz). The aim of our work is to optimize the distribution of currents on the surface by maximizing the magnetic flux in the receiving coil by a new method based on the analytical evaluation of the contribution of the single loop at the total magnetic flux. The best distribution of currents on the surface is obtained by our method in three steps. Firstly, the total magnetic flux from both the driving coil and the metasurface concatenated with the receiver is calculated on the assumption that each coil is radiating as an elementary magnetic dipole fed with unitary source. Secondly, the optimum currents of each unit cell are determined by means of an optimizer whose cost function is the maximization of the total magnetic flux on the receiving coil. Subsequently, in order to achieve the desired currents on each loop of the surface, the loads to be added in series to the ports of the loops are computed by applying the theory developed in [2]. Because this method depends on the matrix of the impedances of the loops present in the scene, evaluable by a full-wave simulation, the real coupling between the unit cells is considered. The proposed procedure allows to design magnetic metasurfaces with arbitrary shapes and able to synthetize the magnetic field distribution required for a given application with a high degree of freedom. A further objective of this work is the application of the presented method to WPT scenarios where an arbitrary distributions of unit cells in space can be the enabling step in order to find the best configuration that maximize the coupling between the transmitting coil and the receiving one.