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This article presents a numerical strategy for actively manipulating electromagnetic (EM) fields in layered media. In particular, we develop a scheme to characterize an EM source that will generate some predetermined field patterns in prescribed disjoint exterior regions in layered media. The proposed question of specifying such an EM source is not an inverse source problem (ISP) since the existence of a solution is not guaranteed. Moreover, our problem allows for the possibility of prescribing different EM fields in mutually disjoint exterior regions. This question involves a linear inverse problem that requires solving a severely ill-posed optimization problem (i.e. suffering from possible non-existence or non-uniqueness of a solution). The forward operator is defined by expressing the EM fields as a function of the current at the source using the layered media Green’s function (LMGF), accounting for the physical parameters of the layered media. This results to integral equations that are then discretized using the method of moments (MoM), yielding an illposed system of linear equations. Unlike in ISPs, stability with respect to data is not an issue here since no data is measured. Rather, stability with respect to input current approximation is important. To get such stable solutions, we applied two regularization methods, namely, the truncated singular value decomposition (TSVD) method and the Tikhonov regularization method with the Morozov Discrepancy Principle. We performed several numerical simulations to support the theoretical framework and analyzes, and to demonstrate the accuracy and feasibility of the proposed numerical algorithms. 

Beamforming by scattering from an array of scatterers carried by a drone is explored. By positioning the vertical heights of the scatterers on the drone, beam focusing can be achieved in a desired direction. Various horizontal layouts of the scatterers on the drone can be used, with a “double-cross” layout used here for the case of 9 scatterers. The formation of a null in the pattern in a desired direction is also possible using optimization of the scatterer positions. 

There may be situations where a direct line of sight between a transmitter and a receiver is blocked. In such a situation it may be possible to transmit a signal upward from a transmitter to a swarm of drones, each of which carries a scattering object. By positioning each drone properly, the scattered signal from the drones can add coherently in a given direction, forming a beam in that direction. The altitude of each drone is used as a degree of freedom in order to change the phase of the signal scattered by the drone. For a given set of horizontal drone positions, the drone altitudes can be determined to produce a main beam in a given direction. The drone positions can also be optimized to focus a beam in a given direction while producing pattern nulls in other prescribed directions with very small sidelobes.