Beamforming with Perfectly-Matched Metamaterials

This work reports an inverse design method for perfectly-matched metamaterials (PMMs) with multi-input multi-output (MIMO) functionality. PMMs are inhomogeneous, anisotropic 2-D metamaterials composed of unit cells that remain impedance-matched to each other and the surrounding medium. These reflectionless devices rely on refractive effects to perform field transformations, exhibiting true time delay behavior and broadband operation. The paper improves on a previously reported inverse design method on two fronts. First, the objective function is modified to match desired voltage magnitudes and phase profiles. Importantly, the objective function allows phase profiles to have an arbitrary phase offset instead of absolute phase values. Second, an absorbing boundary condition is imposed on all boundaries of the computational domain. As an example, a compact and broadband beamformer is presented. The device transforms the field of a line source to the far-field radiation pattern of a Dolph-Chebyshev array of the same size with a -20 dB sidelobe level.