Optimization of Scalar and Bianisotropic Electromagnetic Metasurface Parameters Satisfying Far-Field Criteria (2011.09016v1)

Abstract: Electromagnetic metasurfaces offer the capability to realize almost arbitrary power conserving field transformations. These field transformations are governed by the generalized sheet transition conditions, which relate the tangential fields on each side of the surface through the surface parameters. Ideally, engineers would like to determine the surface parameters for transformations based on their application-specific far-field criteria. However, determining the surface parameters to satisfy these criteria is challenging without direct knowledge of the tangential fields on one side of the surface, which are not unique for a given far field pattern. As a result, current design is restricted to analytical examples where the tangential fields are solvable or other ad hoc methods. This paper presents a convex optimization-based scheme which determines surface parameters, such as surface impedance, admittance, and magneto-electric coupling, which satisfy far-field constraints such as beam magnitude, side lobe level, and null locations. The optimization is performed on a model constructed using the method of moments. This model incorporates edge effects and mutual coupling. The resulting non-convexity from this model is relaxed using the alternating direction method of multipliers. Examples of this optimization scheme performing multi-criteria pattern forming, extreme angle small surface refraction, and Chebyshev beamforming are presented.