Optimization of Electromagnetic Metasurface Parameters Satisfying Far-Field Criteria

Electromagnetic metasurfaces offer the capability to realize 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, designers would solve for the surface parameters based on their application-specific far-field criteria. However, determining the surface parameters for these criteria is challenging without knowledge of the tangential fields on each side of the surface, which are not unique for a given far-field pattern. Current designs are generally restricted to analytical examples where the tangential fields can be solved for, or determined via
ad hoc
methods, although there has been recent work to circumvent this. This article presents an optimization scheme, which determines surface parameters, such as electric impedance, magnetic admittance, and magnetoelectric coupling, satisfying far-field constraints, such as beam level, sidelobe level, and null locations. The optimization is performed using a method of moments-based model incorporating edge effects and mutual coupling. The surface parameters are optimized for using the alternating direction method of multipliers. Examples of this optimization scheme performing multicriteria pattern forming, extreme angle small surface refraction, and Chebyshev-like beamforming are presented.