Designing Anisotropic, Inhomogeneous Metamaterial Devices Through Optimization

A method for designing multi-input, multi-output metamaterial devices is presented. The devices are 2-D anisotropic, inhomogeneous media. The design technique consists of a custom finite-element method solver coupled to a constrained, nonlinear minimization algorithm. The design method has advantages over existing metamaterial design methods such as transformation optics, in that material constraints can be imposed and multi-input, multi-output functionality allowed. Transformation optics devices only achieve multi-input, multi-output functionality through geometrical symmetry. The gradient-based optimization method employed in the metamaterial design process is fast given that an analytic expression for the gradient of the cost function can be written. The proposed technique is demonstrated through the design of two beamforming devices. A commercial full-wave solver is used to validate the design approach. The constitutive parameters of these 2-D designs can be implemented using printed-circuit board metamaterials, such as tensor transmission-line metamaterials.