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A general synthesis technique for beamforming metasurfaces is presented which utilizes accurate modeling techniques and rapid optimization methods. The metasurfaces considered consist of patterned metallic claddings supported by finite grounded dielectric substrates. The metasurfaces are modeled using integral equations which accurately account for all mutual coupling and finite dimensions. A beamforming metasurface is designed in three phases: an initial Direct Solve phase involving the solution of the integral equation via the method of moments to obtain a complex-valued initial design satisfying the desired far-field beam specifications, a subsequent Optimization phase to convert the complex-valued metasurface into a purely reactive metasurface, and a final Patterning phase to realize the metasurface as a patterned metallic cladding. The metasurface is optimized using an adjoint optimization method. The method calculates the gradient of the cost function in only two forward problem solutions. An example metasurface designed using this approach is presented. 

This work presents the experimental realization of a printed-circuit beamformer designed using shape optimization. Shape optimization of the printed-circuit beamformer is enabled through the use of a circuit network solver that utilizes reduced-order models of printed-circuit unit cells to rapidly evaluate device responses, and the adjoint variable method to evaluate gradients. The designed beamformer is patterned on a microwave substrate and interfaces with a 3-D printed tapered aperture antenna. It produces nine orthogonal beams and has isolated input ports that are impedance matched. Experimental results for the performance of the 3-D printed antenna and the beamformer will be presented at the conference. 

In this work, an inverse design method for multi-input multi-output (MIMO) metastructured devices is developed. Large-scale inverse design problems are difficult to solve directly and often require heuristic methods or design optimization to find a solution. Inherent errors introduced by heuristic methods makes design optimization a more promising route to the realization of high performance devices. Here, a fast frequency domain solver for grids of Y-parameter matrices is developed. The solver is used together with an adjoint-based optimization routine to solve inverse metastructured design problems. The design procedure is demonstrated through the realization of a planar beamforming network for a multi-beam antenna. 

Lossless, reciprocal bianisotropic metasurfaces have the ability to control the amplitude, phase, and polarization of electromagnetic wavefronts. However, producing the responses that are necessary for achieving this control with physically realizable surfaces is a challenging task. Here, several design approaches for bianisotropic metasurfaces are reviewed that produce physically realizable metasurfaces using cascaded impedance sheets. In practice, three or four impedance sheets are often used to realize bianisotropic responses, which can result in narrowband designs that require the unit cells to be optimized in order to improve the performance of the metasurface. The notion of a metasurface quality factor is introduced for three-sheet metasurfaces to address these issues in a systematic manner. It is shown that the quality factor can be used to predict the bandwidth of a homogeneous metasurface, and it can also be used to locate problematic unit cells when designing inhomogeneous metasurfaces. Several design examples are provided to demonstrate the utility of the quality factor, including an impedance matching layer with maximal bandwidth and a gradient metasurface for plane wave refraction. In addition to these examples, several metasurfaces for polarization control are also reported, including an isotropic polarization rotator and an asymmetric circular polarizer. 

In one dimension, a circuit network equivalence has been established for omega materials. However, 2-D circuit-based or transmission-line metamaterials have previously been restricted to magnetic and electric responses. This paper proposes 2-D circuit-based omega materials using asymmetric circuits. A general formulation is provided in terms of ABCD-parameters and an example is shown using Pi-networks. These metamaterials could enable the design of compact beamformers, power dividers, and other microwave devices.