Accurate Modeling and Rapid Synthesis Methods for Beamforming Metasurfaces

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.