The Design of Dual Band Stacked Metasurfaces Using Integral Equations.

An integral equation-based approach for the design of dual-band stacked metasurfaces that are invariant in 1-D is presented. The stacked metasurface will generate collimated beams at the desired angles in each band upon reflection. The conductor-backed stacked metasurface consists of two metasurfaces (a patterned metallic cladding supported by a dielectric spacer) stacked one upon the other. The stacked metasurface is designed in three phases. First, the patterned metallic cladding of each metasurface is homogenized and modeled as an inhomogeneous impedance sheet. An electric field integral equation (EFIE) is written to model the mutual coupling between the homogenized elements within each metasurface and from metasurface to metasurface. The EFIE is transformed into matrix equations by the method of moments. The nonlinear matrix equations are solved at both bands iteratively resulting in dual-band complex-valued impedance sheets. In the second phase, optimization is applied to transform these complex-valued impedance sheets into purely reactive sheets suitable for printed circuit board fabrication by introducing surface waves. In the third phase, the metallic claddings of each metasurface are patterned for full-wave simulation of the dual-band stacked metasurface. Using this approach, two dual-band stacked metasurfaces are designed.