  An integral equation-based approach for the design of dual band stacked
metasurfaces is presented. The stacked metasurface will generate collimated
beams at 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.
