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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.

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In recent years, there has been extensive research on planar metasurfaces capable of arbitrarily controlling scattered fields. However, rigorous studies on conformal metasurfaces, such as those that are cylindrical, have been few in number likely due to their more complex geometry. Here, wave propagation in cascaded cylindrical structures consisting of layers of dielectric spacers and azimuthally-varying metasurfaces (subwavelength patterned metallic claddings) is investigated. A wave matrix approach, which incorporates the advantages of both ABCD matrices and scattering matrices (S matrices), is adopted. Wave matrices are used to model the higher order coupling between metasurface layers, overcoming fabrication difficulties associated with previous works. The proposed framework provides an efficient approach to synthesize the inhomogeneous sheet admittances that realize a desired cylindrical field transformation. Design examples are reported to illustrate the power and potential applications of the proposed method in antenna design and stealth technology.

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