Optical metasurfaces are periodic or graded pattern arrays of ultra-thin plasmonic and/or dielectric nanostructures, which are intended to scatter light in manners that cannot be achieved with conventional stratified media. Recent advancements in the theoretical knowledge and fabrication methods of two-dimensional materials, such as graphene, have provided the opportunity to scale down the principles of metasurfaces to atomic dimensions and to offer graded pattern meta-sheets. We present here engineered nanostructures to tailor the beaming pattern of light scattered through such meta-sheets. We obtain designs to precisely control both the in-plane scattering of surface waves associated with the sheets and also out-of-plane scattered far-field beams into a desired direction. We then determine a set of conductivity-balancing conditions to completely confine the surface waves to the meta-sheets at highly scattering sites and demonstrate that under such criterion the propagation of guided surface waves can be described simply using Fresnel equations of plane waves. Furthermore, we cascade three sinusoidally modulated reactance surfaces to realize a broad-beam leaky-wave antenna to completely scatter the surface waves to far-field and also control the steering direction. In addition, conformal patterned 2D sheets will be explored for the first time and how to successfully design and manipulate the light wavefront. For fast and accurate designs of the flat and conformal meta-sheets, we take advantage of our superior auxiliary differential equation finite-difference time-domain (ADE-FDTD) method. Also, an integral equations (IE) model will be applied for large-area system platforms design investigation.
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