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Meta-surface design based on transformation optics

In this study, we propose a new way of designing metasurface based on transformation optics. The major features of the method can be concluded as the following two points: 1) Instead of the conventional sense of determining the proper transformation coordinate first, we try a different way: in terms of the desired radiation properties, electric and magnetic distributions on the boundary are firstly defined from huygens' principle and then inversely derive the coordinate transformation and the associated material parameters. Obviously, the attempts from a field's perspective offers more physical insights in the design of EM devices, thus bringing more flexibility and effectiveness to the manipulation of EM wave using TO. 2) Based on the Maxwell's equation and given the predefined polarization, a simplification procedure to 2D parameters is proposed via carefully choosing the coordinate transformation and effectively eliminating the spatial dependence. As a result, the design can be easily realized by 2D metasurface. The main difference from the meta-surface design based on “flat optics” purely from a 2D perspective, we view it as a 3D model essentially and simplifications are founded on the reasonable cancelation of the normal axial related components. As a result, much more comprehensive understandings can be obtained, thus offering valuable guidelines for further improvement of the design. More importantly, compared to the metasuface design by introducing the abrupt jump of phase on the surface, our design is rooted in transformation optic which has incomparable advantages in dealing with the complex problems, owing to its capability of simultaneously manipulating every single vector of electric and magnetic field. Therefore, our study will provide a more flexible and effective solutions for metasurface design.