Conformal carpet and grating cloaks.

@article{Schmied2010ConformalCA,
  title={Conformal carpet and grating cloaks.},
  author={Roman Schmied and Jad Camille Halimeh and Martin Wegener},
  journal={Optics express},
  year={2010},
  volume={18 23},
  pages={
          24361-7
        }
}
We introduce a class of conformal versions of the previously introduced quasi-conformal carpet cloak, and show how to construct such conformal cloaks for different cloak shapes. Our method provides exact refractive-index profiles in closed mathematical form for the usual carpet cloak as well as for other shapes. By analyzing their asymptotic behavior, we find that the performance of finite-size cloaks becomes much better for metal shapes with zero average value, e.g., for gratings. 

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