Design of magnifying oblate cylindrical hyperlens and planar hyperlens using multi-layer metamaterial

We designed a magnifying oblate cylindrical hyperlens with a planar object surface by taking advantage of the oblate cylindrical coordinate system in association with Pendry\´s coordinate transformation, enabling a sub-diffraction-limited object to be magnified from a plane to a curved elliptical surface beyond the diffraction limit. Then we used the conformal mapping approach to produce another structure, which is added at the top of the oblate cylindrical hyperlens to make the imaging surface flat, here we term it as "magnifying planar hyperlens", the possible implementation method is proposed by using effective anisotropic metamaterial formed by alternating metallic and dielectric thin layers. The magnification performance of the designed multi-layer lensing structure is numerically simulated to confirm our theoretical analysis. This kind of flat-to-flat imaging structure is expected to show its convenience in far-field image measurement and have potential applications in real-time far-field subwavelength imaging as well as in litherphotography.