Overlapping illusions by transformation optics without any negative refraction material

A novel method to achieve an overlapping illusion without any negative refraction index material is introduced with the help of the optic-null medium (ONM) designed by an extremely stretching spatial transformation. Unlike the previous methods to achieve such an optical illusion by transformation optics (TO), our method can achieve a power combination and reshape the radiation pattern at the same time. Unlike the overlapping illusion with some negative refraction index material, our method is not sensitive to the loss of the materials. Other advantages over existing methods are discussed. Numerical simulations are given to verify the performance of the proposed devices.