Transformation optical design for 2D Flattened Maxwell fish-eye lens

In this paper, a 2D Flattened Maxwell fish-eye (MFE) lens is proposed using transformation optics, which transforms a traditional MFE lens into a flattened MFE lens. The coordinate transformation is presented from a circular to a rectangular domain. We also discussed the rotated ray trajectories in MFE lens. The required permittivity and permeability tensors are derived for the flattened MFE lens and full-wave simulations are obtained. The simulated results show that the flatted lens can also provide the image focus opposite to the object focus on the boundary of rectangle.