Using the gradient phase discontinuities that meta-mirrors provide, we show that the incident wave can be reflected anomalously with a broad angle range of negative reflections. Such reversed behaviors promote the immediate applications for the planar meta-mirrors to steer the signals more arbitrarily and the convex meta-mirrors to focus and collimate electromagnetic fields. We practically implement these negative reflecting meta-mirrors through an arrangement of subwavelength ring patches and generate the desired phase distribution by also considering the incident angle. Finally, the experiments are carried out to verify the functionality of the convex meta-mirror firstly, and the performances of the planar meta-mirror are also tested by further building up a dual reflector system with the demonstration of obtaining the plane wave from the convex meta-mirror and then having the well collimated beam negative reflected by the planar meta-mirror. The proposed design should be readily applicable to a wide range of electromagnetic problems, especially for devising smart planar illusion devices, and highly directive antennas mounting on convex surfaces of various platforms.

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Gradient-index dielectric lenses are generated based on the coordinate transformation by compressing the homogeneous air spaces quasi-conformally towards and outwards the primary source. The three-dimensional modeling is then performed through revolving the prescribed transformational media 180 degrees around the focal point to reach the architecture of barrel-vaults. It is found that all these two- and three-dimensional transformation-optical designs are capable of producing fan-beams efficiently over a broad frequency range with their main lobes possessing the narrow beamwidth in one dimension and the wide beamwidth in the other, while having the great ability of the wide angular scanning. Finally, we propose to construct such four types of fan-beam lenses through multiple-layered dielectrics with non-uniformed perforations and experimentally demonstrate their excellent performances in the fan-beam synthesis.