It is well known that the horn antennas have been widely used in wireless communication and satellite communication systems, due to their simple structures, broad operating bandwidth, low loss and high reliability. In this article, we propose a new approach of manipulating the aperture field and succeed to reduce the side-lobe level of radiation patterns by loading GRIN metamaterials in a three-dimensional (3D) horn antenna. But the required inhomogeneous and anisotropic medium is hard to be implemented. More recently, Gok and Grbic presented a method to tailor the electromagnetic fields including the phase and power flow 18. However, this metamaterial lens has to be placed away from the specially designed source so that the far-field radiation patterns of the source can be used to illuminate the surface of the metamaterial lens. 17 to control both the amplitude and phase distributions of the metamaterial lens, in which the spherical waves emitted from a special source (i.e., a well-designed waveguide antenna) are converted to plane waves, achieving a performance-improved lens antenna 17. More specifically, an efficient method was proposed in Ref. In most literatures, the GRIN metamaterials have served to increase the directivity and gain of antennas by transforming spherical waves to plane waves 11, 12, 13, 14, 15, 16.

Since then, the GRIN metamaterials have been utilized in achieving a variety of microwave applications, such as the Luneburg lenses 11, 12, highly directive antennas 13, 14, Maxwell fish-eye lenses 15, 16, low sidelobe lens antennas 17 and beam-scanning antenna 10. The first GRIN metamaterial was implemented in 2005, consisting of split-ring resonators (SRRs) to form the deflection of microwave beam 8. The GRIN metamaterials can be artificially realized with different unit cells with varying geometries and dimensions and therefore, is simple to design. Among various metamaterials in literatures, the gradient refractive index (GRIN) metamaterials which possess gradient permittivity and/or permeability have played an important role. In the past decade, metamaterials composed of periodic structures in the sub-wavelength scales have provided an unprecedented skill to control electromagnetic waves and create new devices such as invisibility cloaks 1, 2, 3, 4, 5, perfect absorbers 6, 7, metamaterial lenses 8, 9, 10, 11, 12, 13, 14, 15, 16 and metamaterial antennas 17, 18, 19, 20, 21.

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