High numerical aperture and large focusing efficiency metalens based on multilayer transmitarray elements

•High numerical aperture and large focusing efficiency metalenses in the microwave spectrum are studied.•Numerical and experimental results demonstrate a high NA metalens in the order of 0.8 and the large focusing efficiency around 40% based on four-layer high transmission gradient element.•Besides, the NA of proposed metalens can be further improved from 0.8 to 0.9 by increasing dielectric thickness and/or the focusing efficiency can be enhanced to above 50% by adding the layer number of the stacked meta-atoms. High numerical aperture (NA) metalenses with large focusing efficiency are crucial for various applications in modern optics and photonics, particularly in high resolution imaging, high directivity lasing process and so on. Recent progresses have been achieved in designing high NA metalenses which can surpass conventional ones but mainly in the visible and infrared regimes by using all-dielectric metasurfaces. Here, multilayer phase gradient metallic metasurfaces sandwiched by filling dielectrics are employed to design high NA and large efficiency metalenses in the low spectrums. Benefiting from its high transmission amplitude and the full phase control to the incident waves of the proposed gradient meta-atoms with a double split ring resonator, the designed ultra-thin and small footprint four-layer metalens (5λ × 5λ × 0.23λ, λ is wavelength) demonstrates a high NA in the order of 0.8 and the large focusing efficiency around 40% according to the full-wave simulations and experimental measurements. Furthermore, the influences of the dielectric thickness and the layer number of stacked meta-atoms on the presented high NA metalens are investigated. The results reveal that the NA of proposed metalens can be surprisingly further improved from 0.8 to 0.9 by increasing dielectric thickness and/or the focusing efficiency can be enhanced to above 50% by adding the layer number of the stacked meta-atoms. These findings also imply that our high NA metalens in low spectrum can be compatible to the standard printed circuit board fabrication and also posses of good robustness to the metasurface layer number. The presented work provides new vistas to develop high NA and large efficiency metalens in low microwave or Terahertz (THz) spectrum, where the metallic metasurfaces are commonly used. Besides, it can benefit to the development of various novel metadevices such as miniaturized high-gain lens antenna, compact cloaks and many others in modern microwave enginee