Optimization-free approach for broadband achromatic metalens of high-numerical-aperture with high-index dielectric metasurface

Broadband achromatic metalenses are highly desirable for realistic applications in focusing and imaging. In this paper, a group of dielectric double-strip meta-atoms of high-index are proposed to achieve a large range of group delay in a broadband near-infrared range. And an optimization-free method is developed for the simple and fast design of broadband achromatic metalenses of high-numerical-aperture, which treats the dispersion as a function of radius and independent of wavelength. To verify the proposed meta-atoms and the optimization-free design approach, an achromatic metalens is designed with a high-numerical-aperture of NA = 0.81 and a broad bandwidth of 120 nm within the wavelength range from 1470 nm to 1590 nm. Numerical simulations reveal that the focal length only has a small variation of 0.27 lambda(0) (0.17 lambda(0)/NA(2), lambda(0) = 1530 nm), the depth of focus is smaller than 2.85.0, and the average transverse size of the focal spot is less than 0.68 lambda(0), which is slightly larger than the diffraction limit of 0.617 lambda(0) (0.5 lambda(0)/NA). Compared to other reported achromatic metalenses, the proposed lens has a larger numerical aperture and smaller depth of focus. In addition, the proposed optimization-free method makes it easier to design achromatic metalens with high-numerical-aperture and improved axial resolution.