THz focusing and imaging include bulky dielectric refractive lenses and parabolic mirrors. Due to the diffraction effect, the resolution of conventional optics is limited by the Abbe diffraction limit (DL) of 0.5λ/NA, [5] where λ and NA are working wavelength and numerical aperture (NA), respectively. Recently, there has been a growing interest in developing far-field super-resolution optical devices, which can achieve point-spread-function (PSF) of size smaller than the Abbe DL without evanescent waves [6] at a distance far beyond the near-field regime. [7,8] Based on the concept of superoscillation, [9-11] a variety of sub-diffraction or super-resolution optical devices have been demonstrated either theoretically or experimentally, including scalar super-resolution metalenses [12-22] and vector super-resolution metalenses. [23-33] Such super-resolution devices have been successfully shown great potential in labelfree super-resolution microscopy [13,21,34,35] and super-resolution telescope. [36] However, most previously reported super-resolution metalenses only work at one single wavelength [37] or several designed discrete wavelengths, [38,39] while broadband achromatic metalenses working in the visible [40-42] and nearinfrared spectrum [43-46] as well as THz regime [47] are restricted by the Abbe DL. To achieve a broadband super-resolution imaging, recently, a broadband super-resolution scheme was proposed and experimentally demonstrated by adopting the combination of a super-oscillatory binary phase filter and a conventional bulk achromatic refractive convex lens. [48] Up to now, it is still a great challenge to realize a sub-diffraction achromatic metalens with a continuous broad bandwidth. To achieve broadband achromatic super-resolution focusing, similar to the conventional optics, dispersion compensation is required to ensure that the wave of different wavelengths is focused at the same focal point. In addition, wave front engineering is also required to achieve the super-resolution PSF. Recent fast development of metasurfaces [49-54] provides effective ways to manipulate the amplitude, [55,56] phase, [57-61] polarization [30,33,62-66] and dispersion properties [67,68] of light waves. To achieve wave front shaping without influences on dispersion, one possible way is to realize broadband achromatic super-resolution by adopting amplitude modulation. Conventionally, pupil filters [69-78] can be used to achieve super-resolution in traditional optical systems. Recently, there are growing interests in developing super-resolution metalenses for applications of focusing and imaging. On one hand, various sub-diffraction metalenses have been demonstrated; however, most of them only work at a single wavelength or multiple discrete wavelengths. On the other hand, the previously reported broadband achromatic metalenses are diffraction-limited, or their focal spots are larger than the corresponding Abbe diffraction limit, 0.5λ/NA, where λ and NA are the lens working wavelength and numerical aperture. In the present wo...

Optical super-resolution diffractive metalenses have been promising candidates for realizing optical imaging and a microscope beyond the Abbe diffraction limit. An achromatic super-resolution metalens is particularly important for practical applications; however, it remains challenging to achieve high-numerical-aperture achromatic super-resolution metalens for subwavelength focusing. Herein, a holographic approach of realizing a multiwavelength achromatic subwavelength super-resolution focusing is proposed. Through wavefront engineering and holographic synthesis, a high-numerical-aperture achromatic super-resolution metalens is demonstrated for subwavelength super-resolution focusing at five different wavelengths of 520, 555, 632.8, 660, and 690 nm. Broadband achromatic performance is also expected. Generally, there is no theoretical limit on the number of achromatic wavelengths. The proposed method could be useful in super-resolution related applications, including imaging, microscopy, and data storage.

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