Introduction
Metasurface has emerged as a practical revolutionary structure composed of engineered arrays of sub-wavelength spaced resonators (called as metaatoms)\cite{Lin2014}. These flat structures have evoked enormous exotic properties due to the ability in simultaneous manipulation of the phase, amplitude, and polarization of the incident light with a subwavelength spatial resolution\cite{Yu2014}. However, the evolution of optical metasurfaces was inevitably associated with metallic metaatoms as the building blocks, these constitutional elements suffer from non-radiative Ohmic losses. Later, the substitution of dielectric metaatoms with their plasmonic counterparts has added a new paradigm to the pioneer optical metasurface to reach beyond moderate efficiency\cite{Yu_2015}. Several dielectric metaatoms such as titanium dioxide TiO2 \cite{Sun2017}, Silicon (Si) \cite{Shalaev2015} and gallium nitride (GaN)\cite{Chen2017} have been employed at optical frequencies. Among the aforementioned materials, Si-based metasurfaces are compatible with the well-established complementary metal-oxide-semiconductor (CMOS) technology. Though amorphous Si metaatoms provide a low loss solution in the infrared domain, they experience a considerable loss in the visible domain due to the higher absorption of Si in this regime. In this regard, thanks to the hydrogenated amorphous silicon (a-Si:H) which provides a high efficient metasurface at visible frequency without adding complexity in the fabrication process \cite{Yoon2018}. During the deposition of a-Si:H, the hydrogen atoms passives the dangling bond defects and reduces the concentration of them \cite{Ramanujam_2012,Pfanner_2013}. Also, It has been demonstrated that a-Si:H metaatoms can provide a \(2\pi\) phase shift at different visible wavelengths \cite{park2017structural,mahmood2018polarisation,ansari2020engineering}.
Various efforts have been employed to enhance the practicality of metalenses as a versatile platform such as designing the multifocal \cite{bao2017enhanced} or achromatic \cite{wang2017broadband} metalenses. A multifocal metasurface gives this opportunity to focus the incident beam into different spots along the longitudinal \cite{chen2015longitudinal}, transverse \cite{lv2019multifocal}\cite{lv2019multifocal} or diagonal \cite{shanei2019all} directions which has significant applications in three-dimensional imaging systems \cite{khorasaninejad2016multispectral}, optical tomography technique \cite{pahlevaninezhad2018nano}, optical data storage \cite{wen2015helicity}, laser printing \cite{carstensen2018holographic} and parallel particle trapping \cite{toprak2007three,ma2017trapping,jin2019metasurface}. Many approaches have been put forward to focus the incident light at multiple focal spots in the bulky refractive/ diffractive optical element elements such as lens arrays \cite{algorri2017tunable}, beam splitters \cite{nielsen2001high}, freeform surfaces \cite{ye2017review}, Fresnel zone plates \cite{de2013multiple} and so on. The advent of flat optics has opened new promising possibilities not only to design efficient multifocal metalenses \cite{chen2015longitudinal,yin2017beam,bao2017enhanced,lin2019multifocal} but also to control the dispersion of the metasurfaces \cite{arbabi2017controlling,wang2018broadband,shrestha2018broadband}\cite{Fan2019}. Recently, the achromatic single spot metalenses have been paid remarkable attention and many kinds of multiwavelength metasurface have been realized theoretically and experimentally \cite{aieta2015multiwavelength,avayu2017composite,khorasaninejad2017achromatic}. Generally, the multiwavelength metasurfaces are realized by two strategies. The first one is rely on the structural/geometrical engineering of the metasurfaces such as stacking or stitching multiple layers of metasurfaces or multiplexing several metasurfaces to each other \cite{zhou2018multilayer,avayu2017composite}. The second strategy is based on the extending of the phase coverage beyond \(2\pi\) and then, implementing an optimization algorithm such as particle swarm optimization \cite{shi2018single,khorasaninejad2017achromatic}. It worth mentioning, the latter technique compensates the chromatic dispersion without adding any fabrication complexity. Here, the chromatic dispersion of a double focal metalens is minimized by the realization of the multiple \(2\pi\) phase coverages by the metaatoms. The multiple chooses of metaatoms can simultaneously satisfy the required phase profiles of discreet wavelengths on the metasurface. To our knowledge, the double focal metalens with an achromatic behavior has not been proposed before.
In this work, we introduce three different double focal metasurfaces focusing the RGB incident lights at two separate spots. Each metasurface is patterned to introduce the corresponded phase and amplitude modulations. The first configuration of the double focal metasurface is patterned by considering a mixed-phase profile. This profile manipulates the impinging lights to interfere constructively at two focal spots. The next configuration is achieved by dividing metasurface to two sub-area. So, we have to consider two different phase profiles for this metasurface which is named as an ophthalmic lens. Finally, for the last configuration, we have applied an extra amplitude mask to the arrangement of an ophthalmic lens. So, in this configuration, the mataatoms should be patterned to introduce a phase and amplitude profiles, simultaneously. This amplitude mask gives an extra degree of freedom to control the unwanted interaction between the zones of metasurface. This configuration is called an engineered ophthalmic lens. Then, we investigate the focusing behavior of each configuration in terms of efficiency, achromaticity and resolution.
This paper is organized as follows: in Section~\ref{sec:2}, we study the designing principle of mixed, ophthalmic and engendered ophthalmic lenses based on the required phase and amplitude modulation. In Section~\ref{sec:3}, the numerical results of the performance of each configuration are investigated. Section~\ref{sec:4} presents the fabrication process, measurement setup and the experimental results of fabricated metasurfaces. Finally, In Section~\ref{sec:5} we study and compare the focusing performance of metasurfaces in terms of efficiency, achromaticity and resolution.