Metasurface Design
In this Section, we study the \(2\pi\) phase coverage mechanisms, working principle of multiwavelength double-focal metasurfaces, three proposed configurations and the optimization algorithm implemented to find the best possible metaatom for the decorating of the metasurface.In this regard, Three different configurations to provide the metasurfaces with two focal spots working at \(\lambda_1=460\ nm\), \(\lambda_2=535\ nm\) and \(\lambda_3=610\ nm\). Then, we introduced the optimization algorithm implemented to find the optimum sizes of metaatoms.
To design a phase gradient metasurface, it is required to provide a complete \(2\pi\) phase coverage by the building blocks of the metasurface. Three different techniques are mainly involved to realize a \(2\pi\) phase shift by dielectric metaatoms. The first mechanism is based on the geometrical phase (Pancharatnam-Berry phase) which achieved by the rotation of the metaatoms around the propagation direction of a circularly polarized incident light \cite{maguid2017multifunctional}. The second scheme is achieved by considering a high aspect ratio resonator with different cross-sections. These resonators can be considered as the truncated waveguides with Fabry–Pérot resonances \cite{kamali2016decoupling,Hu_2019}. Finally, for the third approach, a low aspect ratio resonator is utilized to excite different orders of electric and magnetic Mie resonances. The spectral positions of Mie resonance modes are tuned by the changing of the metaatom cross-section. Then, the phase modulation of the transmitted wave is achieved by the tailoring of the spectral position of the Mie resonances. The advantage of this technique is the capability in providing multiple 0 to \(2\pi\) phase coverages as a function of metaatom size which can later benefit to design an achromatic metasurface \cite{yu2015high}. Moreover, a fine parametric design of metaatom provides a Kerker’s condition \cite{Gao2017}. In this work, due to the variation of the working wavelength, the phase shifts are realized by a combination of Fabry–Pérot and/or Mie mechanisms \cite{li2019mechanisms}.
Figure \ref{897304} shows the working principle of an achromatic multiwavelength metalens consisting a-Si:H nanoblocks rested on the top of the SiO2 substrate. The constitutional elements of metasurface, a-Si:H nanoblocks, take advantage of high-refractive-index and low extinction coefficient at the working wavelengths, especially at \(\lambda_3\) and \(\lambda_2\). However, the absorption of metaatoms at \(\lambda_1\) is not as negligible as the two other wavelengths but, it is still acceptable in comparison to amorphous and polycrystalline silicon. On the other hand, the growth and deposition process of an a-Si:H thin layer is much straightforward than crystalline silicon. So, a-Si:H is a good candidate to preserve the compatibility of designed metasurface with CMOS technology at visible frequencies. The inset of fig 1 demonstrates a scheme of the proposed unit cell. The period of the unit cell is \(P=280\ nm\), while the metaatom features a sub-wavelength thickness of \(h=190\ nm\). As shown in Fig \ref{897304}, the \(y\)-polarized RGB lights are focused at two focal planes by an achromatic metalens while propagating along the metalens axis.