Metasurfaces based on subwavelength scale structures have emerged as a next-generation optical platform for enabling complete control of the properties of light [1–31]. Depending on the geometrical parameters and materials of the designed nanostructures, known as meta-atoms, various metasurfaces that manipulate visible light have been proposed, such as metaholograms [1–11], plasmonic resonators [12–14], phase control devices [15–19], and compact photonic devices [20–31]. All-dielectric metalenses have received great attention in particular, due to having various industrial applications [32–39] and advantages over traditional lenses such as their ultrathin compact integration, multifunctionality [32–35], and high numerical aperture (NA) imaging [36–39] in the visible spectrum.

However, as with conventional refractive lenses, chromatic dispersion is a limiting factor for metalenses, which means that existing all-dielectric metalenses can be operated only by one specific design wavelength. Recently, several methods have been introduced to reduce chromatic dispersion such as control of the group delay dispersion of light by adjusting the geometric parameters and rotation angle of nanofins [40,41]. Chromatic dispersion can be reduced by compensating the optical path difference to the focus of the transmitted light for different wavelengths through the variation of group delay dispersion of nanofins. However, they have an NA of less than 0.2, making them unsuitable for high-resolution imaging systems. Various metalenses have also been demonstrated [42,43] but have NAs of less than 0.3 and do not operate at visible wavelengths. Multilayer stacking and spatial multiplexing have also been reported for achromatic metalenses operating at several discrete wavelengths [44–50]. Multilayer stacking can be demonstrated by Fresnel zone plates or independent phase modulation at different wavelengths [43,44]. However, these metalenses have low efficiency due to noise between stacked metasurfaces. Because of this problem, various metalenses have been integrated into one metalens by spatial multiplexing [46–49]. These metalenses can operate at two [46,47] or three [48,49] discrete wavelengths but are still limited due to low NA ($<0.4$). Such problems can be solved by the spatial integration of different isotropic meta-atoms. The simple integration of isotropic meta-atoms based on unit cell engineering can increase the operating wavelengths of the metalens. Therefore, this method can reduce chromatic dispersion.

Here, we propose a polarization-insensitive RGB achromatic metalens by spatial integration of three distinct meta-atoms to design a metalens that operates at three wavelengths in the visible spectrum (450, 532, and 700 nm). The meta-atoms for two wavelengths (532 and 700 nm) are embedded in the metalens designed to operate at the wavelength of 450 nm. To design a high NA and high-efficiency metalens, dielectric meta-atom transmitter arrays composed of low-loss hydrogenated amorphous silicon (a-Si:H) are used [50]. By controlling the hydrogenation and silicon disorder, a-Si:H is optimized to provide a near-zero extinction coefficient ($k$) in the visible spectrum. Also, it has a higher refractive index than conventional materials such as titanium dioxide (${\mathrm{TiO}}_2$), gallium nitride (GaN), or silicon nitride (SiN). This leads to higher efficiency metalenses than previous results in our group using ${\mathrm{TiO}}_2$ [51]. The calculated efficiencies of the $\mathrm{NA}=0.87$ a-Si:H-based spatial interleaving method (SIM) metalens are 25.2%, 58.7%, and 66.4% at the wavelengths of 450, 532, and 700 nm, respectively. Furthermore, the metalens is successfully fabricated by using simple plasma-enhanced chemical vapor deposition (PECVD) and electron-beam lithography (EBL) processes. The fabricated metalens has $\mathrm{NA}=0.87$ with a diameter of 450 μm and measured efficiencies of 5.9%, 11.3%, and 13.6% at $\lambda =450$, 532, and 700 nm, respectively.

To design an RGB achromatic metalens operating at three discrete wavelengths, the following hyperbolic phase profile must be satisfied to prevent spherical aberration [52]: $$\varphi (r)=2\pi -\frac{2\pi }{\lambda }(\sqrt{r^2+f_d^2}-f_d),$$(1)where $r$ is the radial distance from the center, $\lambda$ is the incident wavelength of light, and $f_d$ is the designed focal length. For polarization-insensitive operation, circular meta-atoms on glass substrate are used [Fig. 1(a)]. To realize the required phase profile $\varphi (r)$, the geometrical parameters such as diameter (D) and height (H) are optimized to provide full phase coverage from 0 to $2\pi$ [Fig. 1(b)]. As D increases, the phase of the transmitted light is modulated from 0 to $2\pi$, showing that the full phase coverage can indeed be achieved. A sufficiently high H is also required for full phase coverage, as the phase change increases when the length of the optical path increases. In addition, since a proper lattice constant (P) is required for high efficiency, transmitted light must be restricted to only the 0th order. This can be predicted by the grating equation at normal incidence as given by $n\sin ({\theta }_m)=m\lambda P^{-1}$, where $n$ is the refractive index of the medium, $m$ is diffraction order, and ${\theta }_m$ is the $m$th diffraction angle. When high-order diffraction occurs (i.e., $m\ge 1$), the transmitted light cannot be focused. Therefore, a sufficiently small P is required to avoid anomalous scattering. To achieve the required phase profile with the following considerations, low-loss a-Si:H is used for meta-atoms [50]. It has a higher refractive index ($n$) than ${\mathrm{TiO}}_2$ or SiN and a lower extinction coefficient ($k$) than conventional silicon-based materials in the visible spectrum [Fig. 1(c)]. Sufficiently high $n$ of a-Si:H makes it suitable for achieving full phase coverage at low height.

Taking these considerations into account, finite-difference time-domain (FDTD) simulations were conducted to optimize the geometrical parameters (D, H, and P) of the meta-atoms and to calculate their transmission properties (see Appendix A). The transmitted phase can be adjusted from 0 to $2\pi$ by varying D from 60 to 104 nm at $\lambda =450\mathrm{nm}$ [Fig. 1(d)]. Full phase coverage was also obtained at $80\mathrm{nm}\le D\le 156\mathrm{nm}$ and $100\mathrm{nm}\le D\le 252\mathrm{nm}$ for $\lambda =532$ and 700 nm, respectively [Figs. 1(e) and 1(f)]. The meta-atoms have been optimized by $H=600\mathrm{nm}$ and $P=230\mathrm{nm}$ at $\lambda =450\mathrm{nm}$. For $\lambda =532$ and 700 nm, optimized P was 460 nm with the same H. Full phase coverage also can be achieved at $H>500\mathrm{nm}$ with high transmittance, resulting in a high aspect ratio (AR). However, high AR and small diameter of meta-atom ($<60\mathrm{nm}$) reduce the feasibility of the fabricated metalens due to a limitation of resolution in EBL; therefore, the H was set to be 600 nm (see Appendix A). In addition, $P$ was optimized to meet the 0th-order diffraction condition of the grating equation and the Nyquist sampling criterion ($P<0.5\lambda {\mathrm{NA}}^{-1}$) for high transmittance (see Appendix A). At $\lambda =532\mathrm{nm}$, $P=460\mathrm{nm}$ does not satisfy the Nyquist sampling criterion but was used to simplify the interleaving process. The transmittance of the meta-atoms at $\lambda =450\mathrm{nm}$ gradually decreases with increasing D due to the nonzero $k$ of a-Si:H.

To realize the RGB achromatic operation of metalens at three wavelengths (450, 532, and 700 nm), SIM is applied to three distinct meta-atoms. Three metalenses for $\lambda =450$, 532, and 700 nm can be integrated by substituting one of four blue meta-atoms with red meta-atoms and, likewise, one of two red meta-atoms with green meta-atoms [Fig. 2(a)]. The light transmitted from the meta-atoms at each wavelength can constructively interfere at the focus when the coupling between neighboring meta-atoms is weak.

To theoretically investigate the focusing properties of an RGB achromatic metalens, the cross-sectional electric-field (E-field) distributions in the focal region with different incident wavelengths of light (${\lambda }_{\mathrm{inc}}$) are calculated using 3D finite-difference time-domain (3D FDTD) simulations (see Appendix A). The designed metalens has a diameter $(D_{\mathrm{lens}})=20\mathrm{\mu m}$, $f_d=5.5\mathrm{\mu m}$, and $\mathrm{NA}=0.87$. The transmitted light with ${\lambda }_{\mathrm{inc}}=450$, 532, and 700 nm is focused at $f=f_d$ through the SIM metalens [Fig. 2(b)]. The focusing efficiency is calculated by the ratio of optical power at the focal spot to the total incident power on the metalens. Focusing efficiencies of 25.2%, 58.7%, and 66.4% are calculated at ${\lambda }_{\mathrm{inc}}=450$, 532, and 700 nm, respectively. The normalized E-field distributions of the SIM metalens at $f=5\mathrm{\mu m}$ confirm that the two metalenses focus the incident light at the almost same spot for ${\lambda }_{\mathrm{inc}}=450$, 532, and 700 nm [Figs. 2(c) to 2(e)]. The focusing efficiency at ${\lambda }_{\mathrm{inc}}=450\mathrm{nm}$ is slightly lower than at ${\lambda }_{\mathrm{inc}}=532$ and 700 nm because of the absorption by nonzero $k$ of a-Si:H. Additionally, the focusing efficiency decreases as ${\lambda }_{\mathrm{inc}}$ decreases due to the phase difference of meta-atoms at three different wavelengths. For ${\lambda }_d=450\mathrm{nm}$, the meta-atoms have $60\mathrm{nm}\le D\le 104\mathrm{nm}$, which is relatively small for ${\lambda }_d=700\mathrm{nm}$; thus, the phase error due to the meta-atoms of ${\lambda }_d=450\mathrm{nm}$ is small when the SIM metalens operates at ${\lambda }_{\mathrm{inc}}=700\mathrm{nm}$. However, when the metalens operates at 450 or 532 nm, a large phase error can be caused by the meta-atoms for ${\lambda }_d=700\mathrm{nm}$. In addition, high-order diffraction ($m\ge 1$) can occur at ${\lambda }_{\mathrm{inc}}=450$ and 532 nm due to the large diameter of meta-atoms for ${\lambda }_d=700\mathrm{nm}$.

The fabricated metalens has $D_{\mathrm{lens}}=450\mathrm{\mu m}$, $f_d=125\mathrm{\mu m}$, and $\mathrm{NA}=0.87$, which is the same NA as the simulated metalens [Figs. 3(a) and 3(b); see Appendix B]. To investigate the focusing properties of the fabricated SIM metalens, we measured the intensity profile in the $x\text{-}y$ focal plane for various propagation distances in the $z$-direction using a custom-built setup [Fig. 3(c); see Appendix C]. The focal spot of the $y$ plane was determined by taking the location of the maximum intensity. The cross-sectional images were combined to produce the optical field intensity profile along the $x\text{-}z$ axis [Fig. 3(d)]. The transmitted light with ${\lambda }_{\mathrm{inc}}=450$, 532, and 700 nm through the fabricated metalens was focused at $f=f_d$, which is consistent with the simulation results.

The point spread function of the metalens at three incident wavelengths (${\lambda }_{\mathrm{inc}}=450$, 532, and 700 nm) was measured at each focal spot [Figs. 4(a)–4(c)]. The focusing efficiency of fabricated metalens is defined as the ratio of optical power at the focal spot to the total incident power. Focusing efficiencies of 5.9%, 11.3%, and 13.6% were measured at ${\lambda }_{\mathrm{inc}}=450$, 532, and 700 nm, respectively. In addition, focusing efficiencies were measured depending on the polarization to confirm the polarization-insensitive characteristic of the SIM metalens (see Appendix D). These are lower than the simulated results, but the trends are similar. It can be improved through further research (see Appendix E). To compare the SIM metalens and the perfect lens, measured intensity profiles and their Airy functions were plotted and normalized at each wavelength [Figs. 4(d) to 4(f)]. The normalized intensity of the Airy function is given as follows [53]: $$\frac{I_A}{I_o}=[\frac{2J_1\left(\frac{\pi Dr}{\lambda f_d}\right)}{\frac{\pi Dr}{\lambda f_d}}{]}^2,$$(2)where $I_0$ is the maximum intensity, and $J_1$ is the Bessel function of the first order. The measured FWHMs of the SIM metalens were 298.5, 323.4, and 457.1 nm at ${\lambda }_{\mathrm{inc}}=450$, 532, and 700 nm, respectively. Diffraction-limited FWHMs at the respective incident wavelengths, derived from the Airy function (i.e., $0.514\lambda {\mathrm{NA}}^{-1}$), are 264.6, 312.8, and 411.6 nm. The measured FWHMs of the SIM metalens are comparable with Airy functions, implying that the fabricated metalens is diffraction-limited. To confirm this, the Strehl ratios (SRs), which are the figure of merit to indicate the imaging quality of the lens, are calculated by normalizing and integrating the ideal Airy functions and measured intensity profiles to obtain the power of the lens. After that, we multiply a compensating factor, so that the calculated powers of the metalens and perfect lens are the same. Finally, we calculate the SR by dividing the central intensity of the Airy function and measured profile [54]. SRs of 0.89, 0.88, and 0.82 were obtained at ${\lambda }_{\mathrm{inc}}=450$, 532, and 700 nm, respectively. Considering that the maximum value of SR is 1, the high enough SR value at each wavelength represents excellent imaging performance of the metalens. Therefore, the fabricated SIM metalens is capable of diffraction-limited operation. Compared with the existing RGB metalens study, the SIM metalens has a high resolution (low FWHM value) and a sufficiently high Strehl ratio value with a high NA (Appendix F).

To characterize the optical system in the spatial frequency domain, the modulation transfer function (MTF) through the Fourier transform relation was obtained [Figs. 4(g)-4(i)]. It is the standard resolution, indicating how the image is blurred by using the lens. We calculated MTF values from three wavelength cases from the equation below [55]: $$\mathrm{MTF}=\left|\frac{\iint I(x,y)\exp [-i2\pi (f_{xx}+f_{yy})]\mathrm{d}x\mathrm{d}y}{\iint I(x,y)\mathrm{d}x\mathrm{d}y}\right|,$$(3)where $I(x,y)$ is the pupil function from the experimentally obtained focusing images, and $f_x$ and $f_y$ are the spatial frequency of the $x$ and $y$ coordinates, respectively. The high spatial frequency value in MTF means that fine patterns are also possible, and the image can be resolved above the cutoff frequency, which is the point where the MTF value decreases to 0. From the MTF result, sharp drops of MTF are shown at all wavelengths, and it can be interpreted that the shorter wavelength light has a better resolution ability.

Also, we confirmed the imaging capabilities of the metalens by using a negative 1951 USAF target (Thorlabs R3L1S4N). The imaging macroscopy setup is shown in Fig. 5(a). The laser light was cropped by a pinhole to adjust it to the proper size and was incident on a negative resolution target. An objective lens (Olympus PLN10X) ensured the diverging light with a wide area of target images focused tightly on metalens. The resulting images were captured with the CCD camera. The image of the resolution target was successfully captured at $\lambda =532\mathrm{nm}$ [Fig. 5(b)]. However, in the case of blue light ($\lambda =450\mathrm{nm}$), the imaging efficiency is low; in the case of red light ($\lambda =700\mathrm{nm}$), the intensity of the supercontinuum laser is weak, so the imaging results could not be captured by CCD camera and sCMOS camera.

The achromatic imaging of the SIM metalens was investigated by using a screen-capture system [Fig. 6(a)]. The image reflected on the screen was taken with the camera. Since the metalens is a high NA lens with an NA of about 0.87, the screen had to be close. Therefore, the magnified image was large (as large as several cm) even if the $4f$ system was used. The same number “5” of the resolution target was compared for each wavelength [Fig. 6(b)]. Even though the images were not clear compared with Fig. 5, and there were some distortions because of the limit of the oblique screen-capture system, the SIM metalens demonstrated the capability of achromatic imaging.

In summary, we successfully designed and experimentally realized an RGB achromatic metalens operating at three wavelengths in the visible spectrum. The spatial interleaving method is used to demonstrate the RGB achromatic metalens by the simple spatial integration of meta-atoms. This method yields a metalens ($D_{\mathrm{lens}}=20\mathrm{\mu m}$, $f_d=5.5\mathrm{\mu m}$, and $\mathrm{NA}=0.87$) that focuses light of $\lambda =450$, 532, and 700 nm with calculated efficiencies of 25.2%, 58.7%, and 66.4%, respectively. The fabricated metalens achieves focusing efficiencies of 5.9%, 11.3%, and 13.6% at the given wavelengths. This efficiency loss was caused by fabrication error, but it can be improved by further optimization during the fabrication process. We also demonstrated that our fabricated metalens is capable of diffraction-limited operation. The spatial interleaving method could be further generalized to multifunctional metasurfaces at specific wavelengths or RGB achromatic operation of more than three wavelengths. Furthermore, RGB achromatic metalenses working at discrete wavelengths have the potential for applicability in various display devices such as CMOS image sensors, which are essential for next-generation display technology.

Acknowledgment. J.R. acknowledges an industry-academia strategic grant funded by Samsung Display Co., Ltd. Y.K. acknowledges the Hyundai Motor Chung Mong-Koo fellowship, and the NRF fellowships (NRF-2022R1A6A3A-13066251 and NRF-2022K1A3A1A12080445), respectively, funded by the Ministry of Education and the Ministry of Science and ICT of the Korean government. J.K. acknowledges the POSTECH Alchemist fellowship.