With the rapid development of smartphones and digital cameras, the pixel size of image sensors is constantly shrinking to meet the requirements of high-resolution imaging^[1]. However, the reduction in pixel size will diminish the sensitivity, signal-to-noise ratio, and dynamic range of image sensors due to each pixel receiving less light energy. Image sensors typically rely on spectral filter arrays embedded above photodetectors to extract color information, only transmitting certain narrowband light while filtering out the rest^[2]. The out-of-band photon loss seriously limits the energy utilization efficiency of image sensors and inevitably degrades the imaging performance, especially for high-density imaging in low-light scenarios. Nanophotonic spectral filters^[3–5] have been developed to replace traditional pigment color filters, but they still cannot fundamentally address the issue of out-of-band energy waste. As for Bayer image sensors, even if the color filters reach 100% transmittance in the passband, the maximum energy utilization efficiencies of red (R), green (G), and blue (B) channels are still limited to only 25%, 50%, and 25%, respectively^[2].

To tackle this problem, spectral splitting techniques that aim to spatially separate light of different bands to corresponding photodetectors have been investigated. Similar to spectrometers, blazed gratings and a microlens array were combined early to converge light of different wavelengths onto distinct pixels^[6]. To avoid the issue of inadequate angular dispersion in the same diffraction order of blazed gratings, color separation gratings that can divide R, G, and B bands to $+1$, 0, and $-1$ order directions, respectively, were proposed^[7,8]. However, they work for the far-field regimes and usually require long propagation distances and large grating periods, which limits the pixel-level integration with photodetector arrays. Many plasmonic nanoantennas capable of achieving wavelength-dependent directional scattering have been studied, but their efficiencies are constrained by the inherent loss of metals^[9,10]. To avert ohmic loss, dielectric scatterers and diffractive optical elements were utilized for spectral routing^[11–15]. Nonetheless, due to severe crosstalk between distinct color channels, most of these designs rely on a post-processing reconstruction algorithm (e.g.,  conversion matrix method) to restore the RGB color information, which will have a poor effect for imaging dark scenarios^[8,11,13]. Additionally, researchers have designed micro-metalens arrays to focus light at different wavelengths onto specific pixels^[16–20]. Most of these designs built a library containing a variety of intricate unit cells in order to approximate routing phase profiles of multiple wavelengths simultaneously. Recently, spectral routers (i.e., color routers) based on code-like or freeform metasurfaces were reported via inverse design^[21–25]. Moreover, inverse design algorithms can be further applied to develop high-performance spectral routers utilizing three-dimensional (3D) metamaterials^[26–36]. However, their topologies are too complicated to be feasible for visible light applications even by state-of-the-art processing technologies.

Herein, we demonstrate a highly efficient pixelated Bayer spectral router that can precisely separate and focus the incident R (600–700 nm), G (500–600 nm), and B (400–500 nm) light to the corresponding pixels of a typical Bayer pattern (RGGB) image sensor, based on a metasurface made of the array of sparse meta-atoms (i.e., unit cells larger than the operating wavelength). We prove that pixel-level dispersion engineering can efficiently split the broadband photons by relatively simple supercells consisting of only four isolated square nanopillars, meeting an excellent balance between structural complexity and device performance. As a result, high average spectral routing efficiencies of 51.13%, 62.91%, and 42.57% for R, G, and B bands, respectively, are obtained, corresponding to a 56.6% signal enhancement beyond the classic Bayer color filter scheme. The spectral router’s applicability in color imaging is experimentally validated. We also show that the response of the router under oblique incidence can be enhanced by introducing a structure shift method, which can expand the maximum acceptable chief ray angle to over 30°. To intuitively demonstrate the advantages of our router, Table S1 in Sec. S12 in the Supplementary Material compares the feature sizes, gaps between nanostructures, pixel sizes, and efficiency enhancement factors of this work with those of previous spectral routers. Our router, based on the sparse meta-atom array simultaneously, realizes high spectral routing performance and fabrication simplicity. The structural layout of the device is very straightforward, comprising only four nanopillars in each supercell, with a large feature size of 150 nm and all gaps between nanopillars larger than 500 nm, which makes it suitable for massive production through conventional nanofabrication technologies, such as deep ultraviolet lithography^[37] and nanoimprinting^[38]. The pixelated Bayer spectral router developed here is believed to be of practical significance for building the next generation of high-performance image sensors.

Figure 1(a) schematically illustrates a conventional image sensor consisting of a microlens array, color filters, and photodetectors. The most common color filter array arrangement for image sensors in the visible band is the RGGB, with each Bayer cell containing one R, two G, and one B color filters. Due to the selective absorption of color filters, a great deal of energy is wasted. The goal of this work is to design a pixelated spectral router that can improve the energy utilization efficiency of image sensors. Figure 1(b) schematically illustrates an image sensor with the spectral router, which is capable of efficiently routing the R, G, and B band light onto corresponding pixels of the Bayer pattern. The color filter array is also configured between the spectral router and photodetectors to filter the routed light to reduce the crosstalk between different color channels.

To manipulate the light field within small apertures, sophisticated nanostructures with complicated distributions have been previously employed to satisfy specific dispersive phase profiles^[17,24]. In this work, to facilitate massive production, we aim to explore the feasibility of realizing color separation at pixel-level dimensions through simple nanostructures made of a few regular-shaped sparse meta-atoms while ensuring high performance. Figures 1(c) and 1(d) illustrate the structural layout of the spectral router, i.e., one supercell of the metasurface. The supercell has a period of $2.24\mathrm{\mu m}\times 2.24\mathrm{\mu m}$, corresponding to four pixels in one Bayer cell (RGGB). Therefore, the spectral router is well matched to image sensors with a pixel size of $1.12\mathrm{\mu m}\times 1.12\mathrm{\mu m}$, which is a common pixel size used in commercial complementary metal–oxide semiconductor (CMOS) image sensors. In this design, each meta-atom includes one ${\mathrm{Si}}_3{\mathrm{N}}_4$ square nanopillar above the ${\mathrm{SiO}}_2$ substrate. ${\mathrm{Si}}_3{\mathrm{N}}_4$ is almost transparent in the visible band and compatible with the CMOS processing technology. The refractive index parameters of ${\mathrm{Si}}_3{\mathrm{N}}_4$ and ${\mathrm{SiO}}_2$ used here are plotted in Fig. S1 in the Supplementary Material. There are four meta-atoms in one supercell, with each grid centered by a ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanopillar. In contrast to the routers made up of subwavelength unit cells, the sizes of sparse meta-atoms used in our design can be larger than the operating wavelength. The transmission phase profile of the supercell will be modulated by ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanopillars and also by the air gaps between them (or corresponding to a gap phase)^[39]. The particle swarm optimization (PSO) algorithm is combined with finite-difference time-domain (FDTD) numerical simulation to iteratively optimize the structures of meta-atoms, aiming to achieve high spectral routing efficiency. The simulation method and optimization process of the spectral router is shown in Fig. S2 in the Supplementary Material. The design parameters include the widths of ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanopillars ($w_1$, $w_2$, and $w_3$), the height of ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanopillars ($h$), and the distance between the nanopillars and the detection plane ($h_{\mathrm{d}}$). Due to the diagonal symmetry of the Bayer pattern (RGGB) and to ensure the polarization insensitivity of the device, nanopillars on the two G pixels have the same width ($w_2$). To endow the spectral router with the potential for massive production, a constraint condition in which the widths of all square nanopillars exceed 150 nm is imposed during the optimization process. As shown in Eqs. (S1)–(S3) in Sec. S2 in the Supplementary Material, the spectral routing efficiency at a specific wavelength is defined as the ratio of the light energy reaching the pixels of the corresponding band to the total energy incident on the supercell at this wavelength. In order to achieve high routing performance across the broadband, the average spectral routing efficiencies of R, G, and B bands serve as crucial indicators in evaluating the device performance, which are defined as $${\mathrm{Eff}}_{\mathrm{R}}=\frac{1}{\mathrm{\Delta }{\lambda }_{\mathrm{R}}}{\int }_{600\mathrm{nm}}^{700\mathrm{nm}}{T}_{\mathrm{R}}(\lambda )\mathrm{d}\lambda ,$$(1)$${\mathrm{Eff}}_{\mathrm{G}}=\frac{1}{\mathrm{\Delta }{\lambda }_{\mathrm{G}}}{\int }_{500\mathrm{nm}}^{600\mathrm{nm}}{T}_{\mathrm{G}}(\lambda )\mathrm{d}\lambda ,$$(2)$${\mathrm{Eff}}_{\mathrm{B}}=\frac{1}{\mathrm{\Delta }{\lambda }_{\mathrm{B}}}{\int }_{400\mathrm{nm}}^{500\mathrm{nm}}{T}_{\mathrm{B}}(\lambda )\mathrm{d}\lambda ,$$(3)respectively, where $T_{\mathrm{R}}(\lambda )$, $T_{\mathrm{G}}(\lambda )$, and $T_{\mathrm{B}}(\lambda )$ are spectral routing efficiencies of R, G, and B channels, respectively, as a function of wavelength, while $\mathrm{\Delta }{\lambda }_{\mathrm{R}}=\mathrm{\Delta }{\lambda }_{\mathrm{G}}=\mathrm{\Delta }{\lambda }_{\mathrm{B}}=100\mathrm{nm}$ are bandwidths of R, G, and B bands. The efficiency enhancement factor is defined as $$\mathrm{Eff}={\mathrm{Eff}}_{\mathrm{R}}+{\mathrm{Eff}}_{\mathrm{G}}+{\mathrm{Eff}}_{\mathrm{B}}.$$(4)

It means that the efficiency enhancement factor of an ideal conventional Bayer filter array is $\mathrm{Eff}=25\%+50\%+25\%=1$. Intending to increase the spectral routing efficiency, the efficiency enhancement factor is set as the figure of merit (FOM) in the optimization.

After sufficient optimization, the ultimate design parameters are determined as follows: $w_1=920\mathrm{nm}$, $w_2=150\mathrm{nm}$, $w_3=278\mathrm{nm}$, $h=998\mathrm{nm}$, and $h_{\mathrm{d}}=4\mathrm{\mu m}$. Figure 2(a) shows the transmission phase profiles of one optimized supercell at three typical wavelengths: 650, 550, and 450 nm. These phase distributions are very close to those of the ideal microlens shown in Fig. 2(b), especially for the R and B light. Therefore, the sparse meta-atoms collectively function as a pixel-level dispersion-engineered micro-metalens, which can separate and focus light of different colors to corresponding pixels. In Sec. S3 in the Supplementary Material, we simulate the focusing effect for R, G, and B colors under a limited aperture, where the incident light only covers nine meta-atoms. For each R/G/B pixel, the nine meta-atoms corresponding to the central pixel and the eight surrounding pixels function as a microlens, focusing light toward the central pixel. In this manner, the central pixel collects the energy that would otherwise be absorbed by color filters of the neighboring pixels of different colors, thereby improving the energy utilization efficiency. For the sparse meta-atom array, Figs. 2(c)–2(e) illustrate the simulated power flow density distributions of R, G, and B light on the detection plane, respectively, which are already the average results under the X- and Y-axis linear polarization incidence conditions. Obviously, most of the R, G, and B light is routed to the targeted pixels. In order to demonstrate the phenomenon of wavelength-dependent routing in the propagation direction intuitively, Figs. 2(f)–2(h) present the power flow density distributions of the XZ cross section at wavelengths of 650, 550, and 450 nm, respectively. The coordinate system is shown in Fig. 1(c). The Y coordinates of the XZ cross section are $Y=0.28\mathrm{\mu m}$ for Fig. 2(f) and $Y=-0.56\mathrm{\mu m}$ for Figs. 2(g) and 2(h). The white horizontal dashed lines in Figs. 2(c)–2(e) represent the cutting plane in Figs. 2(f)–2(g), respectively. Figure 2(i) plots the simulated spectral routing efficiencies of R, G, and B channels. The horizontal dashed lines in Fig. 2(i) represent the maximum spectral routing efficiencies of an ideal traditional Bayer color filter array. The area above the dashed lines and below the spectral routing efficiency curves is the total enhanced energy, which contributes to a higher efficiency enhancement factor. The peak spectral routing efficiencies of the spectral router are 64.3%, 70.43%, and 54.62% for R, G, and B light, respectively. The average spectral routing efficiencies are 51.13%, 62.91%, and 42.57% for R, G, and B bands, respectively. Therefore, the efficiency enhancement factor is 1.566, which means that 56.6% signal enhancement is obtained by the spectral router.

In order to experimentally verify the RGB separating function of the designed device, we have fabricated the metasurface by plasma-enhanced chemical vapor deposition (PECVD), electron beam lithography (EBL), lift-off, and reactive-ion etching (RIE). Details of the fabrication process are presented in Sec. S4 in the Supplementary Material. The top-view and tilted-view scanning electron microscope (SEM) images of the sample are presented in Figs. 3(b) and 3(c). After completing the fabrication, the spectral routing effect of the device is characterized using the optical measurement setup shown in Fig. 3(a). Color filters can be selectively inserted between the collimation system and the spectral router according to the wavelength or band required to be measured. First of all, the spectral router is illuminated by the collimated beam of the white light-emitting diode (LED, Thorlabs MNWHL4, 4900 K). As shown in Fig. 3(d), the image on the detection plane of the spectral router is magnified by the microscope and captured by a color image sensor (HW200). Figures 3(e)–3(g) present the measured intensity profiles of R, G, and B channels on the detection plane, respectively. Agreeing with the simulation results, it can be observed that R, G, and B light is effectively routed to the corresponding pixels of the Bayer pattern. Figure S5 in the Supplementary Material presents the intensity profiles on the detection plane under the illumination of light at different wavelengths (step: 20 nm), which are measured by the same experimental setup with a monochromic image sensor (MV-CS200-10UM). Figure 3(h) plots the measured spectral routing efficiencies of R, G, and B channels. The measured average spectral routing efficiencies of the router are 49.53%, 55.27%, and 37.74% for R, G, and B bands, respectively, which greatly exceed the spectral routing efficiencies of the traditional Bayer color filter array. The deviations between the simulation and experimental results mainly arise from the processing errors of the sample, collimation of the light source, and diffraction limit of the microscope system. The impact of fabrication errors on device performance is shown in Sec. S15 in the Supplementary Material. Besides, the diffraction limit of the microscope system may lead to a slight loss of information on the detection plane and reduce efficiencies in the experiment.

We experimentally verify the applicability of the spectral router in color imaging by the optical setup shown in Fig. 4(a). An object (Rubik’s cube image) is placed 540 mm away from the imaging system and is imaged onto the spectral router by an imaging lens. A microscope, R/G/B bandpass filters, and a monochromic image sensor (MV-CS200-10UM) are combined to mimic the architecture of an image sensor with color filters and photodetectors. Figure S6 in the Supplementary Material depicts the spectra of R/G/B bandpass color filters. Figures 4(b)–4(d) present the measured intensity profiles of R, G, and B channels, respectively, on the detection plane after the image is routed. The mosaic images of R, G, and B channels can be obtained directly according to the calibrated spectral routing efficiency. Details of the reconstruction of the Rubik’s cube image are provided in Sec. S7 in the Supplementary Material. After demosaicing through bilinear interpolation^[40], the images of R, G, and B channels are reconstructed, respectively. Figure 4(e) presents the reconstructed color image after performing white balance^[41]. As a contrast, the reference images of R, G, and B channels obtained using only color filters without the spectral router are also reconstructed through color correction and demosaicing. The reconstructed images with the spectral router are in good agreement with the reference images for all color channels. Figures 4(f) and 4(g) present the reference color image obtained with only color filters, which is consistent with Fig. 4(e). The intensity of Fig. 4(f) is matched to that of Fig. 4(e) for clearer comparison. There is a small speckle in the lower left corner of the reconstructed image due to the fabrication defects at that position. As shown in Sec. 8 in the Supplementary Material, we also performed the color imaging experiment on another object (ColorChecker), showing similar results. Figure S9 in the Supplementary Material presents the efficiency enhancement for color imaging with the Bayer spectral router. The average efficiency enhancement factor is 1.3 compared with the traditional color filter scheme. This value is comparatively lower than the case without an imaging lens (normal incidence). Note that here we apply the combined scheme (spectral router + color filters) to enhance the detection efficiency without a matrix conversion. If only the spectral router is utilized together with the conversion matrix method^[8,11], the energy utilization efficiency can be enhanced by approximately 3 times compared with the conventional filter scheme, as all transmitted energy of the router is utilized. However, this approach will suffer from crosstalk between color channels. Additionally, limited by the finite field of view area caused by the microscopy system, the images of the Rubik’s cube and ColorCheck only occupy 110 pixel × 110 pixel and 132 pixel × 88 pixel, respectively. The numerical aperture and aberrations of the imaging system also blur the images. The spectral router is anticipated to be directly integrated with image sensors in the future, enabling its application in clear, large-area, high-resolution imaging.

To further explore the potential of this Bayer spectral router for practical industrial applications, we discuss its features of polarization response, incident angle tolerance, and fabrication feasibility. The spectral routing efficiencies of R, G, and B channels under the illumination of different polarization states are shown in Fig. S10 in the Supplementary Material. Since the supercell is diagonally symmetric and the overall device exhibits periodicity, the structural layout centered around each R or B pixel satisfies fourfold symmetry, while the structural layout centered around each G pixel satisfies twofold symmetry. It can be seen in Figs. S3(a)–S3(c) in the Supplementary Material. Meanwhile, all nanopillars have fourfold symmetric cross sections. As a result, the spectral router is insensitive to polarization, which is applicable to imaging scenarios with arbitrary polarized illumination. The tolerance to the incident angle is also a significant parameter of spectral routers. Figure S11 in the Supplementary Material presents the calculated spectral routing efficiencies of R, G, and B channels under different incident angles. The average efficiency of R, G, and B channels remains above 33.33% up to a 10° incident angle, which is higher than the efficiency of an ideal Bayer color filter array. According to the same definition (the angle where the efficiency drops to half of the maximum) used in previous studies^[16,26,31], the maximum acceptable incident angle for this spectral router is 14.6°, corresponding to a numerical aperture of 0.252 for the imaging lens.

Under oblique incidence of large angles, a portion of light intended to be routed to the $\mathrm{R}/{\mathrm{G}}_1/{\mathrm{G}}_2/\mathrm{B}$ pixels is misrouted to other neighboring pixels, leading to decreased efficiency and aggravation of crosstalk between channels. As shown in Sec. S11 in the Supplementary Material, referring to the mature microlens design of edge pixels in conventional image sensors^[42], we employ the structure shift method to improve the device performance under oblique incidence. Under the incident angle of $\theta$, we can shift nanostructures by a displacement calculated by $$\mathrm{\Delta }x(\theta )=h\times \tan \left[\arcsin \left(\frac{\sin \theta }{n_{\mathrm{eff}}}\right)\right]{+h}_{\mathrm{d}}\times \tan \left[\arcsin \left(\frac{\sin \theta }{n_{{\mathrm{SiO}}_2}}\right)\right],$$(5)where the former term represents the required shift caused by the nanostructure layer, the latter term represents the required shift caused by the ${\mathrm{SiO}}_2$ spacer layer, $n_{\mathrm{eff}}$ is the effective refractive index of the nanostructure layer^[43], and $n_{{\mathrm{SiO}}_2}$ is the refractive index of ${\mathrm{SiO}}_2$. Most of the misrouted light can be transferred to the desired pixels by shifting the structures according to the chief ray angle corresponding to the pixel position. Our simulation results reveal that the structure shift method can expand the maximum acceptable chief ray angle to over 30°, which is applicable to image sensors with large areas. Moreover, the spectral routing efficiency under oblique incidence can even be further improved by specially optimizing the nanostructures while keeping the height of the nanopillars and the position of the detection plane unchanged.

Compared with previous pixelated light splitting techniques based on micro-metalens arrays^[16,17], as well as code-like and freeform metasurfaces^[21–24], our spectral router based on sparse meta-atoms has a straightforward structural layout comprising only four nanopillars in each supercell, highly promising for massive production through mature processing technologies, such as deep ultraviolet lithography^[37] and nanoimprinting^[38]. The detailed comparison between the structural layouts of this work and code-like metasurfaces is illustrated in Fig. S12 in the Supplementary Material. Moreover, our spectral router notably improves the spectral routing efficiency of the G channel while maintaining the high performance of the R and B channels. As shown in Table S1 in Sec. S12 in the Supplementary Material, compared with past research, our spectral router based on the array of sparse meta-atoms simultaneously realizes high spectral routing performance and fabrication simplicity. Using similar patterns, in Sec. S13 in the Supplementary Material, we also designed Bayer spectral routers that can match the pixel sizes of $1\mathrm{\mu m}\times 1\mathrm{\mu m}$ and $0.5\mathrm{\mu m}\times 0.5\mathrm{\mu m}$, respectively, while the latter belongs to state-of-the-art image sensors with the smallest pixel size. These results indicate that our sparse meta-atom-based spectral router scheme is robust and applicable to image sensors with high-density pixels. Furthermore, in practical applications, the color filter array can be integrated between the spectral router and photodetector array to improve color purity. As shown in Sec. S14 in the Supplementary Material, we simulate the architecture including the spectral router, ${\mathrm{SiO}}_2$ spacer layer, color filters, anti-reflection film, and photodetectors from top to bottom. It is revealed that the crosstalk between different color channels can be significantly suppressed by the color filter array, which is highly beneficial for improving the performance of image sensors.

In conclusion, we demonstrate a pixelated spectral router based on a sparse meta-atom array and experimentally verify its potential in color imaging for true scenarios. This optical hardware can improve the photon collection efficiency of image sensors by a ratio of 56.6% above the classic color filter scheme. The spectral routing efficiency is insensitive to the incident light polarization and keeps high values at large incident angles by flexibly shifting the nanostructures. Compared with the existing blueprints, the simple structural layout and CMOS compatibility processing techniques are the most important features of our design, enabling massive production for industrial applications. Putting these into perspective, it is highly believed that pixelated spectral routers based on sparse meta-atoms can play a key role in developing the new generation of advanced image sensors.