Traditional spectrometers, primarily composed of wavelength-selective devices and detectors, are usually bulky. Therefore, their applications in some scenarios are limited. With the rapid development of metasurface technology in recent years^[1], a new pathway has emerged for achieving more compact and lightweight spectrometers^[2,3]. Metasurfaces, composed of two-dimensional subwavelength structures, demonstrate diverse and flexible control over optical parameters such as amplitude, phase^[4,5], polarization^[6–8], and spectrum^[9], providing a novel platform for the design of miniaturized, high-performance micro-nano optical devices. Customizing the spectral control capabilities of metasurfaces allows them to serve as broadband filters with specific spectral response characteristics in computational spectrometers^[10]. Compared with traditional narrowband filters, it is possible to use fewer metasurface filters to reconstruct spectra over a broader wavelength range.

Recently, Xiong et al. demonstrated a silicon real-time ultraspectral imaging chip based on reconfigurable metasurfaces, comprising 155,216 (356×436) image-adaptive microspectrometers with an ultra-high center-wavelength accuracy of 0.04 nm and a spectral resolution of 0.8 nm^[11]. Wang et al. adjusted the period, the lattice constant, and the hole sizes of photonic crystals, effectively controlling the transmission spectra in different regions. They coupled incident light from free space into lateral propagation modes, focusing it effectively at an imaging plane 1 mm from the metasurface array, achieving a 1 nm resolution spectrometer in the 550–750 nm range^[12]. Yang et al., addressing the limitations of regular-shaped meta-atoms in traditional metasurfaces that restrict spectral imaging performance, proposed a new algorithm for generating freeform-shaped meta-atoms with controllable feature sizes and boundary curvatures to enrich the spectral response of metasurfaces. They achieved an ultraspectral imager composed of a metasurface layer, a microlens layer, and an image sensor layer^[13]. However, most miniature computational spectrometers based on metasurfaces mainly target the visible light range, with few devices capable of covering both visible and near-infrared wavelengths.

In this Letter, we demonstrate visible-to-near-infrared spectrum reconstruction using metasurface filters consisting of amorphous silicon nanopillars. By varying the period and size of the nanopillars, we can achieve rich transmission spectral features due to multimode resonances^[14,15]. These metasurface filters enable effective control over parts of the visible and near-infrared spectra with low correlation between different filters.

As shown in Fig. 1, the light to be measured illuminates the metasurface filter array, and the transmitted light power from each filter is measured by a photodetector. With the measured power and the known transmission spectra of the metasurface filters, we reconstruct the spectra of the incident light using an algorithm matched to the filter model^[16,17]. Both narrow and broadband spectra reconstruction (450–950 nm) are achieved. The metasurface filter array used in this study is 2mm×2mm in size and 0.7 mm in thickness, thus enabling integration with detectors, such as CCDs, and facilitating snapshot spectral measurement and sensing capabilities^[18].

As shown in Fig. 2(a), the metasurface consists of periodically arranged amorphous silicon nanopillars with a unit period, P, selectable among 350, 400, 450, 500, and 600 nm. The ratio of the pillar side length L to the period P ranges between 1/3 and 2/3, with a fixed height H of 620 nm. As the silicon pillars are square-shaped, they exhibit polarization-insensitive characteristics. Figure 2(b) presents the simulation results of the transmission spectra of different metasurfaces under normally incident broadband light. In the 400–700 nm range, the low transmission shown in blue is primarily due to the absorption of light in this spectrum by amorphous silicon. The changes in transmission beyond 700 nm are mainly caused by the excitation of dipole/multipole resonances in the nanostructures by incident light. When light near the bandgap frequency of the amorphous silicon illuminates the nanopillars, it not only excites electric dipole and magnetic dipole resonances but may also stimulate higher-order resonances such as electromagnetic quadrupole resonances^[19,20]. These resonances collectively enable control over the scattering properties of the nano-silicon structures, providing an effective way to design broadband filters for computational spectrometers^[15]. In comparison, previous work has mostly focused on the filters in the visible light spectrum, and the geometrical parameters of the nanostructures are designed accordingly. For example, the silicon metasurfaces designed by Park et al.^[21] have a maximum periodicity of no more than 400 nm. Their design has a height of 80 nm, and the diameters of the nanodisks are 80, 130, and 170 nm respectively. Although these designs perform well in filtering visible light, they do not consider filtering effects in the near-infrared region. In contrast, the silicon pillar metasurface we designed has a height of 620 nm, a maximum periodicity extending to 600 nm, and the side lengths of the nanopillars range from 150 to 400 nm, thereby providing an effective filtering in the near-infrared spectrum as well.

Figure 2(c) shows the transmission images of the metasurfaces when illuminated by a white light source (Thorlabs tungsten halogen lamp SLS201L/M) and magnified through an objective lens (Olympus PLN10X). The different colors in these images result from the specific transmission and absorption of light by different metasurface structures, as described in Fig. 2(b). The experimental results preliminarily prove the filtering functionality of our designed structure. Here, we use 24 metasurfaces, each approximately 280μm×280μm, collectively forming a transmissive broadband filter array.

Figure 3(a) shows the experimental setup used to measure the transmission spectra of the metasurface filter array. The experiment employs a supercontinuum light source from a tunable filtering system, enabling precise measurement of transmission spectra in the 450 to 1000 nm wavelength range, with a step interval of 5 nm. The specific measurement process includes the following steps: First, the collimated beam from the laser illuminates the metasurface array, forming a magnified real image through the objective lens. The size of the real image is adjusted to be larger than the diameter of the small aperture of the aperture stop, ensuring that the measured part completely covers the small hole. The light beam then passes through the small hole and is received and measured by a power meter as the transmitted light power I1. Subsequently, the metasurface is removed from the beam path, and the direct transmitted light power I2 is measured. The transmission spectra at the corresponding wavelength are determined by calculating the ratio of I1 to I2. The measurement data is linearly interpolated with a precision of 1 nm, as shown in Fig. 3(b). Then, we compared the experimental results with the simulation results, as shown in Figs. 3(c) and 3(d). The positions of the four peaks and valleys, 1, 2, 3, and 4 in Fig. 3(c), correspond to the positions of 1′, 2′, 3′, and 4′ in the simulation result in Fig. 3(d), respectively. Due to errors introduced in the manufacturing process, the experimental results exhibit a certain blue shift compared with the simulation results, but both are fundamentally consistent, demonstrating the accuracy of the simulation model and the effectiveness of the experimental setup. The reasons for the absence of high-frequency information are similar to those for the blue shift and are due to errors in experimental fabrication. For example, the size and shape of nanopillars may be different from the design.

In the following, we describe the algorithm to reconstruct the spectrum of light under test. Assume R0(λ) represents the intrinsic response of the photodetector, which refers to the detector’s sensitivity to light signals of different wavelengths, determined by the material and design of the detector. Let Tk(λ) be the transmission spectra of the kth metasurface filter. Then, the overall response of the metasurface filter and the detector, Rk(λ), can be expressed as Rk(λ)=R0(λ)Tk(λ),k=1,2,…,N,(1)where N is the number of metasurface filters. When the incident broadband light passes through the kth metasurface filter, the total optical power is calculated as Pk=∫λ1λ2[Rk(λ)P(λ)+nk(λ)]dλ,(2)where P(λ) represents the power density of the light under test, nk(λ) is the system noise, and λ1 and λ2 are the boundaries of the spectrum under test. Since P(λ) is only unknown, it can be reconstructed from the measured power Pk of N photodetectors and the known detector response spectra Rk(λ).

In practical applications, the elements of Eq. (2) are discretized and expressed in vector form. Specifically, Rk(λ)P(λ) is discretized into Rk[λ] and P[λ]. This approach involves representing the spectral response of the kth filter and the power density of the light as matrices. Rk[λ] is configured as an M-row, 1-column matrix, where each row corresponds to the response coefficient at a specific wavelength λ, and P[λ] is also an M-row, 1-column matrix, each row representing the intensity of the incident light at a specific wavelength λ. This matrix representation allows for the systematic computation and analysis of the spectral data.

When multiplying Rk[λ] by P[λ], we obtain a linear equation, and with N detectors, we have a system of N linear equations. Theoretically, this system should have a unique solution when N=M, allowing us to solve for the unknown spectral data from the known response matrix and measured values. However, in practice, the number of detectors N is often less than the number of reconstruction points M, and due to measurement errors and noise, these linear equations may become inconsistent, i.e., without an exact solution. This noise could originate from instrument errors, environmental interference, or inaccuracies in data processing. Despite these challenges, we can still approximate a solution to these equations using the least squares method to find a set of spectral data that minimizes the error between them and the measured data^[3].

To validate the quality of spectrum reconstruction, we employed a supercontinuum light source and a tunable filtering system to produce narrowband spectra. This was achieved by adjusting the supercontinuum laser to emit a set of beams around the target wavelength. For instance, the narrow band at 850 nm consists of a beam at 850 nm, complemented by beams at 852 and 848 nm with lower power. This is due to the inherent characteristics of the supercontinuum laser. We found that the spectrum of the low-power 850 nm output, measured by a commercial spectrometer, was unstable and oscillating. However, when low power outputs at 848 and 852 nm were also introduced, the measured spectrum became stable and was conductive to the reconstruction. A commercial spectrometer (Thorlabs, CC200/M, measurement range: 200–1000 nm) was used to measure these narrowband spectra, as shown by the blue solid lines in Figs. 4(a)–4(f), allowing for comparison with the reconstructed spectra.

In this study, we implemented spectrum reconstruction using the non-negative linear least squares algorithm, which finds a set of solutions that minimize the sum of squared differences between predicted and actual values while ensuring that the solution vector remains non-negative. This method is suitable for spectral data reconstruction, as spectral intensities cannot be negative. The mean squared error (MSE) was employed to assess the quality of the reconstructed spectra. The results show that the peak wavelengths of each reconstructed spectrum closely match the corresponding reference spectra, with the MSE for narrowband reconstructed spectra at 500, 600, 700, 750, 850, and 950 nm ranging between 0.0017 and 0.0040. For narrowband spectra reconstruction, it is capable of effectively distinguishing light at intervals of 10 nm. While the shapes of the reconstructed spectrum peaks generally align with the reference spectra, there are differences, such as in reproducing fine features and peaks at low intensities, possibly due to the limited number of filters used.

Increasing the number of filters could further improve the quality of the reconstructed spectra. In Fig. 4(g), we demonstrate the comparison between the measured transmitted light power (blue curve) and the calculated light power (red curve) when illuminating 24 metasurface filters with a narrowband light source centered at 600 nm [same as the one used in Fig. 4(b)]. The reconstructed spectra with the previously measured overall response of the metasurface filter/detector are used to estimate the light power value. Comparing the measured light power with the estimated light power allows for assessing the accuracy of the spectrum reconstruction. This approach offers the advantage of providing a direct and intuitive verification of the spectrum reconstruction effectiveness and allows for a quantitative analysis of errors in the reconstruction process, such as those caused by environmental noise. It is evident that the measured light power and the light power calculated using the reconstructed spectrum generally match well. The discrepancies between some filter results and the measured outcomes can be attributed to inaccuracies in the measurement of intrinsic responsivity and the influence of environmental noise^[22].

For the reconstruction of broadband spectra, we employed the least absolute shrinkage and selection operator (Lasso) regression algorithm combined with a Gaussian filter to enhance accuracy. This approach helps avoid overly complex models that fit too closely to specific data (a problem known as overfitting), thereby improving the model’s performance on new, unseen data. This characteristic makes Lasso particularly useful for spectrum reconstruction, as it ensures that only the most relevant features are considered, making the model both simpler and more effective. Gaussian filtering helps data smoothing through weighted averaging. In the context of spectra reconstruction, the Gaussian filter is utilized to smooth the data, removing noise and improving signal quality. In this study, the specific parameters of the Gaussian filter (standard deviation 1.8, window size 150) were determined through training to ensure the best fit for our model. The standard deviation parameter controls the degree of smoothing, with a larger value implying stronger smoothing and a smaller value retaining more detail. The window size dictates the number of data points considered for averaging, with larger windows encompassing more points and thus yielding smoother results. The choice of these parameters depends on the specific spectral characteristics and desired reconstruction accuracy in practical applications. Adjusting and optimizing these parameters can effectively improve the accuracy and reliability of spectrum reconstruction. As shown in Figs. 5(a) and 5(b), the two original spectra for reconstruction are obtained from an LED light source (wavelength range: 500–700 nm) through green (bandwidth 485–565 nm) and red filters (bandwidth 600–2500 nm), respectively. The spectrum in Fig. 5(c) is produced using a tungsten halogen lamp source (bandwidth: 360–2400 nm) after passing through a cutoff filter (bandwidth 485–1100 nm) and a broadband filter (650–2500 nm). It is evident that the reconstruction of broadband spectra also matches the measurements from the commercial spectrometer.

Improvements in spectral resolution and reconstruction accuracy can be achieved by reducing measurement errors. This includes using more stable calibration light sources and employing higher-performance transmittance detection equipment. Additionally, increasing the number of broadband filters helps enhance spectral resolution, as these filters can cover a wider spectral range, enabling a broader spectrum reconstruction. On the other hand, enhancing spectral resolution and reconstruction accuracy also relies on utilizing prior spectral knowledge (such as signal sparsity) and advanced reconstruction algorithms. Methods like L1 and L2 regularization norms, principal component regression (PCR), and genetic algorithms can effectively improve spectrum reconstruction accuracy. These algorithms, by considering specific features and structures of spectral data, can more accurately recover and reconstruct spectral signals. By integrating these techniques, the accuracy and reliability of spectral analysis can be significantly enhanced.

In this Letter, we proposed and experimentally validated a spectral measurement method based on metasurface filters. These filters, composed of amorphous silicon-based nanopillars, have a responsive range covering the visible to part of the near-infrared spectra (450–950 nm) and exhibit rich spectral characteristics. After passing through the filter, the spectral information of the light under test can be reconstructed based on its intensity information. The experiment successfully achieved precise reconstruction of both narrowband and broadband unknown spectra in parts of the visible and near-infrared wavelengths. Therefore, this method has broad application prospects in fields such as chemical analysis, biomedical research, and environmental monitoring.

The process involved depositing a 620-nm-thick amorphous silicon (a-Si) thin film on a 700-µm-thick glass substrate using plasma-enhanced chemical vapor deposition (PECVD). A 100-nm-thick layer of hydrogen silsesquioxane electron beam lithography resist (HSQ, XR-1541) was then spin-coated onto the film and baked on a hot plate at 100°C for 2 min. Subsequent patterning of the resist was carried out using standard electron beam lithography (EBL, Nanobeam Limited, NB5), followed by development in an NMD-3 solution (2.38% concentration) for 2 min. Finally, the designed patterns were transferred from the photoresist to the amorphous silicon film using inductively coupled plasma etching (ICP, Oxford Instruments, Oxford Plasma Pro 100 Cobra300, SF6:C4F8 = 19.8 sccm: 40.2 sccm).