Spectrometers play a crucial role in identifying substances and analyzing their chemical composition and relative content through spectral characteristics^[1]. Traditional spectrometers, which typically incorporate dispersive optical elements, long optical paths, detector arrays, and movable components, provide high resolution and wide spectral coverage. However, their large size and high cost have restricted their applicability in many scenarios^[2]. In recent years, miniaturized spectrometer systems integrated into devices such as smartphones^[3,4] and complementary-metal-oxide-semiconductor (CMOS) imaging systems^[5,6] have been developed for application in fields such as soil and crop analysis, food safety, marine science, and material analysis^[7,8]. Nonetheless, achieving low cost, high stability, and high resolution while minimizing the size remains a challenge in the field of on-chip spectrometer systems.

On-chip computational spectrometers based on filters with diverse transmissions reconstruct spectral information at high resolution using fewer filter structures, offering advantages of compact size and high performance. These features make them an emerging trend in the integration and miniaturization of on-chip spectrometer devices. Various nanostructures used in filter design have been reported, such as micro-ring resonators^[9], optical microcavities^[10], quantum dot arrays^[11], photonic crystal slab arrays^[12–14], and metasurfaces^[15–21]. Among them, the optical parameters of metasurfaces can be flexibly controlled, such as amplitude, phase, and polarization, providing higher degrees of freedom in the filter design for spectrometers, and they can be fabricated using a mature CMOS-compatible process to enable dense integration and mass-production, thereby significantly reducing manufacturing costs. Meanwhile, computational algorithms can be used to reconstruct broadband incident spectra with high precision^[22–25]. In order to improve the robustness of reconstruction results, regularization terms can be added to the reconstruction algorithm, which can suppress noise interference and prevent overfitting. Recent reconstruction methods rely on empirically tuned fixed parameters for regularization, which may cause excessive smoothing or noise amplification; therefore, proper parameter selection is critical to improving reconstruction accuracy.

Various dielectrics have been utilized to fabricate the metasurface filters, such as thin-film silicon (Si), silicon nitride (Si3N4), titanium dioxide (TiO2), and silicon dioxide (SiO2)^[14,20,22], among which thin-film Si provides a higher refractive index with maintained high transmission, enabling high-throughput metasurface filters^[6,21,26]. CMOS-compatible a-Si metasurfaces excel in cost-effectiveness, fabrication simplicity, and thickness tunability^[6,27]. In the future, integrating a-Si metasurfaces with image sensors through bonding or direct thin-film deposition and etching processes will further simplify the manufacturing process, reduce costs, and enhance compatibility. In terms of substrate, Si substrates require complex transfer processes due to strong visible-to-NIR absorption^[5,15], while fused silica offers visible-to-NIR transparency, improving the signal-to-noise ratio and cost-efficiency^[6,14,20]. Additionally, the a-Si/silica platform enables wafer-scale processing, demonstrating its potential for high yield and excellent uniformity, further supporting the scalability and cost-effectiveness of the a-Si/silica platform for large-scale production^[28–30]. Therefore, the a-Si/silica platform enables high-performance, low-cost computational spectrometers for visible-NIR applications.

In this Letter, an on-chip computational spectrometer for visible light using freeform-generated metasurfaces based on the a-Si/silica platform is presented and experimentally demonstrated. Twenty-five a-Si metasurface filters of low correlations are selected from large quantities of generated sample filters to produce distinct transmissions. We introduce a spectral reconstruction algorithm integrated with a genetic algorithm (GA), which is utilized to assist in improving the regularization parameters in the least squares strategy, achieving accurate reconstruction of various complex spectra and an optimal resolution of 1.5 nm with a relatively small number of filter channels. Employing a mature nanofabrication process presents compactness and cost-effectiveness. while addressing challenges of miniaturization and scalability for a broader spectral range. The experimental results support its potential in visible light spectral detection applications, which can also be potentially integrated into image sensor chips for spectral imaging.

The working principle of the computational spectrometer based on a-Si metasurfaces is shown in Fig. 1(a). Incident light illuminates the designed metasurface filter array, producing distinct transmissions and is subsequently captured by a detector array. The responsivity of the detector R0(λ) represents its sensitivity to optical signals at different wavelengths. The transmissions of the mth filter is denoted as tm(λ). The actual response function of the on-chip spectrometer to the incident light, taking account of the detector and the filters, can be expressed as Tm(λ)=tm(λ)·R0(λ),m=1,2,3,…M,(1)where M denotes the total number of metasurface filters. When the incident light f(λ) passes through the mth metasurface filter, the power received by the detector underneath the filter can be expressed as Im=∫λ2λ1[f(λ)Tm(λ)]dλ,(2)where λ1 and λ2 define the wavelength boundaries of the incident light under test. To make a discretization, we can obtain IM=TM×N×fN×1, where I, f, T, and N are the detected power vector by the detector array, the input spectrum vector, the filter response matrix, and wavelength points in the spectral range, respectively. Since M≪N, f has to be computed from I using reconstruction algorithms.

To enhance the reconstruction accuracy of incident light, the correlation coefficient between the transmission of different metasurface filters should be minimized. We introduce the Pearson correlation coefficient^[31] as the optimization objective for the metasurface filters. The correlation coefficient R between the transmission of the ith and jth metasurface filters can be expressed as Rti,tj=∑(ti−ti¯)(tj−tj¯)∑(ti−ti¯)2·∑(tj−tj¯)2,(3)where ti and tj represent the transmittances at different wavelengths, and ti¯ and tj¯ are the mean values of their respective transmission spectra. The average correlation coefficient ρ of the kth transmission spectrum is defined as ρ=∑j=1M|Rkj(tk,tj)|M−1(k≠j).(4)

The metasurface patterns were designed by generating binary images, and C4 symmetric shapes were used to ensure the polarization independence of the metasurface filter; 4000 distinct binary patterns were generated as candidate topological structures for metasurface units. As shown in Fig. 1(b), the metasurface unit has a period of P=1600nm, and a-Si was chosen as the metasurface material with a thickness of d=200nm. The minimal dimension was 50 nm. The metasurfaces were fabricated on a fused silica substrate. Figure 1(c) shows SEM images and transmissions (after calibration) of three types of metasurface filter arrays.

To balance reconstruction time and reconstruction error, the particle swarm clustering optimization (PSCO) algorithm^[31] was employed to select the 25 patterns with the lowest correlation coefficient from 4000 designed metasurface patterns for constructing the metasurface filters shown in Fig. 2. The correlation coefficient matrix for these 25 filters is presented in Fig. 1(d). The average correlation coefficient of the transmissions for the 25 calibrated filters was 0.23 (experimental data). Figure 1(e) shows the fabrication process of the proposed computational spectrometer based on freeform metasurfaces. To enhance the conductivity of the resist, a sputtered chromium (Cr) thin film was added as an additional step. The metasurface patterns were then defined through electron beam lithography (EBL). The a-Si layer was etched using inductively coupled plasma reactive ion etching (ICP-RIE).

To enhance the spectral reconstruction accuracy, we design a spectral reconstruction algorithm based on the least squares method as shown in Fig. 2, with its regularization parameters optimized by a GA to ensure precise spectrum reconstruction. First, we introduce a regularization term based on the least squares method to enhance the accuracy and stability of the reconstructed spectrum: minf′‖I−Tf′‖22+r1‖f′‖1+r2‖Bf′‖2+r3‖f′‖2,(5)where f′ is the reconstructed spectrum. ‖f‖1 represents the L1 regularization term, which helps prevent overfitting. ‖Bf′‖2 is the smoothing regularization term to improve the local smoothness of the data. ‖f‖2 is the L2 regularization term, which improves the accuracy of broadband spectral reconstruction. The parameters r1, r2, and r3 are the regularization coefficients, with values in the range of 0 to 0.5. By selecting appropriate regularization coefficients, the accuracy of the reconstruction algorithm can be significantly improved.

A GA is employed to optimize the regularization coefficients in order to obtain the optimal solution. The fitness function is used to assess the quality of the solutions, and in the proposed optimization process, the fitness function is influenced by both the root mean square error (RMSE) and fidelity (F)^[31]. The fitness function is defined as fit=a×RMSE+b×(1−F). A lower fitness value indicates better reconstruction performance. The tournament selection method is employed to retain individuals with lower fitness values. It is important to note that different regularization parameters are selected for narrowband and broadband light.

The experimental setup shown in Fig. 3(a) was used to validate the spectral reconstruction performance of the fabricated spectrometer chip. Before conducting spectral reconstruction experiments, the transmission of the designed metasurface filters was calibrated using a broadband filter (YSL VLF3580). The calibrated transmission was obtained by normalizing the metasurface filter’s transmitted spectrum, measured with the commercial spectrometer (Ocean SR-2VS400-10), against the base spectrum. The base spectrum was obtained by removing the metasurface filter from the optical path and directly measuring the incident light using the commercial spectrometer. The average correlation coefficient of the transmissions for the 25 calibrated metasurface filters was found to be 0.23. To evaluate the broadband spectral reconstruction performance, the laser (YSL SC-PRO-M) emitted light in the range of 550 to 850 nm through the broadband filter (YSL VLF3580), and by adjusting its cutoff bandwidth, multiple broadband spectra were constructed. After passing through the metasurface filter, the collimated beam was received by a photodetector (Thorlabs S120C), and a reconstruction algorithm was applied to recover the incident broadband or narrowband spectral signals. Simultaneously, a commercial spectrometer (Ocean SR-2VS400-10) was used to measure the incident spectrum as a reference, enabling the assessment of the reconstruction performance of the metasurface spectrometer.

The reconstruction results are shown in Figs. 3(b)–3(e). The shape and trend of the reconstructed spectra closely match the reference spectra measured by a commercial spectrometer. Additionally, we calculated the F and RMSE between the reconstructed spectra and the reference spectra. As shown in Fig. 3(b), the F of the reconstructed spectrum is 97.72%, with an RMSE of 0.0077. Figure 3(c) presents the reconstruction results for broadband light in the 600 to 775 nm wavelength range, with an F of 96.45% and an RMSE of 0.0107. Figure 3(d) shows the reconstruction performance for a broader spectrum, where the F of the reconstructed spectrum is 92.89%, and the RMSE is 0.0263. As shown in Fig. 3(c), when the incident light bandwidth was further increased by adjusting the filter cutoff to 550 to 850 nm, the reconstructed spectrum achieved an F of 88.09% and an RMSE of 0.0561. These results demonstrate that our on-chip spectrometer system effectively reconstructs complex broadband spectra across a range of bandwidths within the 550 to 850 nm wavelength range.

Using the experimental setup shown in Fig. 4(a), the laser emits narrowband light through an acousto-optic tunable filter (AOTF). To assess the narrowband spectral reconstruction performance of the designed on-chip spectrometer system, we performed experiments on narrowband monochromatic spectral reconstruction, multi-channel discrete narrowband spectral reconstruction, and spectral resolution. The reconstruction results for monochromatic spectra with different central wavelengths are presented in Fig. 4(a). The reconstructed spectra closely match the measurements from the commercial spectrometer. We calculated the F and RMSE for each reconstructed monochromatic spectrum, as shown in Fig. 4(b). The results demonstrate the uniformity of spectral reconstruction across the 550 to 850 nm wavelength range for the designed on-chip spectrometer. The average F of the reconstructed monochromatic spectra is 88.12%, with an average RMSE of 0.0224. Furthermore, we evaluated the errors in full width at half-maximum (FWHM) and center wavelength, as shown in Fig. 4(c). The reconstruction error for the center wavelength is in the range of −0.5 to 0.5 nm, while the FWHM error is mostly in the range of 0 to 2 nm. These results demonstrate that the on-chip spectrometer system based on metasurfaces provides accurate monochromatic spectrum reconstruction across the 550 to 850 nm wavelength range.

Spectral resolution is a key parameter for evaluating the performance of a spectrometer. To assess the optimal spectral resolution of the designed on-chip spectrometer system, we generated dual-narrow peak signals using the AOTF, as shown in Figs. 5(a)–5(f). Figure 5(a) shows the reconstruction of dual-narrow peaks at 595 and 596.5 nm (1.5 nm separation), with a zoom-in in Fig. 5(b). The reconstructed spectrum matches the reference, demonstrating a spectral resolution of 1.5 nm. Figures 5(c) and 5(d) show the reconstruction of peaks at 691.5 and 694 nm (2.5 nm separation), while Figs. 5(e) and 5(f) display peaks at 791.5 and 796 nm (4.5 nm separation). The resolution decreases at longer wavelengths because the refractive index of a-Si varies with wavelength, weakening the metasurface’s modulation effect at longer wavelengths and increasing the correlation between transmissions. These results confirm that the optimal spectral resolution of the designed on-chip spectrometer system is 1.5 nm, with slightly reduced performance at longer wavelengths, where it can still resolve dual-narrow peaks with a wavelength separation of 4.5 nm.

To further validate the spectral reconstruction performance of our designed on-chip spectrometer for complex spectra, we tested and reconstructed four multi-channel discrete narrowband spectra. The laser emitted narrowband light from multiple channels simultaneously through the AOTF. Notably, when the laser simultaneously outputs light from multiple channels via the AOTF, the light intensities at different central wavelengths vary. Figure 6(a) shows the reconstruction of four discrete wavelengths spaced 60 nm apart. By adjusting the output channels of the AOTF, we tested and reconstructed spectra for additional channels with varying spacing. Figures 6(b)–6(d) show the reconstruction of discrete wavelengths spaced 50, 40, and 30 nm apart. These results demonstrate that our designed on-chip spectrometer system can effectively reconstruct multi-channel discrete spectra with varying wavelength intervals.

Table 1 shows the comparison of visible light broadband computational spectrometers based on transparent substrates. The number of filter channels is one of the key factors determining the resolution of on-chip spectrometers. A larger number of filter channels can provide richer transmissions^[14,26], thereby enhancing the spectrometer’s resolution. Nevertheless, for further miniaturization and dense integration, it is crucial to reduce filter channels while maintaining high resolution. Here, we achieved a high resolution of 1.5 nm and a wide bandwidth of 300 nm with 25 filter channels. The filter transmissions can be further optimized by improving the metasurface design, thereby reducing the number of sampling channels. Additionally, we optimize the reconstruction process by combining the least squares method with a GA, leveraging the global search capability of the GA compared to traditional least squares methods, which significantly improves the accuracy of spectral reconstruction^[20]. The performance can be further improved by optimizing metasurface filter design and reconstruction algorithms^[5,15]. Furthermore, the a-Si/silica platform utilizes mature thin-film deposition and etching processes on transparent substrates, avoiding the need for transfer printing^[5,15]. This lowers manufacturing complexity while enhancing cost-effectiveness and industrial applicability. Therefore, the demonstrated computational spectrometer using metasurfaces built on an a-Si/silica platform offers advantages in performance, cost-effectiveness, and compactness, which makes it well-suited for high-precision, low-cost, and miniaturized applications.

An on-chip visible light computational spectrometer based on an a-Si/silica material platform is proposed and experimentally demonstrated. By leveraging the mature thin-film deposition and etching processes of the a-Si/silica platform, we address the challenges of achieving high performance while maintaining cost-effectiveness. We introduce a reconstruction algorithm that combines least squares optimization with a GA, effectively mitigating overfitting and data anomalies, thereby improving spectral reconstruction accuracy. Through a series of experimental tests, we evaluate the system’s reconstruction performance and spectral resolution. The experimental results show that the system achieves an optimal resolution of 1.5 nm with a wide bandwidth of 300 nm using a relatively small number of filter channels. These results provide valuable insights into the miniaturization of spectrometers. The integration of this on-chip spectrometer with portable devices holds significant potential for a wide range of applications and enables snapshot spectral imaging through integration with the CMOS technology.