Deep learning-enabled ultra-broadband terahertz high-dimensional photodetector

Abstract

Capturing multi-dimensional optical information is indispensable in modern optics. However, existing photodetectors can at best detect light fields whose wavelengths or polarizations are predefined at several specific values. Integrating broadband high-dimensional continuous photodetection including intensity, polarization, and wavelength within a single device still poses formidable challenges. Here we present a metasurface-mediated high-dimensional detector that projects polarimetric and spectral responses into the Orbital Angular Momentum (OAM) domain via dispersion-driven OAM multiplication. By decoupling the frequency-controlled transmission phase response and polarization-controlled geometric phase response, spectrum and polarization information are encoded into unique polaritonic vortex patterns, which can be accurately deciphered via machine learning technique. Eventually our neural-network assisted metadevice achieves full characterization of intensity-polarization-frequency 3D continuous parametric space, so that light with arbitrarily mixed polarization states across 0.3-1.1 THz can be accurately detected with total error <5.1%. Our technology also showcases application potential as OAM-mediated information encryption, offering impetus for next-generation high-dimensional photodetectors and information security.

Simultaneously capturing polarization and frequency is challenging. This work develops a metasurface-based intelligent photodetector, which can detect arbitrary polarization and frequency within 0.3-1.1 THz with a total error smaller than 5.1%.

Introduction

Intensity, phase, wavelength, and polarization are intrinsic characteristics of light fields. Simultaneously capturing these multi-dimensional optical information is crucial for a comprehensive understanding of transmitted signals¹, facilitating a plethora of applications in optical computing², optical communications³, biomedical characterization⁴, and remote sensing^5,6. However, the detection capability of existing photonic detectors is mainly constrained to two dimensions, that is, measuring the intensity and polarization at a fixed wavelength (polarimeter)^7–15 or detecting the intensity and wavelength at a uniformed polarization (spectrometer)^16–21, while other dimensions of rich information are sacrificed or simplified. Although the collaboration of multiple discrete detectors enables extracting multiple-dimensional information separately²², the bulky volume and low collection efficiency greatly hinder its practicality²³. Integrating higher dimensional (≥3) detection capacity in a single miniaturized device is still challenging no matter in process or performance.

Recently, several studies have attempted high-dimensional information acquisition using integrated optoelectronic techniques. Graphene devices with unique photovoltage mappings successfully achieved full-Stokes parameters measurement at two specific wavelengths (5 μm, 7.7 μm)²⁴ or wavelength differentiation at two circular polarizations²⁵. Nonetheless, these approaches are limited to predetermined discrete frequencies or polarizations and cannot be extended to other bands due to the fixed inherent dispersion of graphene. Similar limitation also exists in other layered 2D material platforms, including misaligned unipolar barrier photodetectors²⁶. Different from natural materials with fixed dispersion²⁷, artificial metasurface structure provides a pioneering platform to flexibly manipulate multiple dimensions of photons in any desired wavelength^28–30. Recently, all-silicon metasurface with focusing functions has demonstrated high-efficiency photodetection across 10 polarizations at 5 mid-infrared wavelengths²³, significantly extending the high-dimensional detection capabilities. However, this wavelength-decoupled approach still loses a certain degree of freedom, failing to fully cover the entire polarization-wavelength continuous parametric system. Whereas in real-world scenarios, light fields to be detected generally carry arbitrarily varying polarizations and intensities across a wide range of wavelengths, hence it is essentially demanded to establish a 3D (or even 4D) photodetector that can accurately characterize an arbitrary light field in complete 3D intensity-polarization-wavelength parametric space.

Here, we introduce an intelligent metasurface-assisted THz photodetector for simultaneously characterizing various polarization, intensity, phase and frequencies of broadband light (0.3–1.1 THz), with the frequency prediction accuracy ≤25 GHz. By appropriately arranging the Pancharatnam–Berry (PB) and transmission phases, the metasurface decouples frequency-dependent (transmission) phase response and spin-dependent (geometric) phase response. This design allows the generation of a broadband vortex whose topological charge and composition coefficients of orbital angular momentum (OAM) modes, respectively, linearly depend on the frequency and polarization, realizing a unique mapping of spectral and polarimetric information. Furthermore, a residual neural network (ResNet) is introduced to enable precise, robust and continuous detection, with average prediction errors of only 2.8% for polarization and 4.3% for frequency detection. Compared to existing photodetectors, which cannot cover the full polarization-frequency space, our minimized metadevice is a true-sense 3D photodetector across the entire Stokes sphere in a continuous 0.3–1.1 THz range, free of any moving parts or bulk polarization/wavelength optics. The principle can be extended from the microwave to the visible light regime by simply scaling the design. We further demonstrate its application for the information encryption transmission, paving avenues to ultra-compact multi-dimensional photodetectors and information processors.

Results

Approach of our intelligent photodetector

To date, high-dimensional optical detection is constrained to two-dimensional parameter measurement (polarization-intensity or wavelength-intensity detection). In real-world scenes, light fields usually exhibit arbitrary, varied polarization and intensity over a plethora of wavelengths, where conventional photodetectors fail to differentiate. Aimed at the problem, our work proposes an intelligent high-dimensional photodetector, that encodes information into frequency-polarization sensitive surface plasmon polariton (SPP) vortices, with the data accurately decoded by a neural network.

The core device for generating polarization-wavelength-dependent interferograms is a spatially dispersive metasurface comprising a set of nanoslits, as exhibited in Fig. 1a. When light with diverse polarization and frequency is incident upon the metadevice from the substrate side, distinct SPP vortices are generated through on-chip spin–orbit interaction¹¹. Via dispersion-driven OAM multiplication mechanism³¹, the generated OAM topological charge is linearly proportional to the driven frequency, and the mode purities and relative amplitudes of vortex fields depend on the polarization. The superposition of these OAM modes leads to polarization-wavelength-sensitive exotic intensity distributions, enabling the differentiation of high-dimensional information.

Fig. 1. Design principles of our intelligent high-dimensional photodetector.

a Underlying mechanism of our multi-dimensional photodetector. The specially designed meta-slit array generates distinct polaritonic vortices over a broad spectral range under different polarizations and wavelengths. Since the topological charges and mode purities of generated OAM beams, respectively, rely on the incident wavelength and polarization states, the interference of these OAM beams results in various plasmonic distribution under different incidences, enabling the differentiation of multi-dimensional information. b Via training on the trends of metasurface-generated plasmonic patterns with a deep residual neural network, the effective identification of intensity, polarization and wavelength information can be implemented in the frequency range of 0.3–1.1 THz within 25 GHz accuracy.

Furthermore, deep-learning techniques are incorporated to learn collected data and accomplish precise recognition of multiplexing vortex pattern, enabling the wavelength and polarization information retrieval over a wide spectral range (0.3–1.1 THz). Figure 1b displays the conceptual diagram of our proposed intelligent high-dimensional photodetector. When light with an unknown wavelength and polarimetric information illuminates the device, the resulting SPP pattern is collected and input into the established ResNet model. Via this process, the wavelength and full-Stokes information of the incoming wave can be accurately characterized.

Metamaterial design of high-dimensional photodetector

Here, the core design principle of multi-dimensional spectral detection lies in the realization of a sensor with the capability to resolve both wavelength and polarization information. Figure 2a shows the schematic of our innovative photodetector that excites customized vortices interference. The metasurface transforms the left circularly polarized (LCP) and right circularly polarized (RCP) components into l+1th and l−1th order Bessel vortex beams, respectively, where the topological charge l varies monotonically with the incident frequency. Meanwhile, for arbitrarily polarized incident light, which can be regarded as the superposition of LCP and RCP, the transmitted plasmonic field distribution behaves as a superposition of two vortex beams, whose mode purities directly correspond to the composition coefficients of LCP and RCP components. Hence, the polarization state can be determined by the mode purity spectra extracted from the field distribution, and meanwhile, the topological charges of predominant OAM modes directly reflect the wavelength information.

Fig. 2. Metasurface design with high-dimensional identification capability.

a Schematic of the metasurface-mediated interferometric photodetector. b Theoretical results of generated OAM topological charges under LCP and RCP incidences at different frequencies, with both lines having slopes of -m/f₀. c Simulated plasmonic field distributions (real part of E_z component) and d corresponding mode purities under different illuminations when structural parameters m = 1 and f₀ = 0.3 THz. The OAM mode purity exhibits high purity (≈1.0). e The normalized amplitude of two generated OAM beams |M_l-1|, |M_l+1| and their phase difference angle (M_l-1–M_l+1) versus different QWP (quarter-waveplate) angle at three different frequencies, where l-1th and l+1th order vortices theoretically are the two predominant modes in OAM spectrum. Here, the QWP angle changes from −90° to 90° in increments of 22.5°, causing the polarization state to change from yLP to right-handed elliptical polarization, then back to yLP and finally transition to left-handed elliptical polarization. The OAM coefficient variation trends under diverse frequencies are basically the same.

The achievement of aforementioned functionalities on a single fixed device demands frequency-spin-dependent phase modulation among a broadband range. However, spin-dependent PB metahologram based on rotated classical meta-atoms is dispersionless among a broad spectra^13,32, and Archimedes or ring shaped slit pairs only work for a single wavelength as another strategy to construct vortices^11,33,34. Here, instead of slit pairs with certain lateral spacing, a single subwavelength slit is adopted as the unit cell. The adoption of a single slit on a silica substrate avoids the frequency dispersion arising from the inner spacing of paired slits, so each unit cell solely determines the spin-dependent Berry phase, whereas the spatial arrangement of unit cells only controls the frequency-dependent propagation phase. Subsequently, the frequency-dependent phase response and spin-dependent response can be modulated independently.

To generate frequency-polarization-controlled polaritonic vortices, the subwavelength slits are placed along an Archimedean spiral ρ_s(θ)=ρ₀ + m ⋅ λ_SPP0/2π ⋅ θ with rotation angles α_s(θ)=α₀ + n₀ ⋅ θ, where ρ₀ represents the initial radius in cylindrical coordinates (ρ_s, θ), m is an integer and λ_SPP0 is the SPP wavelength at frequency f₀, α₀ and n₀ are the initial angle and rotation factor of the slits, which are set as α₀ = π/4 and n₀ = 1 here. Unlike conventional methods to achieve interference of different plasmonic vortices that use two or more sets of nanoslit pairs¹¹, we employs only a single set of nanoslits to achieve such interference, empowering broadband continuous mapping into OAM topological charges. Notably, the spatial distribution ρ_s induces frequency-dependent vortex (transmission) phase and the rotation α_s induce spin-dependent vortex (PB) phase.

When light at frequency f and polarization characterized by E_in∝(1, ae^iξ) is incident upon the specially designed slit array from the back side, where a and ξ respectively denote the amplitude ratio (a = E_0y/E_0x) and phase difference (ξ = φ_y – φ_x) of the electric field in the x and y directions (Supplementary Note 1), each slit approximately behaves as a magnetic dipole source^35–38, and the transmitted plasmonic field can be written as (for details see Supplementary Note 3):

$$E_z\left(\rho ,\phi \right)\propto e^{i{\alpha }_0}\left(1+\frac{a{e}^{i\xi }}{i}\right)J_{l+1}\left(k_{\mathrm{SPP}}\rho \right)e^{i\left(l+1\right)\phi }-e^{-i{\alpha }_0}\left(1-\frac{a{e}^{i\xi }}{i}\right)J_{l-1}\left(k_{\mathrm{SPP}}\rho \right)e^{i\left(l-1\right)\phi }$$ 1

where J($*$) is Bessel function, k_SPP is the SPP wave number with wavelength λ_SPP, and $l=-m\cdot f/f_0$ is the induced topological charge.

From Eq. (1), we can see that the single spiral-shaped structure simultaneously yields l − 1th and l + 1th order Bessel functions. Hence, based on the existing OAM topological charges |l − 1〉 and/or |l + 1〉, the incident frequency f can be determined. Moreover, only l − 1 (l + 1) order plasmonic vortex is generated under RCP (LCP) incidence, whose theoretical relationship is displayed in Fig. 2b. The ability of our metadevice to generate vortices with topological charges that vary continuously with frequency and polarization lies solid foundation for all-space continuous polarization and frequency prediction. The broadband vortex generation is confirmed by simulated near-field distributions under different spins and frequencies (f₀, 2f₀, and 3f₀), which are depicted in Fig. 2c. Intriguingly, these plots demonstrate that a single fixed metadevice can lead to the creation of vortices with different topological orders that varies with incident chirality and frequency, and the OAM topological charge at frequency f = p·f₀ equals -f / f₀·m + σ with different integer p and spin σ (Fig. 2d), showing excellent consistence with our theory. These plasmonic vortex patterns confirm that our device could effectively distinguish light with different frequencies and circular polarization states.

Besides circular polarizations, the device also enables identifying other uniform polarization states, including linear and elliptical polarizations. Since the two complex weights of l − 1th and l + 1th order OAM modes, respectively, relate to the RCP and LCP components, the composition of LCP and RCP can be determined by the OAM mode spectra. Here we define the complex OAM mode spectra to characterize the amplitude and phase of different modes as

$$a_p\left(\rho \right)=\frac{1}{\sqrt{2\pi }}{\int }_0^{2\pi }{E}_z\left(\rho ,\phi \right)e^{-ip\phi }d\phi ,p=-N,\cdots ,0,\cdots$$ 2

which is calculated using the measured SPP field distribution. Theoretically, from Eq. (1), we have the OAM coefficients $M_{l\pm 1}=a_{l\pm 1}\left(\rho \right)/J_{l\pm 1}\left(k_{\mathrm{SPP}}\rho \right)\propto \pm e^{\pm i{\alpha }_0}\left(1\pm a{e}^{i\xi }/i\right)$ and $M_p=0$ for $p\ne l\pm 1$. In Fig. 2e, M_l−1 and M_l+1 are exhibited under distinct polarizations at three frequencies. The polarized lights with various polarization states correspond to OAM vortices with uniquely different complex spectra M_l−1 and M_l+1, while the variation trends of M_l−1 and M_l+1 remain basically consistent across different frequencies, demonstrating the broadband effectiveness of our design.

For quantitatively verifying the performance of our high-dimensional detector, we set f₀ = 0.3 THz and m = 1 to characterize the designed structure and conduct simulations and experiments. For a more noticeable effect, the segmented spiral composed of nanoslits is rotated by 6π (3 turns) to enhance the field strength. The detailed device characterization is revealed in Supplementary Note 2. Figure 3 illustrates the results across seven polarizations including four linear polarizations (xLP with S = (1,0,0), 45 °LP with S = (0,1,0), yLP with S = (−1,0,0), and –45 ° LP with S = (0,–1,0)), one elliptic polarization with S = (0.83,0,−0.55), and two circular polarizations (LCP with S = (0,0,−1), and RCP with S = (0,0,1)). The field measurement by THz time-domain spectroscopy system³⁹ achieves a high spatial resolution of 10 um (Supplementary Note 5). As illustrated in Fig. 3b, c, the simulated and measured intensity patterns on the x–y cross-section show high consistence, while the non-uniformity of measured SPP petals arises from fabrication errors and experimental noise. Meanwhile, the radial variation of fields agrees well with Bessel functions, with the intensities at ρ = 0 always being zero except the 0 order mode. According to our theoretical model shown in Fig. 2b, the potential OAM topological charges at distinct frequencies are restricted to specific values: −2, 0 at 0.3 THz; −3, −1 at 0.6 THz; and −4, −2 at 0.9 THz. Hence, the extracted OAM mode spectra from measured field distributions (Fig. 3d) supports direct discrimination of incident frequency, except a specific case of pure −2nd order OAM. Since LCP incidence at 0.9 THz and RCP incidence at 0.3 THz both can generate the pure −2nd order OAM, the frequency identification at the two specific cases requires additional spatial pattern analysis. As the Bessel functions of the same order at higher frequencies have denser radial distribution with more “donuts”, the specific case with a single “donut” pattern indicates 0.3 THz, while a denser distribution corresponds to 0.9 THz. Finally, all the three frequencies across different polarizations could be correctly identified, which confirms the frequency identification functionality.

Fig. 3. High-dimensional detection results for distinct polarizations at three bands.

a Calculated Stokes parameters from simulated and experimental results, under various polarizations and frequencies. b Simulated plasmonic electric field intensity profiles under different incident frequencies and polarizations, whose corresponding polarizations are the same with those depicted in (a). c Experimentally measured SPP intensity profiles. The measurement scope is 1.5 × 1.5 mm. d Extracted OAM purities under incidences of different polarizations and frequencies, which are one key basis for frequency identification. The ordinates represent the seven tested polarization states.

Based on the OAM purities and identified frequency, we could further calculate the polarization state. Because theoretcially$M_{l\pm 1}\propto \pm e^{\pm i{\alpha }_0}\left(1\pm a{e}^{i\xi }/i\right)$, we find $a{e}^{i\xi }=\left(-\gamma -i\right)/\left(1+i\gamma \right)$ with ${\alpha }_0=\mathrm{\pi }/4$ applied and $\gamma =M_{l+1}/M_{l-1}$ computed using Eq. (2). Then the normalized Jones vector can be directly calculated by $\left(1,a{e}^{i\xi }\right)/\sqrt{1+a^2}$, and the Stokes parameters can be further derived accordingly (see Supplementary Note 3), as given in Fig. 3a. It can be clearly observed that the calculated S parameters closely match the theoretical values in all three bands, validating the broadband polarimetry capability of our photodetector.

Machine-learning-based detection of polarization and frequency

The high-dimensional detection demonstrated so far is restricted to frequencies f = p · f₀ with integer p, which limits the resolution of frequency detection to be f₀. For frequencies f with p = f/f₀ being nonintegers, our device generates fractional-order vortex (see Eq. (1)), which is equivalent to a superposition of countless integer OAM states^40,41. Owing to the complicated OAM compositions under these frequencies, our aforementioned calculation method using OAM decomposition fails to directly capture the multi-dimensional information at these cases. However, Eq. (1) indicates that the interferometric patterns generated by our metadevice are uniquely defined under each combination of frequency and polarization, and the field patterns at two distinct incidences must be distinct (Supplementary Note 4). Hence, deep-learning technique⁴² can be induced to recognize these unique vortex patterns, meanwhile quickly extracting the polarization and frequency information from the patterns with high accuracy.

The architecture of adopted neural network is illustrated in Fig. 4b. It is noteworthy that, although our method can capture both phase and intensity distributions with high spatial resolution (Fig. 4a), the neural network functions well using only the intensity patterns as inputs. The plasmonic intensity images encoded with different polarizations and spectra are used as the training dataset, and a total of 381 * 16 = 6096 types of distributions are generated, involving 381 polarization states and 16 wavelengths. To enhance the system robustness and obtain a sufficient training dataset in a short time, we utilize data augmentation to process simulated and measured patterns, including adding noises and performing image translation. These operations help partly alleviate the impacts of environmental fluctuations, making the neural network system more robust for practical applications.

Fig. 4. Realization of an intelligent polarization spectrum detector based on deep-learning techniques.

a Demonstration of the measured phase and intensity distributions under specific incidence. b Architecture of the employed neural network for high-dimensional detection, with metasurface-generated intensity patterns as network inputs. The output layer is a vector indicating Stokes parameters and wavelength information. c The neural network predictions of wavelength (left panel) and polarimetric information (right panel) on the test set, which comes from simulations. The numbers on the diagonal of the left matrix reveal the count of precisely identified samples, while those off the diagonal reflect the number of incorrect predictions. The distinct polarization states are represented on the Poincaré sphere (the second inset), and the ResNet-predicted polarization results are projected onto the S₁–S₂ and S₂–S₃ planes for clarity. The different colors represent selected incident frequencies among 0.3–1.1 THz. d The prediction results based on a test set of real laboratory data. Our model can accurately predict wavelength (left panel) and polarimetric information (right three panels) in experimental testing.

For the employed neural network, we modify the ResNet-50 model⁴³ by adding a fully connected layer as the output layer and replacing the activation function of Stokes parameters with tanh (instead of softmax), which ensures the output Stokes parameters within the range of −1 to 1. The modified residual neural network is trained based on the previously prepared intensity images, and the cost function for multiple-output regression tasks is defined using mean square error: $\mathrm{Cost}={\alpha }_1{\sum }_{i=1}^3{\left({S_i}^{real}-{S_i}^{pre}\right)}^2+{\alpha }_2{\left({freq}^{real}-{freq}^{pre}\right)}^2$, where S_i^real (freq^real) is the real Stokes parameters (frequency) label for the input image, and S_i^pre (freq^pre) is the predicted S parameters (frequency) by the ResNet; α₁ and α₂ denote adjusting contribution weights.

When the training dataset all comes from simulations, the training loss at the final epoch reaches 0.26‰. The performance of ResNet model is then evaluated using a simulated test dataset without overlapping with the training dataset, and the predicted results by ResNet are displayed in Fig. 4c. Notably, the frequency and stokes parameters prediction is a multiple-output regression task (rather than category task) that supports continuous prediction. For clearer visualization, the predicted frequencies are categorized with a 0.05 THz interval and presented in a 16 * 16 confusion matrix (left panel in Fig. 4c), whose diagonal entries denote the number of precise predictions. The matrix reflects that our frequency prediction accuracy can at least reach 25 GHz across an ultra-wide band of 0.3–1.1 THz. It is clearly observed that high-accuracy multi-dimensional prediction is retrieved, with low average deviations of 0.014 for frequency and 0.011 for Stokes vector S = (S₁, S₂, S₃). Remarkably, this approach fully covers the entire frequency-Stokes parameters continuous space.

To further assess the model’s applicability in non-ideal and real-world scenarios, we retrained the ResNet using a mixed dataset combining both simulation and experimental data. The test results on the additional experimental dataset are demonstrated in Fig. 4d. After retraining, the final training loss of our ResNet model is 0.32‰, and our system achieves precise discrimination of high-dimensional information in the test dataset, with the average errors as low as 0.043 and 0.028 for frequency and polarization predictions, respectively. It well verifies the feasibility and robustness of our high-dimensional photodetector.

Beyond detecting a single beam with arbitrary polarization and spectrum, our methodology also enables the extraction of higher-dimensional information from two or more light beams. As displayed in Supplementary Note 6, we experimentally validated the extraction of high-dimensional information under three unknown incident beams. Furthermore, while our current approach employs solely intensity distribution, incorporating high-spatial-resolution phase distribution in the future may unlock the potential for simultaneously extracting even higher-dimensional information, like inhomogeneous polarizations¹⁰.

High-dimensional information encryption transmission with metasurface

Since our metadevice maps high-dimensional polarization and spectral information into unique multiplexed OAM states (Fig. 5a), where vortices with fractional topological charge may exhibit confusing OAM spectrum, it holds significant potential in OAM-mediated high-security information encryption. By analyzing the one-to-one mapping in the system, we identify valuable keys embedded in the physical process, say (1) Utilizing two (or more) OAM orders, and (2) Adjusting the metasurface design parameters such as m, n₀, f₀. Different keys unlock distinct OAM-related information, and only correct keys can decrypt the data, providing resistance to eavesdropping in point-to-point free-space transmission⁴⁴.

Fig. 5. Experimental demonstration of information encrytion using designed metasurface.

a The one-to-one mapping between incident states (Stokes parameters and wavelength) and OAM spectrum enabled by the designed metasurface. b The OAM spectra under several distinct incident states, where 0th order (blue) and 2nd order (red) OAM modes are selected to encode information in this example. c By selecting incident states with the two (0th and −2nd orders) appropriate OAM mode intensities, the longitude and latitude coordinate information of Beijing (116.2°E, 39.6°N) are respectively encoded into two sets of incident states (Input states 1, Input states 2). d When obtaining correct keys (metasurface, 0th and −2nd orders), the receiver can encrypt the longitude (116.2° E) and latitude (39.6°N) information of Beijing by analyzing the metasurface-generated OAM mode intensities under the two sets of incident states. The letters “E” and “N” are revealed by the spatial arrangement of −2nd order OAM mode intensities in a square format, and the number “116.2″ and “39.6″ are decoded through binary encoding of 2nd order OAM mode intensities along each line, where a value greater than 0.4 is taken as “1” and a value less than 0.4 is considered as “0”. Here, the highest (leftmost) order is defined as a decimal point.

Here we define Key 1 as the designed metasurface in the previous section, and Key 2 as 0th and −2nd order OAMs. Based on the meatasurface-generated OAM spectrum (Fig. 5b), a set of incident states with varying polarizations across the frequency range of 0.3–0.9 THz is selected as parallel channels to transmit information. Under distinct incident states, the amplitude coefficients of output 0th and −2nd order OAMs can be encoded into (0, 0), (1, 0), (0, 1), (1, 1) (upper panel in Fig. 5c). For example, under LCP incidence at 0.3 THz, the coefficients of 0th and −2nd order OAMs are 0.03 and 0.88, which can thus be encoded into (0,1). This encoding scheme enables the transmission of two independent information sequences carried by the two OAM orders. More design details are provided in Supplementary Note 7. A notable feature of this system is that different incident states may produce identical OAM amplitude information, for instance, RCP at 0.3 THz and LCP at 0.9 THz carrying the same information (“0” for 0th order and “1” for −2nd order). This feature significantly enhances the security of the encrypted information.

Figure 5c depicts the encryption of geographical coordinates (116.2°E, 39.6°N) for Beijing. We assume transmitter Alice aims to send the position information to receiver Bob. The transmitter requires two sets of incident states (states 1 and states 2) to encode longitude (116.2°E) and latitude (39.6°N) coordinate information. These two sets of incident states, shown in Fig. 5c, allow the −2nd order OAM to carry the letters E/N, while the 0th order OAM carries the numeric coordinates.

To decode the information, Bob illuminates the metasurface with the two selected sets of incident states (Fig. 5d). The high security of information transmission is ensured through experimental measurements. By using Key 1 (our metasurface) and Key 2 (0th, −2nd order), Bob can decode incident light by arranging the OAM results in a 5 × 5 square format. In this decoding rule, letter information is revealed through the spatial arrangement of −2nd order OAM mode intensity in square format, such as “E” and “N”. Numeric information is obtained via binary encoding of each line’s 0th order OAM mode intensity, such as “116.2” and “39.6”. Here, the highest (leftmost) order is defined as a decimal point. As such, the encrypted information is quite hard to decrypt for unauthorized parties, greatly enhancing the security of the conveyed information. The combination of high-dimensional encoding and OAM-based encryption offers a powerful tool for secure communication.

Discussion

To summarize, we propose an intelligent high-dimensional photodetection method based on a single multifunctional metasurface, eliminating the need for a cascade of polarization- and wavelength-sensitive devices in time or space domains. Via on-chip spin-to-OAM conversion, the metadevice generates frequency-polarization-controlled vortices. Through vortex pattern recognition by ResNet, arbitrary polarization states and wavelength information among 0.3–1.1 THz can be precisely and simultaneously deciphered. Distinct from conventional photodetectors, which cannot cover the full 3D parametric space, our method enables fully characterizing arbitrary light in the entire three-dimensional polarization-frequency-intensity parametric space with an error as low as 0.043 for frequency and 0.028 for polarization prediction. Moreover, the metadevice can be readily applicable as high-security information encryption in almost any band (More demonstrations are provided in Supplementary Note 9.)^45,46. The innovative methodology may offer possibilities for information encryption and higher-dimensional detection.

Compared with existing photodetectors, our metasurface enables full characterization of intensity-polarization-frequency continuous parametric space without the need for complicated material systems or cumbersome fabrication processes. Our metasurface fabrication procedure is easy and well-established, offering better controllability and reproducibility in comparison with heterojunction²⁶ or moiré systems. Meanwhile, in contrast to anisotropic natural material with fixed dispersion, which encounters certain bandwidth and function limitations, our device design maintains adjustable and significant distinguishability over ultra-broadband. More importantly, via dispersion-driven OAM multiplication mechanism³¹, high-dimensional photon information is linearly and continuously mapped into the OAM dimension. Unlike devices generating discrete mapping (e.g., frequency-polarization dependent focuses²³), the continuous nature of OAM topological order allows continuous detection in ultra-broadband 3D complete parametric space. A detailed comparison of the present approach with existing works is listed in Table 1 (for more discussion see Supplementary Note 8).

Table 1.

Comparison with existing works

Reference	Polarization coverage	Spectrum coverage	Detected information	Relative bandwidth	3D space continuous
Commercial spectrometer	\	0.35–1.1/… /1–12 μm	Wavelength	Different	×
Nature 523, 67–70 (2015)52	\	0.39–0.69 μm	Wavelength	0.56	×
Science 365,1017–1020 (2019)53	\	0.49–0.63 μm	Wavelength	0.25	×
Sci. Adv. 7, eabe 3196 (2021)21	LPs	0.4–0.8 μm	LPs wavelength	0.67	×
Science 378, 296–299 (2022)54	\	405–845 nm	Wavelength	0.70	×
Nat Commun 13, 4627 (2022)	\	1.15–1.47 μm	Wavelength	0.24	×
Commercial polarimeter	Full-Stokes	Known single wavelength	Polarization	\	×
Science 365, eaax 1839 (2019)55	Full-Stokes	532 nm	Polarization	\	×
Nat. Photon. 15, 614–621 (2021)12	Full-Stokes	\	Polarization	\	×
Nature 604, 266–272 (2022)24	Full-Stokes	5 μm, 7.7 μm	Polarization, 2 wavelengths	\	×
Light Sci Appl 12, 105 (2023)23.	10 selected polarizations	5 wavelengths in 3–4.5 μm	10 polarizations 5 wavelengths	0.40	×
Nat Commun 15, 8347 (2024)25	2 CPs	1.0–7.5 μm	2 CPs wavelength	1.53	×
Nat Commun 15, 7071 (2024)26	LPs	3–4.2 or 4.2–5 μm	LPs only 2 bands	0.5	×
Present work	Full-Stokes	0.3–1.1 THz	Wavelength polarization	1.14	√

CP circular polarization, LP linear polarization, MWIR mid-wave infrared.

Methods

Device fabrication

First, the quartz substrates are cleaned via sonication in acetone and isopropanol. After cleaning, 20 nm of chromium (Cr) and 100 nm of Au are deposited onto the substrates using the magnetron sputtering technique. A thin layer of photoresist (AZ521) is then spin-coated on top of the Au layer, which is prebaked and exposed to UV light through a pre-designed mask. Next, the exposed Au is etched by the ion beam etch technique, and the rest photoresist is cleaned by an acetone application process. Finally, a polyimide layer is coated on top of the structure.

Experimental characterization

The SPP spatial distributions in the x–y plane at 200 µm above the metadevice on the air side are characterized using a near-field terahertz microscopy system based on terahertz time-domain spectroscopy (THz-TDS)⁴⁷. The schematic of the experimental configuration is illustrated in Fig. S4 (Supplementary Note 5). This system employs photoconductive antenna technology for both terahertz wave generation and near-field detection. The incident terahertz beam, with a spot diameter of approximately 1 cm, fully covers the slits array of plasmonic structure. A microscope is employed to precisely adjust the probe-to-sample distance, while a three-dimensional translation stage is incorporated to fix the detection probe and help scan the SPP field distributions at the desired plane. After scanning, the temporal field distributions across the whole plane are collected by near-field coupled probes. Then by performing Fourier transforms on these data, the field information at different frequencies can be obtained.

In the future, some real-time terahertz near-field microscopy techniques^48,49 can be adopted to significantly minimize imaging acquisition time (<0.1 s) and enhance the efficiency and speed for high-dimensional information acquisition.

Neural network training details

The AdamW optimizer with a learning rate of 0.001 is applied for training using Python (v3.9.7) with the machine-learning framework PyTorch (v2.4.1). The ResNet model is trained using an AMD Ryzen 9 7950 × 16-core CPU (Advanced Micro Devices Inc.). After 100 iterations, the entire process converges, with a running time less than 1 h.

Numerical simulation

For the neural network training, 10,000s of training patterns under distinct incidences need to be generated within a limited time. To save simulation time, an equivalent theoretical model is applied, which can reproduce the simulation result very well^36,50,51. The model considers each nanoslit as an in-plane SPP magnetic dipole source. When the nanoslits are arranged into an array, the SPP field at an arbitrary observation point $\left(\rho ,\phi ,z\right)$ can be calculated by superposing these point magnetic dipole sources (see the Eq. (S3) in Supplementary Note 3): $\mathit{E}\left(\rho ,\phi ,z\right)={\sum }_{m}C\left({\mathit{E}}_{\mathrm{in}}\cdot {\widehat{n}}_m\right){\overrightarrow{e}}_m{e}^{-i{k}_{\mathrm{SPP}}\mid \overrightarrow{\rho }-{\overrightarrow{\rho }}_m\mid }{e}^{-\alpha z}/\sqrt{R_m}$, where $R_m=\sqrt{{\mid \overrightarrow{\rho }-{\overrightarrow{\rho }}_m\mid }^2+z^2}$ is the distance from the mth slit to the observation point, ${\widehat{n}}_m$ represents the unit vector perpendicular to the mth slit, $\alpha =\sqrt{k_{\mathrm{SPP}}^2-k_0^2}$ denotes the attenuation coefficient of the SPP transmission in the z direction, and ${\overrightarrow{e}}_m={\widehat{a}}_m\times {\widehat{R}}_m$ indicates the direction of field generated by the mth slit with ${\widehat{a}}_m$ and ${\widehat{R}}_m$ being the orientation of the slit and the direction from the slit to the observation point, respectively.

Author contributions

Z.-K.Z., M.-Y.X., and Z.Y.F. conceived the project idea. Z.-K.Z. developed the principle and conducted numerical simulations. Z.-P.Z. developed the neural network. Z.-K.Z. and M.-Z.C. fabricated the samples. T.Z. and X.F.Z. built the experimental setup and performed the measurements. Z.-K.Z. wrote the original draft. Z.-K.Z., T.Z., Z.-P.Z., M.-Z.C., M.Q.X., P.P., P.J.F., H.N.S., Z.P.Z., X.F.Z., Z.Y.F., and M.-Y.X. discussed and analyzed the results.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

All the corresponding data, including OAM spectra generated in this study are available via Zenodo [10.5281/zenodo.15873561] without accession code. All data that support the findings of this study are provided in the Supplementary Information and Source Data file. Source data are provided with this paper. Any correspondence and material requests should be addressed to the corresponding authors. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-025-63364-8.