The terahertz (THz) spectrum lies between the infrared and microwave regions and offers many unique advantages for imaging purposes. Its use opens up a wide range of applications across fields that include cosmology and astronomy^[1], chemical identification^[2], food and agricultural product quality^[3], to the structural properties of materials^[4]. In particular, the noninvasive and non-ionizing nature of THz radiation offers important opportunities in the fields of biomedical imaging and diagnostics^[5–10].

In the past, existing THz spectrum analyzers could measure targets’ spectra in the THz frequency range using integrated circuits with silicon photonics technology^[11]. These optical systems are either formed from a THz frequency comb and a power meter^[12,13], or are based on the Fourier transform theory^[14]. Misra et al. introduced a silicon-photonic integrated optical spectrum analyzer featuring two cascaded filters with thermal-tunable ring resonators and matched free spectral ranges^[11]. However, this concept may be more suitable for signal measurements rather than for analyzing the spectra of objects. THz spectrum analyzers integrated with a frequency comb and a power meter can also measure the incident wave, although this method requires additional femtosecond lasers and is thus bulkier and more complicated. Iida et al. presented a Fourier transform THz spectrum analyzer, employing a Martin–Puplett interferometer and Fermi level-managed barrier diode to measure the target spectra with a frequency range between 0.1 and 1.5 THz and a best resolution of 3 GHz^[14]. However, their Fourier transform infrared spectroscopes (FTIRs) use several kinds of mirrors to collimate the incident wave and do the Fourier transform, introducing bulky mechanical systems.

Traditional hyperspectral systems often use complex arrangements of diffractive optics comprising prisms, diffraction gratings, etc., plus their supporting structures, to split the incident light into multiple wavelengths by deflecting it at different angles for subsequent detection and processing. As a result, these kinds of optical systems typically require thousands of operations to tune the incident light, resulting in slow detection rates^[15–17]. Numerous spectrometers based on random filter-based encoders and deep neural networks (DNNs) have been proposed, ranging across the visible^[18] to the near-infrared (NIR)^[19]. For example, in Ref. [18], a minimum of 16 random filter-based encoders were used to do the hyperspectral reconstruction, generating 301 bands. As their detectors were not tunable, and each encoder needed one detector to absorb the optical signal from the incident light, 16 detectors were required in total.

Recently, it was expected that the absorption properties of tunable metamaterials formed from graphene and metasurfaces could be dynamically controlled by electrically tuning their Fermi energies. Prior examples, such as the tunable broadband metamaterial absorber in Refs. [19–23], comprise monolayer graphene with a metallic or dielectric structure that can switch the absorption spectrum via varying the bias voltages. However, in none of these cases do the spectra contain sufficient spectral information (e.g.,  multiple peaks and valleys at different wavelengths), and thus are unsuitable as an encoder for spectrum analysis.

We introduce an electrically tunable metamaterial incorporating graphene and plasmonic nanostructures. The absorption characteristics of the metamaterial can be dynamically adjusted by applying external voltages to modulate the Fermi energies. Therefore, as few as eight encoders based on four detectors are needed to recover 396 spectral bands. With the assistance of a deep residual network (DRN) trained on a data set comprising 64,000 spectra, the study demonstrates the reconstruction of incident spectra within the 1–5 THz range with a high localization precision of 0.3 GHz and a nearest distinguishable center frequency of 120 GHz for double-peak spectra. The results showcase the efficiency of our proposed technology, which is also expected to significantly reduce the size of current THz spectral analyzers.

It can be seen from the block diagram in Fig. 1 that the device comprises two basic parts: the tunable metamaterial-based detector as an encoder, and the DRN decoder. The detector comprises a plasmonic structure built from multiple metallic coaxial square arrays on top of a graphene monolayer acting as a semiconductor channel. The DRN was trained on a data set that is representative of the spectral response of the encoder and then used to reconstruct the unknown target spectra. These components are described in more detail below.

We chose graphene as the absorption layer in the metamaterial-based detector, since it has a zero bandgap, resulting in a wide absorption wavelength range. Furthermore, its semiconductor properties make it a good candidate to serve as the channel of the optoelectronic devices to convert the optical signal to an electrical one. The permittivity of graphene is mainly dependent on its conductivity^[24], which can be described with the combination of electronic interband and intraband transitions according to the Kubo formulas (see Supplement 1 to view the details of Kubo formulas).

It can be deduced that, at shorter wavelengths such as visible or NIR, the conductivity of graphene is dominated by the electronic interband transition. Thus, its permittivity is difficult to tune. On the other hand, at longer wavelengths, such as in the THz region, the permittivity is mostly dependent on the electronic intraband transition and thus can be tuned simply by varying the Fermi energy.

The Fermi energies can be tuned by applying different voltages between two sides of the graphene monolayer with the formula below,EF=ℏvF×πns=ℏvF×εrε0Ved,(1)where vF is the Fermi velocity with 106m/s, and εr and ε0 are the dielectric relative dielectric constant and vacuum dielectric constant, respectively. V is the biased voltage between the gate and the source, e is the elementary charge, and d is the thickness of the dielectric layer. The above results are promising, despite the fact they are based on numerical simulations of the thickness of the dielectric layer. From the above equation, we can conclude that by varying the biased voltages, we can tune the Fermi energy. Furthermore, with a higher dielectric constant and less thickness of the dielectric layer, we can tune the Fermi energies to a wider range.

We consider a graphene monolayer as the channel of a field effector transistor (FET), which has three pads for voltage supply as the drain, source, and gate. Between the graphene channel and the gate, a thick dielectric layer with a large dielectric constant was used as the depletion layer of the transistor.

Then, we used the semiconductor module in COMSOL software to simulate the biased voltage-controlled Fermi energy shown in Fig. 2. To reach a wider tuning range of Fermi energies, we used the material with the highest dielectric constant known so far for the dielectric layer, which is HfO2 with the dielectric constant of 25. HfO2 also has a small extinction coefficient between 0.19 and 0.21 in the THz band. The thickness is 30 nm. Gold (Au) material with a work function of 5.1 V was used for the source, drain, and gate pads. A 0.34 nm thick graphene monolayer dielectric constant of 9 was integrated into the HfO2 layer. Its doping concentration was set as n-type with the value of 1.5×1010cm−3, and the mobility is 10,000cm2/(V·s). The higher doping concentration also can increase the Fermi energy, so we used a medium doping value that needs to be considered during the device simulation. The Shockley–Read–Hall model was used for the trap-assisted recombination conditions. The device was simulated at room temperature around 293 K by applying the drain-source voltage as 0 V, and sweeping the gate-source voltages from 0 to 8 V. Figure 3 shows the Fermi energies can be tuned from 0 to 0.9 eV by applying the gate-source voltage from 0 to 8 V.

It is also evident that the graphene monolayer has a very broad absorption spectrum but is limited by its low absorption value of only 2.3%^[15,25] and uniform shape. For reconstructing the spectrum using deep-learning methods, the encoder needs to have abundant information in terms of amplitude variations at each frequency, indicating that an additional mechanism is needed to manipulate the light amplitude and wavelength. In our case, we used a micrometer-scale plasmonic structure to achieve this manipulation.

Plasmonic structures exciting surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs) have been widely used for optical filtering technologies, manipulating the light by controlling the size and/or period of metallic structures. The peak wavelengths of SPP structures mainly depend on the period, as given by^[15], λ=psinθε1ε2ε1+ε2,(2)where p is the period, θ is the angle of incidence, and ε1 and ε2 are the dielectric constants of two adjacent materials, one of which is metal and the other is dielectric. Note that Ref. [6] also shows that SPP structures are sensitive to the angle of incidence.

On the other hand, the peak wavelengths for LSP structures are determined by the size of the individual structures^[15], andβ=mπ−φd,(3)where β is related to the peak frequencies λ, m is an integer, φ is the reflection phase, and d is the size of the structure.

Our proposed plasmonic structure comprises multiple metallic coaxial square arrays, as shown within the red-dotted region in Fig. 4(a). Au coaxial squares can generate LSP resonances surrounding its surface, which will be turned into SPP resonances when two adjacent Au coaxial squares with different widths are sufficiently close. The width and spacing dimensions need to be about one-third of the shortest wavelength (i.e., highest frequency). In this case, the highest frequency is 5 THz, equivalent to 60 µm, and thus the primary width and space are set to 20 µm. Positioned below the Au coaxial square array is a graphene monolayer, which acts as a channel for the device, absorbing the incident radiation and transforming it into an electrical signal. Below that, at the base of the structure is a metallic substrate, which reflects most of the incident radiation back into the channel.

The wave optics module in the COMSOL Multiphysics software package was used to develop and optimize the structural parameters. The unit cell is shown in Fig. 4(c). The incident THz plane wave was excited from the top of the structure along the z axis. A perfectly matched layer (PML) was placed on the top of the structure above the incident plane wave and was surrounded by scattering boundary conditions (SBCs). Periodic boundary conditions (PBCs) were applied along the x and y directions, repeating the unit cell to reduce overall computation time. The graphene monolayer was set up with transition boundary conditions, and its optical properties were applied based on its conductivity parameter. The substrate was defined as a metallic block surrounded by a PBC, and a perfect electric conductor (PEC) was added to the bottom layer. Metallic pads placed at two sides of the plasmonic structure and monolayer graphene supply the operating voltages and vary the Fermi energies. We swept the Fermi energies to vary the permittivity of the graphene using Eqs. (1)–(4) in Supplement 1 and generated a group of absorption spectra.

We used DRNs for the spectra reconstruction. The general architecture of the DRN used in this work is shown in Fig. 1(a). First, the input signal was connected with 1024 neurons, followed by the leaky ReLu. Then the residual block embedded with a multilayer perceptron (MLP) was fully connected for only 12 layers, which could assist in avoiding gradient vanishing and gradient explosion. Then it connected with an output layer with 396 neurons and another leaky ReLu.

The above models were trained with a mini-batch size of 128 on a GPU (RTX 4090). We started at a learning rate of 0.0001 for 100 iterations with a weight decay of 0.8 and terminated training at 2 k iterations.

The LSP and SPP resonances result in numerous narrow peaks appearing across the spectrum to generate randomness by varying the width and spaces of the plasmonic structure. We calculated 21 absorption spectra with seven random detectors under the Fermi energies only of 0, 0.1, and 0.3 eV, which can be generated by reasonably low biased voltages from 0 to 3.67 V. Then we calculated the correlation to select eight spectra from four random encoders, which have the minimum correlation; their absorption spectra are presented in Fig. 5. The eight random absorption spectra shown in Figs. 5(a)–5(h) exhibit very small correlation but can cover a wide range in the absorptance graph of Fig. 5(i). We also show its angle tolerance; when the incident angle is less than 2°, the absorption spectra are nearly unchanged (see Supplement 4 to view the details).

Based on the selected encoder data, we input these eight spectra into the DRN to train the network. The training set has included 14,720 Gaussian spectra, 12,880 two-peak Gaussian spectra, and 36,400 random wide spectra. Additionally, the reconstructed spectra in Fig. 6 were not in the training data set. The resulting precision for localizing the peak frequency is close to 0.3 GHz [Fig. 6(a)] with a full width at half maximum (FWHM) of 100 GHz. The reconstructed two-peak spectrum was distinguishable and had a closest center frequency distance of around 120 GHz [Fig. 6(b)]. When the center-to-center frequency is smaller than 120 GHz, we can hardly distinguish two adjacent Gaussian peaks. The red lines shown in Figs. 6(a) and 6(b) are the ground truth, and the black dashed lines are experimental results. We also reconstructed some random wide spectra in Fig. 6(c). These five spectra have different peak-and-valley frequencies. The average mean squared error (MSE) between the ground truths and experimental results of all the reconstructed spectra are as minimum as 6.9×10−5 and are shown in Fig. 6(d).

We present the concept behind a tunable THz spectrum analyzer with hyperspectral resolution formed from electrically tunable metamaterial and plasmonic structures. As few as eight encoders based on four detectors are needed to recover 396 spectral bands. The incident spectra in the range of 1–5 THz can be reconstructed with a localization precision of 0.3 GHz and a minimum average MSE of 6.9×10−5. Our proposed analyzer is faster and more portable than those with a frequency comb and a power-meter-based system and more accurate than existing Fourier transform techniques, showing its promising ability to quickly distinguish abnormalities with small features in, for example, biological samples, making it ideally suited to fields such as pathology and biomedical imaging.