Full-Stokes polarimeters have various potential applications in the fields of image processing, biological diagnosis, military detection, and optical communication^[1−7]. Conventional full-Stokes polarimeters are based on either bulky or complicated optical systems or combined complex metasurface structures^[8−13]. Nowadays, optoelectronic devices are developing towards integration and low power consumption. Therefore, traditional full-Stokes polarimeters with bulky systems cannot fulfill the requirements for the present integrated chips technology. Over the last decade, significant progress has been achieved in on-chip full Stokes polarimeters^{[14, 15]}. However, those on-chip full-Stokes polarimeters have either the limited detection wavelength range or relatively poor device performance that need to be further improved^{[16, 17]}. Therefore, it is of great significance to develop the broadband high performance on-chip full-Stokes polarimeters for integrated optoelectronic devices.

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) have drawn vast attention because of their unique optoelectronic properties such as tunable bandgaps, high carrier mobility and good flexibility^[18−25]. Among them, optical anisotropic materials such as rhenium disulfide (ReSe₂)^{[26, 27]}, germanium selenide (GeSe)^{[28, 29]}, palladium diselenide (PdSe₂)^{[30, 31]}, are widely used in linearly polarized photodetectors. However, it would be hard to simultaneously distinguish LP from CP light by using above mentioned devices. Different from most group-Ⅵ TMDCs with in-plane symmetry, ReS₂ in group-Ⅶ has attracted great attention because of its distorted octahedral (1T) structure. Furthermore, ReS₂ is a direct band gap independent of the thickness with a bandgap around 1.6 eV because of weak interlayer coupling, which is suitable for visible light detection^[32−36]. Due to its anisotropic structure, direct band gap and great air-stability, ReS₂ has received extensive attention among the research area of polarization-sensitive photodetectors. However, ReS₂ has been primarily focused on LP light detection and its potential to detect CP light or even full-Stokes parameters remains elusive.

Here, we have successfully presented a broadband full-Stokes polarimeter by using a single ReS₂ nanobelt. The anisotropic structure of the ReS₂ introduces the in-plane optical anisotropy for LP light detection while the Schottky contacts formed by the ReS₂−Au could break the symmetry, introducing circularly photogalvanic effect (CPGE) that allows to sense CP light. Our device delivers a photoresponsivity of 181 A/W and a detectivity of 6.8 × 10¹⁰ Jones, and can sense the four Stokes parameters from 565 to 800 nm with reasonable average errors. We believe our research can provide a simple way to fabricate on-chip full-Stokes polarimeter.

The 10 nm Cr/50 nm Au electrodes on SiO₂ (300 nm)/Si wafer with 10 μm long channel were fabricated by photolithography with subsequent thermal evaporation and lift-off procedure. ReS₂ nanobelt was transferred onto electrodes using a dry transfer method after being exfoliated on polydimethylsiloxane (PDMS) stamp using scotch tape. Ultimately, the device was annealed under Ar gas environment at 300 °C for 1 h to improve the electrical contact.

Optical microscope (OM) images were obtained using an Olympus BX53 microscopy and scanning electron microscopy (SEM) (Tescan Vega3) was used to take SEM image. Photoconductivity was measured using home-built photoconductivity measurement system in ambient condition. A halogen lamp dispersed by a monochromator (Horiba JY iHR320) was served as the light source. The diameter of the incident light is about 1 cm. A polarizer, a half-wave plate and a quarter-wave plate combined together to tune the polarization states of light for polarization resolved photodetection measurement. The photocurrent signal was acquired by combining of a low-noise amplifier (Stanford SR570), a lock-in amplifier (Stanford SR830), a Model SR770 FFT analyzer and a digital oscilloscope (Tektronix MDO3032). The detailed information and measurement procedure can be found in our previous paper^[37].

The crystal structure of ReS₂ is schematically presented in Fig. 1(a), which has a distorted octahedral (1T) crystalline structure. The adjacent four Re atoms are first connected into Re₄ cluster and subsequently grouped into parallelograms along the Re–Re atomic chain (b-axis). Thus, the ReS₂ crystals can be easier exfoliated along the direction of the Re–Re atomic chain. As a result, the stripped ReS₂ nanobelts on polydimethylsiloxane (PDMS) are usually along with the long b-axis.

Fig. 1(b) shows the OM image of the device structure. The thickness of the ReS₂ nanobelt is further measured via atomic force microscopy (AFM) (Fig. 1(c)), with the inset revealing a thickness of approximately 21 nm. Fig. 1(d) shows the SEM image of the ReS₂ nanobelt. It can be seen that the nanobelt is about 500 nm in width and has relatively flat and smooth surface.

In order to further investigate the optoelectronic properties of the ReS₂ nanobelt, we have carried out the photoconductivity measurement of our ReS₂ nanobelt photodetector. The device configuration and measurement setup are schematically presented in Fig. 1(e). The current−voltage curves of our device both in dark and under a 665 nm illumination with a power density of 7.8 μW/cm² are shown in Fig. 1(f). It shows that the obvious photoresponse is present under light illumination.

Responsivity (the ratio of the photocurrent generated under illumination to the incident light power on the device) is a critical parameter to justify the performance of a photodetector. Fig. S1(a) displays the photocurrent spectrum of the ReS₂ device under a bias of 2, 1.5, 1 and 0.5 V and Fig. 2(a) shows the corresponding spectral response of the ReS₂ device extracted from Fig. S1(a). The device delivers a maximum responsivity of 181 A/W under 2 V, which is relatively low compared with that of a photoconductivity device. This can be ascribed to the thinner nanobelt (~21 nm) we used and the electrical contact barrier between the ReS₂ and the Au electrodes.

Fig. 2(b) presents the time-dependent photoresponse of the device under different biases. The corresponding optical switch characteristic indicates the good photoresponse stability of the device. Fig. 2(c) displays the photocurrent and responsivity versus the light power density. The photocurrent gradually increases while the responsivity gradually decreases as the light power density increases, which might arise from the increased recombination among the photocarriers under the high light power density^{[38, 39]}.

The 3 dB bandwidth of our device can be obtained via scanning the photocurrent versus the modulation frequencies, which was calculated to be about 16 Hz at 0.5 V bias (Fig. 2(d)). Furthermore, the rising (falling) time of our device is estimated to be 139 (196) ms (Fig. S1(b)). Fig. 2(e) presents the noise power density spectrum which reveals that 1/f noise dominates the noise spectrum at the low frequency. The estimated noise equivalent power (NEP) spectrum from Fig. 2(e) is about 2.2 × 10⁻²⁶ A²·Hz⁻¹ at 16 Hz. This small bandwidth might be due to the large channel length and non-ideal electrical contact of our device as well as the low carrier mobility of ReS₂. Combining with the spectral response and noise current of the devices, the specific detectivity can be calculated by using formula $D^{*}={\text{(AB)}}^{1/2}/\text{NEP}$ (where A is the effective area of the photodetector and B is the bandwidth). The calculated maximum detectivity is about 6.8 × 10¹⁰ Jones at a bias of 0.5 V (Fig. 2(f)).

In order to measure the Stokes parameters, it requires the photodetector to distinguish LP and CP of light simultaneously. In general, ReS₂ can distinguish LP light due to its anisotropic structure and the ability of LP detection of our ReS₂ device is displayed in Fig. 3(a). Here, the direction along the b-axis (Fig. 1(b)) is defined as 0 degree for the polarization direction of incident light. By continuously rotating the half-wave plate, we obtained linearly-polarization-dependent photoresponse under a 665 nm light excitation (Fig. S2(a)). Photocurrent evolves periodically with the polarization angle scanning from 0 to 360 degrees. The measured data points can be well fitted by the formula $I(\theta )=a\cos (2\alpha +\beta )+b$, where α is the polarization direction of the incident light, $\beta$ is the initial phase parameter when the polarization direction is 0°, a and b are fitting parameters representing polarization-dependent and polarization-independent photocurrent, respectively. The polarization ratio (I_max/I_min, where I_max is the maximum photocurrent and I_min is the minimum one) is about 1.8, which suggests the ability of LP detection of our ReS₂ photodetector (Table S1).

In addition to the intrinsic capability of LP detection arising from the anisotropic optical properties of ReS₂, we can introduce the CP detection capability to our device by establishing Schottky barriers that could break the symmetry, similar to the case in Si^[40], MoSe₂^[41], and black phosphorus^[42]. The Schottky electric field works as a perturbation, which would mix the Bloch states with orthogonal orbital polarizations. The perturbed states lead to an energy-splitting of valance band. The split two valence bands exhibit unbalanced orbital population for a non-zero momentum along out-of-plane direction, leading to the CPGE current under CP light illumination, which has been illustrated in details in Ref. [40]. Fig. S2(b) displays the time-dependent photocurrent when we rotated the λ/4 plate and fixed the λ/2 plate with its fast-axis at 0°. When rotating the λ/4 plate by 15° in turns, the incident light evolves from linear (0°), right-handed circular (45°), linear (90°), left-handed circular (135°) and finally to linear (180°) polarization states again. The measured photocurrent (black curve) versus the angle θ of the λ/4 plate is extracted from Fig. S2(b) and displayed in the upper part of Fig. 3(b), which can be phenomenologically described by:

1$I=C\sin 2\theta +L_{\text{1}}\sin 4\theta +L_{\text{2}}\cos 4\theta +A\mathrm{,}$

where C is the amplitude of the CPGE current, L₁ and L₂ are related to the linearly-polarization-dependent photocurrent contributed from linear photogalvanic effect (LPGE) and/or linear photon drag effect (LPDE) while A is the background current which is polarization-independent. It is obvious that the photocurrent is significantly different between the right-handed (I_r = 58.9 pA) and the left-handed (I_l = 53.6 pA) circularly polarized illumination. The extracted CPGE (red curve) is current component contributed from CP light illumination, which is shown in the lower part of Fig. 3(b). The circular polarization ratio is estimated to 0.047((I_l− I_r)/(I_l+ I_r)). The CPGE current mainly originated from the symmetry broken induced by the Schottky barriers formed at the ReS₂−Au contact.

Now that we have demonstrated both the linear- and circular-polarization-dependent photoresponse of our ReS₂ nanobelt device (Figs. 3(a) and 3(b)), according to our previous work, such devices are capable of detecting Stokes parameters, which we have further attempted to realize, as shown in Fig. S3. In order to detect all the four Stokes parameters, we first have to calibrate our device based on the polarization-dependent photoresponse displayed in Figs. 3(a) and 3(b). We extracted the maximum and the minimum photocurrents (I_M and I_m, respectively) under the LP illumination and the photocurrents under the left- and the right-handed CP illumination (I_l and I_r, respectively), which are the basic parameters for the subsequent calculation process. During the full-Stokes measurement of unknown light, we should keep the incident angle normal to the device while we have to rotate the device and measure the generated photocurrents at several different angles. With all the calibration parameters and the measured photocurrents, we can simply calculate the four Stokes parameters based on the model we have developed in our previous work^{[16, 17]}.

We finally used polarized light with known Stokes vector S (consisting of four Stokes parameters S₀, S₁, S₂, and S₃) to illuminate our device and measured its Stokes vector S’ with our ReS₂ device to examine the performance of the full-Stokes detection based on the device and the model. For the convenience of calculation, we decided to rotate our device to 5 typical angles, which are 0°, 45°, 90°, 135°, and 180°, to measure the photocurrents generated by the incident light. Specifically, we used 9 kinds of polarized light, including LP lights (Fig. 3(c)), CP lights and elliptically polarized lights (Fig. 3(d)), to respectively illuminate the device. It is very clear that the 5 measured photocurrents are all fully polarization dependent, indicating excellent polarization-sensitivity of our device, which can facilitate the subsequent calculation process. By substituting the measured photocurrents into the model, we can obtain the Stokes vector S’. By comparing S and S’, we can evaluate the measurement error and assess the performance of our full-Stokes polarimeter. Fig. 3(e) shows that the average measurement errors of S₁, S₂, and S₃ are 7.3%, 8.9%, and 15.6%, respectively, suggesting decent performance of full-Stokes detection. The polarized light we used here is tuned at 665 nm with a power density of 7.8 μW/cm².

We have also examined the detection performance of our device when the incident light is at different wavelengths and at different intensities. Fig. 4(a) shows the average measurement errors in a wide range of wavelength from 565−800 nm. The calibration and the measurement data are presented in Fig. S4−Fig. S6. The measurement errors of S₁, S₂, and S₃ are all minimized at the wavelength of 665 nm, when the maximum photocurrent is achieved due to the synergistic effect of the photocarrier generation and transport (Fig. S1(a)). On the one hand, the stronger absorption at the shorter wavelength would contribute more photocarriers. On the other hand, the stronger absorption also leads to the fact that the photocarriers are generated at the very surface of devices due to the shorter penetration length, which could result in a lower carrier collection efficiency owing to the surface recombination^[43]. Those two effects together give rise to the largest photocurrent near 665 nm.

Fig. 4(b) presents the power-density-dependent average measurement errors, with the calibration and the measurement data presented in Fig. S7 and Fig. S8. For all S₁, S₂, and S₃, the measurement errors gradually decrease with the increase of the power density. The trends of the measurement errors with the wavelength and the power density may be both because the larger photocurrents can generate a larger difference between I_M and I_m (also I_l and I_r), improving the calculation accuracy of our model, which is exactly the case for 665 nm or higher-power-density irradiation. In addition, the measurement error of S₃, which is related to CP component, is generally larger than S₁ and S₂, which are related to the LP component. The worse performance of measuring S₃ is possibly because the difference between I_l and I_r is much smaller than that between I_M and I_m.

To sum up, a high-performance broadband ReS₂ nanobelt full-Stokes polarimeter has been achieved. The ReS₂ nanobelt device delivers a maximum responsivity of 181 A/W and a detectivity of 6.8 × 10¹⁰ Jones. ReS₂ nanobelt photodetector exhibits a large polarization sensitive photoresponse evidenced via a linear dichroic ratio of 1.80 at 665 nm. Due to the different response to both LP and CP light, our device would be able to sense the full-Stokes parameters of light in a wide range of wavelength from 565 to 800 nm and the minimum errors are 7.3%, 8.9%, and 15.6% at a 665 nm light illumination respectively. We believe our finding provides a simple way to achieve full-Stokes polarimeter with a high-performance.

Supplementary materials to this article can be found online at https://doi.org/10.1088/1674-4926/24080023.