Metasurfaces, by introducing phase discontinuities at the interface, are capable of modulating incident waves on a subwavelength scale [1]. This breaks the limitations of traditional optics and provides greater freedom in controlling electromagnetic waves. Based on the generalized Snell’s law, researchers have proposed versatile metasurfaces [2,3], realizing various physical phenomena and devices such as metaholography [4–6], metalenses [7–10], vortex beams [11–13], vector polarization [14,15], and surface waves [16]. Lenses are widely used in optics, biology, medicine, security, and other fields. The emergence of metalenses has made these devices more compact and introduced new functionalities. Researchers have designed various metalenses, including polarization-insensitive, polarization-tunable, and achromatic metalenses [17–22]. Chen et al. demonstrated a planar lens based on helicity-dependent phase discontinuities [17]. By controlling the incident polarization, controllable real and virtual focal planes were observed using the same metalens. Capasso et al. used high-aspect-ratio nanopillars to construct a millimeter-scale metalens, achieving imaging performance comparable to advanced commercial objectives [18]. Wang et al. proposed a method for achromatic metasurfaces, successfully eliminating chromatic aberration in the wavelength range of 1200 to 1680 nm [19]. Duan et al. presented a polarization-switchable multifocus metalens, demonstrating applications such as polarization detection and zoom imaging [20].

Polarization, as important information carried by electromagnetic waves, is crucial in imaging, encryption, image processing, and other fields. How to generate specific polarization states, how to identify the polarization state of electromagnetic waves, and how to utilize polarization are all research hotspots. For the recognition of polarization states, traditional approaches include measurement through rotating polarizers or phase retarders, as well as the divisions of amplitude and aperture [23–25]. These traditional methods are bulky and not conducive to integration. Researchers have combined the manipulation characteristics of metasurfaces to propose some polarization detection devices [26–32]. Wen et al. utilized the principle of geometric phase to deflect the left-handed and right-handed components of the incident wave in opposite directions, thereby measuring the ellipticity and handedness of polarized light [28]. Zhang et al. proposed a dielectric metasurface for wide-angle polarization detection [29]. Hu et al. used polarization filters to propose Stokes metasurfaces in the near-infrared waveband [30]. Wang et al. proposed a single-layer metasurface spectrometer based on the intrinsic dispersion and multifocus property of the metalens [31]. Especially for the terahertz band, there is an urgent need to develop efficient and compact polarization detection devices. Wang et al. proposed a reflective four-focus metalens for terahertz polarization detection. The polarization information of terahertz waves is obtained based on the intensity of the focal points [33]. Nowack et al. proposed a metasurface polarization detector for the terahertz band, utilizing three sublattices [34]. Jiang et al. proposed a metasurface-like metallic waveguide array to detect continuous terahertz waves [35]. However, these polarization detection schemes require multiple measurements to obtain the required polarization information. For those metasurfaces using multifocus metalenses for polarization detection, they can obtain the intensities of all foci by a single measurement in the visible or infrared band. However, it should be noted that these foci are of different polarization states, including linear polarizations and circular polarizations. If the above schemes are transplanted to the terahertz band, where only a single polarization field can be measured at a time, the intensities of these foci with different polarization states cannot be obtained by a single measurement.

In this work, we propose a multifocus metalens for polarization detection in the terahertz band. Unlike previously reported two-focus or six-focus metalenses used for polarization detection [28,29,36], or some other polarization detection schemes, the proposed metasurface converts all polarization components used to characterize Stokes parameters into the same polarization state, ensuring that only a single measurement is needed to obtain complete polarization parameters and reconstruct the polarization state of the incident field. This provides a new option for real-time polarization detection in the terahertz band and can be extended to visible light and other electromagnetic bands. The proposed metasurface consists of six subarrays (Fig. 1); each subarray sequentially focuses x-polarized, y-polarized, 45°-polarized, 135°-polarized, left-handed circularly polarized (LCP), and right-handed circularly polarized (RCP) components in the incident wave and converts them into x polarization. These subarrays only focus their corresponding polarization components onto the focal plane, excluding their orthogonal polarization states. This ensures that the intensity at each focus corresponds to the intensity of a certain polarization component in the incident field. The polarization state of the incident wave can be reconstructed using the intensities of the six foci. We employ this metalens to detect linear polarizations, circular polarizations, and elliptical polarizations. Simulations and experimental results demonstrate the feasibility of this metalens for polarization detection. This metalens holds great potential for applications in efficient and compact polarization devices and polarization optics.

The proposed metasurface for polarization detection consists of six subarrays, each of which converts its responsible polarization state into x polarization and focuses on the focal plane. Here, we divide the metasurface into six parts to introduce how to design the meta-atoms of each subarray so as to complete the design of the entire metasurface. At its most basic, the entire metasurface is made of high-resistance silicon with a dielectric constant of 11.9. The heights of all silicon pillars are 200 μm, and their operating frequencies are selected as 0.9 THz.

For the first part, the goal is to focus the x-polarized component of the incident field on the focal plane, discarding the y-polarized component. We select 64 meta-atoms through parametric scanning to ensure that the phase shifts of the transmitted x and y components are independent under the x- or y-polarized incidence. The detailed structural parameters (length and width) of these meta-atoms are listed in Tables 1 and 2 (Appendix A). We select eight of these meta-atoms and plot their phase shifts in Fig. 2(a). Their phase shifts cover the 2π range with a π/4 gradient under the x-polarized incidence. In the case of y-polarized incidence, their phases are almost constant. Using these selected 64 meta-atoms, the phase profiles of x- and y-polarized incidences are expressed as $$\begin{gathered} φxx=−2πλ(r2+f2−f), \\ φyy=2πλ(r2+f2−f), \end{gathered}$$(1)where the focal length is set as f=3mm. With the phase profiles in Eq. (1), the x-polarized component of the incident field can be focused on the focal plane, while the y-polarized component cannot. It is worth noting that the next five parts all adopt the phase profile φxx in Eq. (1).Table 1.

Detailed Structural Parameters (Length L1) of the Selected 64 Meta-atoms

For the second part, we want to convert the incident y-polarized wave into x polarization and focus it. To achieve such a polarization conversion, the Jones matrix of meta-atoms can be written as J1=[0110].(2)

For any polarization state incident [cosα,sinαeiδ]T, the transmitted field can be expressed as Eq. (B1). If we only detect the x-polarized component of the transmitted field, we can find that the intensity of the transmitted x-polarized component is only related to the y-polarized component of the incident wave. In order to maintain a high polarization-conversion efficiency, we place the rectangular pillars in a 45° orientation [as shown in the inset of Fig. 2(b)] and vary their lengths and widths for parametric scanning. The simulated transmission amplitudes and phase shifts of the selected eight meta-atoms are shown in Fig. 2(b). They are the transmitted x-polarized component under the y-polarized incidence. Their amplitudes are around 0.7 and cover a phase range of 2π. Using these meta-atoms to design a metalens, the intensity of the focus can be used to characterize the proportion of the y-polarized component in the incident wave.

The Jones matrix of the meta-atoms in the third part can be written as Eq. (3). These meta-atoms can convert the 45°-polarized component of the incident wave into x polarization and will not perform such a conversion for its orthogonally polarized component (135° polarization), J2=12[111−1].(3)

For an arbitrarily polarized wave incident on this part, the modulation of the meta-atoms on the incident wave can be described by Eq. (B2). It can be seen that the intensity of the x-polarized component of the transmitted field is related to the 45° polarization in the incident wave, which can be used to characterize the intensity of the 45°-polarized component.

Here, we fix the orientation of the meta-atoms to 22.5° and perform parametric sweeps. The amplitudes and phase shifts of the selected eight meta-atoms are shown in Fig. 2(c). They are the transmitted x-polarized component under the 45°-polarized incidence.

We rotate the meta-atoms of the third part by 45° to obtain the meta-atoms of the fourth part. Their Jones matrix can be written as Eq. (4), which converts the incident 135° polarization into x polarization [as described in Eq. (B3)]. In this case, the intensity of the transmitted x-polarized component is related to the 135° polarization in the incident field, J3=12[1−1−1−1].(4)

For the fifth part, the meta-atoms convert the incident LCP wave into an x-polarized component. This requires that these meta-atoms are all quarter-wave plates, which means that they have the same amplitudes under the x- and y-polarized incidences, but a phase difference of π/2. For a quarter-wave plate with a rotation angle of 45°, its Jones matrix can be written as $$\begin{gathered} J4=[cosπ4sinπ4−sinπ4cosπ4][100i][cosπ4−sinπ4sinπ4cosπ4] \\ =12[1+ii−1i−11+i]. \end{gathered}$$(5)

For the LCP and RCP components in the incident wave, the modulations of Jones matrix J4 can be described by Eq. (B4). The intensity of the x-polarized component of the transmitted field is related to the LCP component in the incident wave.

We select eight quarter-wave plates by parametric scanning, and their amplitudes and phase shifts of the transmitted x polarization under the LCP incidence are shown in Fig. 2(e). For the sixth part, we just need to rotate the meta-atoms in the fifth part by 90°. Their Jones matrix is expressed as Eq. (6). This allows only the RCP component of the incident wave to be converted into the transmitted x polarization, J5=12[1+i1−i1−i1+i].(6)

Using these six groups of meta-atoms, a metalens is constructed in each part, and the polarization parameters of the incident field can be quickly obtained using the intensity of the x-polarized component at the focal plane, and then reconstructing its polarization state. The relationships between the Stokes parameters of the incident polarization state and the intensities of each focus are defined as follows: $$\begin{gathered} S1=Ix−Iy=II−III, \\ S2=I45°−I135°=IIII−IIV, \\ S3=IRCP−ILCP=IVI−IV. \end{gathered}$$(7)

Considering the differences in the polarization conversion efficiencies of the meta-atoms in the six subarrays, first x polarization, y polarization, 45° polarization, 135° polarization, LCP, and RCP components are incident to this metalens to obtain the maximum value of each focus. Their intensity distributions are shown in Fig. 7 (Appendix C). In the subsequent applications, the values of each focus will be normalized with these six values, and then the Stokes parameters will be calculated.

To validate the capability of the proposed metalens in polarization detection, we first set the incident polarization to a series of linear polarization states with different azimuth angles (−π/4, −3π/16, −π/8, −π/16, π/16, π/8, 3π/16, and π/4). We simulate the transmitted field of the metalens under each linearly polarized incidence in turn. Please note that we only need the information of the x-polarized component of the transmitted field, not the other polarized components or the total field. The same condition applies to all the analyses that follow. The intensity distributions of the transmitted x-polarized component are shown in the first row in Figs. 3(c)–3(j). The intensity of the fourth focus gradually decreases, and the intensity of the third continues to increase as the azimuth angle increases from −π/4 to π/4. Correspondingly, the Stokes parameter S2 gradually increases from −1 to 1 (Fig. 8 in Appendix C). Using the solved Stokes parameters (S1, S2, S3), we can also calculate the amplitude ratios and phase differences of the x and y polarizations in the incident waves and plot the polarization ellipses of each polarization state. The comparisons of the detected polarization states and the incident ones are shown in the second row of Figs. 3(c)–3(j). The detected polarization states maintain the same azimuthal angles as the incident polarizations. We plot the comparison of the azimuth angles of the detected polarizations and the incident ones in Fig. 3(b), and their consistency can be seen quantitatively. We also present them as points on the Poincaré sphere in Fig. 3(a), which follow the equatorial direction from the negative to the positive direction of the S2 axis. The consistencies of the detected polarizations with the incident ones are compared through a variety of polarization representations, demonstrating the accuracy of the proposed metalens for the detection of linear polarization states.

In this part, we select eight elliptically polarized incidences to examine the performance of the proposed polarization detector, all of which have an azimuthal angle of zero. Their axial ratios are 0.8, 0.6, 0.4, and 0.2. The first four polarization states have right-handed spins and the last four are left-handed. The simulated intensity distributions of the transmitted x-polarized component are shown in the first row of Figs. 4(c)–4(j). For the first four results [Figs. 4(c)–4(f)], their incident waves are all right-handed elliptically polarized. As the axial ratio decreases from 0.8 to 0.2, the intensity difference between the first focus and the second one becomes larger, resulting in a gradual increase in the value of S1 [Fig. 4(b)]. At the same time, the intensity differences between the sixth and fifth foci gradually decrease, resulting in a decreasing trend in S3. Figures 4(g)–4(j) show the corresponding intensity distributions and the comparisons of polarization ellipses when the incident waves are left-handed elliptically polarized. Their axial ratios are 0.2, 0.4, 0.6, and 0.8, respectively. The intensity of the first focus gradually weakens with respect to the second focus, and the corresponding Stokes parameter S1 gradually decreases. The fifth focus gradually strengthens, leading to a continued decrease in the parameter S3. Throughout the process, the intensities of the third and fourth foci remain consistent, with parameter S2 almost equal to zero. This aligns with the incident polarizations having an azimuth angle of zero. According to the parameters of the detected polarization states, we also represent them as points on the Poincaré sphere in Fig. 4(a). Their trajectory follows the meridian from the positive direction to the negative direction of the S3 axis. The detected polarization states remain essentially the same as the incident ones.

In addition to the detection of some linear polarizations and elliptical polarizations with an azimuthal angle of zero in the previous two parts, we also detect some elliptical polarizations with arbitrary azimuthal angles and ellipticities. The first five states are left-handed elliptical polarizations, and their axial ratios and azimuth angles are (0.4, π/4), (0.6, π/8), (0.8, −π/8), (0.8, 3π/16), and (0.2, π/8), respectively. For the last three right-handed elliptical polarizations, their parameters are (0.5, 3π/16), (0.3, −3π/16), and (0.7, −π/4), respectively. Their intensity distributions of the transmitted x-polarized component are shown in Fig. 9 (Appendix C). Under the first five elliptically polarized incidences, the intensities of the fifth focus are larger than that of the sixth, demonstrating a larger proportion of left-handedness in the incident polarizations. For the last three, the right-handedness is more predominant than the left-handedness. Based on the intensity differences among these three pairs of foci, three Stokes parameters are calculated, as shown in Fig. 5(a). These elliptical polarizations all have a larger percentage of x-polarized components than y polarizations, and their parameters S1 are essentially positive. For the parameter S2, they are greater than zero when the values of the azimuth angles are positive. The comparisons of polarization ellipses between the detected polarization states and the incident ones are shown in Figs. 5(c)–5(j). The red ellipses basically show the same curves as the blue ones. Their points on the Poincaré sphere almost coincide, again demonstrating the accuracy of the detected polarization states.

We fabricate a sample of the multifocus metalens proposed in this work using standard ultraviolet lithography and inductively coupled plasma etching processes. The height of the fabricated sample is 500 μm, the etching depth is 200 μm, and the size of the sample is 1.56cm×1.04cm. We select two areas and take their scanning electron micrograph (SEM) images, as shown in Figs. 6(a) and 6(b). The focusing behavior and the capabilities of polarization detection are examined by using a laboratory-built terahertz digital holographic imaging system [37]. Figures 6(d)–6(i) illustrate the measured intensity distributions of the transmitted field when the incident waves are x-polarized, y-polarized, 45°-polarized, 135°-polarized, LCP, and RCP, respectively. For x- and y-polarized wave incidences, the incident polarization states can be inferred from the large contrast between the first and second foci. The calculated parameters S1 are close to 1 and −1, respectively. For the 45° and 135° polarizations, the intensities of the third and fourth foci are significantly different, with the parameter S2 close to 1 and −1, respectively. When the incident waves are circularly polarized, the intensity differences are mainly reflected in the fifth and sixth foci, and their corresponding parameters S3 are close to the theoretical −1 and 1, respectively. We similarly compare the experimentally detected polarization states with the incident ones on the same Poincaré sphere, and these six polarization states are in each of the six directions of the three coordinate axes. The experimentally measured points are very close to the theoretical values.

To quantitatively characterize the accuracy of the proposed metasurface polarization detection scheme, we list the Stokes parameters for six typical polarization states in Table 3 (Appendix C) and calculate the detection error for each polarization state. Here, the average error is defined as Δ=(|S1′−S1|+|S2′−S2|+|S3′−S3|)/3.(8)

The maximum detection error of the simulation results is 0.021, and the average error is 0.0136, which is in good agreement with the theoretical results. In the experiment, these two values are 0.0839 and 0.0592, respectively. These errors may originate from: (1) the amplitude and phase responses of the selected meta-atoms (which are not as perfect as theoretically); (2) the signal-to-noise ratio of the test system.

In conclusion, we demonstrate a polarization detection scheme that requires only a single measurement. The implementation of the scheme is based on a six-focus metalens, which converts six polarization states used to characterize Stokes parameters into x polarization and focuses them. Thus, the complete polarization parameters can be obtained by measuring only the transmitted x-polarized response. The full-Stokes parameters of the incident fields can be calculated from the intensities of the six foci, and they are also characterized by polarization ellipse and Poincaré sphere. The detection results of various linear polarizations and elliptic polarizations demonstrate the capability of this scheme in polarization detection. The practicality of this approach is also tested experimentally by fabricating a sample. This efficient polarization detection scheme may find applications in fields such as integrated optics and polarized optics.