As an inherent characteristic of electromagnetic waves, polarization has been widely used in many fields such as information processing^1-3, quantum optics^4-6 and polarization imaging^{7, 8}. Among them, the polarization states of typical electromagnetic waves can be divided into linear polarization, circular polarization and elliptical polarization. For traditional polarization devices, the conversion of arbitrarily polarized waves into the specific polarized wave relies on the combination of linear polarizers and other polarization devices which undoubtedly hinder the development of modern optical devices towards integration and miniaturization.

Recently, the proposal of chiral metamaterials^9-14 which can be constructed from chiral atoms with strong circular dichroism, has provided another option for realizing the polarization conversion from non-polarized waves to circularly polarized (CP) waves. However, limited by processing accuracy and manufacturing cost, chiral metamaterials are not conducive to further promoting the development of circular polarizers. With this, the in-plane chiral structures^15-21 were proposed to construct planar chiral metamaterials, also called chiral metasurfaces, to reduce the size of devices. Various chiral structures with strong circular dichroism have been investigated, such as L-type²², Z-type^{23, 24}, H-type²⁵, asymmetric split ring^{26, 27} and fish-scale²⁸.

In parallel, different from the above-mentioned metasurfaces based on chiral meta-atoms, the metasurfaces formed by combining several anisotropic meta-atoms can also achieve circular asymmetric transmission^29-32. For example, two pair meta-atoms with a specific rotation angle difference are utilized as a cell to form a metasurface, and beam interference is applied to make left-handed circularly polarized (LCP) waves incident only generate right-handed circularly polarized (RCP) waves, nevertheless the metasurface do not engender outgoing wave under RCP incidence³⁰. Besides, linearly polarized (LP) waves also play an important role in high-resolution imaging. In recent years, metasurface linear polarizers that do not rely on external analyzers to directly observe high-resolution imaging have been reported^33-35. For example, by utilizing a double-layer metasurface composed of aluminum nanorods, a full-broadband polarization-selective transmission of light waves in the near-infrared band has been realized³³. Moreover, by independently tailoring the direction angle of each nanorod, nearly arbitrary intensity manipulation of LP beam could be obtained, which could provide another option for imaging or information encoding.

Therefore, circular and linear polarizers relying on metasurfaces efficiently realize polarization manipulation on the sub-wavelength scale. Certainly, metasurfaces that can control the wavefront while realizing polarization manipulation are more attractive. Here, we introduce the Fresnel zone plate into the metasurface to construct the metasurface zone plate^36-38 with focusing function to generate LP or CP wave. For metasurface zone plates, the odd-numbered and even-numbered ring zones are composed of different meta-atoms and the total number of rings is even. Then, once one polarized beam is incident, the outgoing waves in response to the odd-numbered and the even-numbered ring zones are focused on the same point and superimposed to engender a fixed polarized wave. As shown in Fig. 1(a) and 1(b), when the unpolarized beam is incident, the outgoing beams generated are x-LP and RCP, respectively. Such a strategy provides a novel platform for the design of multifunctional polarized metasurfaces and is expected to promote the development of optical devices towards miniaturization and integration.

Here, to realize the polarization conversion from nearly arbitrary polarizations to a fixed polarization, metasurface zone plates are proposed. Compared with the traditional zone plates, each ring in the metasurface zone plates is composed of micro-structured dielectric pillars to realize the independent manipulation of the polarization, phase and amplitude, which empowers the zone plates diversified functions. For one metasurface zone plate, the outer radius of the nth ring can be expressed as (see Supplementary information Section 1 for details):

(1)rn=nfλ0(1+nλ04f)/2,

where λ₀ = 300 μm is the performing wavelength, f =1.7 mm is the focal length corresponding to λ₀, and n represents a positive integer. When the metasurface zone plate meets the following conditions: all the meta-atoms constituting the ring zone are the same, and the number of rings n is less than 20 and greater than 2, the complex amplitude at the focus is (see Supplementary information Section 1 for details):

(2)E=∑j=1nEj≈{m|E1|+eiπ(m−1)|E1|,n=2m−1m|E1|+eiπm|E1|,n=2m,

wherem is a positive integer greater than 1. It is worth noting that when n is an even number, the absolute values of the complex amplitudes generated by the odd-numbered and the even-numbered ring zones at the focus are practically equal.

Next, we discuss the case where the odd-numbered and the even-numbered rings are composed of different meta-atoms, and n is an even number. Assuming that the incident beam E_in with an amplitude of 1 can be expressed as:

(3)Ein=[AB]=A[10]+B[01],|A|2+|B|2=1,

where A and B stand for arbitrary complex numbers. In the Cartesian coordinate system, the Eq. (3) can be rewritten as:

(4)Ein=A+iB2[1−i]+A−iB2[1i].

In recent years, coupled mode theory (CMT) has been used to study the relevant properties of transmission metasurfaces^39-42, which further promotes the development of metasurfaces. Here, only the polarization conversion properties of metasurfaces are considered to be studied from the Jones matrix. For a lossless anisotropic meta-atom, the corresponding Jones matrix is:

(5)J=RT[eiφx00eiφy]R,

where R is the rotation matrix with the rotation angle θ, φ_x (φ_y) represents the phase delay propagating along the x (y) direction under x-LP (y-LP) incidence. We set the Jones matrix of the even-numbered zone as J₁ and the Jones matrix of the odd-numbered zone as J₂, then the following transmitted electric field at the focus can be obtained according to Eq. (2) (see Supplementary information Section 2 for details):

(6)Eoute=Ein⋅J1=(A+iB2[1−i]+A−iB2[1i])⋅R1T[eiφx100eiφy1]R1=[A−iB4⋅cos(Δφ12)⋅ei∑φ12+A+iB4⋅sin(Δφ12)⋅ei(∑φ12−π2−2θ1)]⋅[1i]+[A−iB4⋅sin(Δφ12)⋅ei(∑φ12−π2+2θ1)+A+iB4cos(Δφ12)⋅ei∑φ12]⋅[1-i]Eouto=Ein⋅J2=(A+iB2[1-i]+A−iB2[1i])⋅R2T[eiφx200eiφy2]R2=[iB−A4⋅cos(Δφ22)⋅ei∑φ22−A+iB4⋅sin(Δφ22)⋅ei(∑φ22−π2−2θ2)]⋅[1i]+[iB−A4⋅sin(Δφ22)⋅ei(∑φ22−π2+2θ2)−A+iB4cos(Δφ22)⋅ei∑φ22]⋅[1-i],

where E_oute (E_outo) is the transmitted electric field generated by the even-numbered (odd-numbered) ring zones at the focus, φ_x1 and φ_y1 are the corresponding phase delays along the x and y axes in the even-numbered ring zones, φ_x2 and φ_y2 are the corresponding phase delays in the odd-numbered ring zones, and θ₁ (θ₂) represents the rotation angle of the meta-atom in the even-numbered (odd-numbered) ring zones. Besides, the phase summations and differences corresponding to the meta-atoms can be defined as: ∑φ₁ = φ_x1 + φ_y1, Δφ₁ = φ_x1–φ_y1, ∑φ₂ = φ_x2 + φ_y2, and Δφ₂ = φ_x2–φ_y2.

In order to convert the incident arbitrary polarization into linear polarization, the phase difference corresponding to the meta-atom in the odd-numbered ring zones is 0, while the phase difference responses to two orthogonal linear polarizations in the even-numbered ring zones is –π. Therefore, Eq. (6) can be rewritten as:

(7){Eoute=−A−iB4⋅ei(φx1+2θ1)⋅[1−i]−A+iB4⋅ei(φx1−2θ1)⋅[1i]Eouto=iB−A4⋅eiφx2⋅[1i]−A+iB4eiφx2⋅[1−i].

Then, the electric field of the transmitted wave on the focal plane is:

(8)Eout=[−A−iB4⋅ei(φx1+2θ1)−A+iB4eiφx2]⋅[1−i]+[iB−A4⋅eiφx2−A+iB4⋅ei(φx1−2θ1)]⋅[1i]

When Eq. (8) satisfies the following conditions:φ_x1 = π, φ_x2 = 0, we can get:

(9)Eout=[A−iB4ei2θ1−A+iB4]⋅[1−i]+[iB−A4+A+iB4e−i2θ1]⋅[1i]=(−Asinθ1+Bcosθ1)[sinθ1−cosθ1].

According to Eq. (9), it can be determined that the outgoing wave on the focal plane is the LP wave related to θ₁. Since θ₂ does not affect the result, the metasurface zone plate can be rotated at an arbitrary angle along the optical axis to generate a corresponding LP wave on the focal plane. For example, substitute θ₁ = π/2 into Eq. (9):

(10)Eout=(−Asinπ2+Bcosπ2)[sinπ2−cosπ2]=−A[10].

Surprisingly, as long as A is not equal to 0, the polarization state of the transmitted wave on the focal plane remains x-linear polarization. Specifically, as long as the incident polarized wave is not a y-LP wave, the wave generated by the metasurface zone plate only exists an x-LP component on the focusing plane.

To further verify the correctness of the above results, CST microwave studio is utilized to construct and determine the required all-silicon meta-atoms with dielectric constant ε = 11.9. After parameter scanning, the structure diagram shown in Fig. 2(a) is obtained. The period of all the meta-atoms constituting the metasurface zone plate is P = 150 μm, the length and width of the dielectric pillars in the even-numbered ring zones are L₁ = 50 μm and W₁ = 120 μm, and the length and width of the other dielectric pillars in the odd-numbered ring zones are L₂ = 60 μm and W₂ = 60 μm (see Supplementary information Section 3 for details). In order to obtain the designed metasurface zone plate (see Fig. 2(a)), these two meta-atoms are arranged according to Eq. (1). Figure 2(b) illustrates the intensity distributions of the x-LP and y-LP components of the exit wave on the xz plane under x-LP incidence. It can be seen that the x-LP component is focused on a point, while the intensity of the y-LP component at this point is negligible, indicating that the metasurface zone plate generates x-LP waves on the focal plane under the incidence of x-LP wave. Figure 2(c) depicts the simulated results on the x-o-z plane under y-LP illumination, which are consistent with the above theoretical results. Figure 2(d) shows the intensity profiles on the focal plane at a distance of 1.7 mm from the metasurface zone plate under the incidences of LP, CP and elliptically polarized (EP) waves. It is worth noting that under y-LP incidence, the metasurface zone plate cannot generate the electromagnetic wave on the focal plane, while under the incidences of other polarized waves, the transmitted waves possess only x-LP components on the focusing plane. In addition, it can be concluded that under the incidence of x-LP waves, the corresponding polarization conversion ratio of the focal plane is close to 100%. Meanwhile, the polarization conversion ratio under the CP incidence is close to 50%. That is to say, the more x-LP components occupied in the incident polarized wave, the greater the polarization conversion efficiency of the x-LP wave generated by the metasurface zone plate.

The sample with a size of 1.4 mm ×1.4 mm is fabricated exploiting standard UV lithography and inductively coupled plasma (ICP) etching techniques, whose scanning electron microscopy (SEM) image is illustrated in Fig. 3(a). The sample is placed in a terahertz digital holographic imaging system to characterize its optical properties. By introducing a half-wave plate, the polarization state of the probe beam can be changed, and then the two-dimensional terahertz field distribution of the corresponding polarization state can be obtained. Figure 3(b) shows the measured intensity distributions of LP waves under LP incidences, indicating that the designed metasurface zone plate is a linear polarizer with focusing characteristics.

By introducing two kinds of meta-atoms with a phase difference of π to construct the other metasurface zone plate, it can convert incident polarized waves into a focused CP wave. Thus, substituting Δφ₁ = Δφ₂ = π into Eq. (6) can be simplified to:

(11){Eoute=−A+iB4⋅ei(φx1−2θ1)⋅[1i]+iB−A4⋅ei(φx1+2θ1)⋅[1−i]=G⋅[1i]+H⋅[1−i]Eouto=A+iB4⋅ei(φx2−2θ2)⋅[1i]+A−iB4⋅ei(φx2+2θ2)⋅[1−i]=I⋅[1i]+J⋅[1−i].

According to Eq. (11), to generate only CP wave at the focal plane, the following conditions need to satisfy:

(12){G−I=−A+iB4⋅[ei(φx1−2θ1)+ei(φx2−2θ2)]≡0H+J=iB−A4⋅[ei(φx1+2θ1)−ei(φx2+2θ2)]≡0,

(13){G+I=−A+iB4⋅[ei(φx1−2θ1)−ei(φx2−2θ2)]≡0H−J=iB−A4⋅[ei(φx1+2θ1)+ei(φx2+2θ2)]≡0.

Equations (12) and (13) are exploited to engender RCP and LCP waves at the focal plane, respectively. Here, we discuss the situation where the metasurface zone plate generates RCP waves at the focal plane under nearly arbitrary polarization incidence. After careful calculations, we have obtained a set of solutions to Eq. (12): φ_x1 =θ₁ = 0, φ_x2 = 3π/2 and θ₂ = π/4. In the same way as in SectionLinear polarizer with focusing function, the CST microwave studio is utilized to determine the suitable meta-atoms which are depicted in Fig. 4(a) and 4(b). These two types of meta-atoms are defined as Meta-atom 1 and Meta-atom 2, respectively. For Meta-atom 1, its period, length and width correspond to P = 150 μm, L₁ =118 μm and W₁ = 50 μm. While the Meta-atom 2 is obtained by rotating a rectangular silicon pillar with length of L₂ = 48 μm and width of W₂ = 78 μm along the +x axis by π/4. Figure 4(c) (Fig. 4(e)) plots the relationship between the amplitudes of the CP components generated by the designed meta-atoms and the incident frequency, under LCP (RCP) incidence. Obviously, when the frequency of the incident CP wave is 1 THz, the amplitude of the co-polarized component of the outgoing wave is almost zero, demonstrating that the outgoing wave is a cross-polarized wave. Figure 4(d) shows the phase shift of cross-polarized waves in response to different incident frequencies under LCP illumination, while the relationship between the phase shift of the transmitted LCP component and incident frequency under RCP incidence is plotted in Fig. 4(f). For LCP incidence, the phase difference between the phase shifts generated by Meta-atom 1 and Meta-atom 2 is π at 1 THz, which can be seen from Fig. 4(d). For RCP incidence, the phase shifts of the transmitted waves generated by these two meta-atoms are equal (see Fig. 4(f)).

With this, the Meta-atom 1 and Meta-atom 2 are utilized as the basic unit to construct the even-numbered and odd-numbered ring zones in the metasurface zone plate, respectively. Figure 5(a) shows a cross-sectional view of the metasurface wave zone plate designed based on the above concept. Figure 5(b) and 5(c) illustrate the simulated intensity profiles of the focal plane under LCP and RCP incidence, respectively, whose inset is the corresponding two-dimensional display. Comparing Fig. 5(b) and 5(c), it can be found that the designed metasurface zone plate can generate RCP waves at the focus under LCP incidence, but cannot engender any outgoing waves at the focus under RCP incidence, that is to say, the metasurface zone plate has a chiro-optical response. It is worth noting that the polarization conversion ratio is a crucial parameter to measure the polarizer, which can be expressed as PCR= P_R/(P_R+P_L), where P_R is the power of the transmitted RCP component and P_L is the power of the LCP. Through simulated calculation, we obtain that the polarization conversion ratio is 89.12% under LCP incidence, indicating such a metasurface zone plate has an efficient polarization conversion ratio. Moreover, the simulated results in response to other incident polarized waves are shown in Fig. 5(d). Obviously, under LP or EP incidence, the outgoing wave on the focal plane generated by the metasurface zone plate keeps as the RCP wave throughout.

Next, the sample is fabricated exploiting the same etching technique as in Section Linear polarizer with focusing function, whose corresponding SEM image is shown in Fig. 6(a). The intensity distributions (see Fig. 6(b)) of different polarized components are obtained by changing the polarization state of the incident wave in the imaging system. It can be seen that the experimental results in Fig. 6 are consistent with the simulated results in Fig. 5: once the polarization state of the incident wave is not right-handed circular polarization, the outgoing wave at the focusing plane is the RCP wave. In short, the results of experiments and simulations manifest that the fixed polarization conversion can be effectively achieved via the metasurface zone plate.

In conclusion, we introduce the Fresnel zone plate into the metasurface to construct the metasurface zone plate, which can convert nearly arbitrary polarizations into a fixed polarization. As demonstrations, in the designed metasurface zone plates, the odd-numbered and even-numbered ring zones, which can be regarded as independent regions, are composed of different meta-atoms. Arbitrarily polarized beams incident on the metasurface zone plates will generate the outgoing wave which are superimposed at the focal plane to form a x-LP or RCP beam. The feasibility and practicability of such design scheme are verified by theory, simulation and experiment. We firmly believe that this strategy can effectively reduce the difficulty of fabricating polarized generators and may improve the versatility and integration of optical devices

We are grateful for financial supports from the National Key Research and Development Program of China (Nos. 2021YFB2800703 and 2017YFA0700202), and the National Natural Science Foundation of China (Nos. 61675147, 61735010 and 91838301).

The authors declare no competing financial interests.

Supplementary information for this paper is available at https://doi.org/10.29026/oes.2022.210014