The arbitrary control of light waves or photons is a core topic for modern optics and photonics, and it is also the foundation of optical devices and systems¹. In recent decades, the rapid development of ultrafast laser, quantum optics, Fourier optics and other fields has promoted the new applications of laser and terahertz wave such as communication, imaging, and advanced manufacturing². However, with the growing demand for diversified and intelligent optical systems, the number and complexity of optical devices are increasing, posing higher requirements for their integration level and optical field control dimension. Traditional optical devices such as lenses, wave plates and polarizers are bulky and highly dependent on the characteristics of their constituent materials. It is difficult for a single device to achieve multi-dimensional manipulation of light, and many optical components require precise processing or human experiences. In the past decade, nanophotonics and metasurfaces have provided an important alternative solution for this problem³⁻⁵. The planar and ultra-thin structures of optical metasurfaces are conducive to the efficient integration of multiple devices, and their preparation methods are in line with the progress of modern micro/nano processing technology^6,7. More importantly, dual- or even multi-parameters control of light such as amplitude, phase, polarization and wavefront can be achieved via a single meta-device⁸⁻¹⁰. It provides important ways for emerging fields such as manipulation of photon state^11,12, light control in momentum space^13,14, and micro-nano laser sources^15,16.

Chiral nanophotonics is an important part of the micro-nano optics, and its achievements have covered light sources^17,18, optical devices and photodetectors¹⁹⁻²². The chiral optical responses in metasurfaces include optical activity (OA) and circular dichroism (CD), which are obtained through intrinsic or extrinsic chirality^23,24. Electromagnetic resonances can be selectively excited by circularly polarized light in chiral meta-atoms to generate optical chirality much greater than free space wave at the micro-nano scale, which have been applied in biochemical sensing²⁵, circularly polarized light detection²⁶, optical display²⁷, and other scenarios²⁸. Combined with Pancharatnam-Berry (P-B) phase, its polarization sensitive far-field control capability can be used for multi-channel holography, full space beam focusing and dynamic polarization modulation²⁹⁻³³. The optical activity and circular dichroism of intrinsic chiral meta-atoms can be considered as originating from differences in real and imaginary parts of their equivalent refractive indices (caused by electromagnetic mode in subwavelength scale) for left and right circularly polarized (LCP and RCP) waves, resulting in differences in their phase and amplitude³⁴. For a single chiral meta-atom, achieving controllable OA without CD in far-field region by adjusting structural parameters is difficult, as the rotation of polarization angle are often accompanied by changes in the amplitude of the orthogonal circularly polarized components, i.e. changes in ellipticity³⁵. How to obtain arbitrary polarization rotation without CD using chiral metasurfaces while designing other optical parameters simultaneously is still an attractive topic. Specifically, chiral metasurfaces in terahertz band can achieve novel applications such as dynamic polarization manipulation and biochemical sensing³⁶⁻⁴⁴.

In this paper, we propose a new method for arbitrary polarization rotation and wavefront manipulation based on racemic dielectric metasurfaces, inspired by the mixture of chiral molecular isomers. Without loss of generality, we demonstrate an example of all-silicon meta-device in the terahertz band. By combining a pair of isomers with mirror patterns to form a "super-unit" instead of a single chiral meta-atom, arbitrary polarization rotation angles are obtained while maintaining almost constant ellipticity. At the same time, relative phase shift is introduced between the "super-units" based on P-B phase, and the wavefront of the transmitted wave is also can be designed. In addition, the racemic dielectric metasurfaces can still be excited for enhanced chiral near-field, but it does not show circular dichroism in the far-field region. We do not choose metal meta-atoms here, mainly considering that dielectric metasurfaces can provide high transmission efficiency while stimulating strong chiral responses, and are more conducive to the independent existence of chiral near-field near the two isomers. This novel characteristic may not only plays an important role for light field manipulation, but also has the potential to be applied in the sensing of chiral biochemical substances.

The new scheme for polarization and wavefront manipulation based on racemic dielectric metasurface is shown in Fig. 1. Here, meta-devices in the terahertz band are used as demonstration examples, and we can design the transmitted wave for a specific wavefront (such as beam deflection, focusing and vortex generation) with arbitrary polarization rotation angle. A basic unit of a racemic metasurface consists of a pair of S-shaped chiral isomers, totaling four chiral meta-atoms as a “super-unit”. The metasurface is an all-silicon device, with both the substrate and upper structure composed of high resistance silicon (ρ>20000 Ω). The geometrical parameters are shown in the figure, with substrate thickness H₁=300 μm, resonance unit height H₂=200 μm, period P=216 μm, and other in-plane dimensions L₁=72 μm, L₂=60 μm, W₁=36 μm, W₂=56 μm. All the samples we will demonstrate in the subsequent sections are composed of 30×30 "super-units" or 60×60 chiral meta-atoms.

The prerequisite for above functions is to obtain sufficient transmission circular dichroism (TCD) in chiral meta-atoms. By simulating and optimizing the S-shaped structure, we have found the size values listed earlier. We calculated four transmission coefficients using commercial software, as shown in Fig. 2(a) and 2(b), where the illustrations represent the corresponding unit shapes. The transmitted and incident terahertz waves can be correlated by the Jones matrix of meta-atoms⁴⁵:

$\left(\begin{array}{c}{E}_{\text{t}}^x\\ E_{\text{t}}^y\end{array}\right)=\left(\begin{array}{cc}{t}_{xx}& t_{xy}\\ t_{yx}& t_{yy}\end{array}\right)\left(\begin{array}{c}{E}_{\text{i}}^x\\ E_{\text{i}}^y\end{array}\right)=T\left(\begin{array}{c}{E}_{\text{i}}^x\\ E_{\text{i}}^y\end{array}\right)\mathrm{,}$（1）

where $E_{i\mathrm{,}j}^{x\mathrm{,}y}$are different incident and transmitted polarized electric fields, t_i,j(i,j=x,y) are transmission coefficients in linear polarization basis. Based on the simulation results of transmission matrix T, we calculate the transmission matrix for circularly polarized waves

$\left(\begin{array}{cc}{t}_{\text{RR}}& t_{\text{RL}}\\ t_{\text{LR}}& t_{\text{LL}}\end{array}\right)=\frac{1}{2}\left(\begin{array}{cc}{t}_{xx}+t_{yy}+\text{i}(t_{xy}-t_{yx})& t_{xx}-t_{yy}-\text{i}(t_{xy}+t_{yx})\\ t_{xx}-t_{yy}+\text{i}(t_{xy}+t_{yx})& t_{xx}+t_{yy}-\text{i}(t_{xy}-t_{yx})\end{array}\right)\mathrm{,}$（2）

where t_i,j(i,j=R,L) are transmission coefficients in circular polarization basis. The red unit shows strong TCD at the frequency of 1 THz, and the t_RL component in its transmission coefficients has the maximum value while the other quantities are very small. The situation for a blue unit is exactly opposite, with its t_LR component showing the maximum value. In addition, we also need the selected structure to be used for standard chiral geometric phase, as not all chiral meta-atoms can obtain P-B phase through rotation²⁹⁻³³. Figure 2(c) shows the transmission amplitude (t_RL component) and rotation angle of the aforementioned red unit after in-plane rotation around its geometric center. The step size of the rotation angle θ is 22.5 degrees. Obviously, these curves only show slight fluctuations and remained above 0.6 at the peak of the curve. More intuitively, we extracted the transmission amplitude and phase at different rotation angles at a frequency of 1 THz and displayed them in Fig. 2(d). It can be observed that the phase change satisfies good linearity, and we have obtained the standard chiral geometric phase. On the other hand, the spin selective transmission is mainly due to the high-order electric multipole excited by specific circularly polarized terahertz waves in chiral meta-atoms, which exhibit significant backward scattering. To prove this, we present the electric field distribution of the "red" meta-atoms under LCP and RCP waves excitations in Fig. 2(e), where there is a significant electric field enhancement when RCP waves are incident, while LCP waves are almost unable to excite localized strong electric fields. More importantly, this selective enhancement can be almost maintained when the meta-atoms undergo in-plane rotation, which is also the direct reason for the appearance of chiral geometric phases.

We prepared the metasurface samples mentioned in Fig. 2(a) and 2(b) using standard UV lithography and ICP (Inductively Coupled Plasma) etching techniques. The samples with a same size of 1.4 cm × 1.4 cm are composed of meta-atoms without rotation (θ=0°). Scanning electron microscope (SEM) images of the structure (red unit) are presented in Fig. 3(a), and several photos from different perspectives and magnifications demonstrate the standardization of our sample preparation. We use a home-built polarization resolved terahertz time-domain spectroscopy (PTDS) system to measure the chiral transmission spectra of the samples, which contains four metal wire grid polarizers based on the standard TDS system. As shown in Fig. 3(b), by rotating polarizers P₂ and P₃ to 45° and –45° as new reference frames, four linearly polarized transmission coefficients are measured and then the circularly polarized transmission matrix are calculated according to Eq. (2). In the optical path, P₁ and P₄ are used to improving the polarization purity and enhancing measurement accuracy, where P₂ and P₃ are used for polarization projection. More detailed operating methods and theoretical basis can be seen in the Supplementary information Section 2. Figure 3(c) and 3(d) show the final experimental results, with the sample structures shown in red and blue patterns, respectively. The four circularly polarized transmission coefficients are in good agreement with the simulation results in Fig. 2, and there is a slight shift in the peak frequency, which may be a deviation generated during the sample etching process.

Then we will demonstrate the function of "super-units". Based on the transmission coefficients in Fig. 2(a) and 2(b), we calculated the transmission circular dichroism T_CD of the two mirror units using the following equation:

$T_{\text{CD}}={\left|t_{\text{RL}}\right|}^2+{\left|t_{\text{LL}}\right|}^2-{\left|t_{\text{LR}}\right|}^2-{\left|t_{\text{RR}}\right|}^2\mathrm{.}$（3）

It can be seen in Fig. 4(a) and 4(b) that the peak value of enantiomer A in the curve is positive, with a maximum value close to 0.4. On the contrary, the peak value of enantiomer B is around −0.4. This already means high chirality efficiency, after all, terahertz waves show significant reflection losses at the air-silicon interface. It is interesting that when we combine the two enantiomers, the new "super-unit" in Fig. 4(c) becomes a racemic structure without circular dichroism because it has a mirror symmetry axis. Meanwhile, we present the near-field excitation of the three units mentioned above at 1 THz in Fig. 4(d−f). Compared with a single chiral meta-atom, the chiral near-field excited in hybrid structures has slightly weakened, but still maintains significant spin selectivity, providing assurance for the manipulation of transmitted waves.

In fact, enantiomers A and B serve as circular polarizers in the hybrid structure. When we introduce geometric phase by rotating the meta-atom, the transmitted orthogonal circularly polarized components combine to form a controllable rotated linearly polarized wave, which means the symmetry of the racemic structure has been disrupted. This can be analyzed from the classical polarization theory. Assuming that the transmitted components of two chiral isomers are RCP and LCP waves, with an initial phase of 0 and a rotation angle of red meta-atoms β. The two orthogonal components can be written by a Jones matrix as⁴⁶:

$E_{\text{L}}=\frac{1}{2}\left[\begin{array}{c}1\\ \text{i}\end{array}\right]\text{exp}(\text{i}{\phi }_{\text{L}})\mathrm{,}{E}_{\text{R}}=\frac{1}{2}\left[\begin{array}{c}1\\ \text{i}\end{array}\right]\text{exp}[\text{i}({\phi }_{\text{R}}+2\beta )]\mathrm{,}$（4）

where φ_R and φ_L are phase shifts of circularly polarized components caused by the metasurface. The Jones vector of the terahertz wave synthesized after passing through a metasurface can be written as

$\begin{array}{ll}E\hfill & =\frac{1}{2}\left[\begin{array}{c}1\\ \text{i}\end{array}\right]\text{exp}(\text{i}{\phi }_{\text{L}})+\frac{1}{2}\left[\begin{array}{c}1\\ -\text{i}\end{array}\right]\text{exp}[\text{i}({\phi }_{\text{R}}+2\beta )]\hfill \\ \hfill & =\frac{1}{2}\text{exp}\left[\frac{\text{i}}{2}({\phi }_{\text{L}}+{\phi }_{\text{R}}+2\beta )\right]\hfill \\ \hfill & \cdot \left\{\left[\begin{array}{c}1\\ -\text{i}\end{array}\right]\text{exp}(\text{i}\beta )+\left[\begin{array}{c}1\\ \text{i}\end{array}\right]\text{exp}(-\text{i}\beta )\right\}\mathrm{.}\hfill \end{array}$（5）

Make $\psi =({\phi }_{\text{L}}+{\phi }_{\text{R}}+2\beta )/2$，and

$E=\text{exp}\left[\text{i}\psi \right]\left[\begin{array}{c}\frac{1}{2}[\text{exp}(\text{i}\beta )+\text{exp}(-\text{i}\beta )]\\ \frac{1}{2}[\text{exp}(\text{i}\beta )-\text{exp}(-\text{i}\beta )]\end{array}\right]=\text{exp}\left[\text{i}\psi \right]\left[\begin{array}{c}\cos \beta \\ \sin \beta \end{array}\right]\mathrm{.}$（6）

Obviously, the rotation angle of the synthesized linearly polarized wave is equal to the in-plane rotation angle of the chiral unit, which provides a very convenient method for polarization manipulation. Of course, the rotation angle of unit here is a relative value, and different absolute angles can be used to design the transmitted wavefront. We have shown three examples in Fig. 4(g−i), assuming that the rotation angle of the red unit is β. The incident wave in the simulation is horizontally polarized (along the x-axis). The figure provides unit diagrams for each scenario and the polarization state of the transmitted wave, when β=0°, the polarization state of the transmitted wave is consistent with that of the incident wave. When β=45° or β=90°, the polarization state of the transmitted wave rotates by a corresponding angle.

Based on the above results, we can now achieve the final functionality of the meta-device. Firstly, we simulate the polarization rotation performance of a "super-unit" with a relative rotation angle of 90 degrees, as shown in Fig. 5(a). The incident x-polarized terahertz wave is efficiently converted into y-polarized at near f=1 THz. Based on the structure shown in Fig. 5(a), we assume that the angles at which the red and blue chiral meta-atoms rotate clockwise and counterclockwise, respectively, are β₁, then the relative phase shift obtained by the super-unit is φ=2β₁. We refer to the relative phase between super-units as the second-order Pancharatnam-Berry phase to distinguish the phase shift between the red and blue units mentioned earlier (first-order Pancharatnam-Berry phase). Figure 5(b) shows several different scenarios. Without loss of generality, we take focusing beams as an example to demonstrate the functions of our metasurface. Figure 5(c) shows the phase profile required for focusing, calculated by the following equation:

$\phi (x\mathrm{,}y)=-\frac{2\pi }{\lambda }(\sqrt{x^2+y^2+f^2}-f)\mathrm{.}$（7）

In our design, the focal length is f=15 mm, and the pixel size is 432 μm × 432 μm, with a total of 30 × 30 phase points. Through full wave simulation of the metasurface, the obvious focusing effect of incident plane waves on the focal plane is observed. Figure 5(d) shows the simulation results in the xoz plane, where the incident wave is x-polarized and the y-polarized component in the transmitted wave is significantly stronger. Similarly, in Fig. 5(e) and 5(f), we present the electric field intensity of the x- and y-polarized waves in the xoy plane (actual focal plane is z=14 mm), respectively. This result presents the focused beam while the polarization plane is rotated 90 degrees. In the experiment, we prepared all-silicon metasurfaces using the method that is same as Fig. 3. Figure 5(g) shows SEM images for the sample, with white boxes marking some of the super-units. Finally, we conduct the measurement of focused beam using a terahertz near-field system, scanning terahertz electric fields for both x- and y-polarized components in the focal plane. The experimental results (at 1.08 THz) are shown in Fig. 5(h) and 5(i), which are basically consistent with the simulation results. Additionally, we calculate the focusing efficiency based on the data in Fig. 5(f) and 5(i), the results indicate that the efficiency values for simulation and experiment are η_s=45.9% and η_e=25.7%, respectively. The focusing efficiency of our racemic metasurface is not as high as many other reports, after all, we use four meta-atoms as a phase pixel. The difference between the two efficiency values may be mainly caused by the low signal-to-noise ratio of the measurement results. The near-field TDS system we use is shown in Fig. 5(j), consisting of terahertz emitter, lens, polarizer and microprobe. The detection of different polarization components in the transmitted beam is achieved by replacing the microprobe. The above results effectively demonstrate the powerful terahertz wave manipulation ability of racemic metasurfaces. In addition, as the enantiomers in the “super-units” provide left- and right-handed circularly polarized components with specific phase differences, the racemic metasurface may serve as a new polarization multiplexing method for devices such as multifunctional meta-lenses and holographic plates, as well as for vector beam generation.

In conclusion, we have demonstrated a new scheme for polarization and wavefront control of terahertz wave based on racemic dielectric metasurfaces, both on simulation and experiment. To alleviate the interference between CD and OA in ordinary chiral metasurfaces, we use the combination of chiral isomers to form a "super-unit" instead of using a single meta-atom as the minimum working unit. Firstly, we obtained an S-shaped structure with strong chiral response through parameter optimization and processed two isomer samples for experimental verification. We built a polarization resolved TDS system to complete transmission spectrum measurement. Then, we mix and arrange the validated chiral meta-atoms to form a new working unit and introduce P-B phase between the atoms (which is called the first-order geometric phase) to obtain a polarization rotation angle. To design the wavefront of the transmitted beam, we next introduced an additional P-B phase between the super-units, i.e. second-order geometric phase. We further validated the wavefront control function of the hybrid metasurface through simulation of the whole sample and measurement of the transmitted focused beam within the focal plane. Our scheme effectively unlocks the CD and OA of chiral metasurfaces while maintaining the wavefront design and also separates the correlation between near-field and far-field chirality of a meta-device, which is of great significance for optical field manipulation and chiral sensing. In terms of light field manipulation, simultaneous control of chiral near-field and far-field can be used for image encryption and multiplexing display. For optical sensing, Racemic metasurfaces can enhance the chirality of the analyte while eliminating background signals, making sensing more accurate.