Chirality is a special geometric asymmetry in nature, which exists widely in microscopic matter and macroscopic objects [1]. The chiral structure of the optical medium may trigger a chiral optical response, which can be explained as different refractive indices for left- and right-handed circularly polarized (LCP and RCP) light [2]. The difference between real and imaginary parts of the refractive index is manifested as optical activity and circular dichroism (CD), that is, the difference in the propagation speed or absorption of the two components. CD has become one of the important expressions of the molecular conformation of biological macromolecules, DNA, and many drug molecules, which is widely used in biology, medicine, chemistry, and other fields [3,4]. However, the inherent CD in natural materials is extremely weak, which requires a high-precision testing system [5].

Metamaterials are new artificial structures composed of subwavelength meta-atoms, which have achieved a variety of electromagnetic manipulation and novel physical phenomena. Metasurfaces are two-dimensional metamaterials that have realized efficient electromagnetic control on extremely small longitudinal scales [6]. Both metamaterials and metasurfaces have achieved broadband or giant chiral optical phenomena, including CD [7,8], chiral wavefront control [9], circular polarization imaging or detection [10,11], and tunable chiral response [12]. In addition, both metasurfaces with or without chirality have been reported for greatly enhancing the CD of chiral molecules [13–15]. In the past 20 years, various chiral phenomena have been observed in metasurfaces includes intrinsic chirality caused by asymmetric meta-atoms and extrinsic chirality caused by achiral structures under oblique incidence [16,17]. The realized functions include spin-selective absorption or reflection [18,19], polarization rotation, and so on [20–27]. However, these implementations require careful design of asymmetric units or large incident angles, and most of them can only work in a narrow frequency band or cannot achieve arbitrary wavefront control.

In this paper, we propose a new method to achieve chiral optical response based on phase manipulation rather than asymmetry meta-atoms. Simultaneously introducing geometric phase and dynamic phase into an all-silicon metasurface, spin-decoupled phase control of the transmitted terahertz wave is realized. The randomly arranged phase of one of the circularly polarized components causes giant circular dichroism-like effect in transmission. The CD can be controlled by the size of the incident terahertz beam. Not only that, but we also demonstrate another metasurface that achieves arbitrary wavefront control of the circularly polarized wave which is not scattered. This scheme provides a new idea for spin-dependent terahertz wave control.

In order to achieve the above functions, design of the metasurface units with spin decoupling function is necessary, so the dynamic phase and geometric phase (Pancharatnam–Berry phase, P-B phase) need to be introduced at the same time. The P-B phase means an additional phase in circularly polarized electromagnetic waves determined by the geometric orientation of the meta-atoms, which appears in anisotropic structures. The P-B phase is spin-dependent, which means the two circular polarization components always obtain opposite phases, while the dynamic phase is determined by the geometry of the meta-atom. Assuming that the dynamic phases of the anisotropic element for x and y polarization components are φx and φy, the geometric phase can be obtained by rotating the element around the z axis by an angle of θ. To achieve the independently controllable circular polarization phase, the dynamic phase and rotation angle of the units need to meet the following equations [28]: {φx=(φRCP+φLCP)/2φy=(φRCP+φLCP)/2−πθ=(φRCP−φLCP)/4,(1)where φRCP and φLCP represent the circular polarization phase response of the metasurface units.

Figure 3(c) is the far-field pattern of the transmitted wave with a phase matrix of Φ0, where the incident wave only undergoes a phase shift after passing through the metasurface, and the transmission direction is almost unchanged. According to Figs. 3(d)–3(f), after the incident wave passes through the random phase matrix (Φ1,Φ2,Φ3), the transmitted wave is scattered in almost all directions, and the energy will be dispersed in a large angle range. When monitoring the transmitted wave at a certain point in the far field, only a small amount of energy will be observed. Then a CD-like response of the transmitted wave is obtained. In order to obtain a higher scattering efficiency, we compared the far-field patterns of several phase matrices with different repetition rates, that is, the phase matrix is composed of 1×1, 2×2, and 4×4 identical elements. It can be found that a larger number of repetitions cause a smaller scattering range and efficiency in the far field. Among them, Fig. 3(d) has the highest scattering efficiency.

Figure 4(c) shows the experiment setup for the transmission spectrum measurement of sample 1. We placed four wire grid polarizers in a typical terahertz time-domain spectroscopy system to form a terahertz polarization test system [30]. Among them, the polarizers P1 and P3 are placed on the side close to the emitter and the receiver, respectively, to ensure that the polarization states of the transmitting and receiving waves remain unchanged during the measurement. In addition, P2 and P4 are rotated by ±45deg (observed along the propagation direction of the terahertz beam) as the x and y coordinate axes of the measurement, as shown by the red and blue arrows in Fig. 4(c). Using the system in the figure, the four transmission coefficients for linear polarization components (txx, tyx, txy, and tyy) can be obtained. Then the transmission matrix of circularly polarized waves can be calculated as [31] Tcir=(trrtrltlrtll)=12(txx+tyy+i(txy−tyx)txx−tyy−i(txy+tyx)txx−tyy+i(txy+tyx)txx+tyy−i(txy−tyx)).(3)We define the transmission difference of the two circular polarization components measured in a certain direction as TCD, which can be calculated by [19] TCD=TR−TL=(|trr|2+|tlr|2)−(|tll|2+|trl|2).(4)Since our metasurface is a non-periodic structure, different numbers of cells may produce different circular polarization responses, thereby achieving tunable CD. In order to verify this function, we place the sample at different positions of the focused terahertz beam during the measurement, so that different numbers of units are illuminated by the terahertz wave. Before that, we first simulated the transmission coefficients of two metasurfaces with 60×60 elements and 120×120 elements, respectively, in which we placed the electric field probe directly in front of the center of the metasurface. Then we calculated the TCD spectrum in the range of 0.5–2.5 THz using Eq. (4), as shown in Fig. 4(d). It can be found that the maximum value of TCD and the curve width are slightly different in the two cases. The red curve reaches a maximum value of about 0.4 around 1.3 THz, and the peak range is narrow. The maximum value of the black curve is about 0.3, while the curve width is larger. It is worth mentioning that due to the reflection loss of high-resistance silicon, the maximum initial transmission coefficient is about 0.7. The maximum value of TCD is as high as about 0.4, showing a polarization conversion efficiency of about 80%. In order to experimentally verify the circular dichroism of the sample, we use the experiment setup shown in Fig. 4(c) to perform the polarization spectrum measurement of sample 1. First, we place the sample at the focal plane (position A, d=0cm) of the off-axis parabolic lens, and the measured linear and circular polarization spectra are shown in Figs. 4(e)–4(g). It can be seen in the circularly polarized transmission spectrum that the values of the two co-polarized components (trr and tll) are relatively small. For the cross-polarization components, trl is as high as about 0.55, but tlr is close to zero. Therefore, the calculated TCD value in Fig. 4(g) reaches about 0.3 near 1.4 THz. Then, we moved the sample about 4 cm along the incident direction and placed it in position B for a similar measurement. The results can be seen in Figs. 4(h)–4(j). The diameter of the terahertz beam at position B (d=4cm) is larger than that at position A, so there will be more units in the sample working. It can be found that the TCD curve in Fig. 4(j) is narrower than that in Fig. 4(g), and the maximum value reaches 0.4 near 1.4 THz. This change rule is consistent with the simulation results in Fig. 4(d), and the tunable CD is obtained. The slight deviation of the working frequency may be caused by the processing deviation of the sample.

We use the terahertz imaging system in Fig. 5(b) to measure the electric field and phase of the transmitted wave. The beam output from the amplified femtosecond laser system (the pulse width is 50 fs, repetition frequency is 1 kHz, and center wavelength is 800 nm) is divided into two paths, which are used as the pump beam and probe beam for terahertz imaging. The terahertz wave generated by the ZnTe crystal on the left is vertically polarized (y axis). After passing through the metasurface, the THz wave is irradiated on the crystal on the right and the probe laser beam experiences an electro-optic modulation effect. Then the modulated laser transmits the terahertz electric field image to the CCD camera through the optical imaging system (lenses L2 and L3, quarter-wave plate, and Wollaston prism). During the measurement, the incident and detected terahertz polarization is changed by rotating the sample or the optical polarizer and the half-wave plate at the pump end, and the terahertz electric fields Exx, Eyx, Eyy, Exy of the four linear polarization components are observed; then the circularly polarized terahertz electric field of the sample can be obtained by Eq. (3).

Before measuring the sample 2, we simulated the transmitted electric field of it with commercial software. Figures 5(c) and 5(d) show the electric fields of the RCP and LCP waves at the focal plane, and Figs. 5(e) and 5(f) show the phase distributions. It can be seen that the RCP component is a vortex beam, while the LCP component is a messy scattered light field. The experimental results at z=6000μm are shown in Figs. 5(g)–5(j), with a working frequency of 1.38 THz. It can be seen that the measured electric field and phase are basically consistent with the simulation results. It should be pointed out that due to the limitation of the aspect ratio in the etching process, we select the designed etching depth as 150 μm, which results in our optimal design working frequency of about 1.3 THz. More importantly, the actual operating frequency is 1.38 THz due to the processing deviation. The terahertz imaging system we use shows a low signal-to-noise ratio (SNR) at 1.38 THz, which led to the deviation in the results of Fig. 5. Fortunately, we believe that the SNR is still acceptable. This may also show that our scheme has good fabrication tolerance.

In summary, we propose a new method to achieve giant chiral response of transmitted terahertz waves based on phase control. By introducing geometric phase and dynamic phase at the same time, we designed a spin-decoupled all-silicon terahertz metasurface, which can set different phase matrices for LCP and RCP incident waves. We analyzed the required conditions of the spin-decoupled metasurface elements, and then simulated and selected their geometric parameters. Using the equivalent phase matrix and the random number phase matrix, we achieve the CD-like effect of the transmitted terahertz wave. Simulated and measured results show that the maximum polarization conversion efficiency is about 80%, and the maximum CD value is 0.4. The CD value can be adjusted by the relative position of the sample in the focused terahertz beam. In addition, we also show that this method is used to achieve spin-dependent arbitrary wavefront control. Measurement results of the two-dimensional terahertz electric field are consistent with the simulation results. The proposed method does not require complex asymmetric chiral units, but only needs to set the phase matrix of the metasurface, which is expected to be used in the design of new chiral devices for terahertz wave.