Terahertz (THz) waves refer to the electromagnetic wave spectrum with a frequency range of 1011 to 1013Hz, occupying a critical spectral region between microwaves and infrared radiation. This unique position confers distinctive properties, including non-ionizing radiation, material penetration capability, and spectral fingerprint specificity, which have driven extensive research across applications such as non-destructive imaging, communication, spectral detection, and biochemical sensing [1–9]. Particularly, THz communication has emerged as a leading candidate for next-generation wireless technology due to its potential to deliver ultra-high data rates and ultra-low latency. Central to advancing the design and manufacturing of THz communication components is the precise modulation of electromagnetic waves. Metasurfaces, ultrathin planar structures comprising subwavelength metaatoms engineered via generalized Snell’s law principles [10], can precisely customize the amplitude, phase, and polarization of electromagnetic waves at a sub-wavelength resolution [11], enabling diverse functionalities such as beam deflection, focusing, complete absorption, specific mode production, and holography [12–18]. Such versatility establishes metasurfaces as a transformative platform for designing miniaturized, reconfigurable THz devices with tailored spectral responses.

Among metasurface devices, metalenses represent a prevalent research area, which can fulfill functions such as beam focusing and high-resolution imaging. In 2013, Hu et al. designed a cylindrical lens and a spherical lens at 0.75 THz by using a V-shaped gold slit antenna unit [19]. In 2016, Capasso’s team invented the metalens with a high numerical aperture that can effectively operate in the visible light range and form a single focal point [20]. Further, to increase the number of channels, multi-focal focusing can be achieved through the precise design of each unit [21]. Lu et al. generated a large number of foci with high-precision intensity distributions by reverse-engineering and optimizing the orientation of individual metaatoms [22]. However, once manufactured, the performance of metalenses is usually fixed and the performance of metalenses, such as focus and focal length, can only be controlled by adjusting parameters such as the polarization state and frequency of incident waves [23]. Fortunately, researchers have found that combining metalenses with adjustable materials allows for flexible control over imaging scenarios, with typical adjustable materials including phase change materials, semiconductors, magneto-optical materials, graphene, and liquid crystals [24–31].

Liquid crystals (LCs) have attracted widespread attention due to their good broadband anisotropy in the THz band and their ability to be flexibly manipulated by optical [32,33], electrical [34–39], or magnetic fields [40–42]. Early research on LC cascaded metasurfaces mainly focused on utilizing the birefringence properties of LCs to achieve optical phase modulation and polarization control, but there was relatively little discussion on multi-focal metalenses. In 2009, Zhang et al. tested the frequency shift of left-handed metamaterials using magnetron LCs birefringence [43]. Over the past decade, significant progress has been made in the research of LC cascaded metalenses. There have been some reports of the cascade of LCs and metalenses to control the number of focal spots, focal length, polarization state of the focal spots, and other parameters. The dynamic THz metalens developed by Wang et al. can switch between polarization-independent single-focal point and spin-selective two-focal points by switching the anisotropy of LCs [44]. Bosch et al. combined LCs with metasurfaces to achieve electro-driven continuous focal length changes and active bifocal imaging at low applied voltage [45]. Ansari et al. demonstrated a metalens enabling simultaneous control over focal spot position, polarization state, and focal wavelength [46]. The integration of LCs into the design of metalenses is expected to enhance the active tunability of the device.

In this study, we propose and experimentally demonstrate a liquid crystal (LC) integrated dynamic THz multi-focal metalens. The device combines the advantages of electronically controlled dynamic anisotropy of LC layers and the ability of silicon-based metasurface structures to control the wavefront phase. The output left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) waves are separated into different focusing modes, and present different multi-focal distributions in a single focal plane. By adjusting the applied voltage, the molecular orientation of the LC can be changed, so as to realize the flexible reconstruction of the multi-focal distribution mode. Simultaneously, dynamic polarization conversion control can be achieved at the central single focal point. The consistency of the simulation and experiment verifies the efficient performance and dynamic reconfigurability of the device in THz wavefront control.

In this work, we design a device that cascades an anisotropic LC layer and a silicon dielectric metalens layer, which enables spatial-spin separation and focusing control under the incidence of a 45° linearly polarized (LP) wave. The LP wave can be decomposed into orthogonal components consisting of equal-amplitude LCP and RCP waves: E45°=12[11]=1−i2·12[1i]+1+i2·12[1−i]=1−i2·ELCP+1+i2·ERCP.(1)

Upon propagation through the glass substrate, the decomposed LCP and RCP components maintain spin coherence without undergoing spin decoupling. The transfer matrix of LCP and RCP components passing through the LC layer satisfies [47]TLC=[tRRLCtRLLCtLRLCtLLLC]=[cos(δ2)isin(δ2)isin(δ2)cos(δ2)],(2)where the first letter in the subscript represents the output polarization, and the second letter represents the incident polarization. Through careful design of the LC thickness, the phase difference δ realizes the conversion from −π/2 to π/2. The metalens layer has independent wavefront control capabilities for each spin state, with its transfer matrix satisfying [47] TML=[tRRMLtRLMLtLRMLtLLML].(3)

According to Eqs. (1)–(3), the transmission characteristics of THz waves can be obtained. When the metalens has only one focal point, the spatial phase distribution of the metalens can be calculated according to the following formula [21–23]: Φ(x,y)=2πλ((x−x0)2+(y−y0)2+f02−f0),(4)where λ is the operating wavelength, x and y denote the coordinates of the unit structure at each position, the position of the focus within the focal plane is denoted as (x0,y0), and the distance from the focal plane to the surface of the metasurface is f0. To achieve independent control of multiple channels, the size and orientation angle of each element are carefully designed so that the cumulative phase generated by the combination of PB phase and propagation phase can be modulated independently of each channel. Furthermore, to preemptively design different focusing effects for various mutually independent spin states, parameters such as focal position, number of focal points, focal length, and operating frequency are incorporated. The transmission coefficients tRRML,tRLML,tLRML,tLLML in Eq. (3) sequentially satisfy [22] tRRML=tLLML=A1exp(2π·iλ((x−xj)2+(y−yj)2+f02−f0)),(5)tRLML=∑j=12A2exp(2π·iλ((x−xj)2+(y−yj)2+f02−f0)),(6)tLRML=∑j=14A4exp(2π·iλ((x−xj)2+(y−yj)2+f02−f0)),(7)where there are three mutually independent spin polarization states: LL (RR), LR, and RL. In particular, for the RL (LR) state, the energy is equally distributed between the two (four) focal points, leading to the amplitudes satisfying: A1=2A2=2A4. The position of focal points is defined as (xj,yj). The transmission coefficients tRRML,tRLML,tLRML,tLLML contain the spatial phase distribution and amplitude required to achieve different focusing configurations with different spin components. Then, the matrix transformation is used to obtain the transmission coefficients txxML,txyML,tyxML,tyyML under the linear polarization basis vector. Combined with the Jones matrix of the input LP wave, the target electromagnetic vector information ExxML,ExyML,EyxML,EyyML can be obtained. The matrix transformation satisfies [47] [txxMLtxyMLtyxMLtyyML]=12[(tRRML+tLLML)+(tRLML+tLRML)i(tRRML−tLLML)−i(tRLML−tLRML)−i(tRRML−tLLML)−i(tRLML−tLRML)(tRRML+tLLML)−(tRLML+tLRML)].(8)

At the same time, establish a database. The numerical simulations are modeled by the finite-difference time-domain (FDTD) method in the commercial software FDTD Solution. The x and y directions are periodic boundaries, and the z direction is surrounded by perfectly matched layers. The light source is set to a plane wave along the x-axis or y-axis, with the frequency at 0.5 THz. The parameters of the material in the numerical simulation can be found in Appendix C. Sweep the parameters (lx, ly, β) of the unit structure shown in Fig. 1(d), obtain information of four electromagnetic vectors (Exx, Exy, Eyx, Eyy) for each structure unit, and save the data to establish a database. Next, the optimal structure is searched by comparing the electromagnetic information in the established database with the target electromagnetic vector information at each position in space. Finally, import all structural units into the FDTD Solution simulation software to simulate the overall effect of the device.

Based on the above principles, we consider the LC cascaded metasurface as a whole. The schematic diagram of THz spatial-spin separation and focusing manipulation is shown in Figs. 1(a) and 1(b). The angle between the LC axis and the positive direction of the y-axis is defined as θ. When the LC axis is aligned along the y-axis (θ=0°), the LCP exhibits a single focal point at the center of the focal plane, whose focal length is 3.8 mm. Meanwhile, the RCP features two focal points separated by a distance of 9.2 mm on the straight line passing through the center of the focal plane. When the LC director is oriented along the x-axis (θ=90°), the LCP presents four focal points located at the four vertices of a square with a side length of 6.4 mm on the focal plane, whereas the RCP has a single focal point at the center of the focal plane. The physical photo of the LC cascaded metalens is shown in the inset of Fig. 1(b).

The device structure encompasses a glass substrate, a rubbed polyimide (PI) alignment layer (which enables the LC molecules to be orderly arranged along the y-axis, completed by Nanjing Ningcui Optical Technology Co., Ltd.), a 700-μm-thick LC layer, and a silicon dielectric metasurface. The LC used in this work is a kind of high-birefringence nematic LC (HTD028200) from Jiangsu Hecheng Technology Co., Ltd., of which ne and no are 1.90 and 1.60 within a certain THz range, respectively. Details of device fabrication can be found in Appendix A. Details of the optical response of LC can be found in Appendix D. The experimental characterization system used in this work is a near-/far-field scannable THz spectroscopy (N/F-STS) system depicted in Fig. 1(c); the near-field probe in it can obtain rich electromagnetic field information [48–50], and more details of the N/F-STS system can be found in Appendix B. Each metaatom and corresponding geometric dimensions are shown in Fig. 1(d), and the scanning electron microscope (SEM) images of the metalens are shown in Fig. 1(e). The period of the unit is Px=Py=300μm. The etching depth (h1) of the silicon structure and the height of the remaining silicon substrate (h2) are both 500 μm. The width of the silicon structure in the unit is w=80μm. Both lx and ly vary from 50 to 250 μm, and the angle β varies from −90° to 90°.

Firstly, we simulate the optical field distribution of the LC integrated dynamic THz multi-focal metalenses at a focal plane of z=38mm under different LC directors, and characterize the device in the N/F-STS system shown in Fig. 1(c). The intensity distributions in the focal plane obtained in the simulation and experiments are shown in Figs. 2(a) and 2(b), respectively. Multi-focal focusing with different spin wave spatial-spin separations has been observed, and this multi-focal focusing effect can also be flexibly manipulated by changing the LC anisotropic state. The results show that with the increase of θ from 0° to 90° in Fig. 2(a), the RCP wave gradually transforms from bifocal focusing to single focal focusing, and the two focal points and the single focal point are distributed at (0 mm, −4.6mm, 38.0 mm), (0 mm, 4.6 mm, 38.0 mm), and (0 mm, 0 mm, 38.0 mm), respectively. At the same time, the LCP wave gradually transforms from single focal point focusing to four focal points focusing, and the single focal point and the four focal points are distributed at (0 mm, 0 mm, 38.0 mm), (3.2 mm, 3.2 mm, 38.0 mm), (3.2 mm, −3.2mm, 38.0 mm), (−3.2mm, 3.2 mm, 38.0 mm), and (−3.2mm, −3.2mm, 38.0 mm), respectively. More numerical simulation details can be found in Appendix C.

The experimental results shown in Fig. 2(b) demonstrate the independent manipulation and dynamic adjustability of focusing configurations for different spin waves, which are similar to the simulation results. This further proves that the spatial light field of the metadevice evolves with the applied voltage from 0 to 200 V, which lays a foundation for the feasibility of flexible control between different focusing states under different bias voltages. In addition, the slight differences between the experimental and the simulation results are due to errors in device fabrication and simplification of material models (such as absorption and dispersion) in simulations.

Subsequently, we selected the positions y=0mm (RCP) and y=−3.2mm, y=0mm, and y=3.2mm (LCP) on the focal plane, as shown in Fig. 3(a). The normalized intensity distribution curve on the selected section is plotted, along with the corresponding full width at half maximum (FWHM, the distance between two positions when the light intensity reaches half of the maximum value in the light intensity distribution curve [21–23]). In the simulation, for RCP waves, the normalized intensity distribution shows a shift from two focal points (0°) to one point (90°) as shown in Figs. 3(b) and 3(c). The FWHM and focusing efficiency (the ratio of the total energy in the diameter of three times the FWHM at the focus to the total energy of the incident wave [21–23]) of the bifocal function are 1.52 mm (1.52 mm) and 44.9% (44.9%), and the FWHM and focusing efficiency of the single focal function are 1.70 mm and 95.4%. At the same time, for the LCP wave, the normalized intensity distribution shows a shift from one point (0°) to four points (90°) as shown in Figs. 3(d) and 3(e). The FWHM and focusing efficiency of the single focal point are 1.70 mm and 82.0%, and the FWHM and focusing efficiency of the four focal points are 1.55 mm (1.55 mm, 1.55 mm, and 1.55 mm) and 22.9% (22.9%, 22.9%, and 22.9%).

In the experiment, for RCP waves, normalized intensity profiles demonstrate a transition from two focal points (0 V) to a single point (200 V) as shown in Figs. 3(f) and 3(g). The FWHM and focusing efficiency of the bifocal function are 1.65 mm (1.65 mm) and 33.7% (44.7%), and the FWHM and focusing efficiency of the single focal function are 1.80 mm and 70.4%. Moreover, for the LCP wave, the normalized intensity distribution shows a shift from one point (0 V) to four points (200 V) as shown in Figs. 3(h) and 3(i). The FWHM and focusing efficiency of the single focal point are 1.80 mm and 65.1%, and the FWHM and focusing efficiency of the four focal points are 2.35 mm (2.35 mm, 2.35 mm, and 2.35 mm) and 14.3% (13.1%, 13.1%, and 18.2%).

Furthermore, the output vector optical fields on the focusing plane and ellipticity at the center of focal points of the LC integrated dynamic THz multi-focal metalens are presented in Fig. 4. We designate the center of the focal point of single focal, two focal, and four focal points as F1, F2, and F4, which are shown in Fig. 4(b), with their two-dimensional coordinates on the focal plane as (0,0), (−4.6,0), and (3.2,−3.2), respectively. Figure 4(a) presents the simulated output vector fields distribution as the θ increases from 0° to 90°. By extracting the polarization ellipticity of the focal center (F1, F2, and F4), the separation effect of the spatial-spin states and the dynamic polarization modulation characteristics controlled by voltage can be observed, as shown in Fig. 4(c). The results show that LCP and RCP states are completely separated spatially. As the θ increases, the polarization state at the central focus gradually transitions from LCP to RCP, while only energy changes occur without polarization state transformation at the two focal points and four focal points. When θ≤45°, the ellipticity at F2 remains below 36.5°, indicating the optical fields at these focal points approximate RCP waves. For θ>45°, rapid energy reduction makes polarization state measurements lose reference value. Similarly, polarization state measurements of the four focal light fields are only meaningful when θ≥45°, where ellipticity values at F4 all exceed 34.7°, indicating approximate LCP waves. F1 experiences almost no energy variation, but its polarization state gradually transforms from LCP to LP and then to RCP with ellipticity from 44° to 0° and then to −39.5°.

Figure 4(b) shows the polarization states at each focal point in the experiment, which are similar to the simulation. The statistically analyzed ellipticity values are presented in Fig. 4(d). The experimental results demonstrate complete spatial-spin separation of LCP and RCP states. As the applied voltage increases from 0 to 200 V, F1 undergoes a gradual polarization transition from LCP to RCP, while F2 and F4 only exhibit energy variations without polarization state transformation. Ellipticity at F2 remains below −25.7°, and at F4 exceeds 11.6°. At 0 V and 200 V conditions, these can still be characterized as RCP and LCP waves, respectively. F1 experiences a gradual polarization evolution from LCP to LP and finally to RCP with ellipticity from 30.8° to 0° and then to −34°. In short, the experimental results are consistent with the simulation results, proving that the device can achieve electrically modulated spatial-spin separation and multi-focal focusing. However, there are slight differences between the experimental results and the simulation results, mainly due to unsatisfactory Gaussian beams used in the experiment, discrepancies between the material model settings in the simulation and reality, and errors in device fabrication. Through the above improvements, it is believed that the actual working effect of the device can be further improved.

To investigate the spectral response properties of the experimentally generated beams, the intensity transmission spectra of the LCP and RCP at the geometric centers of F1, F2, and F4 are measured, as presented in Fig. 5. Firstly, the polarization conversion effect of the LC cascaded metasurface and the absorption characteristics of the LC material resulted in a higher intensity transmission of the single focus of the co-circularly polarized component at low frequencies, which gradually decreased with the increase of THz frequency, as shown in Figs. 5(a) and 5(d). Secondly, for the multi-focal focusing of cross circularly polarized components, the polarization conversion effect of LC cascaded metasurfaces also causes lower transmittance at the low frequency, while the high frequency is mainly due to the resonance effect of metasurfaces, which makes the structure unable to meet the spatial phase distribution required for focusing, resulting in an overall decrease in the transmittance of the device, as shown in Figs. 5(b) and 5(f). Moreover, as the applied voltage increases from 0 to 200 V, the single focal point demonstrates a monotonic increase in RCP wave transmittance as shown in Fig. 5(a) concurrent with a corresponding decrease in LCP wave transmittance as shown in Fig. 5(d): at 0.5 THz, RCP transmittance rises from 1.0% to 37.0% while LCP transmittance drops from 44.7% to 3.9%. The configuration of two focal points exclusively supports RCP waves, with intensity decreasing from 24.7% to 3.4% at 0.5 THz under increasing voltage, as shown in Figs. 5(b) and 5(c). Conversely, the four focal points configuration maintains LCP output because the transmittance is close to 0% as shown in Fig. 5(e), showing an intensity enhancement from 0.7% to 10.9% at 0.5 THz across the same voltage range as shown in Fig. 5(f). It can be seen that the dynamic modulation characteristics of the spectrum at a center frequency of 0.5 THz can still be observed. The working bandwidth of the device is defined as the frequency range where all channels meet an intensity transmittance of not less than half the intensity corresponding to the case when the intensity exceeds the center frequency (0.5 THz). Therefore, the working bandwidth is 0.44–0.55 THz.

Further, to investigate the spatial light field characteristics of the LC cascaded dynamic THz multi-focal metalens over a wide frequency band, we measured the intensity distribution and normalized total output power in the focal planes of 0 V and 200 V. The results at the selected three special frequency points are shown in Fig. 6. Figures 6(a) and 6(c) reveal the intensity distribution in the focal plane at different frequencies at 0 V and 200 V, respectively. At 0 V, the energy of the LCP wave is always concentrated at the center of the focal plane, while the RCP is distributed at the two focal points. At 200 V, the RCP exhibits a single focal point pattern, while the LCP is distributed at the four focal points. As shown in Fig. 6(b), despite the decrease in light intensity at non-design frequencies, the normalized total output power remains above 59.3% across 0.44–0.55 THz. At the center frequency (0.5 THz), the focusing effect is better, and the total normalized emission energy in the operating band is more than 54.9%, as shown in Fig. 6(d). These results are in good agreement with the prediction results, which confirm the tolerance of the broadband metasurface design to the spectral deviation and the effectiveness of the modulation mechanism.

Additionally, the performance of our proposed multi-focal metalens compared with other related research works in terms of working frequency, FWHM, focusing efficiency, and dynamic control method is exhibited in Table 1, which further indicates that the proposed device has excellent overall performance.Table 1.

Comparison with Other Metalenses

In summary, we propose a voltage-controlled LC cascaded THz multi-focal metalens, which enables electrically modulated spatial-spin separation and multi-focal focusing through cascading LC with tunable anisotropy and a metalens with spin-dependent focusing phase control. It combines spatial-spin separation with LC active control techniques, including the advantages of broadband, high efficiency, and dynamic control of the number of focal points and energy distribution. Within the 0.44–0.55 THz frequency band, by tuning the dielectric anisotropy of LCs, the cascaded device can change the focusing configuration of different circularly polarized waves: single-to-quadruple switching for LCP waves and dual-to-single transitions for RCP waves, and dynamic polarization conversion control can be performed at the central focus. Experimental results show that the LC-cascaded metalens achieves a measured FWHM of <2.35mm and a peak focusing efficiency of 70.4%. The normalized total output power exceeds 54.9% (LCP) and 85.1% (RCP) when the LC is along the x-axis, and exceeds 98.1% (LCP) and 59.3% (RCP) when the LC is along the y-axis. This device integrates spin multiplexing, spatial multiplexing, and LC active control technology, achieving precise dynamic non-mechanical control over the focus position, quantity, and distribution pattern of THz waves at the sub-wavelength scale. It is expected to achieve multi-target tracking, parallel data processing, and multi-area detection and spectral analysis, making it have broad application prospects in THz multi-channel wireless communication, high-throughput biosensing and imaging, and other fields.