Asymmetric transmission is defined as the difference in the total transmission between the forward and backward directions, exhibiting great potential applications such as directionally sensitive beam splitting [1,2], multiplexing [3], communications [4], and optical interconnection [5]. A typical method for asymmetric transmission is to break the time-reversal symmetry using an external magnetic field [6], time-varying component [7,8], or nonlinear materials [9], leading to a topological-protected edge mode (nonreciprocal transmission). Although this nonreciprocal edge mode is immune to backscattering, it suffers from complicated materials, external biases, and bulk configurations. Based on the conventional passive and linear materials (chiral metamaterials [10–14], asymmetric metallic gratings [15], traditional polarization devices [16], and photonic crystals [17]), the reciprocal asymmetric transmission is realized by manipulating the propagation direction of electromagnetic (EM) waves.

Metasurfaces, two-dimensional counterparts of metamaterials, can tailor the propagation direction, phase, and polarization of EM waves, providing a platform to manipulate asymmetric transmission in multiple degrees of freedom, i.e., polarization and phase modulation. Benefiting from the superior capability in the local manipulation of the wavefront of EM waves, a plethora of applications such as metalenses [18–26], wave plates [27–30], vortex beam convertors [31–33], and holograms [34–39] have been demonstrated. Nevertheless, devices based on a single-layered metasurface show symmetric transmission, i.e., identical transmission between the forward and backward directions. Recently, multilayered plasmonic metasurfaces have been proposed to demonstrate the asymmetric transmission. For example, Frese et al. [40] and Chen et al. [41] designed dual/triple-layered plasmonic metasurfaces to realize an asymmetric meta-hologram and directional Janus, respectively. Sun et al. [42] reported asymmetric dual-frequency meta-holograms based on a triple-layered transmissive metasurface. These metasurface-based asymmetric devices work in a narrow band because of their resonant unit cells. In addition, study on metasurface-based asymmetric focusing is limited. Here we propose and experimentally demonstrate the broadband asymmetric focusing in the terahertz (THz) region triggered by simultaneous manipulation of the propagation direction, phase, and polarization of THz waves. This directional device for asymmetric focusing consists of a geometric metasurface (with a nonresonant unit cell) and metallic gratings. Unlike previously demonstrated resonant metasurfaces with different structured unit cells, the geometric metasurface consists of identical microrods, and the manipulation of phase, polarization, and energy flux is realized by rotating the microrods (to generate geometric phase). Our designed dual-layered metasurfaces for asymmetric focusing can work in a wide bandwidth ranging from 0.6 to 1.1 THz. The approach for designing directional meta-devices may provide a robust platform in developing future high-performance devices that can manipulate EM waves in multiple degrees of freedom.

Figure 1 shows the schematic of an asymmetric focusing device. Upon the illumination of x-polarized THz waves in the forward direction, a focal point with orthogonal polarization is observed after the dual-layered metasurfaces. In contrast, for backward incidence, the focal point is not generated, leading to asymmetric focusing. This directional device consists of a geometric metasurface with spatially rotated microrods and metallic gratings, which act as a linear polarizer that can transmit x-polarized THz waves and reflect y-polarized THz waves. The geometric metasurface is designed to simultaneously control the phase (for focusing) and polarization (for polarization rotation), generating a focal point with orthogonal polarization relative to incident THz waves. Since a linearly polarized THz beam consists of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) components with the same amplitude, two opposite phase profiles [see Eq. (1)] should be required to focus both the LCP and RCP components: where f is the focal length and λ is wavelength. Therefore, the focused LCP and RCP components [induced by phase modulations in Eq. (1)] with the same amplitude can be combined into a linearly polarized focal spot. Another bulk phase α that can be generated by rotating each microrod with an angle of α/2 should be introduced into the geometric metasurface to rotate the polarization orientation of the focal spot. Therefore, the desired phase profile of the geometric metasurface is governed by where α=90° is the polarization rotation angle of the focal spot.

To manipulate the incident THz waves based on geometric phase, each microrod should be designed as a quasi-perfect half-wave plate. The optimized structure parameters of a gold microrod are as follows: the width and length of the rods are w1=50μm and l=160μm [see Fig. 2(a₁)], and the period is 170 μm. Under the illumination of circularly polarized THz waves, the transmitted THz waves will contain two parts: one is the co-polarized THz waves, and the other is the cross-polarized THz waves. When the microrod is rotated counterclockwise/clockwise with an angle θ, the cross-polarized THz waves will be added with an additional phase delay of ≈±2θ as shown in Fig. 2(a₂). Figure 2(b₁) shows the schematic of metallic gratings where the long side of each grating is along the y axis. The width and period of these metallic gratings are 20 μm and 40 μm, respectively. As shown in Fig. 2(b₂), the transmission for the incident x-polarized THz waves is much higher than that of the incident y-polarized THz waves. By introducing a geometric metasurface (with gold microrods) and metallic (gold) gratings [on the other side of the polyimide film (with permittivity of ε=3.5+0.035i)], asymmetric transmission is realized [see Figs. 2(c₁) and 2(d₂)]. For forward x-polarized incidence, the transmission is more than 82%, ranging from 0.6 to 1.1 THz, while it is lower than 52% under the the illumination of x-polarized THz waves from the backward direction, demonstrating an asymmetric transmission that can work in a broad bandwidth.

Figure 3 shows numerical simulations of asymmetric focusing. The size of this final metasurface composed of 80×80 microrods is 1.36cm×1.36cm. Based on the finite-difference time-domain (FDTD) method, the electric field distributions of asymmetric focusing are calculated and shown in Figs. 3(a₁)–3(f₂). For simplicity, we calculated (and measured) electric field distributions at 0.6, 0.85, and 1.1 THz to show the broadband characteristic of our directional devices. Figure 3(a₁) shows the electric field distribution of x-polarized transmission for forward THz waves at f=0.6THz. The polarization of one focal spot observed at z=2.0mm is along the y axis, which is orthogonal to the polarization of the incident THz waves, while the focal spot [see Fig. 3(b₁)] is not generated for backward incidence, leading to asymmetric focusing. Here the mechanism of the asymmetric focusing can be understood as follows: for forward incidence, the x-polarized THz waves are almost completely transmitted through the metallic gratings and simultaneously interact with the metasurface (microrods with different orientations). Therefore, the transmitted x-polarized THz waves are partly converted into y-polarized THz waves and simultaneously focused into a focal spot. In contrast, for backward incidence, a portion of the waves interact with the metasurface and are converted into y-polarized THz waves. Then the converted waves are reflected completely after interacting with metallic gratings. The other part of nonconverted (x-polarized) THz waves can pass through metallic gratings. However, the nonconverted THz waves are not modulated by the metasurface and thus cannot be focused into a focal spot for backward waves. The detailed mechanism of asymmetric focusing under the illumination of x-polarized (and y-polarized) THz waves in the forward and backward directions is given in Appendix A. Figures 3(a₂) and 3(b₂) show electric field distributions in the x−y plane (z=±2.0mm). For forward transmission, a circularly shaped focal spot is observed at the real focal plane (z=2.0mm), while it cannot be generated (at z=−2.0mm) for the backward case [see Figs. 3(a₂) and 3(b₂)]. When f=0.85 THz (1.1 THz), a focal point located at z=3.5mm (z=5.5mm) with polarization along the y axis is observed for forward incidence as shown in Figs. 3(c₁) and 3(e₁). In comparison with Figs. 3(a₁), 3(c₁), and 3(e₁), the distance between the focal spot and the device is getting longer and longer due to the chromatic aberration. The focal spot cannot be generated for backward incidence [see Figs. 3(d₁) and 3(f₁)]. The corresponding electric field distributions in the x−y plane are shown in Figs. 3(c₂)–3(f₂), demonstrating asymmetric focusing between the forward and backward directions. The calculated efficiencies of the directional device at these three frequencies are 23.03%, 26.7%, and 21.34%, respectively. The calculated electric field (|Ex|2) distributions and the performances (broadband property, size, and excitation ratio of the focal spot) of this directional device are given in Appendix B and Appendix C, respectively. In addition, the focusing properties under the illumination of THz waves with different incident angles are shown in Appendix D.

In experiment, we utilize near-field terahertz microscopy (NSTM) [26,43] to detect field distributions. The position of the THz source and THz tip are fixed while the sample is rotated along the y axis to measure the field distributions under the illumination of THz waves in the forward and backward directions. For forward x-polarized incidence (with working frequency of 0.6 THz), a focal point is generated with polarization along the y axis (at z=2.0mm) as shown in Fig. 4(a₁). In contrast, the focal spot is not generated for backward incidence [see Figs. 4(b₁)], resulting in asymmetric focusing. Figures 4(c₁)–4(f₁) show the measured electric field distributions at 0.85 THz and 1.1 THz, respectively. Under the illumination of x-polarized THz waves in the forward direction, a focal spot located at 3.5 mm (or 5.5 mm) is observed as shown in Figs. 4(c₁) and 4(e₁), while this focal spot cannot be generated for backward incidence [see Figs. 4(d₁) and 4(f₁)]. The measured electric field distributions in the x−y plane at z=±2.0mm, ±3.5mm, ±5.5mm are shown in Figs. 4(a₂)–4(f₂), and they also reveal the asymmetric functionality. The measured efficiencies of the directional device at f=0.6, 0.85, and 1.1 THz are 20.6%, 25.3%, and 20.3%, respectively. The experimental results are matched well with the numerical simulations, except for a slight discrepancy, which can be attributed to the fabrication error and nonperfect half-wave plate of each microrod. In addition, the signal-to-noise ratio of the THz source (in the experiment) decreases with the increase of the frequency, and thus the focal spot is distorted in comparison with the case in simulation. The measured electric field (|Ex|2) distributions and the performances (size and excitation ratio of the focal spot) of the directional device are given in Appendix B and Appendix C, respectively.

Our approach can not only manipulate asymmetric transmission with one focal point but also enable the capability to harness the multiple focal points with functionality of asymmetric transmission. We numerically demonstrate the asymmetric transmission with longitudinal and transverse multiple focal spots as shown in Fig. 5. The corresponding phase profile requirements of the longitudinal and transverse multiple focal spots are written as where φLCP1/φRCP1 and φLCP2/φRCP2 have the same formula as shown in Eq. (1) but different focal length [f1 (focal length) for φLCP1 and φRCP1, while f2 (focal length) for φLCP2 and φRCP2]. φLCP3(x,y)=−φRCP3(x,y)=2πλ[(x−xi)2+y2+f2−f] and φLCP4(x,y)=−φRCP4(x,y)=2πλ[(x−xj)2+y2+f2−f]. The designed parameters are xi=−xj=1mm, f1=4mm, f2=6mm, and f=4mm. Figure 5(a) shows the electric field (|Ey|2) distribution of the asymmetric transmission of longitudinal multiple focal spots upon the illumination of x-polarized THz waves (at 0.85 THz) from the forward direction. Two separated focal points located at z=3.9mm and z=5.9mm are observed along the longitudinal direction. Here the discrepancy in focus spot position between theoretical design and numerical simulation results from the nonperfect half-wave plate of the microrods. When the x-polarized THz waves interact with the geometric metasurface (with the phase profile shown in ΦT), two transversely distributed focal points located at (x=1mm, z=3.9mm) and (x=−1mm, z=3.9mm) are generated as shown in Fig. 5(c). These two focal points are not generated for backward incidence as shown in Figs. 5(b) and 5(d). The calculated efficiencies of the asymmetric transmission with longitudinal and transverse focal spots are 23.93% and 25.35%. The calculated electric field (|Ex|2) distributions and the performances (excitation ratio of the focal spot) of the directional device are given in Appendix B and Appendix C, respectively.

The approach can be utilized to design ultrathin and ultraflat geometric metasurfaces by simultaneously controlling the polarization, phase, and transmission direction in all spatial dimensions, leading to unprecedented capabilities in developing multifunctional components and ultrathin systems. Typically, the asymmetric functionality of our designed metasurfaces can be traditionally realized by putting together a lens, a half-wave plate, and a linear polarizer. However, the conventional devices should typically be thick enough and exhibit certain surface topography to ensure the gradual phase accumulation (along the propagation direction) to realize the desired wave-manipulating functionalities. The thickness of these traditional THz elements is up to the order of centimeters, resulting in a large and bulky functional device. Since device miniaturization and system integration are two continuing trends for next-generation integration-optics applications, our designed directional device opens a new avenue to address the aforementioned issues. The thickness of the metasurface and metallic gratings is 0.15 μm, while it is 30 μm for the spacer (polyimide). The total thickness of the device is 30.3 μm, which is an order of 0.09λ0 (λ0 is the central working wavelength of the designed device). Therefore, the uniqueness and robustness of our proposed approach may provide a platform for designing future multifunctional and ultracompact devices. The sample fabrication is given in Appendix E. In addition, the efficiency plays an important role for device performance. The efficiency of the directional device is more than 20% [in simulation (see Fig. 10)] ranging from 0.6 to 1.1 THz. For the traditional devices, the efficiency of the THz lens (half-wave plate and linear polarizer) is about 52% (75% and 90%). Therefore, the total efficiency of the asymmetric focusing (realized by traditional devices) is about 35%. In comparison with the traditional bulk devices, our designed directional device not only shows a comparable performance in the efficiency but also enables the ability to design ultrathin devices.

From the practical point of view, some other distinct properties of the designed directional device are of great interest. Unlike traditional asymmetric transmission, which only controls the propagation direction of EM waves, the developed directional device can simultaneously control the polarization, phase, and transmission direction, leading to a directional metalens. As is well known, lenses can be applied for imaging. Recently, various types of metalenses such as dual-polarity plasmonic metalenses [18,19], achromatic metalenses [23,44], metalens arrays [45], and polarization-dependent metalenses [26,46] have been developed for imaging. However, all of the previous metalenses are symmetric in the forward and backward directions. The developed directional metalens can be applied for unidirectional imaging, which means that we can grab information/imaging from the “enemy” side and avoid our own information being detected. As a result, the designed ultrathin device can have an immediate impact on information security and cloaking. Moreover, the proposed approach can be extended to design asymmetric transmission with multiple focal points, while a traditional lens generates only one focal point. Therefore, the flexible design will enable the directional metalens with unprecedented functions that are impossible to achieve by traditional lenses. Due to the simplicity and robustness of the method, our approach can be easily extended into the visible and IR frequency regions by designing the metasurface and metallic gratings with proper sizes, i.e., the same structure with reduced size. While remarkable progress has been achieved, great challenges, i.e., further enhancement of the focusing efficiency and asymmetric focusing under oblique incidence, exist that provide new opportunities for future studies.

In conclusion, we have proposed and experimentally demonstrated an approach to realizing asymmetric focusing in the THz region. Based on a geometric metasurface and polarization-selective gratings, a focal spot is observed under the illumination of x-polarized THz waves in the forward direction, while this focal spot is not generated for backward incidence. This metasurface-based directional device works in a broad bandwidth ranging from 0.6 to 1.1 THz. The robust approach can be also extended to design asymmetric transmission with multiple focal points. The presented dual metasurfaces are a powerful tool that can not only flexibly control the wavefront of EM but also open a new window to manipulate the propagation direction of EM waves.