1Terahertz Technology Innovation Research Institute, Terahertz Spectrum and Imaging Technology Cooperative Innovation Center, Shanghai Key Laboratory of Modern Optical System, University of Shanghai for Science and Technology, Shanghai 200093, China
2Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai 200092, China
The manipulation of polarization in the longitudinal direction using metasurfaces introduces a new dimension for controlling polarization states. Previous research has primarily focused on creating a single beam with a linearly polarized state that varies along the optical path. Nevertheless, this unexplored territory offers vast opportunities for longitudinally polarization-variant applications. Here, we present and experimentally demonstrate an innovative approach that can transform the linearly polarized (LP) terahertz (THz) waves into multiple pencil-like beams, featuring diverse, longitudinally varying polarization behaviors. We characterize a series of metadevices capable of mimicking the longitudinal polarization evolution between two orthogonal LP states, i.e., circularly polarized (CP) states and hybrid-polarized states (elliptically and arbitrarily polarized states) (i.e., the evolution between orthogonal LP and CP states), in the longitudinal direction. In addition, we experimentally demonstrate a wide range of polarization-switchable imaging modalities in the propagation direction, which we term “polarization-evolutive imaging.” This work not only expands the role of polarization in imaging with multiplexed functionalities but also paves the way for developing other metadevices that can perform unique tasks such as ultrahigh-bandwidth data exchange and versatile light–matter interactions.
【AIGC One Sentence Reading】:Metasurfaces enable multiplexing of pencil-like beams with varying polarization states, paving the way for polarization-evolutive imaging and versatile applications.
【AIGC Short Abstract】:Metasurfaces enable the creation of multiple pencil-like THz beams with longitudinally varying polarization states. We demonstrate metadevices that transform LP waves into diverse polarization behaviors, including CP and hybrid states. Polarization-evolutive imaging, showcasing a range of imaging modalities, is also achieved. This work advances polarization control in imaging and opens avenues for novel metadevice applications.
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1. INTRODUCTION
Polarization is a fundamental property of electromagnetic waves. Manipulation of polarization field in the transverse plane has revolutionized various fields, including its applications to polarization imaging [1,2], optical displays [3], and quantum communication [4]. Moreover, polarization plays a crucial role as an essential information carrier in light–matter interactions, enabling unprecedented capability in identifying and detecting materials’ composition [5,6], morphology [7], and structural information [8]. Therefore, the versatile manipulation of polarization plays a vital role in fundamental research and practical applications. For scalar fields with homogeneous polarization distributions, traditional techniques for manipulating polarization include specular reflection, birefringence, and dichroism. These methods enable the conversion of initial polarization state into desired output by using spatial phase modulators, wave retarders (e.g., polarizers and wave plates), beam splitters, etc. However, electromagnetic (EM) waves with nonuniform polarization distributions (that are vector fields) require a more sophisticated approach. By introducing cascaded polarizing elements [9,10], such nonuniform polarization distribution can be realized. Unfortunately, the traditional techniques for manipulating polarization states are often limited to modulating polarization states in the transverse plane and typically require complex systems comprising multiple optical elements.
The advent of metasurfaces has revolutionized the manipulation of electromagnetic waves. By designing 2D meta-atoms with precise shapes and orientations, metasurfaces offer an ultracompact and flexible platform to accurately tailor the amplitude, phase, and polarization of EM waves at subwavelength resolution [11,12]. Benefiting from the ultrathin, integrated, and miniaturized characteristics, metasurfaces have been proposed to design a plethora of efficient functional devices, including beam steering [13–16], vortex generators [17–22], metalens [23–30], and holograms [31–36]. By leveraging metasurfaces with delicately designed structures, researchers have developed innovative approaches to manipulate polarization along the optical path. For instance, metasurface-based platforms have enabled the generation of homogeneous polarization distributions [37–42] and inhomogeneous polarization distributions with spiral phase named “vector vortex generators” [43–47]. Further, recent advancements have demonstrated the manipulation of polarization states along the optical path, transforming an incident waveform into an ensemble of pencil-like beams with varying polarization states in the longitudinal direction [41,42]. This capability can be extended to the generation of scalar vortex beams with topological charges evolving along the optical path. Additionally, metasurfaces have been used to create longitudinally varying vector vortex beams or structured vector fields by tailoring orthogonal helical components [48–50]. Moreover, spin-polarization multiplexing encoding techniques have enabled the longitudinal manipulation of scalar fields to vector fields [51]. These breakthroughs have expanded our capabilities in modulating polarization and opened avenues for exploring new applications. While existing architectures primarily focus on the generation of a single beam with linear polarization states varying along the optical path, there remains an unexplored avenue for applying polarization-switchable functions in the propagation direction.
In this paper, we present a unique approach for designing all-dielectric metasurfaces that can produce multiple pencil-like beams with longitudinally varying polarization states, leading to polarization-switchable imaging. By breaking the spin-locking constraint in geometric metasurfaces, we demonstrate the ability to tailor separate phase functions within two orthogonal helical channels, allowing for the creation of multiple pencil-like beams with varied polarization states along the propagation direction. Our approach is based on synthesizing two orthogonal helical components into - and -polarized focal points with partial overlap by precisely controlling each focal length. Upon illumination of LP THz waves, we numerically and experimentally demonstrate the generation of two pencil-like beams with longitudinally inhomogeneous LP, CP, and hybrid-polarized states using three designed metasurfaces. Furthermore, we experimentally verify polarization-switchable imaging capabilities, including linear- and circular-polarization switching along the optical path. This unique approach enables the manipulation and superposition of two helical components, allowing for the generation of multiple pencil-like beams with longitudinally inhomogeneous versatile polarization distributions and polarization-evolutive applications, which has significant implications for tunable structured light and light–matter interactions in three dimensions.
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2. PRINCIPLE AND DESIGN
The operating principle behind our designed metasurface for generating multiple pencil-like beams with longitudinally inhomogeneous versatile polarization states is illustrated in Fig. 1(a). Under the illumination of LP THz waves, the designed metasurface is capable of transforming incident light into two distinct pencil-like beams. One beam exhibits a longitudinal polarization evolution, transitioning from to polarized along the propagation direction, while the other beam enables a different polarization evolution from the LCP to RCP state. The LP incidence of THz waves can be decomposed into two orthogonal helical components, i.e., LCP and RCP with identical amplitude. By embedding different focusing phases and initial phases into the incident LCP and RCP components, we can achieve the desired functionality and express the required phase profile as follows: where and are the phase requirements for focusing the incident LCP and RCP components into and focal points, and . is the phase requirement of a metasurface, which can generate multiple pencil-like beams with longitudinally inhomogeneous versatile polarization states, while (, , and ) is defined as a polarization-rotated angle. To generate two pencil-like beams depicted in Fig. 1(a), we manipulate the incident LCP/RCP component using a metasurface with a phase profile encoded according to Eq. (3). The component is then focused into three RCP/LCP focal points with distinct focal lengths, where . When -polarized THz waves are incident and (or ), the incident LCP/RCP component is focused into an RCP/LCP focal point with the focal length of (or ). A -polarized focal point (or -polarized focal point) is generated at the focal plane (or ), and these two LP focal points are partially overlapped, resulting in a pencil-like beam that exhibits longitudinal polarization evolution from a - to -polarized state. Meanwhile, the incident LCP/RCP component is also focused into RCP/LCP focal point with a focal length of and , and these two CP-based focal points are partially overlapped as well, giving rise to another pencil-like beam that exhibits longitudinal polarization evolution from LCP state to RCP state. The polarization-evolutive imaging is schematically illustrated in Fig. 1(b), where imaging samples are placed at different transverse planes within the pencil-like beams to demonstrate polarization-switchable imaging.
Figure 1.Schematic of the spin-decoupled metasurfaces for the generation of multiple pencil-like beams with longitudinally inhomogeneous versatile polarization states and polarization-evolutive imaging. (a) A metasurface that can generate two pencil-like beams with longitudinally inhomogeneous versatile polarization states. (b) Schematic of the same metasurface for polarization-evolutive imaging.
To achieve the proposed functions, we designed and numerically optimized three metasurfaces comprising anisotropic meta-atoms with an identical shape but different in-plane orientations, as shown in Figs. 2(a)–2(f). The operating frequency is fixed at 0.6 THz, and the phase and intensity maps of transmission in copolarization for - and -polarized incidence are shown in Figs. 2(a)–2(d). The optimized structural parameters are as follows: (period); (length); (width); (height of meta-atom); and (thickness of substrate). Each meta-atom can be considered a quasi-half-wave plate that can efficiently control the polarization state of incident THz wave. Under the illumination of - and -polarized THz waves, the transmissivity of the - and -polarizations is 92% [Fig. 2(e)], with an efficiency of polarization conversion between the transmitted RCP THz waves and the incident LCP THz waves of approximately 92% [blue curve in Fig. 2(f)] at 0.6 THz. Additionally, the phase difference between the transmitted electric fields in the and directions is nearly [orange curve in Fig. 2(f)]. It should be noticed that the spin-decoupled functionality of our designed metalenses relies solely on pure geometric phase (see the detailed discussion in Ref. [29]), in contrast with the combination of geometric phase and propagation phase utilized in Refs. [19–22,25,30]. The fabricated samples are shown in Figs. 2(g)–2(i), which demonstrate the generation of two pencil-like beams to mimic longitudinal polarization evolution between two orthogonal LP states [Fig. 2(g)], circularly polarized (CP) states [Fig. 2(h)], and hybrid-polarized states [Fig. 2(i)], respectively.
Figure 2.Design of metasurfaces and optical images of samples. (a) and (b) Phase maps of a meta-atom versus the structural parameters and under the illumination of (a) - or (b) -polarized THz waves. (c) and (d) Intensity maps of transmission in copolarization for (c) - or (d) -polarized incidence. (e) The transmission spectra of the selected meta-atom under the illumination of - (red curve) or -polarized (black curve) THz waves. (f) The polarization conversion efficiency (blue curve) between the transmitted RCP and incident LCP THz waves and phase difference (orange curve) between the transmitted electric fields in the and directions. (g), (h), and (i) Optical images of the three fabricated samples.
As a proof-of-concept study, we designed and experimentally demonstrated a metasurface capable of generating two pencil-like beams with longitudinal polarization evolution between two orthogonal LP states, as shown in Fig. 3. In Figs. 3(a1) and 3(a2) for the incidence of -polarized THz waves, two - and -polarized focal points are generated after the metasurfaces.
Figure 3.Electric-field intensity and polarization distributions of pencil-like beams with the longitudinal polarization evolution between two orthogonal LP states. (a1)–(a3) and (h1)–(h3) The simulated and measured -polarized (a1), (h1), -polarized (a2), (h2), and total (a3), (h3) electric-field intensity distributions after the designed geometric metasurface. (b1)–(b5)/(c1)–(c5) and (i1)–(i5)/(j1)–(j5) The simulated and measured polarized electric-field intensity distributions for the left pencil-like beam at the different transverse () plane. (d1)–(d5) and (k1)–(k5) The simulated and measured polarization distributions for the left pencil-like beam at the different transverse plane. (e1)–(e5)/(f1)–(f5) and (l1)–(l5)/(m1)–(m5) The simulated and measured polarized electric-field intensity distributions for the right pencil-like beam at the different transverse () plane. (g1)–(g5) and (n1)–(n5) The simulated and measured polarization distributions for the right pencil-like beam at the different transverse plane.
The two -polarized focal points are located at (, 0, 6.3 mm) and (1.5 mm, 0, 7.5 mm), while the -polarized focal points are located at (, 0, 7.5 mm) and (1.5 mm, 0, 6.3 mm). Since these two focal points with two orthogonal LP states and located at (, 0, 6.3 mm) and (, 0, 7.5 mm) are partially overlapped with each other, they are merged into a pencil-like beam [the left beam in Fig. 3(a3)]. Similarly, another pencil-like beam can be obtained just by synthesizing two partially overlapped focal points with orthogonal LP states and located at (1.5 mm, 0, 6.3 mm) and (1.5 mm, 0, 7.5 mm) [the right beam in Fig. 3(a3)]. To demonstrate the polarization evolution of these two pencil-like beams, the electric-field intensity distributions and the synthetic polarization distributions (from the electric-field intensity distributions) in the longitudinal direction are numerically simulated in Figs. 3(b1)–3(g5). As shown in Figs. 3(b1)–3(b5) for the -polarized electric-field intensity distributions of the left pencil-like beam, the intensity in the plane is decreased with the detection plane switched from to , while the -polarized electric-field intensity of the left pencil-like beam is increased with the detection plane switched from to , as shown in Figs. 3(c1)–3(c5). The synthetic polarization distributions of the left pencil-like beam in the longitudinal direction are shown in Figs. 3(d1)–3(d5), which demonstrate that the polarization is evolved from the - to -polarized state. In contrast, the polarized electric-field intensity distributions (in the plane) of the right pencil-like beam are increased/decreased with the gradual enhancement of the distance between the metasurface and detection plane, as shown in Figs. 3(e1)–3(f5). The synthetic polarization distributions shown in Figs. 3(g1)–3(g5) demonstrate that the polarization evolution of the right pencil-like beam is transformed from the - to -polarized state. The measured electric-field intensity distributions in the plane are shown in Figs. 3(h1)–3(h3), where two -polarized focal points [Fig. 3(h1)] and -polarized focal points [Fig. 3(h2)] are observed, and two pencil-like beams are generated [Fig. 3(h3)] due to the partial overlap between - and -polarized focal points. The electric-field intensity distributions and polarization evolutions of the left and right pencil-like beams are experimentally demonstrated in Figs. 3(j1)–3(k5) and Figs. 3(l1)–3(n5), respectively. The experimental results show that the polarization evolution of the left/right pencil-like beam is transformed from - to -polarized state. The experimental results are matched well with the numerical simulations, except for a slight discrepancy in polarization distributions, which can be attributed to the fabrication and testing errors. The robust approach can be extended to design a metasurface that can generate much more pencil-like beams with the longitudinal polarization evolution between two orthogonal LP states (Appendix A).
Although a beam with longitudinally inhomogeneous polarization states has been demonstrated, the applications for the varied polarization in the optical path have not been explored thus far. To demonstrate the applications of pencil-like beams in the longitudinal direction, an imaging sample consisting of two letters, W and E, is designed and fabricated [Figs. 4(a) and 4(b)] to realize the polarization-switchable imaging. The letters W and E consist of periodically arranged metal slits coating on the polyimide (PI) film, where the metallic slits in letters W/E are parallel to the axis, resulting in the polarization-selection function (which is demonstrated in Appendix B). To demonstrate the polarization-switchable imaging, the metasurface and THz detector are fixed, while the imaging sample is scanning/shifting at the different transverse plane of a pencil-like beam to reveal the desired imaging. As shown in Figs. 4(c1)–4(c3) for the imaging sample located at the different transverse plane in the left pencil-like beam, the letters E, WE, and W are, respectively, observed at , 6.7, and 7.7 mm, demonstrating the polarization-switchable imaging. In other words, one can display the whole or a part of an image by using such a pencil-like beam. In contrast, when the imaging sample is located in different transverse planes of the right pencil-like beam, the switchable display among letters W, WE, and E can be realized (at , 6.7, and 7.7 mm), as shown in Figs. 4(d1)–4(d3). The numerical demonstrations of polarization-switchable imaging shown in Figs. 4(e1)–4(f3) are matched well with the measured results.
Figure 4.Polarization-switchable imaging based on the designed metasurface that shows two pencil-like beams with the longitudinal polarization evolution between two orthogonal LP states. (a) and (b) The schematic and optical images of the designed imaging sample consisting of the letters W and E. (c1)–(c3) and (e1)–(e3) The simulated and measured electric-field intensity distributions for the imaging sample located at different transverse planes of the left pencil-like beam. (d1)–(d3) and (f1)–(f3) The simulated and measured electric-field intensity distributions for the imaging sample located at different transverse planes of the right pencil-like beam.
Our proposed approach can be further extended to a design metasurface for the generation of multiple pencil-like beams with the longitudinal polarization evolution between two orthogonal CP states. As shown in Figs. 5(a1) and 5(a2) for the incidence of LP THz waves, two LCP [Fig. 5(a1)] and RCP [Fig. 5(a2)] focal points are generated after the designed metasurface, while the left/right two focal points with orthogonal CP states are partially overlapped to form a pencil-like beam, resulting in two pencil-like beams with longitudinally switchable CP states [Fig. 5(a3)]. To reveal the polarization properties of the left pencil-like beam, the electric-field intensity distributions at different transverse planes (in the left pencil-like beam) are as calculated in Figs. 5(b1)–5(b5) and Figs. 5(c1)–5(c5), in which the LCP/RCP electric-field intensity is increased/decreased with the detection plane switched from to . Therefore, the synthetic polarization distributions of such a pencil-like beam in the longitudinal direction are evolved from LCP, LECP (left-handed elliptically polarized), LP, RECP (right-handed elliptically polarized) to RCP state, as shown in Figs. 5(d1)–5(d5). The LCP and RCP electric-field intensity distributions at different transverse planes (in the right pencil-like beam) are numerically simulated and shown in Figs. 5(e1)–5(e5) and Figs. 5(f1)–5(f5), and the synthetic polarization distributions of such a pencil-like beam in the longitudinal direction are transformed from RCP, RECP, LP, LECP to the LCP state, as demonstrated in Figs. 5(g1)–5(g5). The measured electric-field intensity distributions in the plane are shown in Figs. 5(h1)–5(h3), which demonstrate that these two pencil-like beams are generated by combining LCP and RCP focal points with partial overlap. The measured electric-field intensity distributions and polarization evolution at the different transverse planes (in these two pencil-like beams) are as illustrated in Figs. 5(i1)–5(m5), which agree well with the calculated results. The measured focal spots are slightly larger than the simulated focal spots, which can be attributed to the fabrication and measurement errors. The generation of more pencil-like beams with the longitudinal polarization evolution between two orthogonal CP states based on our proposed approach is also numerically simulated and demonstrated in Appendix C. The detailed simulation methods and experimental measurements are supplied in Appendix D.
Figure 5.Electric-field intensity and polarization distributions of pencil-like beams with the longitudinal polarization evolution between two orthogonal CP states. (a1)–(a3) and (h1)–(h3) The simulated and measured LCP (a1), (h1), RCP (a2), (h2), and total (a3), (h3) electric-field intensity distributions after the designed geometric metasurface. (b1)–(b5)/(c1)–(c5) and (i1)–(i5)/(j1)–(j5) The simulated and measured LCP/RCP electric-field intensity distributions for the left pencil-like beam at the different transverse () plane. (d1)–(d5) and (k1)–(k5) The simulated and measured polarization distributions for the left pencil-like beam at the different transverse plane. (e1)–(e5)/(f1)–(f5) and (l1)–(l5)/(m1)–(m5) The simulated and measured LCP/RCP electric-field intensity distributions for the right pencil-like beam at the different transverse () plane. (g1)–(g5) and (n1)–(n5) The simulated and measured polarization distributions for the right pencil-like beam at the different transverse plane.
In addition to realizing the LP-switchable imaging, the designed metasurface for generating multiple pencil-like beams with the longitudinal polarization evolution between two orthogonal CP states also can be applied to the CP-switchable imaging. To demonstrate this application, a CP-dependent imaging sample consisting of numbers 6 and 9 is designed and fabricated, as shown in Figs. 6(a) and 6(b). The sample consists of meta-atoms with a split-ring-stripe hybrid structure and metallic gratings. For the opening orientation of the hybrid structure along the antidiagonal/diagonal direction, LCP/RCP THz waves nearby 0.6 THz can be transmitted through the designed imaging target 9/6. The corresponding transmission spectra for the hybrid structure are also shown in Appendix B. When such CP-dependent imaging sample is located in the left pencil-like beam, the numbers 6, 69, and 9 are, respectively, revealed at , 6.7, and 7.7 mm, resulting in CP-switchable imaging [Figs. 6(c1)–6(c3)]. On the contrary, the numbers 9, 96, and 6 can be observed at , 6.7, and 7.3 mm, when the same CP-dependent imaging sample is located in the right pencil-like beam, as shown in Figs. 6(d1)–6(d3). The numerical demonstrations of the CP-dependent imaging are shown in Figs. 6(e1)–6(f3), which agree well with the measured results.
Figure 6.Polarization-switchable imaging based on the designed metasurface that shows two pencil-like beams with the longitudinal polarization evolution between two orthogonal CP states. (a) and (b) The schematic and optical images of the designed imaging sample consisting of numbers 6 and 9. (c1)–(c3) and (e1)–(e3) The simulated and measured electric-field intensity distributions for the imaging sample located at different transverse planes of the left pencil-like beam. (d1)–(d3) and (f1)–(f3) The simulated and measured electric-field intensity distributions for the imaging sample located at different transverse planes of the right pencil-like beam.
The robust approach cannot only tailor the longitudinal polarization evolution between two orthogonal LP states or CP states but also enables the capability to simultaneously harness the orthogonal LP states and CP states in the propagation direction. Figure 7 shows the simulated and experimental demonstrations of a metasurface to generate two pencil-like beams, in which one beam enables the longitudinally varying CP states, while the other beam possesses the longitudinally varying LP states. Upon the illumination of LP THz waves, the left pencil-like beam in Fig. 7(a4) consists of two partially overlapped focal points with two orthogonal CP states, as shown in Figs. 7(a1) and 7(a2). In addition, the right pencil-like beam in Fig. 7(a4) is composited by two partially overlapped focal points with two orthogonal LP states [Figs. 7(b1) and 7(b2)]. To reveal the polarization evolution of the left pencil-like beam in the longitudinal direction, the electric-field intensity distributions and the synthetic polarization distributions are numerically simulated in Figs. 7(c1)–7(e5). The LCP/RCP electric-field intensity decreased/increased for the detection plane switched from to [Figs. 7(c1)–7(c5) and Figs. 7(d1)–7(d5)], and the synthetic polarization distributions gradually evolved from LCP state to RCP state [Figs. 7(e1)–7(e5)]. Figures 7(f1)–7(h5) show the electric-field intensity distributions and the synthetic polarization distributions in different transverse planes of the right pencil-like beam. The polarized electric-field intensity decreased/increased for the detection plane switched from to [Figs. 7(f1)–7(f5) and Figs. 7(g1)–7(g5)], while the synthetic polarization distributions switched from the - to -polarized state [Figs. 7(h1)–7(h5)]. The measured electric-field intensity distributions and the synthetic polarization distributions are shown in Figs. 7(i1)–7(p5), which are matched with the calculated results, demonstrating the generation of multiple pencil-like beams with the longitudinal polarization evolution between two orthogonal CP and LP states. The generation of more pencil-like beams with the longitudinal polarization evolution between two orthogonal LP and CP states based on our proposed approach is also numerically demonstrated in Appendix E.
Figure 7.Electric-field intensity and polarization distributions of pencil-like beams with the longitudinal polarization evolution between two orthogonal LP and CP states. (a1)–(a3) and (i1)–(i3) The simulated and measured LCP (a1), (i1), RCP (a2), (i2), and total (a3), (i3) electric-field intensity distributions for the left focal point. (b1)–(b3) and (j1)–(j3) The simulated and measured LCP (b1), (j1), RCP (b2), (j2), and total (b3), (j3) electric-field intensity distributions for the right focal point. (a4) and (i4) The simulated and measured electric-field intensity distributions after the designed metasurface. (c1)–(c5)/(d1)–(d5) and (k1)–(k5)/(l1)–(l5) The simulated and measured LCP/RCP electric-field intensity distributions for the left pencil-like beam at the different transverse () plane. (e1)–(e5) and (m1)–(m5) The simulated and measured polarization distributions for the left pencil-like beam at the different transverse plane. (f1)–(f5)/(g1)–(g5) and (n1)–(n5)/(o1)–(o5) The simulated and measured -polarized electric-field intensity distributions for the right pencil-like beam at the different transverse plane. (h1)–(h5) and (p1)–(p5) The simulated and measured polarization distributions for the right pencil-like beam at the different transverse plane.
The polarization-switchable imaging based on the above-mentioned metasurface (Fig. 7) was also experimentally demonstrated, as shown in Fig. 8. Figures 8(a)–8(d) show the theoretical designs and optical images for the CP-based [Figs. 8(a) and 8(b)] and LP-based [Figs. 8(c) and 8(d)] imaging samples. As shown in Figs. 8(e1)–8(e3) for the CP-based imaging sample (consisting of numbers of 7 and 0) located in the left pencil-like beam, the measured electric-field intensities for numbers of 7, 70, and 0 are, respectively, revealed at , 6.7, and 7.3 mm, demonstrating the CP-switchable imaging. When the LP-based imaging sample (which is composite of the letters H and V) is located at the right pencil-like beam, the measured electric-field intensities for letters V, HV, and H are observed at , 6.7, and 7.3 mm, resulting in the LP-switchable imaging [Figs. 8(f1)–8(f3)]. The numerical simulations in Figs. 8(g1)–8(h3) are in accordance with the measured results.
Figure 8.Polarization-switchable imaging based on the designed metasurface that shows two pencil-like beams with the longitudinal polarization evolution between two orthogonal CP and LP states. (a) and (b) The schematic and optical images of the designed imaging sample consisting of two CP-based numbers 7 and 0. (c) and (d) The schematic and optical images of the designed imaging sample consisting of the LP-based letters H and V. (e1)–(e3) and (g1)–(g3) The simulated and measured electric-field intensity distributions for the CP-based imaging sample located at different transverse planes of the left pencil-like beam. (f1)–(f3) and (h1)–(h3) The simulated and measured electric-field intensity distributions for the LP-based imaging sample located at different transverse planes of the right pencil-like beam.
This proposed approach enables the design of geometric metasurfaces that simultaneously manipulate phase in the transverse direction and polarization in the longitudinal direction, resulting in multiple pencil-like beams with longitudinally varying polarization states. The gradual evolution of polarization states from, for example, circularly polarized to linearly polarized states along the beam’s length opens up new avenues for controlling polarizations. This capability may lead to innovative applications in polarization-switchable imaging, allowing for partial and complete display of images. In addition to polarization-switchable imaging, the pencil-like beams may facilitate unprecedented applications in light–matter interactions and biological sample analysis, especially in vivo practices, where they can be used to detect biological features at different depths. In traditional approaches, controlling polarization states requires projecting electromagnetic waves onto analyzers with different orientations. The longitudinally controlled polarization state achieved here dramatically simplifies these processes, potentially leading to the development of new techniques for manipulating and utilizing light, which may develop new techniques for the manipulation and utilization of light.
5. CONCLUSION
In conclusion, we have successfully proposed and experimentally verified an innovative strategy to convert incident LP THz waves into multiple pencil-like beams with longitudinally varying polarization states. By combining focusing phases with different focal lengths in two orthogonally helical components, we designed a geometric metasurface-based platform capable of focusing incident THz waves into multiple focal points. The partial overlap of two focal points with orthogonal polarization states has enabled the creation of two or more pencil-like beams exhibiting longitudinal polarization evolution between two orthogonal LP states and/or CP states. Notably, we experimentally demonstrated, for the first time to our best knowledge, LP/CP-switchable imaging applications that allow for partial or complete display of an image. The unique approach to multiplex focal points and manipulating polarization in the optical path may find new applications for developing optically switchable devices and advancing light–matter interactions.
APPENDIX A: THREE PENCIL-LIKE BEAMS WITH LP LONGITUDINALLY INHOMOGENEOUS VESATILE POLARIZATION STATES
Figure 9 shows the electric-field and polarization distributions of three pencil-like beams with the longitudinal polarization evolution between two orthogonal LP states. These three pencil-like beams are synthesized by three -polarized [Fig. 9(a1)] and -polarized [Fig. 9(a2)] focal points, in which two focal points with orthogonal LP states are partially overlapped with each other, leading to three pencil-like beams [Fig. 9(a3)]. For the left pencil-like beam, the intensity of the -polarized electric-field in the plane is decreased with the detection plane switched from to [Figs. 9(b1)–9(b5)], while the -polarized electric-field intensity is increased with the detection plane switched from to , as shown in Figs. 9(c1)–9(c5). The synthetic polarization distributions of the left pencil-like beam in the longitudinal direction are shown in Figs. 9(h1)–9(h5), which demonstrate that the polarization is evolved from - to -polarized state. In addition, the middle/right pencil beam enables the synthetic polarization distributions evolving from polarized state to polarized state (in the longitudinal direction), which are numerically demonstrated in Figs. 9(d1)–9(e5)/Figs. 9(f1)–9(g5) and Figs. 9(i1)–9(i5)/Figs. 9(j1)–9(j5), respectively.
Figure 9.Electric-field intensity and polarization distributions of three pencil-like beams with the longitudinal polarization evolution between two orthogonal LP states. (a1)–(a3) The simulated (a1) -polarized, (a2) -polarized, and (a3) total electric-field intensity distributions after the designed geometric metasurface. (b1)–(b5)/(c1)–(c5), (d1)–(d5)/(e1)–(e5), and (f1)–(f5)/(g1)–(g5) The simulated polarized electric-field intensity distributions for the left, middle, and right pencil-like beams at the different transverse () plane. (h1)–(h5), (i1)–(i5), and (j1)–(j5) The simulated polarization distributions for the left, middle, and right pencil-like beams at the different transverse plane.
APPENDIX B: TRANSMISSION SPECTRA FOR METAL SLITS AND DUAL-LAYER CHIRAL STRUCTURES
The LP-dependent imaging samples are consisting of metal slits. The transmission spectra of metal slits are shown in Figs. 10(a) and 10(b). For the long axis of the metal slits along the direction, the -polarized THz waves cannot transmit from the designed metal slits, while the -polarized THz waves can transmit through the metal slits, as shown in Fig. 10(a). The transmittance for the incidence of -polarized THz waves at 0.6 THz is about 70%. In contrast, for the long axis of the metal slits along the direction, the -polarized THz waves can transmit from the designed metal slits, while the -polarized THz waves cannot transmit through the metal slits, as shown in Fig. 10(b). The transmittance for the incidence of -polarized THz waves at 0.6 THz is about 70%. The CP-dependent imaging samples are composited of dual-layer chiral structures consisting of a split-ring-stripe hybrid structure and metallic gratings, as shown in the insets of Figs. 10(c) and 10(d). When the opening orientation of the split-ring-stripe hybrid structure is along the antidiagonal direction [inset in Fig. 10(c)], the LCP THz waves can be transmitted through the designed dual-layer chiral structures, while the RCP THz waves cannot be transmitted through the designed structures, as shown in Fig. 10(c). The transmittance for the incidence of LCP THz waves at 0.6 THz is about 85%. On the contrary, for the opening orientation of the split-ring-stripe hybrid structure along the diagonal direction [inset in Fig. 10(d)], the RCP/LCP THz waves can/cannot be transmitted through the designed dual-layer chiral structures, as shown in Fig. 10(d). The transmittance for the incidence of RCP THz waves at 0.6 THz is about 85%.
Figure 10.(a), (b) Transmission spectra of metal slits and (c), (d) dual-layer chiral-structure consisting of split-ring-stripe hybrid structure and metallic gratings. The structural parameters are as follows: ; ; ; ; ; .
APPENDIX C: THREE PENCIL-LIKE BEAMS WITH CP LONGITUDINALLY INHOMOGENEOUS VESATILE POLARIZATION STATES
The generation of three pencil-like beams with the longitudinal polarization evolution between two orthogonal CP states is numerically demonstrated in Fig. 11. In the same way, the three pencil-like beams are also synthesized by three LCP [Fig. 11(a1)] and RCP [Fig. 11(a2)] focal points, in which two focal points with orthogonal CP states are partially overlapped with each other, leading to three pencil-like beams [Fig. 11(a3)]. The left pencil-like beam is synthesized by the LCP and RCP focal points with partial overlapping with the corresponding electric-field intensity distributions, as shown in Figs. 11(b1)–11(b5) and Figs. 11(c1)–11(c5). The polarization distributions in the longitudinal direction are shown in Figs. 11(h1)–11(h5), which means that the polarization is evolved from LCP, LECP, LP, RECP to the RCP state. The middle pencil-like beam enables the same evolution of polarization in the longitudinal direction, as demonstrated in Figs. 11(d1)–11(e5) and Figs. 11(i1)–11(i5). In addition, the right pencil-like beam enables the polarization evolution from RCP, RECP, LP, LECP to the LCP state, which is demonstrated in Figs. 11(f1)–11(g5) and Figs. 11(j1)–11(j5).
Figure 11.Electric-field intensity and polarization distributions of three pencil-like beams with the longitudinal polarization evolution between two orthogonal CP states. (a1)–(a3) The simulated (a1) LCP, (a2) RCP, and (a3) total electric-field intensity distributions after the designed geometric metasurface. (b1)–(b5)/(c1)–(c5), (d1)–(d5)/(e1)–(e5), and (f1)–(f5)/(g1)–(g5) The simulated LCP/RCP electric-field intensity distributions for the left, middle, and right pencil-like beams at the different transverse () plane. (h1)–(h5), (i1)–(i5), and (j1)–(j5) The simulated polarization distributions for the left, middle, and right pencil-like beams at the different transverse plane.
APPENDIX D: SIMULATION METHODS AND EXPERIMENTAL MEASUREMENTS
Numerical simulations: The full-wave simulations are conducted by using Lumerical (FDTD Solutions) software. To optimize each unit cell structure (in metasurface) as a quasi-half-wave-plate, the period boundary conditions are selected in the and directions, while the perfect matching layer (PML) is applied along the direction. For the calculation of electric-field intensity distributions after each metasurface, PMLs are employed along the , , and directions. The thickness of meta-atoms/substrate is 500 μm, while the permittivity of silicon is . In simulation, plane-wave sources are selected and impinge onto the metasurface, while a 2D monitor detects electric-field distributions.
Experimental setup: An all-fiber near-field scanning THz microscopy (NSTM) system is established to detect the electric-field intensity distributions after the designed metalenses. A femtosecond laser beam with central wavelength of 1560 nm is divided into two parts: one part of laser beam is coupled into a fiber and guided into the THz emitter to excite THz radiation; the other part is transmitted from an optical delay and then impinges onto the THz tip, which is mounted on a 3D translation stage. The fabricated samples are fixed between the THz emitter, and the THz tip (after the samples) is moved to scan the generated electric-field intensity distributions.
Measurement of focal points and imaging: Before the experimental measurement of our designed sample, we first measure the electric-field distribution of the THz source. A quasi-Gaussian distributed electric-field distribution of THz source can be achieved. We can control the 3D translation stage and move the THz tip into the center of the THz source and then fix the THz tip in that position. After that, the sample is embedded behind the THz tip. By matching the center of the sample with the THz tip, we can approximately control the center of the sample matching with the center of the THz source. By rotating the THz half-wave plate (after the THz emitter) and the samples, the - and -polarized transmitted electric-field distributions after the sample can be obtained. Thus, the linearly polarized or circularly polarized focal points can be achieved by synthesizing the - and -polarized transmitted electric-field distributions. For the polarization-switchable imaging, another 3D translation stage is used to fix and move the imaging samples. The distance between the imaging sample and THz tip is fixed as 0.2 mm, while the metalens is fixed without moving. By simultaneously moving the imaging sample and THz tip in the longitudinal direction and scanning the electric-field distributions in the plane (after the imaging sample), the electric-field intensity distributions for the polarization-switchable imaging can be revealed.
APPENDIX E: THREE PENCIL-LIKE BEAMS WITH LP AND CP LONGITUDINALLY INHOMOGENEOUS VESATILE POLARIZATION STATES
The generation of three pencil-like beams with the longitudinal polarization evolution between two orthogonal LP and CP states is numerically demonstrated in Fig. 12. These three pencil-like beams are also synthesized by three [Fig. 12(a1)] and [Fig. 12(a2)] focal points, in which two focal points with orthogonal LP/CP states are partially overlapped with each other, leading to three pencil-like beams [Fig. 12(a3)]. The left pencil-like beam is synthesized by - and -polarized focal points with partial overlapping with the corresponding electric-field intensity distributions shown in Figs. 12(b1)–12(b5) and Figs. 12(c1)–12(c5). The polarization distributions in the longitudinal direction are shown in Figs. 12(h1)–12(h5), which means that the polarization is evolved from the - to -polarized state. The middle pencil-like beam enables the same evolution of polarization (i.e., the polarization evolution from the - to -polarized state) in the longitudinal direction, as demonstrated in Figs. 12(d1)–12(e5) and Figs. 12(i1)–11(i5). In addition, the right pencil-like beam enables the polarization evolution from RCP, RECP, LP, LECP to the LCP state, which is demonstrated in Figs. 12(f1)–12(g5) and Figs. 12(j1)–12(j5).
Figure 12.Electric-field intensity and polarization distributions of three pencil-like beams with the longitudinal polarization evolution between two orthogonal LP and CP states. (a1)–(a3) The simulated (a1) -polarized, (a2) -polarized, and (a3) total electric-field intensity distributions after the designed geometric metasurface. (b1)–(b5)/(c1)–(c5) and (d1)–(d5)/(e1)–(e5) The simulated polarized electric-field intensity distributions for the left and middle pencil-like beams at the different transverse () plane. (f1)–(f5)/(g1)–(g5) The simulated LCP/RCP electric-field intensity distributions for the right pencil-like beam at the different transverse () plane. (h1)–(h5), (i1)–(i5), and (j1)–(j5) The simulated polarization distributions for the left, middle, and right pencil-like beams at the different transverse plane.