## Abstract

Metasurfaces employed for generating orbital angular momentum (OAM) beams have drawn tremendous interest since they can offer extensive applications ranging from quantum optics to information processing over the subwavelength scale. In this study, a flexible bilayer metasurface is proposed and experimentally verified in the terahertz (THz) region. Based on Pancharatnam-Berry (P-B) phase, the proposed meta-atom satisfies perfect polarization-flipping at the design frequency and is implemented for the generation of vortex beams under circularly polarized (CP) illumination. Two metasurfaces are designed, fabricated and experimentally characterized with a THz spectral imaging system for linearly polarized (LP) illumination. The transmitted field intensity distribution of *y* component is petal-shaped of gradually varied pieces with the frequency due to the complementary symmetric structure, indicating OAM state transition between a single vortex beam and superposition of two vortex beams. The measured spectral imaging distributions of amplitude and phase show good agreement with the simulation results. Such designs open a pathway for modulation of THz OAM states and bring more possibilities for flexible metasurfaces in a THz application.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1 Introduction

Metasurfaces have received considerable research interests owing to their unique features in Electromagnetic (EM) wavefront manipulation [1–10]. With a negligible thickness as compared to the working wavelength, it is capable of tailoring waves by introducing discontinuous abrupt phases and can be easily made by mature micro-nano processing technology. By deliberately designing phase and amplitude profiles of the metasurfaces in either transmission or reflection mode, many fascinating applications have been successfully realized in various EM wave bands such as beam steering and shaping [11–14], focusing lens [15–18], various vortex beam generators [1,10,19–25], meta-holograms [26,27], to name but a few of the enabled field.

In particular, vortex beam carrying orbital angular momentum (OAM) [28–32] has attracted widespread attention owing to its potential to enhance the spectrum efficiency and expand communication capacity in data communication. Although multifarious methods have been reported to generate vortex beams in recent years, metasurfaces are believed to be a more efficient way owing to their outstanding advantages in comparison with the conventional methods. Especially, terahertz (THz) metasurfaces with Pancharatnam-Berry (P-B) phase [33–37] have a special contribution to the modulation of spin-polarized beams. By changing the geometric orientation of the meta-atoms, a vortex beam with an arbitrary topological mode of interest can be launched. Not only that, they can be also employed for polarization multiplexing for left-handed circular polarization (LCP) and right-handed circular polarization (RCP). However, most of them are in reflection mode or lack of experimentally verification, which restrict their practical applications. Very recently, all-dielectric metasurface for manipulating the superpositions of OAM states [38,39] have been proposed. However, they usually have large optical thickness and suffer from the complicated fabrication procedure in practical application.

Flexible metasurfaces have many advantages, lightweight, low cost as well as chemical stability and mechanical malleability, making it possible to achieve flexible and foldable devices [5,9,40]. Especially, flexible metasurfaces can be easily attached to a radiation source in conformal geometry. Because of the above reasons, we propose a flexible bilayer metasurface for OAM beam generation. The meta-atoms are constructed to generate OAM beams and it is demonstrated that under LCP/RCP illumination the transmitted field are the typical characteristics of RCP/LCP vortex waves in simulation. Moreover, two metasurfaces with topological charge *l*=2 and *l*=3 are fabricated and characterized by a THz spectral imaging system. The OAM superposition is discussed at three different frequencies based on Jones matrix. Both the simulations match well with the experiments and theoretical analysis. This design based on flexible metasurface exhibits extraordinary advantages and provide new insight for OAM manipulation in THz application.

## 2 Theory and design

Generally, for an incident plane wave with an arbitrary polarization state, the transmitted electric field can be characterized by the Jones matrix ${\tilde{E}_{out}} = J{\tilde{E}_{in}}$. Considering a LP wave composed of *x* and *y* components normally impinges upon a metasurface with the meta-atoms rotated by an angle *α* along the *z* axis, the transmitted field is expressed as [41,42]

*t*,

_{xx}*t*,

_{yy}*t*,

_{xy}*t*are linearly co- and cross-polarized transmission coefficients. From Eq. (1) it is apparent that once the coefficients of the meta-atom are determined, the transmitted field in any direction (

_{yx}*x*or

*y*) can be obtained by the corresponding Jones Matrix. When converted into the circularly polarized (CP) incident waves with left- and right-handed components, the Jones matrix

*J*for CP related to LP can be expressed by the equation

^{cir}*t*,

_{rr}*t*,

_{ll}*t*,

_{lr}*t*are circularly co- and cross-polarized transmission coefficients. Obviously, the geometric phase modifications of cross-polarized components are controllable with the rotation angle

_{rl}*α*, which is known as P-B phase. Accordingly, by purposefully tailoring the linear transmission coefficients, the transmitted EM wave can be effectively regulated. We start from analyzing the meta-atoms that can achieve full phase control. For one case, an ideal situation will appear when four linear transmission coefficients are |

*t*|= |

_{xx}*t*|=1,

_{yy}*t*=

_{xy}*t*=0 and

_{yx}*ϕ*-

_{xx}*ϕ*=−180°. Substitute the above values into Eq. (2), we are left with the following matrix [6,8]

_{yy}*α*of the meta-atom. The axially rotated meta-atoms switch the polarized state from RCP/LCP to LCP/RCP and the scatterer theoretically achieves a perfect polarization conversion efficiency between the RCP wave and LCP wave.

Besides, it has been theoretically demonstrated that the single-layer metallic structure is insufficient to achieve the phase range of 180 degree since only electric responses operate [42,43]. Based on theoretical analysis on transmit array [41], the maximum phase range of 170 degrees can be achieved with 1 dB transmission loss for double-layer metallic structures. In other words, we could obtain a phase shift of 180 degrees between *ϕ _{xx}* and

*ϕ*with a transmission coefficient of near −1 dB ((79.4%). Of course, if we choose structures with triple metallic layers, we could obtain a higher transmission efficiency. However, the complexity of the fabrication process will increase significantly. Therefore, bilayer metallic structures are the best choice after balancing the transmission efficiency and complexity of the fabrication process.

_{yy}The bilayer structure composed of complementary double split-ring resonator (DSRR) pairs is illustrated in Fig. 1. To guarantee *t _{xy}*=

*t*=0, the meta-atom exhibits rigorously mirror symmetry with gold (

_{yx}*σ*=4.561×10

^{7}S/m) metallic patterns symmetrically loaded on the upper and lower sides of a transparent polyimide(

*ɛ*=3.5 + 0.003i) spacer. The thickness of the polyimide substrate is extremely subwavelength (∼0.1λ at 0.79 THz), thus introducing very wake EM effect, and meanwhile, providing both mechanical robustness and flexibility. The metallic pattern consists of two types of complementary DSRRs with orientations perpendicular to each other. The inner is a square ring with a slot along

*y*-direction and the external is an annulus with a fan-shaped slot along

*x*-direction. Different sizes of the inner square ring and external annulus with slots in two perpendicular directions make the scatter anisotropic. Consequently, when the structure is illuminated by two orthogonal LP (

*x*- or

*y*-) waves, two distinct resonances occur concurrently and each resonance can be control independently. All the parameters of the structure are shown in Fig. 1(b).

The performance of the proposed meta-atom is investigated and optimized using electromagnetic simulation, by properly applying periodic boundary conditions along *x* and *y* for the case of normal linear or circular plane wave incidence. The simulated amplitude and phase of the transmission coefficients are shown in Fig. 2. It is observed from Fig. 2(a)–2(b) that the amplitude of co-polarized transmission coefficients *t _{xx}* and

*t*are trading off and taking turn in the range of 0.6–0.9 THz due to the complementary symmetric structure. In particular, at the designed frequency of 0.795 THz they are equal in amplitude (nearly 0.84) with the phase difference about 179.8°, and the cross-polarized coefficients

_{yy}*t*and

_{xy}*t*are zero in the whole band as expected, which can ensure the high polarization conversion efficiency.

_{yx}To further demonstrate the relation between the geometric phase modifications of the transmitted electric field and the orientation angle of the meta-atom, eight meta-atoms with rotation angle *α*=22.5° are selected to generate full phase coverage from 0 to 2π. The simulated amplitude and phase response of the meta-atoms under incidence of LCP wave are shown in Fig. 2(c)-(d), their transmission amplitudes remain around 0.8 with slight peak variations at 0.795 THz while their phase shifts cover 2*π* range in increments of about 45° (∼2α) in the whole band, which are in agreement with P-B phase. Encouraged by the simulation results, the samples (seen in Fig. 1(c)) are fabricated and characterized as shown in Fig. 2(e). The measured experimental data match well with the simulations except a slightly frequency shift (the design frequency changes to 0.79 THz) which can be attributed to errors in the process of fabrication and measurement.

Especially, the samples are fabricated by mature micro-nano processing technology including the following procedures [3]. The first step is to spin-coat the bottom polyimide (about 5 µm thickness with a viscosity of 7000–8000 centipoise) layer on a silicon substrate, followed by a curing process. Next to form the photoresist pattern by photolithography, a deposition of the Ti/Au layer (10/200 nm) by magnetron sputtering, and then a lift-off operation to complete the bottom metallic pattern. The rest of the sandwiched polyimide layers and the upper metallic pattern are created by repeating the previous steps in sequence. Finally, the samples are mechanically scored with a sharp tool around its edge and then immersed in a hot water bath with ultrasound for several minutes to help it peel from the silicon substrate. The ultimate samples are shown in Fig. 1(d), which exhibit mechanical flexibility and robustness.

## 3. Results and discussions

To validate the capabilities of the proposed design, we now use the meta-atom as a building block to realize to generate multiple vortex beams with helicoidal equal-phase wavefronts. As known, the beams carrying OAM are characterized by the spatial distributed phase term exp(*ilφ*) in the transverse plane. To create the spiral phase profile in *xoy* plane, the corresponding phase distribution of each meta-atom in the metasurface at position (*x*, *y*) can be expressed as follows [3]:

*φ*is the azimuthal angle and

*l*is the topological charge. Based on P-B phase discussed above, the rotated angle

*α*of each meta-atom should satisfy

*α*=

*lφ*/2, and then OAM of topological charge

*l*can be introduced in the transmitted EM wave.

Due to its perfect polarization-flipping characteristics, theoretically, when the metasurface is illuminated by LCP incident beam, only the transmitted RCP can be detected with the generated vortex carrying topological charge of *l*. As for RCP illumination, only the transmitted LCP can be detected and its topological charge is *-l*. Figure 3 shows the simulated field intensity distribution of the transmitted |*E _{RCP}*|

^{2}/|

*E*|

_{LCP}^{2}component and phase profiles under LCP/RCP illumination for the incident frequency of

*f*= 0.79 THz. Although, the topological charge of the vortex are ±2 and ±3 for LCP/RCP incident THz waves, respectively, both of them are identical in field intensity |

*E*|

^{2}distribution with energy concentrated on a doughnut-shaped ring as shown in Fig. 3(a

_{1})-(a

_{4}), which is the typical characteristics of single-mode vortex waves [28]. However, the phase distributions are reversed with rotation direction counterclockwise and clockwise determined by the positive and negative topological charge. The overall phase shift around the phase singularity in a turn is 2 times of 2

*π*for

*l*=2 and 3 times of 2π for

*l*=3 respectively as shown in Fig. 3 (b

_{1}) - (b

_{4}). Specifically, the nonuniform of the field intensity distribution can be attributed to the diffraction effect and the truncation effect caused by the edges of the metasurfaces. Actually, because of the limitation of the computer resources, the observation

*xoy*plane is set as 1.5 mm (3.9

*λ*when

*f*=0.79 THz) away from the center of the metasurfaces consisting of an array of 25 × 25 elements with an area of 4 × 4 mm

^{2}in the simulation.

For LP illumination, both the LCP and RCP incident beams can excite the THz vortex with different helical phase. Therefore, the superimposed field depends on the charge of the vortices of the component beams and the relative intensity of the two beams. To further characterize the functionality of THz near-field OAM, two metasurfaces consisted of rotated meta-atoms with successive phase step are designed and fabricated. The topological charges are 2 and 3 respectively. Each metasurface is in size 1.2×1.2 cm^{2} consisted of 75×75 meta-atoms. Their superposition states are characterized using THz spectral imaging system as illustrated in Fig. 4. A femtosecond pulse with a central wavelength of 800 nm is divided into one pump light and one probe light by a beam splitter. The wavefront of the pumped light is tilted by a grating. A strong field THz pulse with a peak value of 900 kV/cm is irradiated on the sample by the optical rectification effect of LiNbO_{3}. After the delay line, the probe light arrives at the GaP crystal at the same time with the THz pulse carrying information of the sample. The reflected probe light with THz-induced birefringence is divided into two linearly polarized beams with mutually perpendicular polarization directions through the PBS, and then the THz time-domain signal can be obtained through balanced photodiode detector. Simultaneously, the probe images in two orthogonal polarizations were spatially separated and captured using a near-infrared Charge Coupled Device (CCD) camera [7].

Unfortunately, due to the limited experimental setup, only the LP 2D near-field distribution can be measured under LP incidence. The experimental measurements and numerical simulation for *l*=2 at three different frequencies of 0.7 THz, 0.79 THz (the design frequency) and 0.85 THz for LP illumination(*y*-polarized) are shown in Fig. 5, respectively. A LP incident THz beam is composed of two orthogonal components with opposite helicity and they are coherently superimposed with each other, showing a quite different field distribution from only LCP/RCP incidence (see Fig. 3 of the simulated results) as depicted in Fig. 5(*b*_{1})-(*b*_{4}) at the design frequency of 0.79 THz. This can be attributed to the superposition transmitted field of vortex beams with different topological charges *l*_{1}=2 for LCP and *l*_{2}=−2 for RCP illumination. At 0.79 THz, assuming that *|t _{yy}*|=

*|t*|=1 and

_{xx}*t*= 0 are perfectly satisfied, the corresponding phase and amplitude of the two beams is determined, and the phase and field distribution conform to the case

_{xx}+t_{yy}*l*

_{1}=-

*l*

_{2}[44,45]. We can explain it by Jones matrix in linear base (Eq. (1)), as known, the transmitted intensity of

*y*-polarized component |

*E*|

_{y}^{2}is related to ${|{{t_{yy}}} |^2} = {\left|{{t_{yy}}{{\cos }^2}(\frac{{l \times \varphi }}{2}) + {t_{xx}}{{\sin }^2}(\frac{{l \times \varphi }}{2})} \right|^2}$. That is to say at 0.79 THz the intensity is regarded as $I \propto {|{\cos l \times \varphi } |^2}$. The total amplitude of the intensity distribution is a pretty split petal-like pattern with the number of lobes of the pattern equal to

*N*= |

*l*

_{1}| + |

*l*

_{2}|=4. Moreover, the energy distribution of each side lobe is theoretically uniform. Careful inspection of Fig. 5(a

_{1})-(c

_{1}) reveals hollow field still exist at the center of the beam due to the characteristic of the meta-atom. As for phase distribution, since |

*l*

_{1}| is equal to |

*l*

_{2}|, the transmitted phase distribution should be related to the phase distribution of the beam of topological charge

*l*=2 with phase in the azimuth direction distinctly divided into two symmetric parts. The experimentally measurements and numerical simulations results are shown in Fig. 5(b

_{1})-(b

_{4}), which match well with the theoretical analysis.

As for the other two frequencies, the ideal is no longer satisfied, and the relative phase and amplitude of the two beams are undetermined. However, Jones matrix still works. At the frequency of 0.7 THz, the linear transmission coefficient *t _{xx}* is much smaller than

*t*according to the measured results of the unit cell (see Fig. 2(a)). Now assuming

_{yy}*t*=0 and

_{xx}*t*=1, the intensity is $I \propto {\left|{{{\cos }^2}\frac{{l \times \varphi }}{2}} \right|^2}$ and the transmitted field will be also a pretty petal-like pattern with the number of lobes of the pattern equal to

_{yy}*N*=

*l*= 2. Meanwhile, for

*f*=0.85 THz, the linear transmission coefficient

*t*is much smaller than

_{yy}*t*. Assuming

_{xx}*t*=0 and

_{yy}*t*=1, the intensity is $I \propto {\left|{{{\sin }^2}\frac{{l \times \varphi }}{2}} \right|^2}$ and a petal-like pattern with

_{xx}*l*=2 lobes appear in opposite directions relative to 0.7 THz. Note that the complementary symmetry with orthogonal directions denotes their opposite charge. Figures 5(a

_{1})-(a

_{4}) and 5(c

_{1})-(c

_{4}) show the simulated and measured intensity and phase profiles of transmitted LP components at

*f*=0.7 THz and 0.85 THz respectively. Obviously, the field is double petal–shaped distribution in the horizontal direction with very weak field distributed in the vertical direction at

*f*=0.7 THz. If continuously observed, the electric field gradually weakens with the increasing of the frequency in the horizontal direction, and the two lobes in the vertical direction strengthen, leading to quadruple petal–shaped field distribution at

*f*=0.79 THz. As the frequency continues to increase, the horizontal electric field gradually is weakened to nearly disappear, and at

*f*=0.85 THz, the double petal–shaped petals only distributed in the vertical direction. Although there are fine distinctions between the simulations and experiments due to fabrication errors, measurement error and unexpected scattering on the surface leads to additional errors, they show a good agreement with the analysis. Their unique properties provide a flexible way of generating OAM states in many applications.

Figure 6 shows the simulated and measured intensity and phase profiles of the metasurface with topological charge *l*=3 at three different frequencies of 0.7 THz, 0.79 THz and 0.85 THz, respectively. Now the topological charge of the metasurface is *l*=3. Therefore, for LP illumination, the transmitted field is coherent superposition of vortex beam with topological charge *l*=3 for LCP and *l*_{2}=−3 for RCP incidence at 0.79 THz leading to sextuple petal–shaped field distribution as depicted in Fig. 6(b_{2}). As the frequency ranges from 0.7 THz to 0.85 THz, the field distribution continuously varies from trivalve-shaped to sextuple petal–shaped and then goes back to trivalve-shaped in the direction of rotating 90 degrees clockwise relative to the original shown in Fig. 6(a_{2})-(c_{2}). The corresponding phase profiles are depicted in Fig. 6(a_{4})-(c_{4}). The phase distributions are also matched with the corresponding topological charge exhibiting a sextuple-petal homogeneous intensity with every other petal having almost the same phase along the azimuthal direction. It can be seen that the measured results are in good agreement with the simulations and theoretical analysis, except that the intensity is not uniform due to the errors in the experiment and simulation.

## 4. Conclusions

In summary, we have numerically and experimentally demonstrated a flexible bilayer metasurface to realize the manipulation of OAM states in THz region. Two metasurfaces with topological charge *l*=2 and 3 are designed and fabricated. The simulated results indicate that for LP illumination, the transmitted field intensity and phase are coherently superimposed of the LCP and RCP incidence. We also experimentally investigate the OAM characteristics using THz spectral imaging system. Interesting, the field intensity distribution exhibit that OAM states vary between a single vortex beam and superposition of two vortex beams with the increasing of frequency as a result of the complementary characteristics of the structure. The phase profile is related to the intrinsic topological charge. Both the simulations match well with the experiments. This flexible metasurface greatly facilitates its integration with other device and will be beneficial for the applications utilizing the OAM of THz waves.

## Funding

National Natural Science Foundation of China (61521001); National Key Research and Development Program of China (2017YFA0700202); Fundamental Research Funds for the Central Universities; Jiangsu Provincial Key Laboratory of Advanced Manipulating Technique of Electromagnetic Wave.

## Disclosures

The authors declare no conflicts of interest.

## Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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