Min Zhong(仲敏) and Jiu-Sheng Li(李九生)

Center for THz Research,China Jiliang University,Hangzhou 310018,China

We propose a switchable vortex beam polarization state terahertz multi-layer metasurface, which consists of threelayer elliptical metal crosses,four-layer dielectrics,and two-layer hollow metal circles,which are alternately superimposed.Under the normal incidence of left-handed circularly polarized(LCP)wave and the right-handed circularly polarized(RCP)waves,the proposed structure realizes three independent control functions,i.e.,focused and vortex beam,vortex beam with different topological charges,and polarization states switching,and azimuth switching of two vortex beams with different polarization states.The results show that the proposed metasurface provides a new idea for investigating the multifunctional terahertz wave modulation devices.

Keywords: terahertz wave,switchable vortex beam,polarization states,flexible manipulation

1. Introduction

Metasurface can flexibly manipulate the phase, amplitude, polarization, frequency, and wavefront propagation of electromagnetic wave and possesses many applications in holographic projection,[1,2]focusing,[3–5]photon spin Hall effect,[6–9]Airy beam,[10,11]spectrum,[12]etc. Recently, vortex generators based on metasurface orbital angular momentum (OAM) have attracted much attention.[13–15]For example, in 2019, Liuet al.[16]proposed a multifunctional metasurface vortex beam generator to realize vortex beams with reconfigurable polarization states. In 2020,Jianget al.[17]designed a plasma metasurface vortex beam generator to generate near-field dual-channel vortex beam and far-field dualchannel vortex beam. In 2021, Zhenget al.[18]designed a metasurface by changing the opening angle and direction angle of the square split ring to obtain about 80% high-purity mode vortex beams. More recently, some research teams have drawn their attention towards Pancharatnam–Berry(PB)metasurface vortex generator.[19–21]In 2021, Gaoet al.[22]employed a four-layer metallic PB phase metasurface and a three-layer dielectric PB phase metasurface to obtain a vortex beam with a transmission efficiency of about 79%. Wanget al.[23]utilized a flexible bilayer PB phase metasurface to generate vortex beams for circularly polarized waves incidence.In 2022, Xianget al.[24]proposed a TiO2elliptical cylinder all-dielectric PB phase metasurface for generating annular focused optical vortices. However, PB-phase metasurfaces can only realize spin-locked OAM beams or OAM beams with specific helicity. This effect is the inherent characteristics of geometric phase metasurfaces, which limit the device application. Furthermore, independent control of OAM with two different helicities remains a problem, especially in the terahertz band,which is still a challenge.

In this work, we combine propagation phase and geometric phase to design a switchable vortex beam polarization state multi-layer metasurface in terahertz region. By changing the size parameters and rotation angle of the metal–particle at the same time, the decoupling relationship between the incidence of left-handed circularly polarized(LCP)wave and the incidence of right-handed circularly polarized (RCP) wave is established. Therefore, the two orthogonal circularly polarized waves can generate mutually independent functions. The designed metasurface generates switching between focused beam and vortex beam,switching between vortex beams with different topological charges,azimuth switching between two vortex beams under different circularly polarized waves incident. The designed metasurface has potential applications in terahertz control devices.

2. Device design

Figure 1 shows the schematic diagram of the switchable vortex beam polarization state terahertz multi-layer metasurface, which can exhibit different and independent functions under the incidence of two different circularly polarized waves. This metal particle is composed of three elliptical metal cross layers,four dielectric layers and two hollow metal circle layers. The metallic material is gold with a conductivity of 4.561×107S/m. The thickness of metal layer is 3 μm,and the dielectric layer is polyimide with a thickness of 10 μm.The arm lengths of the elliptical metal cross are marked as a and b, respectively. The radius of the hollow metal circle isr=20 μm, and the period of the metal particle is set to bep=130 μm. We use the commercial CST Microwave Studio to optimize the coding particle under the incidence of LCP wave and RCP wave. Bothxaxis andyaxis are set to be of periodic boundary conditions andzaxis is fixed as open space.

Fig.1. Schematic diagram of switchable vortex beam polarization state terahertz multi-layer metasurface.

Fig. 2. Under linearly polarized terahertz wave incidence, (a) transmission amplitude and (b) phase of particle, (c) phase and (d) amplitude of 15 metal-particles with different sizes.

Under the incidence of circularly polarized terahertz wave,the relationship matrix between the transmitted field and the incident field can be expressed as resent the transmission amplitude and transmission phase of thex-polarized andy-polarized waves, respectively. When the amplitude of the incident polarized wave is 1, the phase difference isπ(i.e.,Rx=Ry= 1,φx-φy= 180°),δ=(Txeiφx+Tyeiφy)/2=0,η=(Txeiφx-Tyeiφy)/2=(eiφxei(φx-180°))/2= eiφx. The transmission matrix can be given by

whereαis the rotation angle of the unit cell,δ=(Txeiφx+Tyeiφy)/2,η=(Txeiφx-Tyeiφy)/2.Tx,Ty,φx, andφyrep-

From the above equation, it can be found that the LCP wave and the RCP wave of the transmitted field each acquire an extra phase (i.e.,φL=φx-2α,φR=φx+2α), which can be expressed as

It can be seen from the above formula that the decoupling of the relationship between the LCP wave and RCP wave can be achieved by adjusting the rotation angleαof the metalparticle,the transmission phaseφxandφyofx-andy-polarized waves.

Fig.3. The 64 kinds of metal-particles.

Figures 2(a)and 2(b)display the transmission amplitude and phase of metal-particle under the incidence of linearly polarized terahertz waves.At a frequency of 0.97 THz,the metalparticle has a high transmission amplitude,and the phase difference between the two linear polarizations is aboutπ. In order to meet the phase requirement under the incidence of RCP wave and LCP wave, 15 kinds of metal-particles cover the 2πphase in steps of 22.5°as shown in Fig.2(c). The corresponding amplitudes are shown in Fig.2(d).The 15 kinds of metal-particles rotate with different values of angleαto form 64 kinds of metasurface arrays as displayed in Fig.3.

3. Calculation and analysis of performance

3.1. Focused and vortex beam manipulation

The proposed metasurface phase distribution satisfies the following relation:

whereφLandφRare the required phase distributions to generate focused and vortex beams under the incidence of LCP wave and RCP wave,andλ,f,andlrepresent operating wavelength,focal length,and topological charge,respectively. Figures 4(a)and 4(b)show the phase distribution of generated focused beam and vortex beam under the incidence of LCP wave and RCP wave, respectively. Figure 4(c) demonstrates the function schematic diagram of the switchable focused/vortex beam function.

Fig. 4. (a) Focusing phase distribution under incidence of LCP wave, (b) vortex beam phase distribution under incidence of RCP wave, (c) function schematic diagram of switchable focused/vortex beam under incidence of LCP wave and RCP wave.

Fig.5. Focusing effect under incidence of LCP wave: (a)energy distribution on xoz and yoz planes,(b)–(c)focal spot electric field strength in xoz and xoy planes,respectively,and(d)full width at half maximum in xoy plane.

Figure 5 displays the focusing effect of the proposed metasurface under the incidence of LCP terahertz wave at a frequency of 0.97 THz. The designed metasurface generates a terahertz focused beam with a focal length off=1500 μm as shown in Fig.5(a). Figures 5(b)and 5(c)show the electric field intensity in thexozplane andxoyplane,respectively.The focused spot can be clearly observed,and the electric field energy is focused on the center point. Figure 5(d)gives the full width at half maximum(FWHM)in thexoyplane,0.224 mm(i.e.0.721λ). That is to say,the proposed metasurface can obtain high-quality terahertz focused beam under the LCP incidence.Figure 6 describes the vortex beam effect with topological chargel=1 when the RCP terahertz wave is vertically incident on the metasurface.The transmitted electric field phase,amplitude, three-dimensional (3D) far field, and mode purity of the vortex beam are shown in Figs.6(a)–6(d),respectively.It can be seen from the figure that the mode purity of the vortex beam is 65.3%. Combining Figs.5 and 6, it can be seen that the metasurface produces the focusing beam function and the vortex beam function under the incidence of LCP wave and RCP wave,respectively.

Fig. 6. Vortex effect under incidence of RCP wave: (a) phase distribution,(b)amplitude distribution,(c)3D far-field,and(d)mode purity.

3.2. Vortex beam manipulation with different topological charges

The metasurface phase distribution satisfies the following relation:

wherelis the topological charge of the vortex beam, specifically,l1=-1 andl2=-2. The phase distributions of the vortex beams with different topological charges are shown in Figs.7(a)and 7(b). Figure 7(c)shows the schematic diagram of vortex beams with different topological charges. Under the incidence of LCP wave, the proposed metasurface generates terahertz vortex beam with topological chargel=-1, and under the incidence of RCP wave, it generates vortex beam with topological chargel=-2. Figure 8 displays that the proposed metasurface generates a terahertz vortex beam with topological chargel=-1 under the incidence of LCP terahertz wave. At a frequency of 0.97 THz,the phase,amplitude,three-dimensional far-field, and mode purity of the generated vortex beam are shown in Figs.8(a)–8(d). We can find that the mode purity is 68.7%. Figure 9 gives terahertz vortex beam with a topological charge numberl=-2 under the illumination of the RCP wave. Figures 9(a)–9(d)represent the electric field phase distribution, amplitude distribution, 3D far field,and vortex beam mode purity of 55.4%, respectively. It can be noted from Figs.8 and 9 that the designed metasurface can control vortex beam with different topological charge numbers under the incidence of LCP wave and RCP wave.

Fig.7. (a)Vortex beam phase distribution with l=-1 under incidence of LCP wave,(b)vortex beam phase distribution with l=-2 under incidence of RCP wave,(c)vortex beam manipulation with different topological charges under incidence of LCP wave and RCP wave.

Fig.8. (a)Phase distribution,(b)amplitude distribution,(c)3D far-field,(d)mode purity for vortex beam with topological charge l=-1 under incidence of LCP wave.

Fig.9. (a)Phase distribution,(b)amplitude distribution,(c)3D far-field,(d)mode purity for vortex beam with topological charge l=-2 under incidence of RCP wave.

3.3. Vortex beam direction manipulation

When the designed metasurface phase distribution satisfies the following formula:

Here,lis the topological charge of the vortex beam,l1=l3=1,l2=l4=2.Figures 10(a)and 10(b)show the phase distribution of the proposed metasurface for generating vortex beams with different topological charges. Figure 10(c) shows that two vortex beams with different topological charges are generated along thexaxis direction and theyaxis direction under the incidence of LCP wave and RCP wave.

Figures 11(a)and 11(b)show the 3D far-field distribution and phase distribution of the terahertz vortex beam generated under the incidence of LCP wave at a frequency of 0.97 THz.It can be seen that the two terahertz vortex beams (marked as VB1 and VB2) with different topological charges (l=1 andl= 2), in which the VB1 and VB2 are located in the-x-axis direction and the-y-axis direction,respectively. The VB2 aperture is slightly larger than the VB1 aperture, which is caused by the increase of the topological charge value. Under the incidence of the RCP wave, the 3D far-field distribution and the far-field phase distribution of the terahertz vortex beams are given in the following Figs. 12(a) and 12(b), respectively. Two terahertz vortex beams with the +x-axis direction (named as VB3) and with +y-axis direction (named as VB4). It can be seen from the figure that the direction of the terahertz vortex beam can be effectively regulated under the incidence of the THz waves with different polarizations(i.e.,LCP/RCP).A comparison with other reported articles is shown in Table 1. According to Table 1 shown below,one can see that the designed metasurface has a relatively good performance and multi-function.

Fig.10. Vortex beam phase distribution under(a)incidence of LCP wave,(b)RCP wave,and(c)function schematic diagram for directions switchable vortex beams with different topological charges under incidence of LCP wave and RCP wave.

Fig. 11. (a) The 3D far-field and (b) phase distribution of generated vortex beam in -x direction and -y direction under incidence of LCP terahertz waves.

Fig.12. (a)The 3D far-field and(b)phase distribution of generated vortex beam in+x-axis direction and+y-axis direction under incidence of RCP terahertz wave.

Table 1. Comparison of performance between proposed metasurface and some previous research results.

4. Conclusions

In this work, we proposed a diversified function metasurfaces under the incidence of LCP terahertz wave and RCP terahertz wave. The structure consists of three-layer elliptical metal crosses,four-layer dielectrics,and two-layer hollow metal circles, which are alternately superimposed. Under the incidence of LCP wave and RCP wave, the designed metasurface can independently control focusing beam and vortex beam, vortex beams with different topological charges, and two vortex beams with topological charges (l=1,l=2) located in different azimuths. The proposed metasurface can independently manipulate two orthogonal circularly polarized waves,which has great application values in the future multifunctional terahertz wave control devices.

Acknowledgements

Project supported by the National Natural Science Foundation of China (Grant Nos. 61871355, 61831012,and 62271460), the Talent Project of Zhejiang Provincial Department of Science and Technology, China (Grant No. 2018R52043), the Zhejiang Key Research and Development Project of China (Grant Nos. 2021C03153 and 2022C03166),and the Research Funds for the Provincial Universities of Zhejiang Province,China(Grant No.2020YW20).