Ying-Hua Wang(王英華) Jie Li(李杰) Zheng-Gao Dong(董正高) Yan Li(李妍) and Xu Zhang(張旭)

1School of Physics and Physical Engineering,Shandong Provincial Key Laboratory of Laser Polarization and Information Technology,Qufu Normal University,Qufu 273165,China

2Gr¨unberg Research Centre,Nanjing University of Posts and Telecommunications,Nanjing 210023,China

3School of Physics,Southeast University,Nanjing 211189,China

Keywords: metamaterial,multi-band,asymmetric transmission,polarization conversion

1. Introduction

Metamaterials and metasurfaces have become an important research field because they present powerful capacities for manipulating the fundamental properties of the propagating electromagnetic waves due to the flexible design of subwavelength geometric shapes and sizes.[1,2]In addition, acoustic metamaterials are also proposed to investigate the transmission spectra and sound insulation performance.[3,4]Since the proposal of the concept of metamaterials,several novel structures have been reported, ranging from microwave to optical regimes,such as I-shaped metamaterials,split-ring resonators,L-shaped metallic antennas, and S-shaped holes.[5-9]Since then, many studies have paid attention to focusing beams,[10]creating orbital angular momentum,[11]and manipulating the polarization states,phases,and modes of TE/TM waves.[12,13]In 2007, Zhouet al.proposed an I-shaped metamaterial to manipulate the polarization of electromagnetic waves and achieved complete conversion between two perpendicular linear polarizations.[9]In 2020, broadband linear-to-circular polarization conversion was realized among reflected waves.[14]In addition, metamaterials have been used to realize perfect absorption,circular dichroism,optical activity,and the asymmetric transmission(AT)effect.[15-20]

In recent decades, the AT effect has garnered increasing attention. To realize outstanding and tunable AT effects in linearly and circularly polarized plane waves, several studies have been conducted, such as changing the shapes of symmetry-broken chiral metastructures,[21,22]increasing the layers of the proposed nanobars,[23,24]and tilting the rectangular nanoholes.[25]With regard to circularly polarized plane waves, high-efficiency broadband and dualband AT effects have been studied and realized from microwave to optical regimes,[20,26-28]and tunable AT effects have also been realized by integrating the graphene layers with metamaterials.[29-31]With regard to linearly polarized plane waves, several studies have focused on enhancing the efficiency and broadening the band of the AT effect. In these studies,the AT effect in the microwave regime achieved better results than those in the optical regime. For instance, dualband, broadband, and multi-band AT effects have been realized in the microwave regime with high efficiency.[21,32,33]In comparison with the microwave regime, most studies on the near-infrared regime have realized the broadband or dual-band AT effect with low efficiencies.[33-35]For example,Zhang realized both circularly and linearly polarized AT effects using one-layer metamaterials, but the AT values were about 0.1.[25,29]To increase the AT values, more works paid attention to bi-layer metamaterials,then I-L-shaped,S-shaped,split ring-shaped Ω-shaped metamaterial, and many other metamaterials were proposed, and the AT values increased to 0.8.[35-40]For further increases in AT effects,multilayer metamaterial has also been proposed and the AT values have been increased to 0.9. But here, the multilayer metamaterials increase the complexity and difficulty of the fabrication process,so it is necessary to enhance and broaden the AT effects using bi-layer metamaterials.[24,41,42]In previous works, the dualband AT effect has also been realized by bi-layer metamaterial with a maximum of about 0.75,[8,32,43,44]but a few studies have reported the multi-band AT effect and its tunable properties. According to the multi-band absorption, multi-band polarization conversion, and multi-band circular dichroism and other multi-band electromagnetic effects, we know that it is useful to study the multi-band AT effect on the near-infrared regime.[45-47]

In this study, we propose a bi-layer windmill-shaped metamaterial and numerically investigate the multi-band AT effect and its tunable properties using the finite-difference time-domain method. In comparison with the split-ring resonator, the windmill-shaped resonators can motivate and enhance more resonant modes. Consequently, the simulated results demonstrate that the AT values are greater than 0.5 at 195,260, and 309 THz. Moreover, the high-efficiency AT effects can be flexibly tuned by modulating the geometric parameters of the proposed metamaterial.For instance,the bandwidth can be tuned by changing the sizes,whereas the polarization state of the transmitted plane wave can be tuned by changing the gap between the first and second layers. The additional operating frequency bands and tunable properties provide more application possibilities for the AT effect in the future.

2. Design and structure

Firstly,we discuss the principles of the bi-layer windmillshaped metamaterial design. When a linearly polarized plane wave is propagating in the +zdirection, the illuminated and transmitted electric field can be given by[48,49]

According to Eqs.(8)-(10)we can getTxx=Tyy. In addition,the windmill arms play an important role in inducing and enhancing multi-band resonances.[50]As a result, the bi-layer windmill-shaped resonator can result in a multi-band AT effect for only linearly polarized plane waves.[48-50]

Fig.1. (a)A unit cell of bi-layer windmill-shaped resonators with blue and red arrows indicating the forward and backward incidences,respectively. (b)and(c)The first and second layers of the unit cell.

Based on the design principles the bi-layer windmillshaped resonator is proposed and shown in Fig.1. Figure 1(a)presents the perspective view of a unit cell of this resonator,where the two windmill-shaped metallic layers are separated(g= 70 nm) by a silicon oxide dielectric spacer layer with a permittivity ofεsio2=2.1. The windmill-shaped metallic layers are made of silver with a Drude-type dispersion, for which the plasma and collision frequencies areωp=1.367×107rad/s andγ=7.73×1013rad/s,respectively,and the highfrequency bulk permittivityε∞=6.0. The blue and red arrows indicate that thex- andy-polarized plane waves propagate along the forward (+z) and backward (?z) directions,respectively. Figures 1(b)and 1(c)respectively show the first and second layers of the windmill-shaped resonators with the periodp=500 nm. The other geometric parameters of the windmill-shaped resonator are set ast=40 nm,w=80 nm,d=100 nm,ands=50 nm.

3. Results and discussion

Fig. 2. Simulated transmission coefficients of windmill-shaped resonators,when x-and y-polarized plane waves incident along the(a)forward and(b)backward directions, respectively. I, II, and III show three resonances at 195 THz,260 THz,and 309 THz,respectively.

By studying the geometric parameters of the windmillshaped metamaterial,we found that the multi-band AT can be flexibly tuned. First, Fig. 4(a) shows that the sizescan easily tune resonant modes II and III,i.e.,whensincreases from 0 nm to 140 nm, the AT parameters decrease from 0.72 to 0.Meanwhile, the AT parameters increase from 0 to 0.72, and the operation bands of the AT are also broadened in resonant mode III.In addition, Fig.4(b)shows that the gapgbetween the first and second layers can tune resonant modes I and III,i.e., whengincreases from 40 nm to 250 nm, the AT parameters decrease. A new resonant mode IV is induced whengis increased. Resonant mode IV results in opposite polarization conversions and the AT phenomenon at 343 THz, where thex-polarized incident plane wave can be transformed into ay-polarized output plane wave when it propagates in the backward direction and the maximum AT parameter is?0.6 wheng=190 nm.In other words,wheng=190 nm,thex-polarized incident plane wave can pass through this bi-layer windmillshaped metamaterial along the backward(?z)direction,which is opposite to resonant modes I,II,and III.

Fig.3. (a)and(b)The calculated total transmittances for x-and y-polarized excitations propagating along the forward and backward directions. (c)The AT parameters for the designed windmill-shaped resonators. Solid and hollow triangular lines correspond to the AT of the x- and y-polarized plane waves,respectively.

To understand the physical mechanism of the multi-band AT phenomenon, we studied the surface current distributions of this bi-layer windmill-shaped metamaterial in resonant modes I, II, III, and IV. The horizontal red arrows in Figs.5(a)-5(c)represent thex-polarized incident plane wave.Figure 5(a) shows that resonant mode I at 195 THz is induced by a design that is parallel to the split arms. Figure 5(b)shows that resonant mode II at 260 THz is induced by the center split rings, identical to the traditional split-ring resonators(SRRs)without windmill-shaped arms.[21,43,49,52]The surface current passes through the spilledsand results in a magnetic dipole resonance; thus, resonant mode II can be easily tuned by changing the size ofs. Figure 5(c) shows that resonant mode III at 309 THz is also induced by the design of the windmill-shaped arms, in contrast to resonant mode I, where the surface focuses on the two corners of the L-shaped arms,which are included and parallel to the split arms; therefore,the parameterscan tune resonant mode III. In other words,resonant modes I,II,and III are induced by anx-polarized incident plane wave propagating in the forward direction,resulting in thex-polarized plane wave passing through the bi-layer windmill-shaped metamaterial along the forward (+z) direction and transformation to they-polarized output plane wave.Figure 5(d) shows that resonant mode IV at approximately 343 THz is induced when they-polarized incident plane wave propagates in the forward direction, and the surface current distributions are localized on the L-shaped arms, which are perpendicular to the spilled arms. In addition,resonant mode IV can only be activated when the gapgincreases and thexpolarized incident plane wave can only pass through the metamaterial along the backward(?z)direction,which results in a negative AT parameter in resonant mode IV in Fig.4(b).

Fig.4. The tunable AT effect by changing the(a)spilled width s and(b)gap g between the first and second layers.

Fig.5.Current distributions of the multi-band resonant modes at polarization conversion peaks for forwarding propagation. (a)-(c)Simulated current distributions at 195,260,and 309 THz for x-polarized incidence. (d)Simulated current distributions at 343 THz for y-polarized incidence.

Finally, we also consider the effect of the geometric parameterspanddon the AT parameter. In Fig. 6(a), when the periodpincreases from 500 nm to 800 nm, the couplings among neighboring periods decrease,and thus the resonances in modes I, II, and III are weakened, which results in a decrease in the AT parameters. In Fig. 6(b), we first setp=500 nm,but setd=0 nm and 100 nm. Whend=0 nm,the traditional SRRs without windmill-shaped arms are substituted for our bi-layer windmill-shaped metamaterial,and consequently,the AT parameter only appears at 260 THz(resonant mode II). Further, whendis increased to 200 nm, the period also increases and,consequently,the AT parameter decreases.

Fig. 6. Calculated AT parameters of the bi-layered windmill-shaped splitring resonators for different(a)periods p and(b)windmill arm distances d.

4. Conclusion

In this study, we proposed a bi-layer windmill-shaped metamaterial that is different from traditional SRRs,as it can induce more resonant modes and result in multi-band AT in linearly polarized plane waves.The AT parameters reach 0.58,0.74,and 0.62 at 195,260,and 309 THz,respectively.Furthermore,the multi-band AT can be tuned freely by changing the geometric parameterssandg. Wheng=190 nm, a reversed AT was realized at 343 THz with the AT parameter reaching?0.6. To further understand the physical mechanism,the surface current distributions of this bi-layer windmill-shaped metamaterial are presented for the underlying resonant modes I,II,III,and IV,respectively. It is believed that the multi-band AT effects will be applied as polarization rotators and switches in the field of optical nano-devices.