Yuhang Gao(高雨航), Yu Tian(田宇), Qingguo Du(杜慶國(guó)),?, Yuanli Wang(王原麗),?, Qin Fu(付琴),Qiang Bian(卞強(qiáng)), Zhengying Li(李政穎),3, Shuai Feng(馮帥), and Fangfang Ren(任芳芳)

1School of Information Engineering,Wuhan University of Technology,Wuhan 430070,China

2School of Electrical Engineering,Navy University of Engineering,Wuhan 430033,China

3National Engineering Research Center of Optical Fiber Sensing Technology and Networks,Wuhan 430070,China

4School of Science,Minzu University of China,Beijing 100081,China

5School of Electronic Science and Engineering,Nanjing University,Nanjing 210023,China

Keywords: asymmetric polarization converter,visible and near-infrared light,chiral metasurface,Fabry–Perot

1.Introduction

Polarization,one of the most important characteristics of electromagnetic waves,has been widely applied in many fields such as wireless communications,[1–4]biosensing,[5–7]and polarization imaging.[8–11]Especially,linearly polarized light is normally required for polarized light therapy,[12]head-up display system,[13]and LCD/OLED applications.[14]Hence,it is highly demanded to design and fabricate high performance polarization converters which could covert the natural light to one particular linearly polarized light with high efficiency to use the natural light more efficiently.Traditionally, polarization state of light could be manipulated by controllers with crystals and polymers exhibiting birefringence.[15]For example, polarizer could convert unpolarized light to linear polarized light by absorbing the light component with polarization perpendicular to the transmission axis, and allow the light component with polarization parallel to the transmission axis passing through.However, polarizers with birefringent crystals/polymers require long propagation distance to obtain phase accumulation which makes the polarizer too bulky for compact devices.Moreover,such polarizers usually encounter low efficiency and high loss.[16,17]The maximum efficiency of the polarizers in theory is only 0.5, which means that at least half of the incident optical energy will be wasted.

Over the past decade,metasurface,planar optical components consisting of patterned nanostructures at subwavelength scale,provides us a variety of opportunities to manipulate amplitude,phase and polarization of light with highly customized meta-atoms.[18–20]Chiral metasurface has been demonstrated to have giant chiroptical effect with optical activity much stronger than that of the natural chiral media.[21–25]Based on chiral metasurface, many different polarization converters have been proposed.[26,27]Asymmetric polarization converter based on metasurface,which has the capability to convert two orthogonal linearly polarized lights with different manner,has shown potential possibility to fabricate a compact and efficient polarizer to surpass the theoretical limit of the conventional polarizers.[28]Recently,several related works realizing asymmetric polarization conversion with chiral metasurface have been reported.Xu and co-workers realized asymmetric polarization conversion of two orthogonal linearly polarized waves around 0.53 THz.[26]Stephen and co-workers demonstrated an asymmetric polarization conversion for two orthogonal linear polarized lights.[29]The proposed structure shows high conversion efficiency of one linearly polarized light to its orthogonal with high transmittance.However, the orthogonal linearly polarized incident light is mostly reflected rather than transmitted.Polarizers based on these structures still suffer from low total linear transmission efficiency of unpolarized incident light.Zhang and co-workers demonstrated a polarizer achieving a total transmission efficiency of 0.44 for linearly polarized transmittance with unpolarized light incidence around 1100 nm.[30]With the development of nanofabrication technology, the research of metasurface has been further developed to design and fabricate high-performance devices working in higher frequency range such as infrared and even visible.[31,32]

In this paper,we propose an asymmetric polarization converter based on multi-layer chiral metasurface which preserves high transmission for one linearly polarized light and convert the orthogonal linearly polarized light to its cross-polarized light with high transmittance.Theoretical results show that normally incidenty-polarized light preserves high transmittance within the working bandwidth from 685 nm to 800 nm while the orthogonal normally incidentx-polarized light is efficiently converted to they-polarized light with high transmittance within the working bandwidth from 725 nm to 748 nm.For unpolarized incident light, transmittance larger than 0.5 has been successfully achieved fory-polarized light in a broadband wavelength range from 712 nm to 773 nm with a maximum totaly-polarized transmittance of 0.58 at 732 nm.The mechanisms of asymmetric transmission for two orthogonal linear polarized light beams have been analyzed in detail.Finally,the surface current distributions are calculated to provide an intuitive image of the coupling between incident light and the metasurface at the resonant wavelength.

Fig.1.Schematic diagram of the proposed asymmetric polarization converter.(a)Three-dimensional structure of 4×4 unit.(b)Top view of the structure in x–y plane of 4×4 unit.(c)Three-dimensional structure of one unit cell.(d)Top view of the structure in x–y plane of one unit cell.(e)Side view of the structure in x–z plane of one unit cell.

2.Device structure and methodology

The schematics of the proposed asymmetric polarization converter are shown in Fig.1,which consists of parallel plates,rectangular gratings, and a dielectric layer inserted between them.Three-dimensional(3D)schematic diagram of 4×4 unit is illustrated in Fig.1(a) with light propagation direction indicated.Thex,yandzdirections are indicated by red, blue,and green arrows, respectively.The colors of linearly polarized light are corresponding to the color of the respective axes.Top view of the structure inx–yplane of 4×4 unit is shown in Fig.1(b).Figure 1(c) indicates a three-dimensional (3D)schematic diagram of one unit cell.Figure 1(d) indicates the top view of the structure inx–yplane.The width of the parallel plates and the gap between them are indicated asg1andg2, respectively.The width of the rectangular grating is indicated asw1.The period of the unit cell inxandydirections are indicated asaxanday, respectively, which are both fixed at 500 nm.Figure 1(e) shows the side view of the structure,and the thicknesses of layers are indicated ash1,h2, andh3,respectively.The top parallel plates and bottom rectangular grating are indicated asL1andL2,respectively.Silica(SiO2)is used as the material of the substrate with a relative permittivity of 2.1[33]and gold (Au) is employed as the material of top parallel plates and bottom rectangular grating with Drude model that is given in the following equation:[34]

whereωp= 1.37×1016Hz andωτ= 4.08×1013Hz are plasma frequency and collision frequency,respectively.Modeling and simulation analyses are performed with the finitedifference time-domain (FDTD) method.Periodic boundary conditions and perfect matched layer are applied inx,y, andzdirections, respectively.[35]To improve the accuracy of the simulation, inhomogeneous mesh settings are applied in the simulation region.A finer mesh size is applied at the interfaces between the metal and the dielectric layer, which is set as 10 nm inxandydirections and 1 nm in thezdirection.A mesh grid of 15 nm is applied to rest of the simulation region.Polarized light is vertically transmitted through the structure in thezdirection from the parallel plates side.

3.Results and discussion

In order to analyze the optical characteristics of the designed metasurface, Jones matrix are used to describe the transmission properties with[36]

wheretxxortyyrepresents co-polarization transmittance ofx- ory-polarized light, respectively, which evaluates the performance of polarization status preservation after passing through the metasurface structure,tyxortxyrepresents crosspolarization transmittance ofx- ory-polarized light, respectively, which evaluates the performance of polarization status conversion.Exiis the amplitude of the incidentx-polarized light andExtis the amplitude of the transmittedx-polarized light.Eyiis the amplitude of the incidenty-polarized light andEytis the amplitude of the transmittedy-polarized light.Figure 2 shows the co-and cross-polarized transmittance spectra ofx- andy-polarized light through the proposed metasurface structure.The cross-polarization transmittancetyxis larger than 0.5 for the wavelength in the range of 725–748 nm with a maximum of 0.53 at the resonant wavelength of 736 nm,while the co-polarization transmittancetxxis close to 0 at the same wavelength.The co-polarization transmittancetyyis larger than 0.5 in the wavelength range from 685 nm to 800 nm with a maximum transmittance of 0.65 at the resonant wavelength of 720 nm, while the cross-polarization transmittancetxyis close to 0 at the same wavelength.With respect to the unpolarized incident light,the total power transmission of light iny-polarization statety=(tyx+tyy)/2 is larger than 0.5 in the wavelength range from 712 nm to 773 nm with a peak value of 0.58 at 732 nm.[30]Accordingly, the proposed metasurface can effectively convert the incidentx-polarized light into its orthogonal polarized light, while the incidentypolarized light mostly maintains the original polarization state after passing through the structure.Asymmetrical manipulation of the polarization status of two orthogonal linearly polarized light beams has been successfully achieved,which means that the energy of the two linearly polarized light could be concentrate into one specific polarized light with reduced energy loss compared to the traditional polarizers.[37,38]

Fig.2.Co- and cross-polarized transmittance and total transmittance in y-polarization state for an unpolarized light incidence of the proposed metasurface.

To further verify the asymmetric conversion performance of the metasurface structure,polarization azimuth angleθand ellipticity angleηare further studied.Polarization azimuth angleθthat represents the rotation angle of the polarization plane of the transmitted light is normally used to evaluate the rotation ability of the metasurface to the polarization plane of incident light.Ellipticity angleηis normally used to evaluate the polarization status of the light,which is defined as the differential transmission between left-handed circularly polarized and right-handed circularly polarized light.Azimuth angleθand ellipticity angleηare obtained as follows:[39]

where the circular transmission coefficientsT++/??can be derived from the linear polarization transmission coefficients byT++/??=[Txx+Tyy±i(Txy ?Tyx)]/2.Whenθ=90?,the polarization plane of the transmitted light has been rotated for 90?.Whenη=0, the light is pure linearly polarized.As shown in Fig.3, polarization azimuth angleθis around 90?and ellipticity angleηis near 5?in the range of 725–748 nm.Accordingly,the transmitted light of incidentx-polarized light is linearly polarized light and the polarization plane has been rotated for 90?.

In order to analyze the effect of chirality,we further study the transmission and absorption differences between left and right circularly polarizations.Figure 4(a)shows the transmittance spectra of left and right circularly polarized light.In Fig.4(a),t++/??represent the circularly polarized transmittance, where ++ and??represent right and left circularly polarizations, respectively.The difference of the circularly polarized transmittance can be obtained by the equation ?t=t++?t??.The right circularly polarized transmittance (t++)is larger than the left circularly polarized transmittance (t??)in the wavelength range from 675 nm to 900 nm.?treaches a peak value of 0.51 at 733 nm,whiletyxreaches a peak value of 0.53 at 736 nm according to Fig.2.From Fig.4(a), large transmission difference between the left and right circularly polarized components of an incoming linearly polarized light has been obtained to be of the proposed chiral structure.In Fig.4(b),A++/??represent the absorption of right and left circularly polarizations,respectively.The difference of the circular absorption which represents circular dichroism(CD)can be obtained by the equation ?A=A???A++.As shown in Fig.4(b), the absorption of left circularly polarized component is larger than the right circularly polarized component in the wavelength range from 675 nm to 900 nm.The difference of the circular absorption reaches a peak value of 0.37 at 716 nm.Transmission and absorption differences between the left and right circularly polarized components of an incoming linearly polarized light finally lead to high cross-polarized transmittance oftyx.

Fig.3.Polarization azimuth angle θ and ellipticity angle η for xpolarized incident light.

Fig.4.Circularly polarized spectra.(a)Transmittance of left and right circularly polarized light.(b) Absorption of left and right circularly polarized light.

To identify the function of each individual layer and to clarify the intrinsic mechanisms,the transmittances of co-and cross-polarization of bothx- andy-polarized incident light beams forL1only and forL1L2(combiningL1withL2) are simulated as shown in Fig.5.For the case ofL1only, the co- and cross-polarization transmittances are almost identical to each other forx- andy-polarized incident light due to the lack of anisotropy of the single layerL1.Bothx- andypolarized light beams could be converted to cross-polarized light.Clearly,there is no asymmetric polarization conversion withL1only.Consequently,L1simply works as a polarization converter.The co-polarization transmittance(txx,tyy)and cross-polarization transmittance (tyx,txy) are smaller than 0.5 in the whole wavelength range studied here.For the case ofL1L2, as shown in Figs.5(b) and 5(d), the cross-polarization transmittancetyxand co-polarization transmittancetyyare significantly improved,which lead to an asymmetric polarization manipulation in the wavelength range from 725 nm to 748 nm.We believe that the asymmetric polarization conversion is due to the symmetry breaking of the metasurface in the direction of propagation with the combination ofL1andL2.

Fig.5.Transmission spectra of L1 and L1L2.[(a),(d)]Co-polarized transmittance txx and tyy.[(b),(c)]Cross-polarized transmittance tyx,txy.

Obviously,L2also play an important role for asymmetric polarization conversion.In order to fully understand the role ofL2,as shown in Fig.6,we simulate and calculate the co-and cross-polarization transmittance and reflectance of bothx-andy-polarized incident light beams.Clearly, the cross-polarized transmittance and cross-polarized reflectance are both nearly zero,denoting that the polarization status of the incident light cannot be rotated withL2only.As shown in Figs.6(a) and 6(c), the co-polarized transmittance ofx-polarized incident light is less than 0.1 and the co-polarized reflectance ofxpolarized incident light is around 0.5 in the wavelength range of 725–748 nm, which means thatL2works as a reflector forx-polarized incident light.On the other hand, as shown in Figs.6(b) and 6(d), the co-polarized transmittance ofypolarized incident light is above 0.85 while the co-polarized reflectance ofy-polarized incident light is less than 0.1 in the same wavelength range, which indicates that most of theypolarized incident light could transmit throughL2.L2with its long axis along they-axis plays a role of polarization filter which allows they-polarized light to pass through and reflects thex-polarized light.

By combing the polarization conversion layerL1with the polarization filter layerL2, a Fabry–P′erot-like resonance is formed in the metasurface structure.[40]As shown in Fig.7,for thex-polarized light, after passing throughL1, thexpolarized light is partially converted toy-polarized light.Most of the convertedy-polarized light is transmitted throughL2.The unconvertedx-polarized light is reflected back toL1and continuously converts toy-polarized light.Finally, owing to the Fabry–P′erot-like resonator,thex-polarized light is mostly converted toy-polarized light.Similarly, for they-polarized light, after passing throughL1, they-polarized light is partially converted tox-polarized light.Most of the unconvertedy-polarized light transmits throughL2, and the convertedxpolarized light is mostly reflected back fromL2,which will be converted toy-polarized light byL1.Finally,y-polarized light shows high co-polarized transmittance throughL1L2.Accordingly, after passing through the proposed structure,x- andypolarized light beams are both transmitted asy-polarized light.

In order to further justify the Fabry–P′erot-like resonance of the proposed structure, the influence of the dielectric substrate thicknessh2,which can be considered as the resonance distance of Fabry–P′erot model,is shown in Fig.8.Clearly,it can be observed that the resonance wavelength of the crosspolarized transmittance forx-polarized incident light redshifts with the increasingh2,conforming to the approximately linear relationship of the resonance distance of Fabry–P′erot modelh2and the resonance wavelengthλ.This observable periodic performance further justifies that the proposed structure has a Fabry–P′erot-like effect.[41]It is worth noting that the strong circular dichroism in both transmission and absorption shown in Fig.4 is benefited from the Fabry–P′erot-like resonance,even though the resonant strength is limited.

Fig.8.Influence of the dielectric substrate thickness h2.

In order to figure out the relationship between transmission performance and the structure period,we depict the influence of the structure period through three transmission spectra, as shown in Fig.9.Cross-polarized transmittance forx-polarized incident light, co-polarized transmittance forypolarized incident light,and total power transmittance of light iny-polarization state are plotted in Figs.9(a)–9(c) for the structure periods of 400 nm,500 nm,and 600 nm,respectively.As shown in Fig.9(a), with the increasing period, the resonance wavelength oftyxredshifts, while the resonance bandwidth and the peak value oftyxare decreased.As shown in Fig.9(b), the peak value oftyyincreases and the resonance wavelength oftyyredshifts with the structure period increasing.As shown in Fig.9(c),total power transmittance of light inypolarization state is larger than 0.5 in the wavelength ranges of 689–723 nm,712–773 nm,and 773–804 nm,corresponding to the structure periods of 400 nm,500 nm,and 600 nm respectively.Total transmission oftygets a maximum transmittance of 0.53 at 707 nm,0.58 at 732 nm,and 0.54 at 786 nm.

Fig.9.Transmission spectra of different structure periods.(a)Cross-polarized transmittance for x-polarized incident light.(b)Co-polarized transmittance for y-polarized incident light.(c)Total power transmittance of light in y-polarization state.

Fig.10.The surface current distribution at L1 and L2 for [(a), (b)] x-polarized incident light, or [(c), (d)] y-polarized incident light at the wavelength of 736 nm.

To analyze the mechanism of the asymmetric polarization conversion in detail, surface current distributions on bothL1andL2at the resonance wavelength of 736 nm are plotted in Figs.10(a)–10(d).Forx-polarized incident light,the instantaneous direction of the current flow ofL1resonator is opposite to that ofL2,which indicates that an equivalent magnetic resonator is formed.[42]Strong coupling from anti-paralleled currents betweenL1andL2promotes the polarization rotation of the incident light.[43]Fory-polarized incident light, instantaneous direction of the current flow ofL1is almost the same as that ofx-polarized incident light with much weaker intensity and the current flow inL2is nearly along the same direction as that inL1.Accordingly, fory-polarized incident light, the equivalent magnetic resonator cannot be excited, which indicates that they-polarized light could pass through the proposed metasurface structure with high transmittance within the working band.

4.Conclusion

In summary, we have proposed a polarization converter with efficient asymmetric polarization conversion for linearly polarized visible and near-infrared light based on a threelayered chiral metasurface.The proposed structure can efficiently convert thex-polarized incident light to its orthogonaly-polarized light and transmit most of they-polarized incident light within the wavelength range from 725 nm to 748 nm.Meanwhile,y-polarized light preserves high transmittance within the working bandwidth from 685 nm to 800 nm after passing through the proposed metasurface structure.Accordingly, for unpolarized incident light, transmittance larger than 0.5 has been successfully achieved in a broadband wavelength range from 712 nm to 773 nm with a maximum totaly-polarized transmittance of 0.58 at 732 nm.Both the ellipticity angle and the polarization azimuth angle verify that the incidentx-polarized light could be successfully converted to cross-polarized light.Transmission and absorption difference of the left and right circularly polarized components of an incoming linearly polarized light indicates the chiral performance,which further verifies the high polarization conversion efficiency.It is also demonstrated that the top parallel plates layer acts as the polarization conversion layer and the bottom rectangular grating layer acts as a polarization filter.The combination of top parallel plates layer and the bottom rectangular grating layer forms an Fabry–P′erot-like resonator, which further boosts the asymmetric polarized conversion efficiency.The redshifts of the resonance wavelengthλwith the increasing resonance distanceh2further verify the Fabry–P′erot-like resonance.Surface current distribution analysis reveals that anti-paralleled currents between top parallel plates layer and the bottom rectangular grating layer promote the polarization rotation, and paralleled currents result in high transmittance of the incident light.We believe that the designed metasurface provides a new route for designing compact and efficient optical asymmetric polarization converter for visible and nearinfrared light with high transmittance, which could break the 0.5 limit of the conventional polarizers.

Acknowledgements

Project supported by the National Natural Science Foundation of China(Grant Nos.62075173 and 12274478),and the National Key Research and Development Program of China(Grant Nos.2021YFB2800302 and 2021YFB2800604).