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Coupling Tai Chi Chiral Metamaterials with Strong OpticalActivity in Terahertz Region

Coupling Tai Chi Chiral Metamaterials with Strong OpticalActivity in Terahertz Region
Coupling Tai Chi Chiral Metamaterials with Strong OpticalActivity in Terahertz Region

Coupling Tai Chi Chiral Metamaterials with Strong Optical Activity in Terahertz Region

Yuanyuan Huang &Zehan Yao &Qian Wang &Fangrong Hu &Xinlong Xu

Received:20October 2014/Accepted:20January 2015/Published online:5February 2015#Springer Science+Business Media New York 2015

Abstract We demonstrated Tai Chi chiral metamaterials of mirror-symmetric and complementary structures in terahertz (THz)region.We investigated the properties of these struc-tures by calculating the transmissions under different circular-ly polarization waves and analyzing the surface current distri-butions.The chiral mirror-symmetric structure has circular dichroism and strong optical activity due to electromagnetic field coupling between layers with sub-wavelength thickness.Moreover,the structures with multiple metallic layers or twist angle between layers can realize chirality tunability,which can be used for THz polarized devices.Besides,the complemen-tary structure has potential applications for polarization-insensitive devices in THz region.

Keywords Chiral metamaterial .Terahertz .Optical activity .Circular polarization

Introduction

Chirality refers to the geometrical property that the original structure cannot be brought to a congruence of its mirror im-age [1].Chirality appears in some natural molecules such as sugar molecules,amino acids,and some organisms like snail

shells.Optical activity and circular dichroism are most unique optical properties induced by chiral structures.Optical activity refers to the polarization rotation due to the different refraction indexes for the left circularly polarized (LCP)light and right circularly polarized (RCP)light.Circular dichroism,however,is due to the differential absorptions of LCP and RCP light [2].These optical properties have a wide range of applications in biology,chemistry,mineralogy,medical science,as well as polarized optoelectronic devices.

However,the weak optical activity and circular dichroism in natural structures are needed to be further enhanced for both theoretical understanding of chirality and potential device de-sign.Strong artificial chirality in metamaterial affords an ef-fective way for this purpose.Metamaterial as a kind of artifi-cial materials consists of sub-wavelength metallic structures with remarkable properties that natural materials do not have [3].Based on the structure-determine-property principle,ex-otic electromagnetic response,ranging from microwave re-gion through terahertz (THz)region to visible region has been demonstrated.For example,Pendry et al.[4]and Tretyakov et al.[5]put forward a Swiss-roll structure to realize negative refraction using chiral metamaterial in the early days.Many chiral structures such as inductor-capacitor circuit structure [6],planar U-shaped split ring resonators [7],and complemen-tary bi-layer cross-wire [8]have been proposed to realize neg-ative refraction afterward.Besides,optical activity [9,10]and circular dichroism [11]in chiral metamaterials are elaborated in many literatures as well,such as rosettes structure [12],U-shaped structure [13,14],twisted-arc structure [15],and many other unique structures [16–19].

THz region is viewed as the gap between the microwave region and infrared region,which is lack of suitable natural materials exhibiting sensitive THz response,especially for THz polarization manipulation.Chirality of natural materials mainly originates from ensembled vibrations (phonons)in THz region,which are different from the electronic responses

Y .Huang :Z.Yao :Q.Wang :X.Xu (*)

State Key Lab Incubation Base of Photoelectric Technology and Functional Materials,International Collaborative Center on

Photoelectric Technology and Nano Functional Materials,Institute of Photonics &Photon-Technology,Northwest University,Xi ’an 710069,China

e-mail:xlxuphy@https://www.wendangku.net/doc/6b6491068.html,

F.Hu

Laboratory for Terahertz,College of Electronic Engineering and Automatization,Guilin University of Electronic Technology,Guilin 541004,People ’s Republic of China

Plasmonics (2015)10:1005–1011DOI 10.1007/s11468-015-9892-7

in visible region,resulting in weak responses for THz wave.Chiral metamaterials in THz region can solve the problem perfectly not only for physics but also for technology.In phys-ics,these chiral metamaterials can harness the chiral electric field,which can enhance the chiral responses of natural mate-rials [20].In technology,chiral metamaterials can fertilize THz devices such as polarization rotator [21,22],wide angle absorber [23],and so on.Thus,the pursuit of strong optical activity is desirable for the development of THz technology.Inspired by traditional Chinese Tai Chi pattern,in this pa-per,we designed chiral metamaterials using chiral mirror-symmetric and complementary structures,of which electro-magnetic responses are in THz region with two resonant modes.We investigated the coupling modes,optical activity,and circular dichroism in these two structures.It is found that mirror-symmetric structure has chirality with much stronger optical activity per wavelength compared with other struc-tures,while complementary structure does not have optical activity.In addition,the chiral properties of mirror-symmetric structure can be tuned with multiple metallic layers and different twist angles between layers for tunable THz chirality.The complementary structure with polarization in-sensitivity can be utilized for polarization-insensitive THz components.

Metamaterial Design and Simulation Metamaterial Design

Figure 1illustrates the geometries of Tai Chi chiral metama-terials.Each unit cell consists of three layers.Mirror-symmetric Tai Chi patterns (Fig.1a )are mirror-symmetric with Z axis direction when we put top and bottom layers in X-Y plane.The top and bottom are metallic layers with thick-ness d =0.2μm and conductivity σ=5.8×107S/m [24,25],separated by a middle layer with polymer of thickness t d =

10μm and permittivity of 2.67[26].In the complementary structure (Fig.1b ),two metallic layers are complementary to generate a whole Tai Chi pattern when they are put in X-Y plane.All parameters are the same as the mirror-symmetric Tai Chi structure:the length of unit cell w =60μm,the radius of two semi-circle r 1=24μm,r 2=12μm,and the radius of the smallest circle r 3=2μm,respectively.Results and Analysis

Numerical simulation using finite integration technique [27]is employed to calculate the transmissions and reflections.Unit cell boundary conditions are set in both X and Y directions,while open boundary condition is set in Z direction.THz waves propagate in ?Z direction.We use frequency domain solver with tetrahedral mesh type,in which case the S-parameters S 21and S 11represent the properties of transmis-sions and reflections,respectively.

Figure 2shows transmission and reflection properties of the chiral mirror-symmetric structure and complementary structure for left-circular polarized (LCP,?)and right-circular polarized (RCP,+)waves.As shown in Fig.2a ,there is no difference between transmission coefficients of LCP (T ??,the first subscript represents the polarization of exit wave and the second represents polarization of incident wave)and RCP (T++)for frequency less than 1.5THz.However,near the resonant frequency F 1=1.85THz,T ??and T++change sharply in the opposite trend.At F 1,T ??gets to maximum 0.787,and the minimum of T++is only 0.106.T ??begins to decrease out of F 1region,while T++begins to increase.At another resonant frequency F 2=2.95THz,T++reaches to maximum 0.777and T ??reaches to minimum 0.13.These results suggest circular dichroism in chiral mirror-symmetric structure.The reflections of LCP and RCP are equal complete-ly and go to minimum in the resonant region.The reason of equal reflections can be deduced by a chiral slab media model in reference [28

].

Fig.1Schematic of chiral metamaterials:a mirror-symmetric Tai Chi structure,b complementary Tai Chi structure.Geometrical parameters of two structures:w =60μm,r 1=24μm,r 2=12μm,r 3=2μm.The

thickness d of metallic layers and td of dielectric layers are 0.2and 10μm,respectively

Compared with mirror-symmetric structure,complementa-ry structure shows similar resonance at F 1=1.75THz,F 2=2.88THz (Fig.2b ).However,the transmission and reflection of the LCP and that of the RCP waves show almost no differ-ence in the whole region,which suggest polarization insensi-tivity for the complementary structure.To deeply understand the mechanism of polarization insensitivity,we studied the surface current distribution in the following.Surface Current Discussion

We have calculated the T ??and T++of mirror-symmetric structure with only one metallic layer on the top,which shows no optical activity.This suggests that the strong chirality in mirror-symmetric structure is induced by the coupling of the top-bottom metallic layers.To better understanding of the mechanism,we analyze the coupling modes referring to the model in reference [29].Firstly,we plot the surface current distributions of the two different structures under LCP and RCP waves at resonant frequencies,which are shown in

Figs.3and 4.Figure 3a,c is surface current distributions under LCP and RCP waves at resonant frequency F 1=1.85THz.We can observe a strong current flowing in an anti-clockwise rotation in the arc cusp pair under RCP wave.This suggests a powerful electromagnetic field twisting under the RCP wave [15]due to strong interaction between chiral struc-ture and THz wave,resulting in much lower transmission (Fig.2a ).However,under LCP wave,the current flowing in top and bottom layers shows the opposite directions with much less intensity,which suggests the limited interaction between THz wave and metamaterial,resulting in high trans-mission (Fig.2a ).Meanwhile,Fig.3b,d is surface current distributions under LCP and RCP waves at resonant frequen-cy F 2=2.95THz.The weak current flowing in a clockwise rotation in the arc cusp pair under RCP wave is observed.Under LCP wave,the strong current flowing in top and bot-tom layers also shows the opposite directions.All analyses above are consistent with the transmission results (Fig.2a ).Figure 3a,b also suggests that the charges of the same sign due to the induced currents in the top and bottom layer

will

Fig.2Transmissions (red and blue curves )and reflections (black curves )of a mirror-symmetric structure and b

complementary structure for LCP (red ,T ??)and RCP (blue ,T++)

waves

Fig.3Surface current of mirror-symmetric structure at F 1=1.85THz:a and c represent LCP and RCP results,respectively;surface current at F 2=2.95THz:b and d represent LCP and RCP results,respectively.The size and pseudo-color of short arrows indicate surface current intensity,and the long arrows point to the directions of current flowing

accumulate in the corners under LCP excitation,which is viewed as antisymmetric modes.However,the opposite charges will accumulate in the corners under RCP excita-tion (Fig.3c,d ),which suggest symmetric modes [30].When the RCP wave impinges on the structure,the charge flowing will decrease the restoring force and energy.On the other hand,the induced charge flowing is repulsive be-tween layers when the structure is under LCP illumination.This will increase the restoring force and lead to higher resonant frequency.

In contrast to chiral mirror-symmetric structure,the sur-face current distributions in complementary structure are independent of LCP and RCP waves (Fig.4a,b ).As shown in Fig.4,we compare the current flowing under LCP and RCP illumination at resonant frequency F 2=2.88THz and find out that the directions of induced currents in top and bottom layer under LCP wave are the same as the directions under RCP wave.The result at the resonant frequency F 1=1.75THz is similar with that of F 2.Based on the analyses,we can explain why the transmissions under two polarized waves are almost equal with each other (Fig.2b ).Thus,the complementary structure is polarization insensitive and leads to low transmissions and reflections in resonant re-gion.This structure could also be used as polarization-insensitive THz components [31].

Optical Properties and Discussion Optical Activity and Circular Dichroism

On account of structural particularity in the chiral structure,

the refractive indexes for LCP and RCP waves are different.This leads to phase retardation between the two circularly polarization waves,which will in turn cause rotation of the THz waves.Optical activity refers to the rotation character of linearly polarized wave.The linearly polarized wave can be regarded as a superposition of coherent LCP and RCP waves with equal amplitude.Thus,optical activity can be

characterized by polarization azimuth rotation angle of circu-larly polarization waves as follows [32]:θ?

1

2

arg T L eT?arg T R eT? e1T

where arg(T L )and arg(T R )represent the phase information of LCP and RCP waves,respectively.In addition to phase retar-dation,different absorption of LCP and RCP waves will in-troduce circular dichroism,which can be characterized by ellipticity and can be expressed as follows [13]:η?12tan

?1T L j j 2?T R j j 2T L j j 2tT R j j 2

!e2T

Figure 5c shows the calculated polarization azimuth rota-tion angle and ellipticity for the mirror-symmetric structure.At resonant frequencies F 1=1.85THz and F 2=2.95THz,the azimuth rotation angles θreach to maximum 145°and mini-mum ?86°,respectively.The ellipticity ηalso transits from 0.37to ?0.37°as the resonant frequency changes from F 1to F 2.Between the two resonant frequencies,there is a small dispersion region (near 2.28THz),where ellipticity ηequals to zero and the pure rotary angle θis approximately 19°.Considering the thickness of only 10.4μm and wave-length λis 162μm at 1.85THz,the peak rotary angle and pure rotary angle of the structure are 2258°/λand 296°/λ.According to the analyses above,we can infer that Tai Chi mirror-symmetric structure with sub-wavelength thickness has strong optical activity,which is bigger than some natural materials such as quartz (0.02°/λat 400nm)[12].Besides,the strength of optical activity characterized by peak rotary and pure rotary is stronger than some other THz chiral metamate-rials,like bi-layer cross structure [33]with maximum rotation angle 70°,U-shaped resonator assembly [34]with maximum ?72°,bi-layer conjugated structure [35]with only 45°.This could have potential applications in ultrathin polarization ro-tator and other polarized THz

devices.

Fig.4Surface current of complementary structure at

resonant frequency F 2=2.88THz under a LCP and b RCP waves illumination.The size and pseudo-color of short arrows indicate surface current intensity,and the long arrows point to the directions of current flowing

layer and four-layer structures

curves for clarity of viewing

Coupling of Multiple Layers and Twist Angle

Unlike the on-plane chirality[9],the chirality in our design is from the electromagnetic field coupling between layers.This coupling could introduce giant polarization rotary[36].The coupling could be understood by the layer stacking and twist of patterns between layers,which in turn can be used to realize tunable chirality.Figure5a shows multi-layer pattern of the mirror-symmetric Tai Chi structure,and the numbers represent the different metallic layers.The parameters of structure and simulation environment are the same as before.We simulate one-layer,three-layer,and four-layer(the thickness td of di-electric layer is15μm)structures.The transmissions of one-layer and three-layer structures under LCP and RCP waves are shown in Fig.5b.It is obvious that the T??and T++of these two structures are almost the same with each other.The one-layer structure has one resonant frequency at F=2.34THz and the three-layer structure has three resonant frequencies:F1= 1.62THz,F2=1.86THz,and F3=3.18THz.It is inferred that the one-layer and three-layer structures are insensitive with the polarization of incident wave.On the other hand,the T??and T++of two-layer and four-layer structures are absolutely dif-ferent,characterized by rotation angle and ellipticity(Fig.5c, d).In two-layer structure,we have calculated the peak rotary angle and pure rotary angle are2258°/λand296°/λ.In the four-layer structure,the peak rotary angle and pure rotary angle are130°at2.92THz(1367°/λ).The maximum of ellip-ticity for the two structures are both0.4.We investigate the properties of multi-layer structures by analyzing the surface current distributions as well.Similar to the coupling model proposed by Liu et al.[37],we have discussed the surface current of two-layer structure,which has symmetric and anti-symmetric modes.For one-layer structure,the induced cur-rents in the layer under LCP wave are the same as the direction under RCP wave at resonant frequency F=2.34THz.For three-layer structure,although the direction and intensity of induced currents under LCP wave are different from that un-der RCP wave at resonant frequencies,the same modes em-body the same energy and resonant intensity.On the contrary, the modes of four-layer structure are totally different under LCP and RCP waves.Thus,the transmissions of one-layer and three-layer structures are independent with the polariza-tion state of incident wave,while the two-layer and four-layer structures are polarization sensitive and generate chirality with strong optical activity.Based on the obvious difference,we can utilize the chiral structures with different metallic layers as chirality switch.

For normal mirror-symmetric structure(Fig.1a),different twist angles between top and bottom layers are able to tune the chirality as well.The schematic of twist structure is shown in Fig.6a,whereαrepresents the twist angle.We simulate the structures whenαequals0,15,30,45,60,75,90°,the trans-missions under LCP and RCP waves are dependent with the angles.We present resonant frequencies F1(under RCP wave) and F2(under LCP wave)as a function of twist angle (Fig.6b).It is obvious that F1increases with the increase of twist angle,while F2decreases with the increase of twist an-gle.The distance between F1and F2decreases whenαin-creases until it gets to minimum at around55°.In addition, the resonance under RCP wave is predominant at low resonant frequency,while the resonance under LCP wave plays a pri-mary role at high frequency.The results are reversed whenαexceeds55°.According to the change of resonant frequencies, we can explain the variation of rotation angle and ellipticity precisely.As shown in Fig.6c,d,the maximum of polariza-tion azimuth rotation angle and ellipticity appear at two reso-nance frequencies.The distances between two resonances de-crease untilαexceeds60°.Moreover,the values of rotation angle and ellipticity begin to reverse whenαgets to60°, indicating the strength of resonance under LCP and RCP waves are reversed as well.As discussed above(Fig.6b), 55°is a critical point,the strong resonance under RCP (LCP)wave at F1(F2)lead to lower transmission whenαless than55°and the strength of resonance and transmission re-verse after55°.Hence,we can observe the reversed phenom-enon whenαequal60,75,and90°.Totally,the multiple metallic layers and twisted mirror-symmetric structures can tune the chiral properties effectively.This remarkable feature could expand THz applications of the chiral Tai Chi structure. Conclusion

In summary,we have designed chiral metamaterials using Tai Chi pattern of mirror-symmetric and complementary struc-tures.The transmissions under LCP and RCP wave illumina-tion of mirror-symmetric structure are tremendously different at resonant frequencies,while the results of complementary structure are polarization independence.The mirror-symmetric structure has circular dichroism and strong optical activity due to coupling between layers,of which the peak rotary angle and pure rotary angle of the structure are2258°/λand296°/λwith sub-wavelength thickness.The values are much higher than some natural and artificial chiral structures in THz region.Moreover,we infer that the mirror-symmetric structure with multiple metallic layers and different twist an-gles between layers can realize the tunable chirality,which could also be benefit for coupling understanding of chirality. Acknowledgments This work was supported by National Science Foundation of China(No.11374240and61265005),Natural Science basic Research Plan in Shaanxi Province of China(No.2012KJXX-27), Ph.D.Programs Foundation of Ministry of Education of China(No. 20136101110007),Key Laboratory Science Research Plan of Shaanxi Education Department(13JS101),National Key Basic Research Program (2014CB339800).

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九年级课文翻译完整版

九年级课文翻译 Document serial number【NL89WT-NY98YT-NC8CB-NNUUT-NUT108】

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