Li Hu(胡莉) Hongxia Dai(代洪霞) Fayin Cheng(程发银) and Yuxia Tang(唐裕霞)

1Chongqing Key Laboratory of Intelligent Perception and BlockChain Technology,Chongqing Technology and Business University,Chongqing 400067,China

2Department of Applied Physics,School of Computer Science and Information Engineering,Chongqing Technology and Business University,Chongqing 400067,China

3Soft Matter and Interdisciplinary Research Center,College of Physics,Chongqing University,Chongqing 400044,China

Keywords: plasmonic resonance,chiral near-field,graphene,metasurface

1. Introduction

Chirality is a geometric property of objects, which indicates that the objects could not overlap with their mirror images through simple translations or rotations. There are a lot of chiral molecules in nature, for instance, proteins, DNA,nucleic acids, and so on.[1,2]Because chiral molecules with the opposite handedness generally show different behaviors in biological processes, the recognition and discrimination of chiral molecules are extremely important in analytical chemistry, biology and pharmacology.[3,4]Nevertheless, the chiral response of natural molecules is very weak and occurs in the ultraviolet region,which hampers their further applications.

In recent years, owing to the excellent properties of the light confinement and local field enhancement, plasmonic nanostructures have drawn a lot of attention owing to their potential applications in light absorption, Raman scattering,chiral response, etc.[5–10]Based on the plasmonic resonance,various metamaterials have been proposed to enhance chiral responses in both the far-field and near-field.[11–14]Especially,the chiral near-field has attracted a lot of interest due to its wide applications, such as molecular recognition, detection,separation,and sensing,[15–18]which are expected with the excellent properties of enough strength,single handedness,large area, etc. Utilizing the plasmonic resonance of metal materials, strong chiral near-fields have been obtained in the visible and near-infrared regions with various chiral and achiral nanostructures.[19–23]In order to obtain chiral responses in the mid-infrared region,graphene is considered to be the best alternative material, because doped graphene nanostructures show strong plasmonic resonances with a relatively low loss.Meanwhile,graphene nanostructures could be accurately fabricated and transferred to various substrates and the plasmonic resonance could be controlled by chemical doping and electrical doping.[24–28]In addition, the twisted bilayer graphene also has chiral properties.[29–31]Therefore, many graphene and graphene-based nanostructures have been designed to generate strong chiral responses.[25,32–35]For example, Konget al.obtained giant circular dichroic (CD) responses with chiral graphene assemblies;[26]Wanget al.designed the achiral metal-nanorods with graphene-nanobelt arrays to achieve CD signals;[36]Fuet al.proposed an achiral nanoring to achieve chiral near-field;[25]chiral near-field also had been achieved with twisted bilayer graphene.[37]For the studies of chiral near-fields, most of them are either complex in structures, or the chiral fields are both left-and right-handed,or the response area is small. As a result, achieving a strong uniform chiral near-field in the mid-infrared region still presents a challenge.

In this work, a graphene metasurface, composed of two same nanosheets in a unit cell, is proposed to produce strong and uniform superchiral fields with both circularly polarized light (CPL) and linearly polarized light (LPL) illuminations. With the metasurface,a one-handed chiral near-field is achieved in the gap of two graphene nanosheets,which could be controlled by the Fermi level of the graphene sheets and the other parameters, and whose handedness could be controlled by the wavelength and the polarization direction of the incident light. To understand the physical mechanism generating the uniform chiral near-field, the distributions of electric and magnetic fields are analyzed.

2. Method and model of simulation

In order to achieve enhanced single-handed near-fields at the mid-infrared region with easily prepared nanostructures, here, we proposed a graphene metasurface composed of single-layer graphene arrays with a symmetric nanosheetdimer in each unit cell on the substrate,as shown in Figs.1(a)and 1(b).The graphene arrays are located on thex–yplane and the exciting light is propagated along thez-axis. The array is a periodic structure with a fixed period of 300 nm both inx-andy-directions. The side lengtha=b=80 nm,and the distance of the gap between the two nanosheets is set asg. The monolayer graphene is deposited on the low resistivity Si substrate(εs=12.04) and the whole nanostructure is placed in the airεm=1. The single-layer graphene nanosheets could be characterized by the surface conductivityσs,which is a function of the frequency of the exciting light and involves contributions from inter-and intra-band transitions,[34]

wheree, ¯h,kB,Ef,T, andτare the electron charge, reduced Planck’s constant, Boltzmann’s constant, Fermi level of graphene, temperature(T=300 K),and carrier relaxation time,respectively. Here,τ=µEf/ev2f,µ(10000 cm2/(V·s))is the moderate carrier mobility,vf(106m/s)is the Fermi velocity, and the angular frequency of the stimulating light isω=2πc/λ(λis the incident wavelength of light in the vacuum;cis the speed of light in the vacuum). The thickness of the monolayer graphene sheets is set astg=1 nm. So, the equivalent relative permittivity of the graphene could be expressed as

whereε0is the permittivity of the vacuum. The sample is easy to prepare in practice.The monolayer graphene grown on copper foil by chemical vapor deposition(CVD)could be repeatedly transferred to the predefined position on the substrate.

Here,to quantify the chiral near-fields,the optical chiralityCis used,[38]

3. Results and discussion

Fig. 1. (a) Top view of a unit cell of graphene metasurfaces with structural parameters. (b) 3D schematic of the graphene metasurface. (c)Absorption spectra of the metasurface stimulated with RCP(black solid line)and LCP(red dot line). Inset: the distributions of surface charge density of graphene nanosheets excited with LCP at two resonance wavelengths (purple dot: 16.25 µm, green dot: 18.4 µm). (d) Averaged optical chirality enhancement spectra of the gap between two graphene nanosheets stimulated with RCP(black line)and LCP(red line). Here Px=Py=300 nm,a=b=80 nm,tg=1 nm,g=10 nm,Ef=0.6 eV,and T =300 K.

To achieve a deep understanding of the physical mechanism of the chiral near-field response, the near-field maps of the metasurface are simulated. Owing to the symmetric properties of chiral responses with LCP and RCP illuminations,here,we only discuss the near-field properties excited by LCP.As depicted in Figs. 2(a) and 2(b), when the incident wavelength is 18.4 µm (the wavelength of the resonance peak),the enhancements of the electric field and magnetic field are stronger than those of the others (18.2 µm: chiral peak II;18.6 µm: chiral peak I, as shown in Fig. 1(d)). For the three scenarios (the wavelengths of the incident light are 18.2 µm(i),18.4µm(ii)and 18.6µm(iii),respectively),the strongest enhancements of the magnetic fields occur on both sides of the graphene nanosheets(Fig.2(a)),but the strongest enhancements of the electric fields are distributed in the gap between the two graphene pieces (Fig. 2(b)). Accordingly, there are chiral near-field responses around the graphene sheets illuminated with the three wavelengths. However,extremely different from the distributions of the electric and magnetic fields,the chiral near-field enhancements in the gap between the two graphene pieces are obviously enhanced at 18.2µm(Fig.2(c)-i) and 18.6 µm (Fig. 2(c)-iii), which could be up to two orders of magnitude, but nearly vanish at 18.4 µm (Fig. 2(c)-ii). Meanwhile,the handedness of the chiral near-fields in the gap is uniform and just opposite for 18.2 µm and 18.6 µm(Figs.2(c)-i and 2(c)-iii), which is very important in applications of chiral separation,sensing,etc.

Therefore, we mainly focus on the chiral near-field between two graphene nanosheets in this work(just as Fig.1(d)).To further explain the chiral flip,the components of the electric field and magnetic field are calculated with the illuminations of 18.2µm,18.4µm,and 18.6µm,respectively. As shown in Figs.3 and 4,the components of the electric fields are consistent and the magnetic fields are exactly opposite for 18.2µm and 18.6 µm, which just lead to the opposite handedness of the chiral near-fields owing toC∝Im(E∗·B). Therefore,we could achieve extremely enhanced single-handed near-fields and the handedness could be tuned by the wavelength and the polarization of the exciting light with the symmetric metasurface.

Fig. 2. The 2D maps of the enhancement of magnetic field (a), electric field (b) and optical chirality (c) in a unit cell at the x–y plane of graphene metasurfaces excited by LCP with the wavelength 18.2µm(i),18.4µm(ii)and 18.6µm(iii). The x–y slices are cut from the middle position of the graphene nanosheets. H0 and E0 are the incident magnetic and electric fields.

Fig.3. The x-components(a),y-components(b)and z-components(c)of electric field maps of an unit cell excited with LCP at the wavelength of 18.2µm(i),18.4µm(ii)and 18.6µm(iii). The x–y slices are cut from the middle position of the graphene sheets.

Fig.4.The x-components(a),y-components(b)and z-components(c)of magnetic field maps of an unit cell excited with LCP at the wavelength of 18.2µm(i),18.4µm(ii)and 18.6µm(iii). The x–y slices are cut from the middle position of the graphene sheets.

As discussed above,the area of chiral near-fields is important in applications such as chiral detection and sensing,here,it could be adjusted by the distance between two nanosheets.Meanwhile, the coupling effect between two metamolecules depends on the distance between the metamolecules. Based on these, it is necessary to discuss the dependence of chiral near-fields on the distance between two nanosheets. As shown in Fig.S1b(supporting information),with the distance(g)increasing from 10 nm to 25 nm and the other parameters keeping the same as those in Fig. 1, the resonant peak of the longer wavelength blue shifts. Correspondingly, the peak (at the longer wavelength) of the averaged optical chirality enhancement blue shifts and the strength decreases (Fig. 5(b)),which is a result of the decrease of the coupling effect between the two graphene nanosheets. Thus, in applications, the area and the strength of the single-handed near-field could be controlled by changing the distance between the two nanosheets.

Besides the gap, the other parameters also affect the response of chiral near-fields. As we all know,the size of plasmonic structures has an influence on plasmonic resonances.When we change the side lengths(aandb,a=b)from 60 nm to 80 nm and fix the other parameters as those in Fig. 1, the resonant peak red shifts and their strength increases,as shown in Fig. S1c (supporting information). However, for the averaged optical chirality enhancement in the gap between the two graphene sheets, as shown in Fig.5(c), the peak of the chiral response red shifts but the strength stays roughly the same with the increase of the side lengths. Meanwhile,the substrate material plays an important role on plasmonic resonances. When the permittivity of the substrate(εs)changes from 8 to 14,and the other parameters remain unchanged,the resonant peak red shifts and the strength decreases (Fig. S1d (supporting information)),which further results in a similar change for the chiral near-field response of the gap (Fig. 5(d)). Therefore, we could adjust different parameters to meet the requests of different applications.

As it has been shown in many studies,owing to the interaction between the incident field and scattered field,the chiral near-field could be achieved in symmetric nanostructures excited with LPL at normal incident.[19,21,40,41]In light of this,here,we also study the chiral near-field of the symmetric metasurface with LPL illuminations at two polarized directions,as shown in Fig. 6(a). For simplicity, we denote the two polarization cases of LPL with ①and ②. Here, ①means the polarization direction along the diagonal of the positivex-axis and the positivey-axis, and ②means the polarization direction along the diagonal of the positivex-axis and the negativey-axis. As that of illuminated with CPL, due to the coupling effect between the two nanosheets, there are two resonance peaks(λ=16.25µm,18.4µm)illuminated with LPL both ①and ②,which coincide with each other,as shown in Fig.6(b).As expected,but different from that of illuminated with CPL,there is a pronounced enhancement of the volume-averaged optical chirality in the gap between the two sheets at the plasmonic resonant peak (λ=18.4 µm) and the handedness of the chiral near-fields is just opposite with two polarizations of ①and ②, as shown in Fig. 6(c). When the metasurface is excited withλ=18.4 µm, similar to that of excited with CPL,the strongest enhancements of magnetic fields(Fig.6(d))and electric fields (Fig. 6(e)) are distributed at different districts, and the maximum uniform enhancement of the chiral near-fields (Fig. 6(f)) still occurs in the gap between the two nanosheets.

Fig.5. Averaged optical chirality enhancement spectra of the gap between two graphene nanosheets of the graphene metasurface with different Fermi levels(a);different gaps(b);different side lengths(c)and different permittivity of substrates(d)excited by CPL.The other parameters are the same as those in Fig.1.

Similarly, the plasmonic resonance and chiral near-field could be tuned by the Fermi level of graphene and the other parameters with LPL illumination. For comparison, we change one parameter every time and the others remain the same as those in Fig. 1. The plasmonic resonances change with the variable parameters, as shown in Fig. S2 (supporting information). For the chiral near-field in the gap between the two graphene nanosheets,as shown in Fig.7(a),with the increase of the Fermi level, the chiral response enhances and the response wavelength has a blue shift. When the gap between the two nanosheets enlarges,the chiral response obviously decreases and the wavelength blue shifts(Fig.7(b)). The wavelength of the chiral response red shifts but the strength change little with the side length (aandb) increasing (Fig. 7(c)).With the increase of the permittivity of the substrate,the chiral response gradually decreases and the wavelength red shifts(Fig. 7(d)). Therefore, we can also tune the wavelength and strength of chiral near-field response by Fermi levels and various structural parameters in different applications with LPL illumination.

Fig.6.(a)Schematic of the polarized direction of the incident electric field, ①represents the incident electric field along the diagonal of+x and+y directions and ②means the incident electric field along the diagonal of+x and −y directions. (b)The absorption spectra of the graphene metasurface excited with linear polarized light. The insets show the surface charge distributions of graphene sheets at resonance peaks. (c)The averaged optical chirality enhancement spectra in the gap between two graphene sheets excited with LPL.Black lines: the polarized direction as shown in ①;red lines: the polarized direction as shown in ②. The 2D maps of the enhancement of magnetic field(d),electric field(e)and optical chirality(f)in a unit cell at the x–y plane of the graphene metasurface excited by LPL at 18.4µm. i: the polarized direction of LPL as shown in ①; ii: the polarized direction of LPL as shown in ②. The x–y slices are cut from the middle position of the graphene nanosheets.H0 and E0 are the incident magnetic and electric fields. All parameters are the same as those in Fig.1.

Fig.7. Averaged optical chirality enhancement spectra of the gap between two graphene nanosheets of the graphene metasurface with different Fermi levels (a); different gaps (b); different side lengths (c) and different permittivity of substrates (d) excited by LPL (Fig. 6(a)- ①). The other parameters are the same as those in Fig.1.

4. Conclusion

In summary,a graphene metasurface with a symmetrical structure is proposed to generate strong chiral near-fields with both CPL and LPL illuminations. Owing to the near-field interaction between different plasmonic modes excited by CPL,a strong single-handed near-field is obtained in the gap between the two nanosheets. With the increase of the Fermi level,the peaks in the averaged optical chirality enhancement spectrum blue shift and the intensities increase. With the distance of the two nanosheets increasing,the area increases but the strength of the chiral near-field in the gap decreases.Meanwhile,the response of the chiral near-field in the gap is influenced by the size of graphene and the permittivity of the substrate. On the other hand, based on the interaction between the incident field and scattered field, one-handed chiral fields could be obtained in the same district with the LPL illumination. Especially,all the handedness of chiral near-fields could be switched by the polarization of the incident light. Thus,the simple graphene metasurface could be used in the detection,sensing and separation of chiral molecules.