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Graphene ribbon based tunable terahertz metalens for dual polarization incidences
Optical Materials 97 (2019) 109325
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Graphene ribbon based tunable terahertz metalens for dual polarization incidences Yuhui Zhanga, Linfeng Maa, Zhiying Liua,b,c, Yuegang Fua,b,c,
T
⁎
a
School of Optoelectric Engineering, Changchun University of Science and Technology, Changchun, 130022, China Key Laboratory of Optoelectronic Measurement and Optical Information Transmission Technology of Ministry of Education, Changchun University of Science and Technology, Changchun, 130022, China c Key Laboratory of Advanced Optical System Design and Manufacturing Technology of the Universities of Jilin Province, 130022, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Tunable metalens Graphene ribbon Terahertz focusing
We propose a graphene ribbon based metalens that can achieve the function of tunable metalens in THz region. Different from these graphene ribbon based metalens that have been reported before, the proposed metalens can focus the x- and y-polarized incident THz wave separately by reconfiguring the Fermi energy distribution of the graphene ribbons. The proposed metalens can also focus the incident wave at different spatial positions and different working frequencies. The simulated results are in good agreement with the designed values. Our findings are beneficial in designing new active terahertz devices.
1. Introduction Metamaterials have attracted much interest due to their unprecedented electromagnetic properties such as negative refraction index [1–3], perfect lens [4] and invisible cloaks [5] in recent years. Metasurface, as a two-dimensional planar version of metamaterial, also possesses novel functions such as optical activity, circular elliptical dichroism and perfect absorption. As a remarkable characteristic, electromagnetic wavefront manipulation, arising from the phase responses of the resonant elements [6,7], is also attracting growing attention in the scientific communities. Various metasurfaces have been reported to achieve the function of metalens [8–12]. However, most of the proposed metalens are composed of metallic or dielectric materials, which lack dynamical control once fabricated and limit the further applications. Recently, graphene has been considered in metasurface construction due to its excellent ability to support THz surface plasmons [13–16] and the conductivity of graphene can be dynamically tuned by manipulating its Fermi energy via chemical doping or electrical gating. Thus, various graphene based THz metalens have been reported [17–19] by researchers. Most recently, graphene ribbon based tunable metalens has been investigated in many reports [20–25], because the Fermi energy of each ribbon can be separately tuned by applying gate voltage, and the phase response can be tuned at will. However, these graphene ribbon based metalenses can focus only one polarization state incident wave. In this paper, we propose and demonstrate a tunable terahertz ⁎
graphene ribbon based metalens, which can separately focus both xand y-polarized incident waves at different spatial positions and different working frequencies via manipulating the Fermi energies of the graphene ribbons. By configuring the Fermi distribution, we first design the metalens with a focal length of F = 300 μm and a working frequency of 6 THz. Both x- and y-polarized incident wave can be focused well by the proposed metalens, and the simulated results agree well with the designed values. Then by reconfiguring the Fermi energies of graphene ribbons, we design the focal spot with off-center focusing, transverse alignment dual focusing, longitudinal alignment dual focusing and a different working frequency of 5.5 THz, respectively. Both x- and y-polarization incidences perform excellent focusing effects. 2. Structure design and theoretical analysis Fig. 1(a) shows the schematic diagram of the proposed graphene ribbon based metalens. The proposed metalens is designed to reflect and focus the incident THz wave. Fig. 1(b) shows the cross-sectional view of the proposed graphene ribbon based metalens. A gold layer is on the bottom of the structure and acts as a reflecting mirror. The graphene ribbons is on the top of the structure, and the two layers are separated by a dielectric polymer spacer due to its low absorption and stable refraction index of about 1.53 across the THz band [26]. The thicknesses of the gold and dielectric layers are set as tg = 2μm and tp = 8μm , which ensure a phase modulation of almost 2π while maintaining high reflectivity at the working frequencies. As we can see from
Corresponding author. School of Optoelectric Engineering, Changchun university of science and technology, Changchun, 130022, China. E-mail address: [email protected] (Y. Fu).
https://doi.org/10.1016/j.optmat.2019.109325 Received 30 May 2019; Received in revised form 3 August 2019; Accepted 15 August 2019 0925-3467/ © 2019 Elsevier B.V. All rights reserved.
Optical Materials 97 (2019) 109325
Y. Zhang, et al.
Fig. 1. (a) Schematic diagram of the proposed graphene metalens. (b) The cross-sectional view of the proposed graphene metasurface. (c) Top view of the unit cell.
Fig. 2. Phase shift (red curves) and reflectance (blue curves) of reflected wave for (a) x-polarization and (b) y-polarization at 6 THz incidence as the Fermi energy changes from 0 to 1 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
the structure, the Fabry-Perot cavity is generated by the three layers, which greatly enhances the interaction between graphene and incident waves and expands the phase shift range [27]. The different Fermi energies of graphene ribbons between 0 and 1 eV [22,25] can be achieved by tuning the gate voltages, and the reflection phase shift resulted by the graphene ribbon resonance can cover a 2π range. In this work, we use finite-difference time-domain (FDTD) method to investigate the performance of the metalens. In the simulation, the minimum mesh is 80 nm along the x, y and z directions, and the graphene is considered as a 2-dimensional sheet, its surface conductivity can be characterized by a Drude-like expression [28].
σg =
e 2EF i π ℏ2 ω + iτ −1
(1)
where e is electron charge, ℏ is reduced Planck's constant, EF is the Fermi energy, and τ is the electron-photon relaxation time (τ = 10−12s [22]). An approximate expression relating EF and bias voltage Vg is given by EF ≈ ℏvf
πεr ε0 Vg etp
, where εr and ε0 are the permittivities of
surrounding medium and vacuum, e is the electron charge and vf is the Fermi velocity (1.1 × 106 m / s ). The top view of the unit cell is shown in Fig. 1(b), The geometric parameters presented in the figure are px = py = 4μm , a = 2μm , b = 3.2μm and w = 0.2μm . Due to the special design of the unit cell, i.e., introducing rectangular graphene structure as resonance antenna instead of solely using graphene ribbon as 2
Optical Materials 97 (2019) 109325
Y. Zhang, et al.
polarization incidences and the designed value, which is due to the approximations in selecting Fermi energy in configuring processes and the insufficient mesh accuracy. Fig. 3(e) and (f) show the intensities of the focusing spots along the x direction, from which we can deduce that both of the full width at half maximum (FWHM) values for x- and ypolarization incidences are 27 μm. The simulated results show that the proposed metalens can focus both x- and y-polarization incident THz waves by manipulating the Fermi energy distribution of the graphene ribbons. By changing the Fermi energy distribution of the graphene ribbons, the metalens can also be designed to focus at other spatial positions. Fig. 4 shows the case of off-center focusing with the focal spot locating at (−200 μm, 300 μm). For x-polarization incidence, the Fermi energy distribution is shown in Fig. 4(a), and the simulated Poynting vector distribution is shown in Fig. 4(c), from which we can see that a offcenter focusing spot is generated and agree well with the designed value. The intensity of the focusing spots along the x direction is shown in Fig. 4(e), a FWHM of 29 μm is acquired. Then we change the Fermi energy distribution, according to Fig. 4(b), to focus y-polarization incident wave. The simulated Poynting vector distribution is shown in Fig. 4(d) and the intensity of the focusing spots along the x direction is shown in Fig. 4(f). The FWHM of the focusing spot is 29 μm for y-polarization incidence. The proposed metalens can be designed with dual focusing spots. We first design the two focusing spots with transverse alignment. The left part of the metalens is designed to focus the spot at the position of (−240 μm, 300 μm) and the right part is for the focusing spot at the position of (−240 μm, 300 μm). Based on Eq. (2), we calculate the Fermi energy distributions for both x- and y-polarization incidences and show them in Fig. 5(a) and (b). The simulated Poynting vector distributions are shown in Fig. 5(c) and (d), from which we can see that the focusing intensity for both x- and y-polarization incidences are reduced and divided into two equal parts with the focal lengths of 290 μm. The x direction intensities of the focusing spots are shown in Fig. 5(e) and (f) and the FWHM of the focusing spots are 35 μm for both
resonance antenna and the graphene ribbon in the designed structure is used for connecting the graphene rectangles, dipole resonances that controlling amplitude and phase of the reflected wave can be excited by both x- and y-polarization incident waves. 3. Results and discussion We first choose the working frequency as 6 THz. Fig. 2(a) and (b) show the phase shift and reflectance of the reflected wave with different Fermi energies when illuminated with x- and y-polarization incident wave, respectively. Note that, the proposed device can realize a near 2π phase shift as shown by the red curves in Fig. 2. The insets in Fig. 2(a) and (b) show the z component of electric field distributions at the resonant Fermi energy, which are dipole resonances along x and y directions, respectively. In addition, a shorter relaxation time of graphene will cause the reduction of the reflectance while has little influence on the reflected phase [24]. In order to realize the function of metalens, the relative phase of the reflected wave at position x should follow the expression
Δϕ (x ) =
2π ( (x + Δx )2 + F 2 − F ) λ0
(2)
where λ 0 is incident wavelength, F represents the designed focal length and Δx is the shift of focal point along x axis. Then we select the Fermi energies of graphene ribbons from Fig. 2(a) and (b) to design metalens for both x- and y-polarization incidences. The focal length is designed as 300μm , and Δx = 0 . The aperture of the metalens is designed as 960μm (240 units of graphene ribbon). The Fermi energy distributions for x- and y-polarization incidences are shown in Fig. 3(a) and (b), respectively. Based on the Fermi energy distributions, we simulate the metalens with x- and ypolarized 6 THz incident wave. The Poynting vector distributions for xand y-polarization incidences are shown in Fig. 3(c) and (d), and the simulated focal lengths are 290μm and 292μm , which agree well with the designed values. Note that there are small deviations among x-, y-
Fig. 3. The Fermi energy distributions of the graphene ribbons for (a) x- and (b) y-polarization incidence. The simulated Poynting vector distributions for the metalens with (a) x- and (b) y-polarization incidences. The intensities of the focusing spots along the x direction for (e) x- and (f) y-polarization incidences. 3
Optical Materials 97 (2019) 109325
Y. Zhang, et al.
Fig. 4. The case of F = 300 μm and Δx = −200μm. (a) Fermi energy distribution, (c) simulated Poynting vector and (e) x direction focusing intensity for xpolarization incidence. (b) Fermi energy distribution, (d) simulated Poynting vector and (f) x direction focusing intensity for y-polarization incidence.
direction are shown in Fig. 6(e) and (f). For x-polarization incidence the FWHM values for the focal lengths of F = 100 μm and F = 300 μm are 27 μm and 25 μm, and that of y-polarization incidence are 27 μm and 25.5 μm, respectively. Further more, The working frequency of the proposed metalens can also be tuned. We then choose the working frequency as 5.5 THz, the phase shift and reflectance resulted by the structure with different Fermi energies are shown in Fig. 7(a) and (b). Based on the phase distributions, we design the metalens focusing at the position of (0, 300 μm) with the working frequency of 5.5 THz for x- and y-polarized
x- and y-polarization incidences. The proposed metalens can also be designed with two longitudinal alignment focusing spots. The middle 120 unit cells are designed to focus the spot at the position of (0, 100 μm) and the side 120 unit cells are designed to focus the spot at the position of (0, 300 μm). The Fermi energy distributions for x- and ypolarization incidences are shown in Fig. 6(a) and (b). Based on the configuration of Fermi energies, the simulated Poynting vector distributions are shown in Fig. 6(c) and (d), from which we can see two longitudinal alignment focal point are generated around the position of (0, 100 μm) and (0, 300 μm). The intensity distributions along x-
Fig. 5. The case of transverse alignment dual focusing with F = 300 μm and Δx = 240 μm. (a) Fermi energy distribution, (c) simulated Poynting vector and (e) x direction focusing intensity for x-polarization incidence. (b) Fermi energy distribution, (d) simulated Poynting vector and (f) x direction focusing intensity for y-polarization incidence.
4
Optical Materials 97 (2019) 109325
Y. Zhang, et al.
Fig. 6. The case of longitudinal alignment dual focusing with F = 100 μm and F = 300 μm. (a) Fermi energy distribution, (c) simulated Poynting vector and (e) x direction focusing intensity for x-polarization incidence. (b) Fermi energy distribution, (d) simulated Poynting vector and (f) x direction focusing intensity for ypolarization incidence.
Fig. 7. Phase shift (red curves) and reflectance (blue curves) of reflected wave for (a) x-polarization incident wave and (b) y-polarization incident wave at the working frequency of 5.5 THz. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
from these graphene ribbon based metalens that have been reported before, the proposed metalens can separately focus the x- and y-polarized incident THz wave by reconfiguring the Fermi energy distribution of the graphene ribbons. Moreover, the proposed metalens can also focus the incident wave at different spatial positions and different working frequencies. The simulated results are in good agreement with the designed values. We believe that our findings provide a new way in designing graphene metalens.
incident waves, respectively. The designed Fermi energy distributions for x- and y-polarization incidences are shown in Fig. 8(a) and (b). The corresponding Poynting vector distributions are show in Fig. 8(c) and (d), respectively. The focal lengths for both cases are 292 μm. The intensity distributions along x-direction are shown in Fig. 8(e) and (f). The FWHM values of the focal spots are calculated to be 29 μm for both the x- and y-polarization incidences. 4. Conclusion
Declaration of competing interest In summary, we have proposed a graphene ribbon based tunable metalens, which can reflect and focus the incident THz waves. Different
The authors declare that they have no known competing financial 5
Optical Materials 97 (2019) 109325
Y. Zhang, et al.
Fig. 8. The case with the working frequency of 5.5 THz. The Fermi energy distributions of the graphene ribbons for (a) x- and (b) y-polarization incidence. The simulated Poynting vector for the metalens with (a) x- and (b) y-polarization incidence. The intensities of the focusing spots along the x direction for (e) x- and (f) ypolarization incidences.
interests or personal relationships that could have appeared to influence the work reported in this paper.
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Acknowledgements This work is funded by National Natural Science Foundation of China (11474041); National Natural Science Foundation of China (61805025); 111 Project of China (D17017). References [1] D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84 (18) (2000) 4184. [2] D.R. Smith, J.B. Pendry, M.C.K. Wiltshire, Metamaterials and negative refractive index, Science 305 (5685) (2004) 788–792. [3] J.F. Zhou, J.F. Dong, B.N. Wang, T. Koschny, M. Kafesaki, C.M. Soukoulis, Negative refractive index due to chirality, Phys. Rev. B 79 (12) (2009) 121104. [4] J.B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 85 (18) (2000) 3966. [5] D. Schurig, J.J. Mock, B.J. Justice, S.A. Cummer, J.B. Pendry, A.F. Starr, D.R. Smith, Metamaterial electromagnetic cloak at microwave frequencies, Science 314 (5801) (2006) 977–980. [6] A.V. Kildishev, A. Boltasseva, V.M. Shalaev, Planar photonics with metasurfaces, Science 339 (2013) 1232009. [7] D. Lin, P. Fan, E. Hasman, M.L. Brongersma, Dielectric gradient metasurface optical elements, Science 345 (2014) 298–302. [8] J. Jiao, Q. Zhao, X. Li, G.F. Liang, X.P. Huang, X.G. Luo, Enhancement of focusing energy of ultra-thin planar lens through plasmonic resonance and coupling, Opt. Express 22 (21) (2014) 26277–26284. [9] J. Zhang, Z. Guo, C. Ge, W. Wang, R. Li, Y. Sun, F. Shen, S. Qu, J. Gao, Plasmonic focusing lens based on single-turn nano-pinholes array, Opt. Express 23 (14) (2015) 17883–17891. [10] D.Y. Lu, X. Cao, K. Wang, M. He, D. Wang, J. Li, X. Zhang, L. Liu, J. Luo, Z. Li, J. Liu, L. Xu, W. Hu, X. Chen, Broadband reflective lens in visible band based on aluminum plasmonic metasurface, Opt. Express 26 (26) (2018) 34956–34964. [11] C. Yang, Y. Shen, Y. Xie, Q. Zhou, X. Deng, J. Cao, Terahertz planar lenses based on plasmonic metasurfaces, Phys. Lett. A 383 (8) (2019) 789–792. [12] Y. Zhu, W. Yuan, W. Li, H. Sun, K. Qi, Y. Yu, TE-polarized design for metallic slit lenses: a way to deep-subwavelength focusing over a broad wavelength range, Opt.
6
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Graphene ribbon based tunable terahertz metalens for dual polarization incidences Yuhui Zhanga, Linfeng Maa, Zhiying Liua,b,c, Yuegang Fua,b,c,
T
⁎
a
School of Optoelectric Engineering, Changchun University of Science and Technology, Changchun, 130022, China Key Laboratory of Optoelectronic Measurement and Optical Information Transmission Technology of Ministry of Education, Changchun University of Science and Technology, Changchun, 130022, China c Key Laboratory of Advanced Optical System Design and Manufacturing Technology of the Universities of Jilin Province, 130022, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Tunable metalens Graphene ribbon Terahertz focusing
We propose a graphene ribbon based metalens that can achieve the function of tunable metalens in THz region. Different from these graphene ribbon based metalens that have been reported before, the proposed metalens can focus the x- and y-polarized incident THz wave separately by reconfiguring the Fermi energy distribution of the graphene ribbons. The proposed metalens can also focus the incident wave at different spatial positions and different working frequencies. The simulated results are in good agreement with the designed values. Our findings are beneficial in designing new active terahertz devices.
1. Introduction Metamaterials have attracted much interest due to their unprecedented electromagnetic properties such as negative refraction index [1–3], perfect lens [4] and invisible cloaks [5] in recent years. Metasurface, as a two-dimensional planar version of metamaterial, also possesses novel functions such as optical activity, circular elliptical dichroism and perfect absorption. As a remarkable characteristic, electromagnetic wavefront manipulation, arising from the phase responses of the resonant elements [6,7], is also attracting growing attention in the scientific communities. Various metasurfaces have been reported to achieve the function of metalens [8–12]. However, most of the proposed metalens are composed of metallic or dielectric materials, which lack dynamical control once fabricated and limit the further applications. Recently, graphene has been considered in metasurface construction due to its excellent ability to support THz surface plasmons [13–16] and the conductivity of graphene can be dynamically tuned by manipulating its Fermi energy via chemical doping or electrical gating. Thus, various graphene based THz metalens have been reported [17–19] by researchers. Most recently, graphene ribbon based tunable metalens has been investigated in many reports [20–25], because the Fermi energy of each ribbon can be separately tuned by applying gate voltage, and the phase response can be tuned at will. However, these graphene ribbon based metalenses can focus only one polarization state incident wave. In this paper, we propose and demonstrate a tunable terahertz ⁎
graphene ribbon based metalens, which can separately focus both xand y-polarized incident waves at different spatial positions and different working frequencies via manipulating the Fermi energies of the graphene ribbons. By configuring the Fermi distribution, we first design the metalens with a focal length of F = 300 μm and a working frequency of 6 THz. Both x- and y-polarized incident wave can be focused well by the proposed metalens, and the simulated results agree well with the designed values. Then by reconfiguring the Fermi energies of graphene ribbons, we design the focal spot with off-center focusing, transverse alignment dual focusing, longitudinal alignment dual focusing and a different working frequency of 5.5 THz, respectively. Both x- and y-polarization incidences perform excellent focusing effects. 2. Structure design and theoretical analysis Fig. 1(a) shows the schematic diagram of the proposed graphene ribbon based metalens. The proposed metalens is designed to reflect and focus the incident THz wave. Fig. 1(b) shows the cross-sectional view of the proposed graphene ribbon based metalens. A gold layer is on the bottom of the structure and acts as a reflecting mirror. The graphene ribbons is on the top of the structure, and the two layers are separated by a dielectric polymer spacer due to its low absorption and stable refraction index of about 1.53 across the THz band [26]. The thicknesses of the gold and dielectric layers are set as tg = 2μm and tp = 8μm , which ensure a phase modulation of almost 2π while maintaining high reflectivity at the working frequencies. As we can see from
Corresponding author. School of Optoelectric Engineering, Changchun university of science and technology, Changchun, 130022, China. E-mail address: [email protected] (Y. Fu).
https://doi.org/10.1016/j.optmat.2019.109325 Received 30 May 2019; Received in revised form 3 August 2019; Accepted 15 August 2019 0925-3467/ © 2019 Elsevier B.V. All rights reserved.
Optical Materials 97 (2019) 109325
Y. Zhang, et al.
Fig. 1. (a) Schematic diagram of the proposed graphene metalens. (b) The cross-sectional view of the proposed graphene metasurface. (c) Top view of the unit cell.
Fig. 2. Phase shift (red curves) and reflectance (blue curves) of reflected wave for (a) x-polarization and (b) y-polarization at 6 THz incidence as the Fermi energy changes from 0 to 1 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
the structure, the Fabry-Perot cavity is generated by the three layers, which greatly enhances the interaction between graphene and incident waves and expands the phase shift range [27]. The different Fermi energies of graphene ribbons between 0 and 1 eV [22,25] can be achieved by tuning the gate voltages, and the reflection phase shift resulted by the graphene ribbon resonance can cover a 2π range. In this work, we use finite-difference time-domain (FDTD) method to investigate the performance of the metalens. In the simulation, the minimum mesh is 80 nm along the x, y and z directions, and the graphene is considered as a 2-dimensional sheet, its surface conductivity can be characterized by a Drude-like expression [28].
σg =
e 2EF i π ℏ2 ω + iτ −1
(1)
where e is electron charge, ℏ is reduced Planck's constant, EF is the Fermi energy, and τ is the electron-photon relaxation time (τ = 10−12s [22]). An approximate expression relating EF and bias voltage Vg is given by EF ≈ ℏvf
πεr ε0 Vg etp
, where εr and ε0 are the permittivities of
surrounding medium and vacuum, e is the electron charge and vf is the Fermi velocity (1.1 × 106 m / s ). The top view of the unit cell is shown in Fig. 1(b), The geometric parameters presented in the figure are px = py = 4μm , a = 2μm , b = 3.2μm and w = 0.2μm . Due to the special design of the unit cell, i.e., introducing rectangular graphene structure as resonance antenna instead of solely using graphene ribbon as 2
Optical Materials 97 (2019) 109325
Y. Zhang, et al.
polarization incidences and the designed value, which is due to the approximations in selecting Fermi energy in configuring processes and the insufficient mesh accuracy. Fig. 3(e) and (f) show the intensities of the focusing spots along the x direction, from which we can deduce that both of the full width at half maximum (FWHM) values for x- and ypolarization incidences are 27 μm. The simulated results show that the proposed metalens can focus both x- and y-polarization incident THz waves by manipulating the Fermi energy distribution of the graphene ribbons. By changing the Fermi energy distribution of the graphene ribbons, the metalens can also be designed to focus at other spatial positions. Fig. 4 shows the case of off-center focusing with the focal spot locating at (−200 μm, 300 μm). For x-polarization incidence, the Fermi energy distribution is shown in Fig. 4(a), and the simulated Poynting vector distribution is shown in Fig. 4(c), from which we can see that a offcenter focusing spot is generated and agree well with the designed value. The intensity of the focusing spots along the x direction is shown in Fig. 4(e), a FWHM of 29 μm is acquired. Then we change the Fermi energy distribution, according to Fig. 4(b), to focus y-polarization incident wave. The simulated Poynting vector distribution is shown in Fig. 4(d) and the intensity of the focusing spots along the x direction is shown in Fig. 4(f). The FWHM of the focusing spot is 29 μm for y-polarization incidence. The proposed metalens can be designed with dual focusing spots. We first design the two focusing spots with transverse alignment. The left part of the metalens is designed to focus the spot at the position of (−240 μm, 300 μm) and the right part is for the focusing spot at the position of (−240 μm, 300 μm). Based on Eq. (2), we calculate the Fermi energy distributions for both x- and y-polarization incidences and show them in Fig. 5(a) and (b). The simulated Poynting vector distributions are shown in Fig. 5(c) and (d), from which we can see that the focusing intensity for both x- and y-polarization incidences are reduced and divided into two equal parts with the focal lengths of 290 μm. The x direction intensities of the focusing spots are shown in Fig. 5(e) and (f) and the FWHM of the focusing spots are 35 μm for both
resonance antenna and the graphene ribbon in the designed structure is used for connecting the graphene rectangles, dipole resonances that controlling amplitude and phase of the reflected wave can be excited by both x- and y-polarization incident waves. 3. Results and discussion We first choose the working frequency as 6 THz. Fig. 2(a) and (b) show the phase shift and reflectance of the reflected wave with different Fermi energies when illuminated with x- and y-polarization incident wave, respectively. Note that, the proposed device can realize a near 2π phase shift as shown by the red curves in Fig. 2. The insets in Fig. 2(a) and (b) show the z component of electric field distributions at the resonant Fermi energy, which are dipole resonances along x and y directions, respectively. In addition, a shorter relaxation time of graphene will cause the reduction of the reflectance while has little influence on the reflected phase [24]. In order to realize the function of metalens, the relative phase of the reflected wave at position x should follow the expression
Δϕ (x ) =
2π ( (x + Δx )2 + F 2 − F ) λ0
(2)
where λ 0 is incident wavelength, F represents the designed focal length and Δx is the shift of focal point along x axis. Then we select the Fermi energies of graphene ribbons from Fig. 2(a) and (b) to design metalens for both x- and y-polarization incidences. The focal length is designed as 300μm , and Δx = 0 . The aperture of the metalens is designed as 960μm (240 units of graphene ribbon). The Fermi energy distributions for x- and y-polarization incidences are shown in Fig. 3(a) and (b), respectively. Based on the Fermi energy distributions, we simulate the metalens with x- and ypolarized 6 THz incident wave. The Poynting vector distributions for xand y-polarization incidences are shown in Fig. 3(c) and (d), and the simulated focal lengths are 290μm and 292μm , which agree well with the designed values. Note that there are small deviations among x-, y-
Fig. 3. The Fermi energy distributions of the graphene ribbons for (a) x- and (b) y-polarization incidence. The simulated Poynting vector distributions for the metalens with (a) x- and (b) y-polarization incidences. The intensities of the focusing spots along the x direction for (e) x- and (f) y-polarization incidences. 3
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Fig. 4. The case of F = 300 μm and Δx = −200μm. (a) Fermi energy distribution, (c) simulated Poynting vector and (e) x direction focusing intensity for xpolarization incidence. (b) Fermi energy distribution, (d) simulated Poynting vector and (f) x direction focusing intensity for y-polarization incidence.
direction are shown in Fig. 6(e) and (f). For x-polarization incidence the FWHM values for the focal lengths of F = 100 μm and F = 300 μm are 27 μm and 25 μm, and that of y-polarization incidence are 27 μm and 25.5 μm, respectively. Further more, The working frequency of the proposed metalens can also be tuned. We then choose the working frequency as 5.5 THz, the phase shift and reflectance resulted by the structure with different Fermi energies are shown in Fig. 7(a) and (b). Based on the phase distributions, we design the metalens focusing at the position of (0, 300 μm) with the working frequency of 5.5 THz for x- and y-polarized
x- and y-polarization incidences. The proposed metalens can also be designed with two longitudinal alignment focusing spots. The middle 120 unit cells are designed to focus the spot at the position of (0, 100 μm) and the side 120 unit cells are designed to focus the spot at the position of (0, 300 μm). The Fermi energy distributions for x- and ypolarization incidences are shown in Fig. 6(a) and (b). Based on the configuration of Fermi energies, the simulated Poynting vector distributions are shown in Fig. 6(c) and (d), from which we can see two longitudinal alignment focal point are generated around the position of (0, 100 μm) and (0, 300 μm). The intensity distributions along x-
Fig. 5. The case of transverse alignment dual focusing with F = 300 μm and Δx = 240 μm. (a) Fermi energy distribution, (c) simulated Poynting vector and (e) x direction focusing intensity for x-polarization incidence. (b) Fermi energy distribution, (d) simulated Poynting vector and (f) x direction focusing intensity for y-polarization incidence.
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Fig. 6. The case of longitudinal alignment dual focusing with F = 100 μm and F = 300 μm. (a) Fermi energy distribution, (c) simulated Poynting vector and (e) x direction focusing intensity for x-polarization incidence. (b) Fermi energy distribution, (d) simulated Poynting vector and (f) x direction focusing intensity for ypolarization incidence.
Fig. 7. Phase shift (red curves) and reflectance (blue curves) of reflected wave for (a) x-polarization incident wave and (b) y-polarization incident wave at the working frequency of 5.5 THz. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
from these graphene ribbon based metalens that have been reported before, the proposed metalens can separately focus the x- and y-polarized incident THz wave by reconfiguring the Fermi energy distribution of the graphene ribbons. Moreover, the proposed metalens can also focus the incident wave at different spatial positions and different working frequencies. The simulated results are in good agreement with the designed values. We believe that our findings provide a new way in designing graphene metalens.
incident waves, respectively. The designed Fermi energy distributions for x- and y-polarization incidences are shown in Fig. 8(a) and (b). The corresponding Poynting vector distributions are show in Fig. 8(c) and (d), respectively. The focal lengths for both cases are 292 μm. The intensity distributions along x-direction are shown in Fig. 8(e) and (f). The FWHM values of the focal spots are calculated to be 29 μm for both the x- and y-polarization incidences. 4. Conclusion
Declaration of competing interest In summary, we have proposed a graphene ribbon based tunable metalens, which can reflect and focus the incident THz waves. Different
The authors declare that they have no known competing financial 5
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Fig. 8. The case with the working frequency of 5.5 THz. The Fermi energy distributions of the graphene ribbons for (a) x- and (b) y-polarization incidence. The simulated Poynting vector for the metalens with (a) x- and (b) y-polarization incidence. The intensities of the focusing spots along the x direction for (e) x- and (f) ypolarization incidences.
interests or personal relationships that could have appeared to influence the work reported in this paper.
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