Dual-layered metasurfaces for asymmetric focusing

Bingshuang Yao; Xiaofei Zang; Zhen Li; Lin Chen; Jingya Xie; Yiming Zhu; Songlin Zhuang

doi:doi:10.1364/PRJ.387672

Photonics Research, 2020, 8 (6): 06000830, Published Online: Apr. 30, 2020

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Bingshuang Yao ¹Xiaofei Zang ^1,2,*Zhen Li ¹Lin Chen ^1,2Jingya Xie ^1,2Yiming Zhu ^1,2,3Songlin Zhuang ¹

Author Affiliations

¹ Terahertz Technology Innovation Research Institute, Terahertz Spectrum and Imaging Technology Cooperative Innovation Center, Shanghai Key Laboratory of Modern Optical System, University of Shanghai for Science and Technology, Shanghai 200093, China

² Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai 200092, China

³ e-mail: ymzhu@usst.edu.cn

Figures & Tables

Fig. 1. Schematic of asymmetric focusing. Under the illumination of x-polarized THz waves in the forward direction, a y-polarized focal spot is observed, while the focal spot is not generated for backward x-polarized incidence.

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Fig. 2. Design of dual-layered metasurfaces: (a₁) and (a₂) schematic and the corresponding geometric phase of the microrod; (b₁) and (b₂) schematic and the corresponding transmission spectra of the metallic gratings; (c₁) and (c₂) schematic and the corresponding transmission spectra of the metasurface combined with metallic gratings; (d₁) and (d₂) optical images of the metasurface and metallic gratings.

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Fig. 3. (a₁)–(f₁) Numerical simulation of electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, and 1.1 THz; (a₂)–(f₂) the corresponding electric field distributions in the x−y plane.

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Fig. 4. (a₁)–(f₁) The measured electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, 1.1 THz; (a₂)–(f₂) the corresponding electric field distributions in the x−y plane.

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Fig. 5. Numerical simulation of asymmetric transmission with (a) and (b) longitudinal and (c) and (d) transversal multiple focal spots.

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Fig. 6. (a₁)–(c₁) Schematics of a microrod, metallic gratings, and a unit cell of the directional device. The intersection angle between the long axis of the microrod and the x axis is 45°, while the long axis of gratings is along the x axis. (a₂)–(a₄) The co-polarized/cross-polarized/total transmission and reflection of the microrod under the illumination of linearly polarized THz waves. (b₂)–(b₄) The co-polarized/cross-polarized/total transmission and reflection of the metallic gratings under the illumination of linearly polarized THz waves. (c₂)–(c₄) The co-polarized/cross-polarized/total transmission and reflection of the unit cell of the directional device under the illumination of linearly polarized THz waves. Tij (Rij) is the transmission (reflection) of the i-polarized THz waves under the illumination of j-polarized THz waves (i,j=x,y). Ti (Ri,i=x,y) is the total transmission (total reflection) under the illumination of i-polarized THz waves.

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Fig. 7. (a₁)–(f₁) Numerical simulation of electric field distributions in the x−z plane under the illumination of y-polarized THz waves in the forward direction at 0.6, 0.85, and 1.1 THz; (a₂)–(f₂) the calculated electric field distributions for backward incidence.

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Fig. 8. The calculated and measured electric field distributions in the x−z plane under the illumination of the x-polarized THz waves from the (a₁)–(f₁) forward and (a₂)–(f₂) backward directions at 0.6, 0.85, and 1.1 THz.

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Fig. 9. The calculated electric field distributions in the x−z plane under the illumination of the x-polarized THz waves in the (a₁), (b₁) forward and (a₂), (b₂) backward directions at 0.85 THz.

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Fig. 10. Calculated efficiency of the directional device under the illumination of x-polarized THz waves in the forward direction.

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Fig. 11. Schematic of multiple transmissions from the dual-layered metasurfaces.

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Fig. 12. Comparison of the numerical (blue curves) and experimental (red curves) focusing properties: (a)–(c) the corresponding electric field distributions at x=0 in the focal plane.

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Fig. 13. Schematics for the extinction ratio defined as (a) TEy/TEx and (b) TEy1/TEy2.

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Fig. 14. (a₁)–(c₁) Calculated electric field (|Ey|2) distributions in the x−z plane under the illumination of x-polarized THz waves (with different incident angles) in the forward directions at 0.85 THz; (a₂)–(c₂) the calculated electric field distributions for backward incidence. Insets show the schematics for the incident THz waves with a tilted wavefront.

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Table1. Size of the Focal Point

Frequency (THz)	Focal Length (mm)	Focal Plane (FWHM/mm)	$x - z$ Plane(FWHM/mm)
0.6	2.0	0.296	0.915
0.65	2.3	0.250	0.825
0.7	2.5	0.236	0.775
0.75	2.8	0.210	0.725
0.8	3.1	0.204	0.575
0.85	3.5	0.194	0.525
0.9	3.9	0.170	0.545
0.95	4.4	0.168	0.580
1.0	4.8	0.166	0.685
1.05	5.2	0.165	0.860
1.1	5.7	0.164	1.150

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Table2. Comparison Between the Diffraction Limit in Theory and the FWHM of the Focal Spots

Frequency (THz)	0.6	0.85	1.1
Diffraction limit (mm)	0.255	0.188	0.159
Sim. (FWHM/mm)	0.296	0.194	0.164
Exp. (FWHM/mm)	0.320	0.294	0.264

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Table3. Extinction Ratio Between ${| E_{y} |}^{2}$ and ${| E_{x} |}^{2}$

Frequency (THz)	0.6	0.85	11.1
Sim. extinction ratio	1.22:1	3.79:1	2.27:1
Exp. extinction ratio	1.6:1	1.7:1	1.6:1

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Table4. Extinction Ratio Between the Forward and Backward Directions

Frequency (THz)	0.6	0.85	1.1
Sim. extinction ratio	36.6:1	81.5:1	76:1
Exp. extinction ratio	17:1	71:1	15.5:1

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Table5. Extinction Ratio for the Directional Device with Two Focal Spots

Extinction Ratio	Longitudinal	Transversal
${\| E_{y} \|}^{2} / {\| E_{x} \|}^{2}$	5.4:1	6:1
${\| E_{y}^{1} \|}^{2} / {\| E_{y}^{2} \|}^{2}$	82:1	38:1

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Bingshuang Yao, Xiaofei Zang, Zhen Li, Lin Chen, Jingya Xie, Yiming Zhu, Songlin Zhuang. Dual-layered metasurfaces for asymmetric focusing[J]. Photonics Research, 2020, 8(6): 06000830.

Dual-layered metasurfaces for asymmetric focusing Download： 748次

Fig. 1. Schematic of asymmetric focusing. Under the illumination of x-polarized THz waves in the forward direction, a y-polarized focal spot is observed, while the focal spot is not generated for backward x-polarized incidence.

Fig. 3. (a₁)–(f₁) Numerical simulation of electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, and 1.1 THz; (a₂)–(f₂) the corresponding electric field distributions in the x−y plane.

Fig. 4. (a₁)–(f₁) The measured electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, 1.1 THz; (a₂)–(f₂) the corresponding electric field distributions in the x−y plane.

Fig. 5. Numerical simulation of asymmetric transmission with (a) and (b) longitudinal and (c) and (d) transversal multiple focal spots.

Fig. 7. (a₁)–(f₁) Numerical simulation of electric field distributions in the x−z plane under the illumination of y-polarized THz waves in the forward direction at 0.6, 0.85, and 1.1 THz; (a₂)–(f₂) the calculated electric field distributions for backward incidence.

Fig. 8. The calculated and measured electric field distributions in the x−z plane under the illumination of the x-polarized THz waves from the (a₁)–(f₁) forward and (a₂)–(f₂) backward directions at 0.6, 0.85, and 1.1 THz.

Fig. 9. The calculated electric field distributions in the x−z plane under the illumination of the x-polarized THz waves in the (a₁), (b₁) forward and (a₂), (b₂) backward directions at 0.85 THz.

Fig. 10. Calculated efficiency of the directional device under the illumination of x-polarized THz waves in the forward direction.

Fig. 11. Schematic of multiple transmissions from the dual-layered metasurfaces.

Fig. 12. Comparison of the numerical (blue curves) and experimental (red curves) focusing properties: (a)–(c) the corresponding electric field distributions at x=0 in the focal plane.

Fig. 13. Schematics for the extinction ratio defined as (a) TEy/TEx and (b) TEy1/TEy2.

Table1. Size of the Focal Point

Table2. Comparison Between the Diffraction Limit in Theory and the FWHM of the Focal Spots

Table3. Extinction Ratio Between ${| E_{y} |}^{2}$ and ${| E_{x} |}^{2}$

Table4. Extinction Ratio Between the Forward and Backward Directions

Table5. Extinction Ratio for the Directional Device with Two Focal Spots

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Dual-layered metasurfaces for asymmetric focusing Download： 748次

Fig. 1. Schematic of asymmetric focusing. Under the illumination of x-polarized THz waves in the forward direction, a y-polarized focal spot is observed, while the focal spot is not generated for backward x-polarized incidence.

Fig. 3. (a1)–(f1) Numerical simulation of electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, and 1.1 THz; (a2)–(f2) the corresponding electric field distributions in the x−y plane.

Fig. 4. (a1)–(f1) The measured electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, 1.1 THz; (a2)–(f2) the corresponding electric field distributions in the x−y plane.

Fig. 5. Numerical simulation of asymmetric transmission with (a) and (b) longitudinal and (c) and (d) transversal multiple focal spots.

Fig. 7. (a1)–(f1) Numerical simulation of electric field distributions in the x−z plane under the illumination of y-polarized THz waves in the forward direction at 0.6, 0.85, and 1.1 THz; (a2)–(f2) the calculated electric field distributions for backward incidence.

Fig. 8. The calculated and measured electric field distributions in the x−z plane under the illumination of the x-polarized THz waves from the (a1)–(f1) forward and (a2)–(f2) backward directions at 0.6, 0.85, and 1.1 THz.

Fig. 9. The calculated electric field distributions in the x−z plane under the illumination of the x-polarized THz waves in the (a1), (b1) forward and (a2), (b2) backward directions at 0.85 THz.

Fig. 10. Calculated efficiency of the directional device under the illumination of x-polarized THz waves in the forward direction.

Fig. 11. Schematic of multiple transmissions from the dual-layered metasurfaces.

Fig. 12. Comparison of the numerical (blue curves) and experimental (red curves) focusing properties: (a)–(c) the corresponding electric field distributions at x=0 in the focal plane.

Fig. 13. Schematics for the extinction ratio defined as (a) TEy/TEx and (b) TEy1/TEy2.

Table1. Size of the Focal Point

Table2. Comparison Between the Diffraction Limit in Theory and the FWHM of the Focal Spots

Table3. Extinction Ratio Between |Ey|2 and |Ex|2

Table4. Extinction Ratio Between the Forward and Backward Directions

Table5. Extinction Ratio for the Directional Device with Two Focal Spots

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Fig. 3. (a₁)–(f₁) Numerical simulation of electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, and 1.1 THz; (a₂)–(f₂) the corresponding electric field distributions in the x−y plane.

Fig. 4. (a₁)–(f₁) The measured electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, 1.1 THz; (a₂)–(f₂) the corresponding electric field distributions in the x−y plane.

Fig. 7. (a₁)–(f₁) Numerical simulation of electric field distributions in the x−z plane under the illumination of y-polarized THz waves in the forward direction at 0.6, 0.85, and 1.1 THz; (a₂)–(f₂) the calculated electric field distributions for backward incidence.

Fig. 8. The calculated and measured electric field distributions in the x−z plane under the illumination of the x-polarized THz waves from the (a₁)–(f₁) forward and (a₂)–(f₂) backward directions at 0.6, 0.85, and 1.1 THz.

Fig. 9. The calculated electric field distributions in the x−z plane under the illumination of the x-polarized THz waves in the (a₁), (b₁) forward and (a₂), (b₂) backward directions at 0.85 THz.

Table3. Extinction Ratio Between ${| E_{y} |}^{2}$ and ${| E_{x} |}^{2}$