Focus control of wide-angle metalens based on digitally encoded metasurface

Yi Chen; Simeng Zhang; Ying Tian; Chenxia Li; Wenlong Huang; Yixin Liu; Yongxing Jin; Bo Fang; Zhi Hong; Xufeng Jing

doi:10.29026/oea.2024.240095

Opto-Electronic Advances, Volume. 7, Issue 8, 240095-1(2024)

Focus control of wide-angle metalens based on digitally encoded metasurface

Yi Chen1... Simeng Zhang1,2, Ying Tian1,*, Chenxia Li1, Wenlong Huang1, Yixin Liu1,2, Yongxing Jin1, Bo Fang3, Zhi Hong2,4, and Xufeng Jing24,** |Show fewer author(s)

Author Affiliations

¹[in Chinese]

²[in Chinese]

³[in Chinese]

⁴[in Chinese]

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Fig. 1. Schematic diagram of metalens unit.

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Fig. 2. (a) Scattering characteristics of the unit structure in the range of 6 to 9 GHz. (b) Curves of the phase and transmission amplitude of the unit with respect to the interlayer circular angle α and symmetry direction β at 8 GHz. (c) Transmission amplitude diagram of the unit structure in the range of −60° to 60°.

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Fig. 3. Schematic diagram of wide-angle metalens focusing.

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Fig. 4. Normalized electric field intensity distribution of the metalens in the x-z plane for θ = −45°, θ = 0°, θ = 30°, θ = 60° at an operating frequency of 8 GHz. (a) Shows the electric field intensity distribution of the metalens with linear phase distribution. (b) Shows the electric field intensity distribution of the wide-angle metalens with quadratic phase distribution.

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Fig. 5. Transmission amplitude plot (a) and phase distribution (b) of the coding unit in the 6–9 GHz range.

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Fig. 6. Coding patterns of each coding sequence (a−d) are the coding patterns of coding sequence S0 after convolution operation with coding sequences S1 (T_S1=12p), S2 (T_S2=16p), S3 (T_S3=32p), and S4 (T_S4=40p), respectively. i) is the coding sequence S0, ii) from top to bottom are S1, S2, S3, S4, iii) the coding sequence after convolution.

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Fig. 7. In the operating frequency of 8 GHz, the normalized electric field intensity distribution on the x-y plane and the y-z plane of the plane wave normal incidence metalens. (a) S0 and S1 are convolved to produce a 51° deflection in the y direction. (b) S0 and S2 are convoluted, a deflection of 38° is produced in the y direction. (c) After convolution of S0 and S3, a deflection of 18° is produced in the y direction. (d) After convolution of S0 and S4, a deflection of 14° is produced in the y direction.

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Fig. 8. In the mixed encoding mode, the normalized electric field intensity distribution of the metalens on the x-y plane and the y-z plane. (a) After the coding sequences S3 and S4 are mixed, the focus of the metalens is deflected by 34° along the y-axis direction. (b) After the encoding sequence S3 and the reverse encoding sequence S1 are mixed, the focus of the metalens is deflected by −31° along the y-axis direction.

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Fig. 9. In the operating frequency of 8 GHz, when the light wave is obliquely incident on the metalens, the normalized electric field intensity distribution on the x-y plane and the y-z plane. (a−d) are the convolution of the coding sequence S0 with S1, S2, S3 and S4 in the y direction respectively, the light wave is incident obliquely on the metalens at an angle of 30°, resulting in a normalized electric field intensity distribution of focus shift. From the column (i), it is observed that the focus shifts in the x and y directions simultaneously. From the column (ii), it is observed that the oblique incidence of the incident wave to the metalens does not change the deflection angle in the y direction, but the focus is offset in the y direction, it is also given an offset in the x-direction, realizing flexible control of the focus in two-dimensional plane.

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Fig. 10. Normalized electric field intensity distribution of the coded metalens based on the addition theorem. (a) The normalized electric field distribution of the x-y section and the y-z section after the addition of the 2-bit coding sequence S7 (0123) with a period of 16p and the 2-bit coding sequence S8 (0123) with a period of 32p. The offset angles of the two focuses are of 18° and 38°, respectively. (b) The normalized electric field distribution of the x-y cross-section and the y-z cross-section after the reverse addition operation of the 2-bit coding sequence S7 (0123) with a period of 16p and the 2-bit coding sequence S8 (0123) with a period of 32p.

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Fig. 11. Physical picture of the middle structural layer of the metalens sample. (a) The metasurface obtained by convolving S0 (focused coding sequence) and S3 (coding sequence with the period of 32p). (b) The metasurface obtained by convolving S0 (focused coding sequence) and S2 (coding sequence with period 16p). (c) The metasurface after mixed coding of the coding sequence S3 and the reverse coding sequence S1. (d) The metasurface obtained using the addition principle of digitally encoded metasurfaces.

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Fig. 12. Experimental testing platform.

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Fig. 13. The experimental test of the metasurface on the x-y plane (i) and y-z plane (ii) in the normal incidence. (a) The light intensity distribution of metasurface focusing effect after S2 sequence convolution. (b) The light intensity distribution of metasurface focusing effect after S3 sequence convolution. (c) The light intensity distribution of the metasurface focusing effect after mixed encoding of the encoding sequence S3 and the reverse encoding sequence S1. (d) The light intensity distribution of multi-focus metasurface realized using the additive principle.

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Fig. 14. The focusing effect of the metasurface in the 30° oblique incidence. (a−d) are the focused light intensity distribution on the x-y plane of the four metasurface samples, respectively.

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Table 1. Operation rules for complex encoding addition from 1-bit to 2-bit, 2-bit to 3-bit.

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Table 1. Operation rules for complex encoding addition from 1-bit to 2-bit, 2-bit to 3-bit.

1 bit→2 bit	2 bit→3 bit
${\dot{0}}_{1} + {\dot{0}}_{1} = {\dot{0}}_{2}$	${\dot{0}}_{2} + {\dot{0}}_{2} = {\dot{0}}_{3}$ ${\dot{1}}_{2} + {\dot{0}}_{2} = {\dot{1}}_{3}$ ${\dot{2}}_{2} + {\dot{0}}_{2} = {\dot{6}}_{3}$ ${\dot{3}}_{2} + {\dot{0}}_{2} = {\dot{7}}_{3}$
${\dot{0}}_{1} + {\dot{1}}_{1} = {\dot{1}}_{2}$	${\dot{0}}_{2} + {\dot{1}}_{2} = {\dot{1}}_{3}$ ${\dot{1}}_{2} + {\dot{1}}_{2} = {\dot{2}}_{3}$ ${\dot{2}}_{2} + {\dot{1}}_{2} = {\dot{3}}_{3}$ ${\dot{3}}_{2} + {\dot{1}}_{2} = {\dot{0}}_{3}$
${\dot{1}}_{1} + {\dot{0}}_{1} = {\dot{3}}_{2}$	${\dot{0}}_{2} + {\dot{2}}_{2} = {\dot{2}}_{3}$ ${\dot{1}}_{2} + {\dot{2}}_{2} = {\dot{3}}_{3}$ ${\dot{2}}_{2} + {\dot{2}}_{2} = {\dot{4}}_{3}$ ${\dot{3}}_{2} + {\dot{2}}_{2} = {\dot{5}}_{3}$
${\dot{1}}_{1} + {\dot{1}}_{1} = {\dot{2}}_{2}$	${\dot{0}}_{2} + {\dot{3}}_{2} = {\dot{7}}_{3}$ ${\dot{1}}_{2} + {\dot{3}}_{2} = {\dot{4}}_{3}$ ${\dot{2}}_{2} + {\dot{3}}_{2} = {\dot{5}}_{3}$ ${\dot{3}}_{2} + {\dot{3}}_{2} = {\dot{6}}_{3}$

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Yi Chen, Simeng Zhang, Ying Tian, Chenxia Li, Wenlong Huang, Yixin Liu, Yongxing Jin, Bo Fang, Zhi Hong, Xufeng Jing. Focus control of wide-angle metalens based on digitally encoded metasurface[J]. Opto-Electronic Advances, 2024, 7(8): 240095-1

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