Design of a double lens freeform miniaturized antenna

Lizhong Hu; Xin Chen; Ping Jiang; Huajun Yang; Yan Qin; Miaofang Zhou; Jing Yang; Junyi He; Jinxin Deng

doi:10.1364/JOSAB.492695

Journal of the Optical Society of America B
Vol. 40,
Issue 9,
pp. 2227-2235
(2023)
•https://doi.org/10.1364/JOSAB.492695

Design of a double lens freeform miniaturized antenna

Lizhong Hu, Xin Chen, Ping Jiang, Huajun Yang, Yan Qin, Miaofang Zhou, Jing Yang, Junyi He, and Jinxin Deng

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Lizhong Hu, Xin Chen, Ping Jiang, Huajun Yang, Yan Qin, Miaofang Zhou, Jing Yang, Junyi He, and Jinxin Deng, "Design of a double lens freeform miniaturized antenna," J. Opt. Soc. Am. B 40, 2227-2235 (2023)

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Abstract

The elliptical laser beam produced by a laser diode (LD) has asymmetrical divergence angle distribution and limits its application in long-distance space optical communication. In this paper, a double lens freeform miniaturized antenna design method is proposed to collimate, shape, and transmit elliptical beams from a LD. Based on the law of conservation of energy, refraction vector theory, equal optical path principle, and the three-dimensional point-by-point construction iterative method, two freeform surfaces on both lenses are constructed simultaneously. According to the simulation results, the maximum divergence angle of the output light is compressed to 4.92 µrad. The volume of the antenna is ${1244.61}\;{{\rm cm}^3}$, which realizes the miniaturization of the antenna. In addition, the performance of the system is evaluated under different wavelength shifts, astigmatism based on the proposed improved line light source model, the offset of the light source, and the offset of both lenses. This paper provides a practical method for designing a simplified antenna that can collimate and shape laser beams and improve transmission efficiency. Furthermore, the proposed improved optimization method can provide a reference for the study of the initial parameters of lens freeform antennas.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	Surface Equations
First freeform surface	$\begin{aligned} F_{1} (x, y, z) & = p_{00} + p_{10} \times \frac{x - a}{b} + p_{01} \times \frac{y - c}{d} + p_{20} \times {(\frac{x - a}{b})}^{2} + p_{11} \times \frac{x - a}{b} \times \frac{y - c}{d} + p_{02} \times {(\frac{y - c}{d})}^{2} \\ + p_{30} \times {(\frac{x - a}{b})}^{3} + p_{21} \times {(\frac{x - a}{b})}^{2} \times (\frac{y - c}{d}) + p_{12} \times \frac{x - a}{b} \times {(\frac{y - c}{d})}^{2} + p_{03} \times {(\frac{y - c}{d})}^{3} \\ + p_{40} \times {(\frac{x - a}{b})}^{4} + p_{31} \times {(\frac{x - a}{b})}^{3} \times \frac{y - c}{d} + p_{22} \times {(\frac{x - a}{b})}^{2} \times {(\frac{y - c}{d})}^{2} + p_{13} \times \frac{x - a}{b} \times {(\frac{y - c}{d})}^{3} \\ + p_{04} \times {(\frac{y - c}{d})}^{4} + p_{50} \times {(\frac{x - a}{b})}^{5} + p_{41} \times {(\frac{x - a}{b})}^{4} \times \frac{y - c}{d} + p_{32} \times {(\frac{x - a}{b})}^{3} \times {(\frac{y - c}{d})}^{2} \\ + p_{23} \times {(\frac{x - a}{b})}^{2} \times {(\frac{y - c}{d})}^{3} + p_{14} \times \frac{x - a}{b} \times {(\frac{y - c}{d})}^{4} + p_{05} \times {(\frac{y - c}{d})}^{5} - \frac{z - e}{f} = 0 \end{aligned}$
Second freeform surface	$\begin{aligned} F_{2} (x, y, z) & = q_{00} + q_{10} \times \frac{x - g}{h} + q_{01} \times \frac{y - i}{j} + q_{20} \times {(\frac{x - g}{h})}^{2} + q_{11} \times \frac{x - g}{h} \times \frac{y - i}{j} + q_{02} \times {(\frac{y - i}{j})}^{2} \\ + q_{30} \times {(\frac{x - g}{h})}^{3} + q_{21} \times {(\frac{x - g}{h})}^{2} \times (\frac{y - i}{j}) + q_{12} \times \frac{x - g}{h} \times {(\frac{y - i}{j})}^{2} + q_{03} \times {(\frac{y - i}{j})}^{3} \\ + q_{40} \times {(\frac{x - g}{h})}^{4} + q_{31} \times {(\frac{x - g}{h})}^{3} \times \frac{y - i}{j} + q_{22} \times {(\frac{x - g}{h})}^{2} \times {(\frac{y - i}{j})}^{2} + q_{13} \times \frac{x - g}{h} \times {(\frac{y - i}{j})}^{3} \\ + q_{04} \times {(\frac{y - i}{j})}^{4} + q_{50} \times {(\frac{x - g}{h})}^{5} + q_{41} \times {(\frac{x - g}{h})}^{4} \times \frac{y - i}{j} + q_{32} \times {(\frac{x - g}{h})}^{3} \times {(\frac{y - i}{j})}^{2} \\ + q_{23} \times {(\frac{x - g}{h})}^{2} \times {(\frac{y - i}{j})}^{3} + q_{14} \times \frac{x - g}{h} \times {(\frac{y - i}{j})}^{4} + q_{05} \times {(\frac{y - i}{j})}^{5} - \frac{z - k}{l} = 0 \end{aligned}$
	Parameters
First freeform surface	$a = - 1.9203 \times 10^{- 9} m m$ , $b = 1.9810$ , $c = - 5.6841 \times 10^{- 10} m m$ , $d = 0.6679$ , $e = 20.7441 m m$ , $f = 0.2181$ , $p_{00} = 0.9036$ , $p_{10} = - 9.4 \times 10^{- 9}$ , $p_{01} = - 1.93 \times 10^{- 10}$ , $p_{20} = - 0.8477$ , $p_{11} = - 2.218 \times 10^{- 11}$ , $p_{02} = - 0.04683$ , $p_{30} = 1.355 \times 10^{- 8}$ , $p_{21} = - 2.774 \times 10^{- 12}$ , $p_{12} = 8.496 \times 10^{- 11}$ , $p_{03} = 2.335 \times 10^{- 10}$ , $p_{40} = - 0.003838$ , $p_{31} = 1.938 \times 10^{- 12}$ , $p_{22} = - 0.0002145$ , $p_{13} = 7.526 \times 10^{- 12}$ , $p_{04} = - 8.735 \times 10^{- 6}$ , $p_{50} = - 5.182 \times 10^{- 9}$ , $p_{41} = 1.536 \times 10^{- 12}$ , $p_{32} = - 1.837 \times 10^{- 11}$ , $p_{23} = - 2.567 \times 10^{- 12}$ , $p_{14} = - 1.595 \times 10^{- 11}$ , $p_{05} = - 5.565 \times 10^{- 11}$
Second freeform surface	$g = - 9.5589 \times 10^{- 9} m m$ , $h = 11.2286$ , $i = - 9.5589 \times 10^{- 9} m m$ , $j = 11.2286$ , $k = 478.1220 m m$ , $l = 0.4007$ , $q_{00} = - 1.189$ , $q_{10} = - 6.194 \times 10^{- 9}$ , $q_{01} = 3.841 \times 10^{- 8}$ , $q_{20} = 0.5544$ , $q_{11} = 1.608 \times 10^{- 8}$ , $q_{02} = 0.636$ , $q_{30} = 3.084 \times 10^{- 9}$ , $q_{21} = 1.204 \times 10^{- 8}$ , $q_{12} = 4.677 \times 10^{- 9}$ , $q_{03} = - 4.992 \times 10^{- 8}$ , $q_{40} = 0.0001028$ , $q_{31} = - 3.002 \times 10^{- 9}$ , $q_{22} = - 0.000686$ , $q_{13} = - 4.019 \times 10^{- 9}$ , $q_{04} = - 0.0004202$ , $q_{50} = - 1.746 \times 10^{- 9}$ , $q_{41} = - 1.36 \times 10^{- 9}$ , $q_{32} = 3.512 \times 10^{- 9}$ , $q_{23} = - 3.253 \times 10^{- 9}$ , $q_{14} = - 2.72 \times 10^{- 9}$ , $q_{05} = 8.196 \times 10^{- 9}$

Abstract

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Tables (1)

Equations (11)

Journal of the Optical Society of America B