Design of a compact off-axis two-mirror freeform optical antenna for shaping and transmitting an elliptical beam emitted by laser diode

Xin Chen; Lizhong Hu; Jianing Liu; Chaoxiang Wang; Chenxi Bai; Yifan Zheng; Yan Qin; Huajun Yang; Ping Jiang

doi:10.1364/AO.505268

Applied Optics
Vol. 63,
Issue 1,
pp. 239-248
(2024)
•https://doi.org/10.1364/AO.505268

Design of a compact off-axis two-mirror freeform optical antenna for shaping and transmitting an elliptical beam emitted by laser diode

Xin Chen, Lizhong Hu, Jianing Liu, Chaoxiang Wang, Chenxi Bai, Yifan Zheng, Yan Qin, Huajun Yang, and Ping Jiang

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Xin Chen, Lizhong Hu, Jianing Liu, Chaoxiang Wang, Chenxi Bai, Yifan Zheng, Yan Qin, Huajun Yang, and Ping Jiang, "Design of a compact off-axis two-mirror freeform optical antenna for shaping and transmitting an elliptical beam emitted by laser diode," Appl. Opt. 63, 239-248 (2024)

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Table of Contents Category
- Optical Design and Fabrication
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About this Article
History
- Original Manuscript: September 8, 2023
- Revised Manuscript: November 25, 2023
- Manuscript Accepted: November 28, 2023
- Published: December 21, 2023

Abstract

Elliptical Gaussian beams generated by laser diodes (LDs) often exhibit asymmetrical divergence angle distribution, which limits their practical applications. In this study, we propose what we believe is a novel approach to shape and collimate the elliptical output beam from a LD. The design process involves the construction of two freeform reflective surfaces on a reference circle using a three-dimensional point-by-point iterative method, based on the law of conservation of energy, the vector reflection theory, and Fermat’s principle. The output beam’s maximum divergence angle is effectively compressed to 3.1579 mrad. The design is compact with a folded optical path and antenna size of $368.8\; {\rm cm}^3$. This paper presents a comprehensive design and optimization process, along with an in-depth analysis of the system’s performance, thereby offering novel insights for emerging optical design practitioners.

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Optical System	Outgoing Spot Radius (mm)	Antenna Volume ( ${c m}^{3}$ )	Reference
①	100	57,200	[22]
②	100	24,200	[20]
③	25	3229.99	[17]
④	25	1244.61	[23]

Mirror	Equation
Secondary Mirror	$\begin{aligned} z_{SM} & = p_{00} + p_{10} \times x_{s} + p_{01} \times y_{s} + p_{20} \times x_{s}^{2} + p_{11} \times x_{s} \times y_{s} + p_{02} \times y_{s}^{2} + p_{30} \times x_{s}^{3} + p_{21} \times x_{s}^{2} \times y_{s} + p_{12} \times x_{s} \times y_{s}^{2} \\ + p_{03} \times y_{s}^{3} + p_{40} \times x_{s}^{4} + p_{31} \times x_{s}^{3} \times y_{s} + p_{22} \times x_{s}^{2} \times y_{s}^{2} + p_{13} \times x_{s} \times y_{s}^{3} + p_{04} \times y_{s}^{4} + p_{50} \times x_{s}^{5} + p_{41} \times x_{s}^{4} \times y_{s} \\ + p_{32} \times x_{s}^{3} \times y_{s}^{2} + p_{23} \times x_{s}^{2} \times y_{s}^{3} + p_{14} \times x_{s} \times y_{s}^{4} + p_{05} \times y_{s}^{5} \end{aligned}$
Primary Mirror	$\begin{aligned} z_{PM} & = q_{00} + q_{10} \times x_{p} + q_{01} \times y_{p} + q_{20} \times x_{p}^{2} + q_{11} \times x_{p} \times y_{p} + q_{02} \times y_{p}^{2} + q_{30} \times x_{p}^{3} + q_{21} \times x_{p}^{2} \times y_{p} + q_{12} \times x_{p} \times y_{p}^{2} \\ + q_{03} \times y_{p}^{3} + q_{40} \times x_{p}^{4} + q_{31} \times x_{p}^{3} \times y_{p} + q_{22} \times x_{p}^{2} \times y_{p}^{2} + q_{13} \times x_{p} \times y_{p}^{3} + q_{04} \times y_{p}^{4} + q_{50} \times x_{p}^{5} + q_{41} \times x_{p}^{4} \times y_{p} \\ + q_{32} \times x_{p}^{3} \times y_{p}^{2} + q_{23} \times x_{p}^{2} \times y_{p}^{3} + q_{14} \times x_{p} \times y_{p}^{4} + q_{05} \times y_{p}^{5} \end{aligned}$
Mirror	Parameters
Secondary Mirror	$\begin{array}{l} p_{00} = 48 .67, p_{10} = 0 .7227, p_{01} = - 1 .058 \times 10^{- 14}, \\ p_{20} = - 0 .004416, p_{11} = - 2.763 \times 10^{- 16}, p_{02} = 0 .005714, \\ p_{30} = 2 .125 \times 10^{- 5}, p_{21} = 3 .873 \times 10^{- 17}, p_{12} = - 5.541 \times 10^{- 5}, \\ p_{03} = 4.721 \times 10^{- 16}, p_{40} = - 6.856 \times 10^{- 7}, p_{31} = - 5.944 \times 10^{- 19}, \\ p_{22} = - 9.511 \times 10^{- 7}, p_{13} = 5.707 \times 10^{- 18}, p_{04} = 1.376 \times 10^{- 5}, \\ p_{50} = 1 .535 \times 10^{- 8}, p_{41} = 2.138 \times 10^{- 20}, p_{32} = 2.259 \times 10^{- 8}, \\ p_{23} = - 1.491 \times 10^{- 18}, p_{14} = - 2.087 \times 10^{- 7}, p_{05} = - 5.644 \times 10^{- 18} . \end{array}$
Primary Mirror	$\begin{array}{l} q_{00} = - 144.1, q_{10} = 5 .481, q_{01} = - 9 .119 \times 10^{- 13}, \\ q_{20} = - 0.1274, q_{11} = 7.549 \times 10^{- 14}, q_{02} = - 0.0004981, \\ q_{30} = 0.002386, q_{21} = - 2 .343 \times 10^{- 15}, q_{12} = 0 .0004273, \\ q_{03} = 1.140 \times 10^{- 16}, q_{40} = - 2 .086 \times 10^{- 5}, q_{31} = 3.232 \times 10^{- 17}, \\ q_{22} = - 1 .022 \times 10^{- 5}, q_{13} = - 4.617 \times 10^{- 18}, q_{04} = - 1 .104 \times 10^{- 6}, \\ q_{50} = 6.989 \times 10^{- 8}, q_{41} = - 1.670 \times 10^{- 19}, q_{32} = 9 .131 \times 10^{- 8}, \\ q_{23} = 4.698 \times 10^{- 20}, q_{14} = 3.553 \times 10^{- 8}, q_{05} = - 2.273 \times 10^{- 21} . \end{array}$

Optical System	Outgoing Spot Radius (mm)	Antenna Volume ( ${c m}^{3}$ )	Reference
①	100	57,200	[22]
②	100	24,200	[20]
③	25	3229.99	[17]
④	25	1244.61	[23]

Mirror	Equation
Secondary Mirror	$\begin{aligned} z_{SM} & = p_{00} + p_{10} \times x_{s} + p_{01} \times y_{s} + p_{20} \times x_{s}^{2} + p_{11} \times x_{s} \times y_{s} + p_{02} \times y_{s}^{2} + p_{30} \times x_{s}^{3} + p_{21} \times x_{s}^{2} \times y_{s} + p_{12} \times x_{s} \times y_{s}^{2} \\ + p_{03} \times y_{s}^{3} + p_{40} \times x_{s}^{4} + p_{31} \times x_{s}^{3} \times y_{s} + p_{22} \times x_{s}^{2} \times y_{s}^{2} + p_{13} \times x_{s} \times y_{s}^{3} + p_{04} \times y_{s}^{4} + p_{50} \times x_{s}^{5} + p_{41} \times x_{s}^{4} \times y_{s} \\ + p_{32} \times x_{s}^{3} \times y_{s}^{2} + p_{23} \times x_{s}^{2} \times y_{s}^{3} + p_{14} \times x_{s} \times y_{s}^{4} + p_{05} \times y_{s}^{5} \end{aligned}$
Primary Mirror	$\begin{aligned} z_{PM} & = q_{00} + q_{10} \times x_{p} + q_{01} \times y_{p} + q_{20} \times x_{p}^{2} + q_{11} \times x_{p} \times y_{p} + q_{02} \times y_{p}^{2} + q_{30} \times x_{p}^{3} + q_{21} \times x_{p}^{2} \times y_{p} + q_{12} \times x_{p} \times y_{p}^{2} \\ + q_{03} \times y_{p}^{3} + q_{40} \times x_{p}^{4} + q_{31} \times x_{p}^{3} \times y_{p} + q_{22} \times x_{p}^{2} \times y_{p}^{2} + q_{13} \times x_{p} \times y_{p}^{3} + q_{04} \times y_{p}^{4} + q_{50} \times x_{p}^{5} + q_{41} \times x_{p}^{4} \times y_{p} \\ + q_{32} \times x_{p}^{3} \times y_{p}^{2} + q_{23} \times x_{p}^{2} \times y_{p}^{3} + q_{14} \times x_{p} \times y_{p}^{4} + q_{05} \times y_{p}^{5} \end{aligned}$
Mirror	Parameters
Secondary Mirror	$\begin{array}{l} p_{00} = 48 .67, p_{10} = 0 .7227, p_{01} = - 1 .058 \times 10^{- 14}, \\ p_{20} = - 0 .004416, p_{11} = - 2.763 \times 10^{- 16}, p_{02} = 0 .005714, \\ p_{30} = 2 .125 \times 10^{- 5}, p_{21} = 3 .873 \times 10^{- 17}, p_{12} = - 5.541 \times 10^{- 5}, \\ p_{03} = 4.721 \times 10^{- 16}, p_{40} = - 6.856 \times 10^{- 7}, p_{31} = - 5.944 \times 10^{- 19}, \\ p_{22} = - 9.511 \times 10^{- 7}, p_{13} = 5.707 \times 10^{- 18}, p_{04} = 1.376 \times 10^{- 5}, \\ p_{50} = 1 .535 \times 10^{- 8}, p_{41} = 2.138 \times 10^{- 20}, p_{32} = 2.259 \times 10^{- 8}, \\ p_{23} = - 1.491 \times 10^{- 18}, p_{14} = - 2.087 \times 10^{- 7}, p_{05} = - 5.644 \times 10^{- 18} . \end{array}$
Primary Mirror	$\begin{array}{l} q_{00} = - 144.1, q_{10} = 5 .481, q_{01} = - 9 .119 \times 10^{- 13}, \\ q_{20} = - 0.1274, q_{11} = 7.549 \times 10^{- 14}, q_{02} = - 0.0004981, \\ q_{30} = 0.002386, q_{21} = - 2 .343 \times 10^{- 15}, q_{12} = 0 .0004273, \\ q_{03} = 1.140 \times 10^{- 16}, q_{40} = - 2 .086 \times 10^{- 5}, q_{31} = 3.232 \times 10^{- 17}, \\ q_{22} = - 1 .022 \times 10^{- 5}, q_{13} = - 4.617 \times 10^{- 18}, q_{04} = - 1 .104 \times 10^{- 6}, \\ q_{50} = 6.989 \times 10^{- 8}, q_{41} = - 1.670 \times 10^{- 19}, q_{32} = 9 .131 \times 10^{- 8}, \\ q_{23} = 4.698 \times 10^{- 20}, q_{14} = 3.553 \times 10^{- 8}, q_{05} = - 2.273 \times 10^{- 21} . \end{array}$

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Applied Optics