Studying near-field propagation of generalized parabolic beams by virtual source method

Li Jia-Ning; Liu Wen; Ren Zhi-Jun

doi:10.7498/aps.73.20241026

Abstract

Generalized parabolic beams have various optical morphologies. They can be used in different research fields, such as component design, aero-optics, and microwave wireless power transmission. Studying the near-field transmission characteristics of these beams is important for improving utilization efficiency. We develop a more accurate theoretical framework to precisely understand the propagation behaviors of complex light fields in the near-field range, especially to break through the limitations of conventional near-axis approximation. This framework fully reveals the propagation mechanism of parabolic beams and their energy transmission modes. Here, based on the principle of independent propagation and the virtual source method, a group of virtual sources are introduced to analyze generalized parabolic beams. These beams can be expanded into the superposition of infinite continuous integer Bessel beams. Then, by combining the Weber integral formula and the Fourier Bessel transform, we rigorously derive an integral expression for generalized parabolic beams during near-field propagation. This expression breaks through the limitation of the traditional paraxial approximation and contains all the key propagation parameters of the family of beams. Based on this integral expression, the intensity distribution and phase characteristics of the generalized parabolic beam along the optical axis are further calculated and analyzed to reveal its energy transfer mode and phase characteristics. By comparing the paraxial approximate solution with the nonparaxial corrected solution for generalized parabolic beams, the far-field propagation of generalized parabolic beams is found to be the same when the propagation distance is sufficiently long. Such simulation results indirectly confirm the correctness of the obtained theoretical solution. The simple paraxial approximation theory can be used conveniently to calculate the far-field propagation of generalized parabolic beams. However, large errors exist when paraxial theory is used to calculate the near-field distribution of generalized parabolic beams. Although calculating nonparaxial propagation is especially complex, the nonparaxial correction solution is necessary when generalized parabolic beams are used in near-field research. Such research results not only deepen the understanding of the propagation mechanism of generalized parabolic beams but also lay a theoretical foundation for studying the precise propagation behaviors of other complex light fields in near-field optics.

Keywords:

Authors and contacts

Key Laboratory of Optical Information Detecting and Display Technology, Zhejiang Normal University, Jinhua 321004, China

Corresponding author: Ren Zhi-Jun, renzhijun@zjnu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12474301).

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References

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图 1 连续参数a = 0时的广义二阶抛物光束的轴上强度

Figure 1. The on-axis intensity distribution of the Parabolic beams with continuous parameter a = 0.

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图 2 连续参数a = 0时的广义二阶抛物光束的轴上相位

Figure 2. The on-axis phase distribution of the Parabolic beams with continuous parameter a = 0.

DownLoad: Full-Size Img PowerPoint

map

[1]	Durnin J, Miceli J J, Eberly J H 1987 Phys. Rev. Lett. 58 1499 Google Scholar
[2]	Durnin J 1987 J. Opt. Soc. Am. A 4 651 Google Scholar
[3]	Gutiérrez-Vega J C, Iturbe-Castillo M D, Chávez-Cerda S 2000 Opt. Lett. 25 1493 Google Scholar
[4]	Sosa-Sánchez C T, Silva-Ortigoza G, Juárez-Reyes S A, et al. 2017 J. Opt. 19 085604 Google Scholar
[5]	Bandres M A, Gutirrez-Vega J C, Chvez-Cerda S 2004 Opt. Lett. 29 44 Google Scholar
[6]	Khonina S N, Ustinov A V, Chávez-Cerda S 2018 J. Opt. Soc. Am. A 35 1511 Google Scholar
[7]	Liang Y S, Yan S H, Wang Z J, Li R Z, Cai Y N, He M R, Yao B L, Lei M 2020 Rep. Prog. Phys. 83 032401 Google Scholar
[8]	Gu S Y, Yu X H, Bai C, Min J W, Li R Z, Yang Y L, Yao B L 2022 Front. Phys. 10 1111023 Google Scholar
[9]	Deschamps G A 1971 Electron. Lett. 7 684 Google Scholar
[10]	Felsen L B 1976 J. Opt. Soc. Am. A 66 751 Google Scholar
[11]	Seshadri S R 2002 Opt. Lett. 27 998 Google Scholar
[12]	Borghi R, Santarsiero M 1997 Opt. Lett. 22 262 Google Scholar
[13]	Li Y J, Lee H, Wolf E 2004 J. Opt. Soc. Am. A 21 640 Google Scholar
[14]	Song L B, Ren Z J, Fan C J, Qian Y X 2021 Opt. Commun. 499 127307 Google Scholar
[15]	Gori F, Guattari G, Padovani C 1987 Opt. Commun. 64 491 Google Scholar
[16]	Seshadri S R 2002 Opt. Lett. 27 1872 Google Scholar
[17]	Yan S H, Yao B L, Lei M, Dan D, Yang Y L, Gao P 2012 Opt. Lett. 37 4774 Google Scholar
[18]	Seshadri S R 2003 Opt. Lett. 28 595 Google Scholar
[19]	Khonina S N, Ustinov A V, Porfirev A P 2019 Opt. Commun. 450 103 Google Scholar
[20]	陈鑫淼, 李海英, 吴涛, 孟祥帅, 黎凤霞 2023 72 100302 Google Scholar Chen X M, Li H Y, Wu T, Meng X S, Li F X 2023 Acta Phys. Sin. 72 100302 Google Scholar
[21]	岳东宁, 董全力, 陈民, 赵耀, 耿盼飞, 远晓辉, 盛政明, 张杰 2023 72 125201 Google Scholar Yue D N, Dong Q L, Chen M, Zhao Y, Geng P F, Yuan X H, Sheng Z M, Zhang J 2023 Acta Phys. Sin. 72 125201 Google Scholar
[22]	尹培琪, 许博坪, 刘颖华, 王屹山, 赵卫, 汤洁 2024 73 095202 Google Scholar Yin P Q, Xu B P, Liu Y H, Wang Y S, Zhao W, Tang J 2024 Acta Phys. Sin. 73 095202 Google Scholar

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Vol. 73, Issue 21 - 2024-11-05

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