Characterization of mode field distribution in optical Fabry-Perot cavity based on nanofiber

Hu Yu-Dong; Song Li-Jun; Wang Chen-Xi; Zhang Pei; Zhou Jing; Li Gang; Zhang Peng-Fei; Zhang Tian-Cai

doi:10.7498/aps.71.20221538

Abstract

The composite cavity optomechanical system combining optical Fabry-Perot (F-P) cavities, particles, and micro/nano mechanical oscillators is becoming more significant in the researches and applications of the fundamental physics, quantum information processing, and precision measurement. Characterizing the mode field distribution of optical F-P cavity is significant prior to the application of optical F-P cavity. In this paper, we propose and demonstrate a method to measure the waist of an optical F-P cavity and to characterize the mode field distribution of the optical F-P cavity by using a nanofiber nondestructively. In experiment, a nanofiber is placed in the mode of the optical F-P cavity with a fineness of around 1500. The optical F-P cavity is composed of two mirrors each with high reflectivity of 99.8%. The radius of curvature of the each mirror is 50 mm. The cavity length is ($ 80 \pm 4 $) mm. The nanofiber is fabricated from a single-mode fiber by the flame-brush method. The nanofiber diameter is around 440 nm. The transmission spectra of the optical F-P cavity are measured by scanning the cavity length. The free spectrum ranges and the inner cavity losses can be obtained from the transmission spectra. First, the influence of the nanofiber on the optical F-P cavity fineness is investigated. The fineness as a function of nanofiber position along the radial direction of the optical F-P cavity is measured. The fineness caused by the nanofiber decreases to a minimum value of about 240. Second, it is investigated that the optical F-P cavity inner loss caused by the nanofiber as a function of the nanofiber position along the radial direction of the optical F-P cavity when the nanofiber is placed at the waist of the optical F-P cavity. The inner loss of the optical F-P cavity caused by the nanofiber is related to the intensity distribution of the optical F-P cavity mode field, which is predicted theoretically. Thus, by making the Gaussian fitting of the optical F-P cavity inner loss as a function of the nanofiber position, we can obtain a waist radius of the optical F-P cavity to be ($ 72 \pm 1 $) μm. This is in good agreement with the theoretical calculation. Finally, the mode field distribution of the optical F-P cavity along the cavity axis is characterized. This method can be used for precisely controlling the coupling between the particles on the surface of nanofiber and optical F-P cavity. Besides, this method provides a good platform for studying the hybrid optomechanical system combining cavities, photons and quantum emitters.

Keywords:

Authors and contacts

1.
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
2.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Corresponding author: Zhang Peng-Fei, zhangpengfei@sxu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. U21A6006, U21A20433, 11974223, 11974225, 12104277, 12104278) and the Fund for Shanxi “1331 Project” Key Subjects Construction, China.

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References

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Cited By

图 1 (a) 理论模型结构示意图, 灰色阴影表示高斯光束, 红色阴影表示高斯光束在径向光功率密度分布, 蓝色长棒表示纳米光纤; (b) 光学F-P谐振腔的精细度随纳米光纤在y轴位置的变化关系的模拟结果, 红色三角块为纳米光纤造成光学F-P谐振腔的内腔损耗, 蓝色实线为光学F-P谐振腔腔内高斯光束的强度分布, 橙色圆点为光学F-P谐振腔精细度

Figure 1. (a) Schematic of the model for numerical simulations. Gray shaded areas represent the Gaussian beams, red shaded areas represent the intensity distribution of Gaussian beams and long blue bars represent the nanofiber. (b) F-P cavity finesse as a function of the nanofiber position along y-axis. The orange circles are the finesse of F-P cavity. The red triangular blocks are the F-P cavity losses and the blue solid line is the intensity distribution of the Gaussian beam in the F-P cavity.

DownLoad: Full-Size Img PowerPoint

图 2 (a) 实验装置示意图; (b) 纳米光纤的电镜照片

Figure 2. (a) Schematic of experimental setup; (b) SEM image of the nanofiber.

DownLoad: Full-Size Img PowerPoint

图 3 光学F-P谐振腔的精细度随纳米光纤在y轴位置的变化关系

Figure 3. Finesse of the F-P cavity as a function of nanofiber position along y-axis.

DownLoad: Full-Size Img PowerPoint

图 5 光学F-P谐振腔中轴向(z轴)的腔内模场分布

Figure 5. Mode distribution in the F-P cavity along z-axis.

DownLoad: Full-Size Img PowerPoint

图 4 纳米光纤处于光学F-P谐振腔腔模腰斑处, 光学F-P谐振腔内腔损耗随纳米光纤在y轴位置的变化关系

Figure 4. F-P cavity loss as a function of the position of the nanofiber in the y-axis when the nanofiber is at the waist of the cavity.

DownLoad: Full-Size Img PowerPoint

map

[1]	张智明 2015 量子光学 (北京: 科学出版社) 第184—193页 Zhang Z M 2015 Quantum Optics (Beijing: Science Press) pp184–193 (in Chinese)
[2]	李刚, 张鹏飞, 杨鹏飞, 王志辉, 张天才 2022 光学学报 42 76 Li G, Zhang P F, Yang P F, Wang Z H, Zhang T C 2022 Acta Opt. Sin. 42 76
[3]	Walther H, Varcoe B T H, Englert B-G, Becker T 2006 Rep. Prog. Phys. 69 1325 Google Scholar
[4]	张天才, 毋伟, 杨鹏飞, 李刚, 张鹏飞 2021 光学学报 41 392 Zhang T C, Wu W, Yang P F, Li G, Zhang P F 2021 Acta Opt. Sin. 41 392
[5]	Vahala K J 2003 Nature 424 839 Google Scholar
[6]	宋丽军, 张鹏飞, 王鑫, 王晨曦, 李刚, 张天才 2019 68 074204 Google Scholar Song L J, Zhang P F, Wang X, Wang C X, Li G, Zhang T C 2019 Acta Phys. Sin. 68 074204 Google Scholar
[7]	McCall S L, Levi A F J, Slusher R E, Pearton S J, Logan R A 1992 Appl. Phys. Lett. 60 289 Google Scholar
[8]	Kahl M, Thomay T, Kohnle V, Beha K, Merlein J, Hagner M, Halm A, Ziegler J, Nann T, Fedutik Y, Woggon U, Artemyev M, Pérez-Willard F, Leitenstorfer A, Bratschitsch R 2007 Nano Lett. 7 2897 Google Scholar
[9]	Ruddell S K, Webb K E, Herrera I, Parkins A S, Hoogerland M D 2017 Optica 4 576 Google Scholar
[10]	Hunger D, Steinmetz T, Colombe Y, Deutsch C, Hänsch T W, Reichel J 2010 New J. Phys. 12 065038 Google Scholar
[11]	Zhang Q Q, Fan Z Y, Zhang J P, Zhang F B, Zhang Q, Li Y M 2020 Appl. Opt. 59 8959 Google Scholar
[12]	成凡, 张鹏飞, 王鑫, 张天才 2017 量子光学学报 23 74 Cheng F, Zhang P F, Wang X, Zhang T C 2017 J. Quantum Opt. 23 74
[13]	Vučković J, Lončar M, Mabuchi H, Scherer A 2001 Phys. Rev. E 65 016608 Google Scholar
[14]	Chen Y T, Szurek M, Hu B L, Hond J D, Braverman B, Vuletic V 2022 Opt. Express 30 37426
[15]	Kuhn A, Hennrich M, Rempe G 2002 Phys. Rev. Lett. 89 067901 Google Scholar
[16]	Yang P F, Xia X W, He H, Li S K, Han X, Zhang P, Li G, Zhang P F, Xu J P, Yang Y P, Zhang T C 2019 Phys. Rev. Lett. 123 233604
[17]	Yang P F, Li M, Han X, He H, Li G, Zou C L, Zhang P F, Zhang T C 2019 arXiv 1911.10300
[18]	Chen W L, Beck K M, Bücker R, Gullans M, Lukin M D, Tanji-Suzuki H, Vuletic V 2013 Science 341 768 Google Scholar
[19]	Colombe Y, Steinmetz T, Dubois G, Linke F, Hunger D, Reichel J 2007 Nature 450 272 Google Scholar
[20]	Haas F, Volz J, Gehr R, Reichel J, Estève J 2014 Science 344 180 Google Scholar
[21]	Albrecht R, Bommer A, Deutsch C, Reichel J, Becher C 2013 Phys. Rev. Lett. 110 243602 Google Scholar
[22]	Takahashi H, Kassa E, Christoforou C, Keller M 2020 Phys. Rev. Lett. 124 013602 Google Scholar
[23]	Kobel P, Breyer M, Köhl M 2021 npj Quantum Inf. 7 6 Google Scholar
[24]	Kiraz A, Michler P, Becher C, Gayral B, Imamoğlu A, Zhang L D, Hu E 2001 Appl. Phys. Lett. 78 3932 Google Scholar
[25]	Lodahl P, Mahmoodian S, Stobbe S 2015 Rev. Mod. Phys. 87 347 Google Scholar
[26]	Metcalf H J, Van der Straten P 2003 J. Opt. Soc. Am. B: Opt. Phys. 20 887 Google Scholar
[27]	Ye J, Vernooy D W, Kimble H J 1999 Phys. Rev. Lett. 83 4987 Google Scholar
[28]	Münstermann P, Fischer T, Pinkse P W H, Rempe G 1999 Opt. Commun. 159 63 Google Scholar
[29]	Fortier K M, Kim S Y, Gibbons M J, Ahmadi P, Chapman M S 2007 Phys. Rev. Lett. 98 233601 Google Scholar
[30]	Kuhr S, Alt W, Schrader D, Dotsenko I, Miroshnychenko Y, Rosenfeld W, Khudaverdyan M, Gomer V, Rauschenbeutel A, Meschede D 2003 Phys. Rev. Lett. 91 213002 Google Scholar
[31]	Zhang Y C, Li G, Zhang P F, Wang J M, Zhang T C 2009 Front. Phys. Chin. 4 190 Google Scholar
[32]	Zhu J G, Ozdemir S K, Xiao Y F, Li L, He L, Chen D R, Yang L 2010 Nat. Photonics 4 46 Google Scholar
[33]	Wang X, Song L J, Wang C X, Zhang P F, Li G, Zhang T C 2019 Chin. Phys. B 28 073701
[34]	Nayak K P, Sadgrove M, Yalla R, Kien F L, Hakuta K 2018 J. Opt. 20 073001 Google Scholar
[35]	Vetsch E, Reitz D, Sague’ G, Schmidt R, Dawkins S T, Rauschenbeutel A 2010 Phys. Rev. Lett. 104 203603 Google Scholar
[36]	Davanco M I, Srinivasan K A 2009 Opt. Express 17 10542 Google Scholar
[37]	Tong L M, Gattass R R, Ashcom J B, He S, Lou J Y, Shen M Y, Maxwell I, Mazur E 2003 Nature 426 816 Google Scholar
[38]	Zhang P F, Wang X, Song L J, Wang C X, Li G, Zhang T C 2020 J. Opt. Soc. Am. B: Opt. Phys. 37 1401 Google Scholar
[39]	Kien F L, Gupta S D, Balykin V I, Hakuta K 2005 Phys. Rev. A 72 032509 Google Scholar
[40]	Fenton E F, Khan A, Solano P, Orozco L A, Fatemi F K 2018 Opt. Lett. 43 1534 Google Scholar
[41]	Wuttke C, Cole G D, Rauschenbeutel A 2013 Phys. Rev. A 88 061801 Google Scholar
[42]	Fogliano F, Besga B, Reigue A, Heringlake P, Lépinay M de L, Vaneph C, Reichel J, Pigeau B, Arcizet O 2021 Phys. Rev. X 11 021009
[43]	Pennetta R, Xie S, Russel P S 2016 Phys. Rev. Lett. 117 273901 Google Scholar
[44]	Bernd W, Thorsten O, Sebastian S, Thomas H, Arno R 2021 Phys. Rev. Appl. 16 064021 Google Scholar
[45]	Sakai H, Honda Y, Sasao N, Araki S, Higashi Y, Okugi T, Taniguchi T, Urakawa J, Takano M 2002 Jpn. J. Appl. Phys. 41 6398 Google Scholar
[46]	You Y, Urakawa J J, Rawankar A, Aryshev A, Shimizu H, Honda Y, Yan L X, Huang W H, Tang C X 2012 Nucl. Instrum. Methods. Phys. Res. Sect. A 694 6 Google Scholar
[47]	Sakaue K, Washio M, Araki S, Fukuda M, Higashi Y, Honda Y, Omori T, Taniguchi T, Terunuma N, Urakawa J, Sasao N 2009 Rev. Sci. Instrum. 80 123304 Google Scholar
[48]	Zhang P F, Cheng F, Wang X, Song L J, Zou C L, Li G, Zhang T C 2018 Opt. Express 26 31500 Google Scholar

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