Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Photon number distribution and second-order degree of coherence of a chaotic laser: analysis and experimental investigation

Lan Dou-Dou Guo Xiao-Min Peng Chun-Sheng Ji Yu-Lin Liu Xiang-Lian Li Pu Guo Yan-Qiang

Citation:

Photon number distribution and second-order degree of coherence of a chaotic laser: analysis and experimental investigation

Lan Dou-Dou, Guo Xiao-Min, Peng Chun-Sheng, Ji Yu-Lin, Liu Xiang-Lian, Li Pu, Guo Yan-Qiang
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • The researches on higher-order coherence and quantum statistics of light field are the important researching issues in quantum optics. In 1956, Hanbury-Brown and Twiss (HBT) (Hanbury-Brown R, Twiss R Q 1956 Nature 177 27) revolutionized optical coherence and demonstrated a new form of photon correlation. The landmark experiment has far-reaching influenced and even inspired the quantum theory of optical coherence that Glauber developed to account for the conclusive observation by HBT. Ever since then, the HBT effect has motivated extensive studies of higher-order coherence and quantum statistics in quantum optics, as well as in quantum information science and cryptography. Based on the HBT scheme, the degree of coherence and photon number distribution of light field can be derived from correlation measurement and photon counting technique. With the rapid development of the photoelectric detection technology, single-photon detection, which is the most sensitive and very widespread method of optical measurement, is used to characterize the natures of light sources and indicate their differences. More recently, HBT scheme combined with single-photon detection was used to study spatial interference, ghost imaging, azimuthal interference effect, deterministic manipulation and detection of single-photon source, etc. Due to broadband RF spectrum, noiselike feature, hypersensitivity to the initial conditions and long-term unpredictability, chaotic laser meets the essential requirements for information security and cryptography, and has been developed in many applications such as chaos-based secure communications and physical random number generation, as well as public-channel secure key distribution. But the research mainly focused on macroscopic dynamics of the chaotic laser. Moreover, the precision of measurement has reached a quantum level at present. Quantum statistcs of light field can also uncover profoundly the physical nature of the light. Thus, it is important to exploit the higher-order degree of coherence and photon statistics of chaotic field, which contribute to characterizing the field and distinguishing it from others. In this paper, photon number distribution and second-order degree of coherence of a chaotic laser are analyzed and measured based on HBT scheme. The chaotic laser is composed of a distributed feedback laser diode with optical feedback in fiber external cavity configuration. The bandwidth of the chaotic laser that we obtain experimentally is 6.7 GHz. The photon number distribution of chaotic laser is fitted by Gaussian random distribution, Possionian distribution and Bose-Einstein distribution. With the increase of the mean photon number, the photon number distribution changes from Bose-Einstein distribution into Poissonian distribution and always accords with Gaussian random distribution well. The second-order coherence g(2)(0) drops gradually from 2 to 1. By changing the bias current (I = 1.0Ith-2.0Ith) and feedback strength (010%), we compare and illustrate different chaotic dynamics and g(2)(0). From low frequency fluctuation to coherence collapse, the chaotic laser shows bunching effect and fully chaotic field can be obtained at the broadest bandwidth. Furthermore, the physical explanation for sub-chaotic or weakening of bunching effect is provided. It is concluded that this method can well reveal photon statistics of chaotic laser and will open up an avenue to the research of chaos with quantum optics, which merges two important fields of modern physics and is extremely helpful for the high-speed remote chaotic communication.
      Corresponding author: Guo Yan-Qiang, guoyanqiang@tyut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61405138, 61505136, 61505137, 61671316), the Funds for International Science and Technology Cooperation Program of China (Grant No. 2014DFA50870), and the Shanxi Nature Science Foundation of China (Grant Nos. 201601D011015, 201601D021021).
    [1]

    Loudon R 2000 The Quantum Theory of Light (USA: Oxford Science Publications) p92

    [2]

    Hanbury-Brown R, Twiss R Q 1956 Nature 177 27

    [3]

    Glauber R J 1963 Phys. Rev. 130 2529

    [4]

    Glauber R J 1963 Phys. Rev. Lett. 10 84

    [5]

    Arecchi F T 1965 Phys. Rev. Lett. 15 912

    [6]

    Arecchi F T, Gatti E, Sona A 1966 Phys. Lett. 20 27

    [7]

    Morgan B L, Mandel L 1966 Phys. Rev. Lett. 16 1012

    [8]

    Kimble H J, Dagenais M, Mandel L 1977 Phys. Rev. Lett. 39 691

    [9]

    Short R, Mandel L 1983 Phys. Rev. Lett. 51 384

    [10]

    Hadfield H R 2009 Nat. Photon. 3 696

    [11]

    Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Żukowski M 2012 Rev. Mod. Phys. 84 777

    [12]

    Banaszek K, Demkowicz-Dobrzaski R, Walmsley I A 2009 Nat. Photon. 3 673

    [13]

    Zhai Y H, Chen X H, Zhang D, Wu L A 2005 Phys. Rev. A 72 043805

    [14]

    Paul H 1982 Rev. Mod. Phys. 54 1061

    [15]

    Zhang S H, Gao L, Xiong J, Feng L J, Cao D Z, Wang K 2009 Phys. Rev. Lett. 102 073904

    [16]

    Schultheiss V H, Batz S, Peschel U 2016 Nat. Photon. 10 106

    [17]

    Liu X F, Yao X R, Li M F, Yu W K, Chen X H, Sun Z B, Wu L A, Zhai G J 2013 Acta Phys. Sin. 62 184205 (in Chinese) [刘雪峰, 姚旭日, 李明飞, 俞文凯, 陈希浩, 孙志斌, 吴令安, 翟光杰 2013 物理学报 62 184205]

    [18]

    Ryczkowski P, Barbier M, Friberg A T, Dudley J M, Genty G 2016 Nat. Photon. 10 167

    [19]

    Magaa-Loaiza O S, Mirhosseini M, Cross R M, Hashemi Rafsanjani S M, Boyd R W 2016 Sci. Adv. 2 e1501143

    [20]

    Diao W T, He J, Liu B, Wang J Y, Wang J M 2014 Acta Phys. Sin. 63 023701 (in Chinese) [刁文婷, 何军, 刘贝, 王杰英, 王军民 2014 物理学报 63 023701]

    [21]

    Guo Y Q, Li G, Zhang Y F, Zhang P F, Wang M J, Zhang T C 2012 Sci. China: Phys. Mech. Astron. 55 1523

    [22]

    Soriano M C, Garca-Ojalvo J, Mirasso C R, Fischer I 2013 Rev. Mod. Phys. 85 421

    [23]

    Wang S T, Wu Z M, Wu J G, Zhou L, Xia G Q 2015 Acta Phys. Sin. 64 154205 (in Chinese) [王顺天, 吴正茂, 吴加贵, 周立, 夏光琼 2015 物理学报 64 154205]

    [24]

    Argyris A, Syvridis D, Larger L, Annovazzi-Lodi V, Colet P, Fischer I, Garcia-Ojalvo J, Mirasso C R, Pesquera L, Shore K A 2005 Nature 438 343

    [25]

    Reidler I, Aviad Y, Rosenbluh M, Kanter I 2009 Phys. Rev. Lett. 103 024102

    [26]

    Wang A B, Li P, Zhang J G, Zhang J Z, Li L, Wang Y C 2013 Opt. Express 21 20452

    [27]

    Yoshimura K, Muramatsu J, Davis P, Harayama T, Okumura H, Morikatsu S, Aida H, Uchida A 2012 Phys. Rev. Lett. 108 070602

    [28]

    van Wiggeren G D, Roy R 1998 Science 279 1198

    [29]

    Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimori S, Yoshimura K, Peter Davis P 2008 Nat. Photon. 2 728

    [30]

    Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58

    [31]

    Tang X, Wu J G, Xia G Q, Wu Z M 2011 Acta Phys. Sin. 60 110509 (in Chinese) [唐曦, 吴加贵, 夏光琼, 吴正茂 2011 物理学报 60 110509]

    [32]

    Li N Q, Kim B, Locquet A, Choi D, Pan W, Citrin D S 2014 Opt. Lett. 39 5949

    [33]

    Albert F, Hopfmann C, Reitzenstein S, Schneider C, Hfling S, Worschech L, Kamp M, Kinzel W, Forchel A, Kanter 2011 Nat. Commun. 2 366

    [34]

    Lebreton A, Abram I, Braive R, Sagnes I, Robert-Philip I, Beveratos A 2013 Phys. Rev. A 88 013801

    [35]

    Kong L Q, Fan L L, Wang A B, Wang Y C 2009 Acta Phys. Sin. 58 7680 (in Chinese) [孔令琴, 樊林林, 王安邦, 王云才 2009 物理学报 58 7680]

    [36]

    Gooodman J W 2000 Statistical Optics (New York: Wiley-Interscience) p34

  • [1]

    Loudon R 2000 The Quantum Theory of Light (USA: Oxford Science Publications) p92

    [2]

    Hanbury-Brown R, Twiss R Q 1956 Nature 177 27

    [3]

    Glauber R J 1963 Phys. Rev. 130 2529

    [4]

    Glauber R J 1963 Phys. Rev. Lett. 10 84

    [5]

    Arecchi F T 1965 Phys. Rev. Lett. 15 912

    [6]

    Arecchi F T, Gatti E, Sona A 1966 Phys. Lett. 20 27

    [7]

    Morgan B L, Mandel L 1966 Phys. Rev. Lett. 16 1012

    [8]

    Kimble H J, Dagenais M, Mandel L 1977 Phys. Rev. Lett. 39 691

    [9]

    Short R, Mandel L 1983 Phys. Rev. Lett. 51 384

    [10]

    Hadfield H R 2009 Nat. Photon. 3 696

    [11]

    Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Żukowski M 2012 Rev. Mod. Phys. 84 777

    [12]

    Banaszek K, Demkowicz-Dobrzaski R, Walmsley I A 2009 Nat. Photon. 3 673

    [13]

    Zhai Y H, Chen X H, Zhang D, Wu L A 2005 Phys. Rev. A 72 043805

    [14]

    Paul H 1982 Rev. Mod. Phys. 54 1061

    [15]

    Zhang S H, Gao L, Xiong J, Feng L J, Cao D Z, Wang K 2009 Phys. Rev. Lett. 102 073904

    [16]

    Schultheiss V H, Batz S, Peschel U 2016 Nat. Photon. 10 106

    [17]

    Liu X F, Yao X R, Li M F, Yu W K, Chen X H, Sun Z B, Wu L A, Zhai G J 2013 Acta Phys. Sin. 62 184205 (in Chinese) [刘雪峰, 姚旭日, 李明飞, 俞文凯, 陈希浩, 孙志斌, 吴令安, 翟光杰 2013 物理学报 62 184205]

    [18]

    Ryczkowski P, Barbier M, Friberg A T, Dudley J M, Genty G 2016 Nat. Photon. 10 167

    [19]

    Magaa-Loaiza O S, Mirhosseini M, Cross R M, Hashemi Rafsanjani S M, Boyd R W 2016 Sci. Adv. 2 e1501143

    [20]

    Diao W T, He J, Liu B, Wang J Y, Wang J M 2014 Acta Phys. Sin. 63 023701 (in Chinese) [刁文婷, 何军, 刘贝, 王杰英, 王军民 2014 物理学报 63 023701]

    [21]

    Guo Y Q, Li G, Zhang Y F, Zhang P F, Wang M J, Zhang T C 2012 Sci. China: Phys. Mech. Astron. 55 1523

    [22]

    Soriano M C, Garca-Ojalvo J, Mirasso C R, Fischer I 2013 Rev. Mod. Phys. 85 421

    [23]

    Wang S T, Wu Z M, Wu J G, Zhou L, Xia G Q 2015 Acta Phys. Sin. 64 154205 (in Chinese) [王顺天, 吴正茂, 吴加贵, 周立, 夏光琼 2015 物理学报 64 154205]

    [24]

    Argyris A, Syvridis D, Larger L, Annovazzi-Lodi V, Colet P, Fischer I, Garcia-Ojalvo J, Mirasso C R, Pesquera L, Shore K A 2005 Nature 438 343

    [25]

    Reidler I, Aviad Y, Rosenbluh M, Kanter I 2009 Phys. Rev. Lett. 103 024102

    [26]

    Wang A B, Li P, Zhang J G, Zhang J Z, Li L, Wang Y C 2013 Opt. Express 21 20452

    [27]

    Yoshimura K, Muramatsu J, Davis P, Harayama T, Okumura H, Morikatsu S, Aida H, Uchida A 2012 Phys. Rev. Lett. 108 070602

    [28]

    van Wiggeren G D, Roy R 1998 Science 279 1198

    [29]

    Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimori S, Yoshimura K, Peter Davis P 2008 Nat. Photon. 2 728

    [30]

    Kanter I, Aviad Y, Reidler I, Cohen E, Rosenbluh M 2010 Nat. Photon. 4 58

    [31]

    Tang X, Wu J G, Xia G Q, Wu Z M 2011 Acta Phys. Sin. 60 110509 (in Chinese) [唐曦, 吴加贵, 夏光琼, 吴正茂 2011 物理学报 60 110509]

    [32]

    Li N Q, Kim B, Locquet A, Choi D, Pan W, Citrin D S 2014 Opt. Lett. 39 5949

    [33]

    Albert F, Hopfmann C, Reitzenstein S, Schneider C, Hfling S, Worschech L, Kamp M, Kinzel W, Forchel A, Kanter 2011 Nat. Commun. 2 366

    [34]

    Lebreton A, Abram I, Braive R, Sagnes I, Robert-Philip I, Beveratos A 2013 Phys. Rev. A 88 013801

    [35]

    Kong L Q, Fan L L, Wang A B, Wang Y C 2009 Acta Phys. Sin. 58 7680 (in Chinese) [孔令琴, 樊林林, 王安邦, 王云才 2009 物理学报 58 7680]

    [36]

    Gooodman J W 2000 Statistical Optics (New York: Wiley-Interscience) p34

  • [1] Ge Shan-Shan, Wang Teng-Wu, Ge Jing-Yi, Zhou Pei, Li Nian-Qiang. Evolution of extreme events in chaotic light-injected semiconductor lasers. Acta Physica Sinica, 2023, 72(16): 164201. doi: 10.7498/aps.72.20230759
    [2] Liu Qi, Li Pu, Kai Chao, Hu Chun-Qiang, Cai Qiang, Zhang Jian-Guo, Xu Bing-Jie. Short-time prediction of chaotic laser using time-delayed photonic reservoir computing. Acta Physica Sinica, 2021, 70(15): 154209. doi: 10.7498/aps.70.20210355
    [3] Wu Jia-Chen, Song Zheng, Xie Yi-Feng, Zhou Xin-Yu, Zhou Pei, Mu Peng-Hua, Li Nian-Qiang. High-quality random number sequences extracted from chaos post-processed by phased-array semiconductor laser. Acta Physica Sinica, 2021, 70(10): 104205. doi: 10.7498/aps.70.20202034
    [4] Zhang Yi-Ning, Feng Yu-Ling, Wang Xiao-Qian, Zhao Zhen-Ming, Gao Chao, Yao Zhi-Hai. Time delay signature and bandwidth of chaotic laser output from semiconductor laser. Acta Physica Sinica, 2020, 69(9): 090501. doi: 10.7498/aps.69.20191881
    [5] Wang Long-Sheng, Zhao Tong, Wang Da-Ming, Wu Dan-Yu, Zhou Lei, Wu Jin, Liu Xin-Yu, Wang An-Bang. 14-Gb/s physical random numbers generated in real time by using multi-bit quantization of chaotic laser. Acta Physica Sinica, 2017, 66(23): 234205. doi: 10.7498/aps.66.234205
    [6] Fan Hong-Yi, Wu Ze. Statistical properties of binomial and negative-binomial combinational optical field state and its generation in quantum diffusion channel. Acta Physica Sinica, 2015, 64(8): 080303. doi: 10.7498/aps.64.080303
    [7] Liu Ying-Ying, Pan Wei, Jiang Ning, Xiang Shui-Ying, Lin Yu-Dong. Isochronal chaos synchronization of a chain mutually coupled semiconductor lasers. Acta Physica Sinica, 2013, 62(2): 024208. doi: 10.7498/aps.62.024208
    [8] Xiao Bao-Jin, Hou Jia-Yin, Zhang Jian-Zhong, Xue Lu-Gang, Wang Yun-Cai. The effect of the relaxation oscillation frequency of chaotic semiconductor laser on the rate of random sequence. Acta Physica Sinica, 2012, 61(15): 150502. doi: 10.7498/aps.61.150502
    [9] Liu Liu, Zheng Jian-Yu, Zhang Ming-Jiang, Meng Li-Na, Zhang Zhao-Xia, Wang Yun-Cai. Photonic generation and transmission of chaotic ultra wideband signals. Acta Physica Sinica, 2012, 61(8): 084204. doi: 10.7498/aps.61.084204
    [10] Wei Yue, Fan Li, Xia Guang-Qiong, Chen Yu-Lin, Wu Zheng-Mao. Bidirectional chaos communication based on two semiconductor lasers subjected to incoherent optical injection of common-chaotic-signal. Acta Physica Sinica, 2012, 61(22): 224203. doi: 10.7498/aps.61.224203
    [11] Huang Yi-Ze, Li Yi, Wang Hai-Fang, Yu Xiao-Jing, Zhang Hu, Zhang Wei, Zhu Hui-Qun, Sun Ruo-Xi, Zhou Sheng, Zhang Yu-Ming. Coherence collapse of the dual fiber Bragg grating external cavity semiconductor laser. Acta Physica Sinica, 2012, 61(1): 014201. doi: 10.7498/aps.61.014201
    [12] Zhang Jian-Zhong, Wang An-Bang, Zhang Ming-Jiang, Li Xiao-Chun, Wang Yun-Cai. Elimination of time-delay signature in an external cavity semiconductor laser by randomly modulating feedback phase. Acta Physica Sinica, 2011, 60(9): 094207. doi: 10.7498/aps.60.094207
    [13] Chen Sha-Sha, Zhang Jian-Zhong, Yang Ling-Zhen, Liang Jun-Sheng, Wang Yun-Cai. One Gbit/s random bit generation based on chaotic laser. Acta Physica Sinica, 2011, 60(1): 010501. doi: 10.7498/aps.60.010501
    [14] Meng Li-Na, Zhang Ming-Jiang, Zheng Jian-Yu, Zhang Zhao-Xia, Wang Yun-Cai. Chaotic ultra-wideband microwave signal generation utilizing an optical injection chaotic laser diode. Acta Physica Sinica, 2011, 60(12): 124212. doi: 10.7498/aps.60.124212
    [15] Zhang Ji-Bing, Zhang Jian-Zhong, Yang Yi-Biao, Liang Jun-Sheng, Wang Yun-Cai. Randomness analysis of external cavity semiconductor laser as entropy source. Acta Physica Sinica, 2010, 59(11): 7679-7685. doi: 10.7498/aps.59.7679
    [16] Cao liang-Ping, Xia Guang-Qiong, Deng Tao, Lin Xiao-Dong, Wu Zheng-Mao. Bidirectional chaos communication based on semiconductor laser with incoherent optical feedback. Acta Physica Sinica, 2010, 59(8): 5541-5546. doi: 10.7498/aps.59.5541
    [17] Niu Sheng-Xiao, Wang Yun-Cai, He Hu-Cheng, Zhang Ming-Jiang. Tunable photonic microwave generation using optically injected semiconductor laser. Acta Physica Sinica, 2009, 58(10): 7241-7245. doi: 10.7498/aps.58.7241
    [18] Liu Si-Ping, Zhang Yu-Chi, Zhang Peng-Fei, Li-Gang, Wang Jun-Min, Zhang Tian-Cai. Experimental study on the properties of the AR-coated external cavity diode lasers. Acta Physica Sinica, 2009, 58(1): 285-289. doi: 10.7498/aps.58.285.1
    [19] Zhao Yan-Feng. Chaos characteristics of the semiconductor laser with double external cavity optical feedback. Acta Physica Sinica, 2009, 58(9): 6058-6062. doi: 10.7498/aps.58.6058
    [20] Wang Yun-Cai. Experimental study on the timing jitter of gain-switched laser diodes with photo n injection. Acta Physica Sinica, 2003, 52(9): 2190-2193. doi: 10.7498/aps.52.2190
Metrics
  • Abstract views:  5605
  • PDF Downloads:  415
  • Cited By: 0
Publishing process
  • Received Date:  24 January 2017
  • Accepted Date:  27 March 2017
  • Published Online:  05 June 2017

/

返回文章
返回