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光学谐振腔的传输特性

王雅君 王俊萍 张文慧 李瑞鑫 田龙 郑耀辉

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光学谐振腔的传输特性

王雅君, 王俊萍, 张文慧, 李瑞鑫, 田龙, 郑耀辉

Transmission characteristics of optical resonator

Wang Ya-Jun, Wang Jun-Ping, Zhang Wen-Hui, Li Rui-Xin, Tian Long, Zheng Yao-Hui
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  • 量子噪声已成为当前精密测量应用中的一种重要限制因素, 与其相关的问题已成为研究热点. 光学谐振腔作为操控量子噪声的一种重要光学器件, 其传输特性决定了输出信号噪声的演化特性. 本文通过理论分析光学谐振腔输出的强度、相位与频率的对应关系, 对比了过耦合腔、阻抗匹配腔与欠耦合腔传输函数、能量传输、噪声传递的频谱特性, 证明其具有功率分束、频率滤波、噪声转换等特性, 为量子噪声的分析与操控等应用研究提供了基础, 将推动精密测量领域的发展.
    Quantum noise has become an important limiting factor in the application of precision measurement, and its relevant problems have become a research hotspot. As an important optical device to manipulate quantum noise, the optical resonator possesses the transmission characteristics that determine the evolution characteristics of output signal’s noise. According to their impedance matching factor a values, the resonators can be divided into three categories: over-coupled cavity for $a \in [ - 1, 0)$, impedance matched cavity for $a{{ = }}0$, and under-coupled cavity for $a \in (0, 1]$. When the resonator fully meets the resonant conditions, its output field can be regarded as a low-pass filter, the high-frequency noise is directly reflected. The high-frequency noise at the output end is greatly suppressed, and the noise at the frequency far larger than the linewidth reaches the shot noise standard. Therefore, the noise of the optical field beyond the linewidth range can be greatly suppressed by the narrow linewidth optical resonator. At the same time, from the three kinds of optical resonator phase diagrams it can be found that the over-coupled cavity is in a state of half a detuning and the sideband frequency phase rotates ± 90° relative to the carrier frequency. In this case, the phase noise of light field can be converted into amplitude noise by an over-coupled cavity, which can be used for the phase noise measurement or squeezing angle rotation of squeezed light and has important applications in analyzing the laser noise component and manipulating the quantum noise. At the same time, the energy loss of the over-coupled cavity is the largest among the three types of cavity structures. Through theoretically analysing the corresponding relation among optical resonator output intensity, phase and frequency, and by making a comparison of comparing transfer function, energy transmission, spectrum characteristics of noise transmission among over-coupled cavity, impedance matched cavity and under-coupled cavity, in this paper the power splitter, frequency filtering, and noise transformation features of the optical resonator are demonstrated. The analysis results in this paper provide a basis for applying various optical resonators to different occasions, and promote the development of using the optical resonators to control the quantum noise of light field and improving the precision of precision measurement.
      通信作者: 郑耀辉, yhzheng@sxu.edu.cn
    • 基金项目: 国家重点研发计划(批准号: 2020YFC2200402)、国家自然科学基金(批准号: 62027821, 11654002, 11874250, 11804207, 11804206, 62035015, 62001374)、山西省重点研发计划(批准号: 201903D111001)、山西省三晋学者特聘教授项目、山西省“1331”重点建设学科和山西省高等学校中青年拔尖创新人才项目资助的课题
      Corresponding author: Zheng Yao-Hui, yhzheng@sxu.edu.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant No. 2020YFC2200402), the National Natural Science Foundation of China (Grant Nos. 62027821, 11654002, 11874250, 11804207, 11804206, 62035015, 62001374), the Key R&D Project of Shanxi Province, China (Grant No. 201903D111001), the Program for Sanjin Scholar of Shanxi Province, China, the Fund for Shanxi “1331 Project” Key Subjects Construction, China, and the Program for Outstanding Innovative Teams of Higher Learning Institutions of Shanxi Province, China
    [1]

    聂丹丹, 冯晋霞, 戚蒙, 李渊骥, 张宽收 2020 物理学报 69 094205Google Scholar

    Nie D D, Feng J X, Qi M, Li Y J, Zhang K S 2020 Acta Phys. Sin. 69 094205Google Scholar

    [2]

    翟泽辉, 郝温静, 刘建丽, 段西亚 2020 物理学报 69 184204Google Scholar

    Zhai Z H, Hao W J, Liu J L, Duan X Y 2020 Acta Phys. Sin. 69 184204Google Scholar

    [3]

    刘奎, 马龙, 苏必达, 李佳明, 孙恒信, 郜江瑞 2020 物理学报 69 124203Google Scholar

    Liu K, Ma L, Su B D, Li J M, Sun H X, Gao J R 2020 Acta Phys. Sin. 69 124203Google Scholar

    [4]

    周瑶瑶, 田剑锋, 闫智辉, 贾晓军 2019 物理学报 68 064205Google Scholar

    Zhou Y Y, Tian J F, Yan Z H, Jia X J 2019 Acta Phys. Sin. 68 064205Google Scholar

    [5]

    葛瑞芳, 杨鹏飞, 韩星, 张鹏飞, 李刚, 张天才 2020 量子光学学报 26 21Google Scholar

    Ge R F, Yang P F, Han X, Zhang P F, Li G, Zhang T C 2020 Acta Sin. Quantum Opt. 26 21Google Scholar

    [6]

    石柱, 郭永瑞, 徐敏志, 卢华东 2018 量子光学学报 24 237Google Scholar

    Shi Z, Guo Y R, Xu M Z, Lu H D 2018 Acta Sin. Quantum Opt. 24 237Google Scholar

    [7]

    Wang Y, Shen H, Jin X L, Su X L, Xie C D, Peng K C 2010 Opt. Express 18 6149Google Scholar

    [8]

    王俊萍, 张文慧, 李瑞鑫, 田龙, 王雅君, 郑耀辉 2020 物理学报 69 234204

    Wang J P, Zhang W H, Li R X, Tian L, Wang Y Jun, Zheng Y H 2020 Acta Phys. Sin. 69 234204

    [9]

    Villar A S 2008 Am. J. Phys. 76 922Google Scholar

    [10]

    Wang Y J, Zheng Y H, Shi Z, Peng K C 2012 Laser Phys. Lett. 9 506Google Scholar

    [11]

    Zhang W H, Wang J R, Zheng Y H, Wang Y J, Peng K C 2019 Appl. Phys. Lett. 115 171103Google Scholar

    [12]

    Zhao G, Hausmaninger T, Ma W G, Axner O 2017 Opt. Lett. 42 3109Google Scholar

    [13]

    胡悦, 曹凤朝, 董仁婧, 郝辰悦, 刘大禾, 石锦卫 2020 物理学报 69 224202

    Hu Y, Cao F Z, Dong R J, Hao C Y, Liu D H, Shi J W 2020 Acta Phys. Sin. 69 224202

    [14]

    Schreiber K U, Gebauer A, Wells J P R 2013 Opt. Lett. 38 3574Google Scholar

    [15]

    Leibrandt D R, Heidecker J 2015 Rev. Sci. Instrum. 86 123115Google Scholar

    [16]

    Liu K, Zhang F L, Li Z Y, Feng X H, Li K, Lu Z H, Schreiber K U, Luo J, Zhang J 2019 Opt. Lett. 44 2732Google Scholar

    [17]

    Kwee P, Willke B, Danzmann K 2011 Opt. Lett. 36 3563Google Scholar

    [18]

    Kaufer S, Kasprzack M, Frolov V, Willke B 2017 Classical Quantum Gravity 34 145001Google Scholar

    [19]

    Junker J, Oppermann P, Willke B 2017 Opt. Lett. 42 755Google Scholar

    [20]

    Kaufer S, Willke B 2019 Opt. Lett. 44 1916Google Scholar

    [21]

    Zhao Y H, Aritomi N, Capocasa E, et al. 2020 Phys. Rev. Lett. 124 171101Google Scholar

    [22]

    McCuller L, Whittle C, Ganapathy D, et al. 2020 Phys. Rev. Lett. 124 171102Google Scholar

    [23]

    Capocasa E, Barsuglia M, Degallaix J, Pinard L, Straniero N, Schnabel R, Somiya K, Aso Y, Tatsumi D, Flaminio R 2016 Phys. Rev. D 93 082004Google Scholar

    [24]

    Kwee P 2010 Ph. D. Dissertation (Hannover: Leibniz Universität Hannover)

    [25]

    Kaufer S 2018 Ph. D. Dissertation (Hannover: Leibniz Universität Hannover)

    [26]

    Brozek O S 1999 Ph. D. Dissertation (Hannover: Universität Hannover)

    [27]

    Guo X M, Wang X Y, Li Y M, Zhang K S 2009 Appl. Opt. 48 6475Google Scholar

  • 图 1  两镜腔结构简图

    Fig. 1.  Structure diagram of two-mirror cavity.

    图 2  不同腔型的特性 (a)能量传输特性; (b)循环功率特性

    Fig. 2.  Characteristics of different cavity types: (a) Energy transfer characteristic; (b) cyclic power characteristic.

    图 3  传输函数$G\left( f \right)$随频率f的变化

    Fig. 3.  Diagram of the transfer function $G\left( f \right)$ with respect to frequency f.

    图 4  光学谐振腔光强反射率和反射位相${\theta _{\rm{R}}}$与失谐量Δ的关系 (a) 过耦合腔, ${R_1} = 0.99$, ${R_2} = 0.998$; (b)欠耦合腔, ${R_1} = 0.998$, ${R_2} = 0.99$; (c)阻抗匹配腔, ${R_1} = {R_2} $$ = 0.994$

    Fig. 4.  Relations between optical intensity reflectivity and reflection phase ${\theta _R}$ and detuning Δ in optical resonator: (a) Over-coupled cavity, ${R_1}{{ = }}0.99$, ${R_2} = 0.998$; (b) under-coupled cavity, ${R_1} = 0.998$, ${R_2} = 0.99$; (c) impedance matched cavity, ${R_1} = R_2 = 0.994$.

    图 5  三镜环形谐振腔的噪声模型

    Fig. 5.  Noise model of three-mirror annular resonator.

    图 6  腔输出场的量子噪声限制 (a)阻抗匹配腔中噪声随频率的变化; (b)非阻抗匹配腔中噪声随频率的变化; (c)反射光场噪声随阻抗匹配因子a的变化

    Fig. 6.  Quantum noise limitation of cavity output field: (a) Variation of noise with frequency in impedance matched cavity; (b) variation of noise with frequency in a non-impedance matched cavity; (c) variation of noise of the reflected light field with impedance matching factor a.

  • [1]

    聂丹丹, 冯晋霞, 戚蒙, 李渊骥, 张宽收 2020 物理学报 69 094205Google Scholar

    Nie D D, Feng J X, Qi M, Li Y J, Zhang K S 2020 Acta Phys. Sin. 69 094205Google Scholar

    [2]

    翟泽辉, 郝温静, 刘建丽, 段西亚 2020 物理学报 69 184204Google Scholar

    Zhai Z H, Hao W J, Liu J L, Duan X Y 2020 Acta Phys. Sin. 69 184204Google Scholar

    [3]

    刘奎, 马龙, 苏必达, 李佳明, 孙恒信, 郜江瑞 2020 物理学报 69 124203Google Scholar

    Liu K, Ma L, Su B D, Li J M, Sun H X, Gao J R 2020 Acta Phys. Sin. 69 124203Google Scholar

    [4]

    周瑶瑶, 田剑锋, 闫智辉, 贾晓军 2019 物理学报 68 064205Google Scholar

    Zhou Y Y, Tian J F, Yan Z H, Jia X J 2019 Acta Phys. Sin. 68 064205Google Scholar

    [5]

    葛瑞芳, 杨鹏飞, 韩星, 张鹏飞, 李刚, 张天才 2020 量子光学学报 26 21Google Scholar

    Ge R F, Yang P F, Han X, Zhang P F, Li G, Zhang T C 2020 Acta Sin. Quantum Opt. 26 21Google Scholar

    [6]

    石柱, 郭永瑞, 徐敏志, 卢华东 2018 量子光学学报 24 237Google Scholar

    Shi Z, Guo Y R, Xu M Z, Lu H D 2018 Acta Sin. Quantum Opt. 24 237Google Scholar

    [7]

    Wang Y, Shen H, Jin X L, Su X L, Xie C D, Peng K C 2010 Opt. Express 18 6149Google Scholar

    [8]

    王俊萍, 张文慧, 李瑞鑫, 田龙, 王雅君, 郑耀辉 2020 物理学报 69 234204

    Wang J P, Zhang W H, Li R X, Tian L, Wang Y Jun, Zheng Y H 2020 Acta Phys. Sin. 69 234204

    [9]

    Villar A S 2008 Am. J. Phys. 76 922Google Scholar

    [10]

    Wang Y J, Zheng Y H, Shi Z, Peng K C 2012 Laser Phys. Lett. 9 506Google Scholar

    [11]

    Zhang W H, Wang J R, Zheng Y H, Wang Y J, Peng K C 2019 Appl. Phys. Lett. 115 171103Google Scholar

    [12]

    Zhao G, Hausmaninger T, Ma W G, Axner O 2017 Opt. Lett. 42 3109Google Scholar

    [13]

    胡悦, 曹凤朝, 董仁婧, 郝辰悦, 刘大禾, 石锦卫 2020 物理学报 69 224202

    Hu Y, Cao F Z, Dong R J, Hao C Y, Liu D H, Shi J W 2020 Acta Phys. Sin. 69 224202

    [14]

    Schreiber K U, Gebauer A, Wells J P R 2013 Opt. Lett. 38 3574Google Scholar

    [15]

    Leibrandt D R, Heidecker J 2015 Rev. Sci. Instrum. 86 123115Google Scholar

    [16]

    Liu K, Zhang F L, Li Z Y, Feng X H, Li K, Lu Z H, Schreiber K U, Luo J, Zhang J 2019 Opt. Lett. 44 2732Google Scholar

    [17]

    Kwee P, Willke B, Danzmann K 2011 Opt. Lett. 36 3563Google Scholar

    [18]

    Kaufer S, Kasprzack M, Frolov V, Willke B 2017 Classical Quantum Gravity 34 145001Google Scholar

    [19]

    Junker J, Oppermann P, Willke B 2017 Opt. Lett. 42 755Google Scholar

    [20]

    Kaufer S, Willke B 2019 Opt. Lett. 44 1916Google Scholar

    [21]

    Zhao Y H, Aritomi N, Capocasa E, et al. 2020 Phys. Rev. Lett. 124 171101Google Scholar

    [22]

    McCuller L, Whittle C, Ganapathy D, et al. 2020 Phys. Rev. Lett. 124 171102Google Scholar

    [23]

    Capocasa E, Barsuglia M, Degallaix J, Pinard L, Straniero N, Schnabel R, Somiya K, Aso Y, Tatsumi D, Flaminio R 2016 Phys. Rev. D 93 082004Google Scholar

    [24]

    Kwee P 2010 Ph. D. Dissertation (Hannover: Leibniz Universität Hannover)

    [25]

    Kaufer S 2018 Ph. D. Dissertation (Hannover: Leibniz Universität Hannover)

    [26]

    Brozek O S 1999 Ph. D. Dissertation (Hannover: Universität Hannover)

    [27]

    Guo X M, Wang X Y, Li Y M, Zhang K S 2009 Appl. Opt. 48 6475Google Scholar

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出版历程
  • 收稿日期:  2021-02-01
  • 修回日期:  2021-05-11
  • 上网日期:  2021-08-18
  • 刊出日期:  2021-10-20

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