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外腔共振和频系统中阻抗匹配的理论研究

闫晓娟 马维光 谭巍

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外腔共振和频系统中阻抗匹配的理论研究

闫晓娟, 马维光, 谭巍

Theoretical investigation of impedance matching in the process of sum-frequency generation in an external resonator

Yan Xiao-Juan, Ma Wei-Guang, Tan Wei
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  • 外腔共振是提高和频效率的有效方法. 实现外腔共振高效和频需要基频光高效地耦合到外部谐振腔中, 因此系统要达到阻抗匹配. 本文分别建立了双波长和单波长外腔共振和频系统的理论模型, 分析了腔增强因子与耦合腔镜反射率、入射基频光功率等参数的依赖关系, 通过数值模拟获得最优化的共振光耦合腔镜反射率, 使系统达到阻抗匹配, 提高和频效率. 研究表明, 无论双波长还是单波长外腔共振和频系统, 共振基频光的最佳耦合腔镜反射率只会随着另一束共振或者不共振的基频光入射功率的增加而减小, 而其本身的入射功率变化则影响较小; 进一步分析表明, 若共振基频光的耦合腔镜反射率超过阻抗匹配值, 和频光功率将会迅速减小, 而小于阻抗匹配值时, 和频光功率减少速度相对较慢, 因此实验过程中要尽量避免过耦合的情况出现. 本文的理论分析过程将对外腔和频实验有一定的指导意义.
    The sum-frequency conversion efficiency is directly proportional to the product of two fundamental laser powers. Therefore, sum-frequency conversion efficiency is rather low when the fundamental beams pass through a nonlinear crystal only once. External resonant technique as an effective means of improving the powers of the fundamental light has been widely applied to the field of nonlinear frequency conversion. This technique can greatly improve the sum-frequency conversion efficiency and is particularly suitable for the situation in which the input power of the fundamental frequency lasers bas been limited. The implementation of high efficient sum-frequency generation in an external resonator requires that the fundamental frequency laser should be efficiently coupled to the external cavity. Therefore, the system needs to achieve impedance matching. In the part of theoretical analysis, first, we derive the enhancement factor when travelingwave cavity is resonant, and then, establish the theoretical models of doubly resonant and singly resonant sum-frequency generation in an external resonator respectively. The variation of enhancement factors as functions of reflectivity of the input couplers and power of the input fundamental light for doubly resonant and singly resonant sum-frequency systems is derived from Boyd-Kleinman theory in detail based on the theoretical models described in the text. The expressions of enhancement factors reflect the nonlinear correlation characteristics of two fundamental light beams in the process of sum-frequency generation. In the part of numerical simulation, firstly, we draw contour plots of output power as functions of reflectivity of the input couplers at two input frequencies in the doubly resonant sum-frequency system by theoretical simulation, and achieve an optimum reflectivity of the input couplers under the condition of different powers of input fundamental light. Secondly, we draw the contour plots of output power as functions of the reflectivity of the input coupler at the resonant frequency, and the input power of non-resonant frequency light in the singly resonant sum-frequency system by theoretical simulation, and achieve an optimum reflectivity of the input coupler at the resonant frequency. These optimum values enable the system to achieve impedance matching; consequently, the sum-frequency conversion efficiency is improved. Finally, this paper analyzes the influence of input power on the impedance matching, and shows that the optimal coupling mirror reflectivity of the resonant fundamental frequency will decrease with the increase of incident power of the other resonant or non-resonant fundamental frequency laser, otherwise, the resonant incident power of its own has less influence on the optimal coupling mirror reflectivity, whether the system undergoes doubly resonant or singly resonant sum-frequency. In addition, if the coupling mirror reflectivity exceeds the optimum value, the power of sum-frequency light will decrease rapidly, while if it is less than the optimum value, the power of sum-frequency light decreases relatively slowly. Therefore an input coupler that may yield over-coupling should be avoided. These results will have a certain guiding significance to related experiments.
      通信作者: 闫晓娟, yanxj@sxu.edu.cn
    • 基金项目: 国家重点基础研究发展计划(批准号: 2012CB921603)、国家自然科学基金(批准号: 61178009, 61275213, 11304189)和山西省青年科学基金(批准号: 2015021105)资助的课题.
      Corresponding author: Yan Xiao-Juan, yanxj@sxu.edu.cn
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2012CB921603), the National Natural Science Foundation of China (Grant Nos. 61178009, 61275213, 11304189), and the Natural Science Foundation of Shanxi Province, China (Grant No. 2015021105).
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    [3]

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    Foltynowicz A, Ban T, Masłwski P, Adler F, Ye J 2011 Phys. Rev. Lett. 107 233002

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    [6]

    Hollemann G, Braun B, Dorsch F, Hennig P, Heistulf P, Kutschki U, Voelckel H 2000 Proc. SPIE 3954 140

    [7]

    Wang P Y, Xie S Y, Bo Y, Wang B S, Zuo J W, Wang Z C, Shen Y, Zhang F F, Wei K, Jin K, Xu Y T, Xu J L, Peng Q J, Zhang J Y, Lei W Q, Cui D F, Zhang Y D, Xu Z Y 2014 Chin. Phys. B 23 094208

    [8]

    Yan X J, Li Z X, Zhang Y Z, Tan W, Fu X F, Ma W G, Zhang L, Yin W B, Jia S T 2012 Acta Sin. Quantum Opt. 18 197 (in Chinese) [闫晓娟, 李志新, 张永智, 谭巍, 付小芳, 马维光, 张雷, 尹王保, 贾锁堂 2012 量子光学学报 18 197]

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    [10]

    Wen X, Han Y H, Bai J D, He J, Wang Y H, Yang B D, Wang J M 2014 Opt. Express 22 32293

    [11]

    Yang W H, Wang Y J, Zheng Y H, Lu H D 2015 Opt. Express 23 19624

    [12]

    Yan X J, Li Z X, Zhang Y Z, Wang L, Hu Z Y, Ma W G, Zhang L, Yin W B, Jia S T 2011 Acta Phys. Sin. 60 104210 (in Chinese) [闫晓娟, 李志新, 张永志, 王乐, 胡志裕, 马维光, 张雷, 尹王保, 贾锁堂 2011 物理学报 60 104210]

    [13]

    Tan W, Fu X F, Li Z X, Zhao G, Yan X J, Ma W G, Dong L, Zhang L, Yin W B, Jia S T 2013 Acta Phys. Sin. 62 094211 (in Chinese) [谭巍, 付小芳, 李志新, 赵刚, 闫晓娟, 马维光, 董磊, 张雷, 尹王保, 贾锁堂 2013 物理学报 62 094211]

    [14]

    Bienfang J C, Denman C A, Grime B W, Hillman P D, Moore G T, Telle J M 2003 Opt. Lett. 28 2219

    [15]

    Kumagai H 2007 Opt. Lett. 32 62

    [16]

    Andersen M T, Schlosser P J, Hastie J E, Tidemand-Lichtenberg P, Dawson M D, Pedersen C 2009 Opt. Express 17 6010

    [17]

    Mimoun E, Sarlo L D, Zondy J J, Dalibard J, Gerbier F 2010 Appl. Phys. B 99 31

    [18]

    Samblowski A, Vollmer C E, Baune C, Fiurek J, Schnabel R 2014 Opt. Lett. 39 2979

  • [1]

    Franken P A, Hill A E, Peters C W, Weinreich G 1961 Phys. Rev. Lett. 7 118

    [2]

    Maker P D, Terhune R W, Nisenoff C M, Savage C 1962 Phys. Rev. Lett. 8 21

    [3]

    Giordmine J 1962 Phys. Rev. Lett. 8 19

    [4]

    Foltynowicz A, Ban T, Masłwski P, Adler F, Ye J 2011 Phys. Rev. Lett. 107 233002

    [5]

    Sugiyama K, Kawajiri S, Yabu N, Matsumoto K, Kitano M 2010 Appl. Opt. 49 5510

    [6]

    Hollemann G, Braun B, Dorsch F, Hennig P, Heistulf P, Kutschki U, Voelckel H 2000 Proc. SPIE 3954 140

    [7]

    Wang P Y, Xie S Y, Bo Y, Wang B S, Zuo J W, Wang Z C, Shen Y, Zhang F F, Wei K, Jin K, Xu Y T, Xu J L, Peng Q J, Zhang J Y, Lei W Q, Cui D F, Zhang Y D, Xu Z Y 2014 Chin. Phys. B 23 094208

    [8]

    Yan X J, Li Z X, Zhang Y Z, Tan W, Fu X F, Ma W G, Zhang L, Yin W B, Jia S T 2012 Acta Sin. Quantum Opt. 18 197 (in Chinese) [闫晓娟, 李志新, 张永智, 谭巍, 付小芳, 马维光, 张雷, 尹王保, 贾锁堂 2012 量子光学学报 18 197]

    [9]

    Boyd G D, Kleinman D A 1968 J. Appl. Phys. 39 3597

    [10]

    Wen X, Han Y H, Bai J D, He J, Wang Y H, Yang B D, Wang J M 2014 Opt. Express 22 32293

    [11]

    Yang W H, Wang Y J, Zheng Y H, Lu H D 2015 Opt. Express 23 19624

    [12]

    Yan X J, Li Z X, Zhang Y Z, Wang L, Hu Z Y, Ma W G, Zhang L, Yin W B, Jia S T 2011 Acta Phys. Sin. 60 104210 (in Chinese) [闫晓娟, 李志新, 张永志, 王乐, 胡志裕, 马维光, 张雷, 尹王保, 贾锁堂 2011 物理学报 60 104210]

    [13]

    Tan W, Fu X F, Li Z X, Zhao G, Yan X J, Ma W G, Dong L, Zhang L, Yin W B, Jia S T 2013 Acta Phys. Sin. 62 094211 (in Chinese) [谭巍, 付小芳, 李志新, 赵刚, 闫晓娟, 马维光, 董磊, 张雷, 尹王保, 贾锁堂 2013 物理学报 62 094211]

    [14]

    Bienfang J C, Denman C A, Grime B W, Hillman P D, Moore G T, Telle J M 2003 Opt. Lett. 28 2219

    [15]

    Kumagai H 2007 Opt. Lett. 32 62

    [16]

    Andersen M T, Schlosser P J, Hastie J E, Tidemand-Lichtenberg P, Dawson M D, Pedersen C 2009 Opt. Express 17 6010

    [17]

    Mimoun E, Sarlo L D, Zondy J J, Dalibard J, Gerbier F 2010 Appl. Phys. B 99 31

    [18]

    Samblowski A, Vollmer C E, Baune C, Fiurek J, Schnabel R 2014 Opt. Lett. 39 2979

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  • 收稿日期:  2015-09-10
  • 修回日期:  2015-10-23
  • 刊出日期:  2016-02-05

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