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Ultra-short pulse (picosecond) anti-Stokes laser can be obtained by using Raman frequency converter in a crystal medium by the coherent anti-Stokes Raman scattering effect. The crystalline Raman frequency converter based on the pump-probe method can realize the collinear interaction of coherent anti-Stokes Raman scattering, thus effectively improving the conversion efficiency of the anti-Stokes light. Theoretical simulation is an important means to study laser operation. Coupled wave equation is widely used to study the characteristics of Raman laser and anti-Stokes laser. Although the coupling wave theory of anti-Stokes Raman frequency shifter reported previously can reflect the operation law of the frequency shifter, the optimization of the frequency shifter and the influence of the frequency shifter parameters on the output characteristics of anti-Stokes laser have not been reported so far. In this paper, the picosecond anti-Stokes Raman frequency converter based on the pump-probe method is studied theoretically. Considering the generation of the first Stokes light in the probe channel and the second Stokes light in the pump channel, the coupled wave equation of the collinear picosecond anti-Stokes Raman frequency converter is established under the plane wave approximation. Without loss of generality, four dimensionless comprehensive parameters are introduced to normalize the equations. A set of universal theoretical curves describing the operation of the Raman frequency converter is obtained. The numerical solutions of the equations show that the performance of the Raman frequency converter mainly depends on three parameters: the normalized phase mismatch parameter ΔK, the normalized Raman gain coefficient G, and the energy ratio of the probe light to the fundamental light rprobe. The reasonable values of normalized variables are determined when the high efficiency anti-Stokes conversion is realized. Experimental data are used to verify the correctness of the theoretical model. The theoretical value of the anti-Stokes conversion efficiency is basically consistent with the literature data. The normalized coupled wave theory proposed in this paper is helpful in understanding the operation law of the picosecond anti-Stokes Raman frequency shifter, and has guiding significance for the design of the frequency converter.
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Keywords:
- coherent anti-Stokes scattering /
- collinear four-wave mixing /
- coupled wave equation /
- normalization theory
[1] 孙瑛璐, 段延敏, 程梦瑶, 袁先漳, 张立, 张栋, 朱海永 2020 物理学报 69 124201
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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[4] Sheng Q, Li R, Lee A J, Spence D J, Pask H M 2019 Opt. Express 27 8540
Google Scholar
[5] Wei L J, Chen M T, Zhu S Q, Dai S B, Yin H, Chen Z Q 2018 Laser Phys. Lett. 15 125001
Google Scholar
[6] Duan Y M, Sun Y L, Zhu H Y, Mao T W, Zhang L, Chen X 2020 Opt. Lett. 45 2564
Google Scholar
[7] Liu J, Ding X, Jiang P B, Sheng Q, Yu X Y, Sun B, Wang J B, Shi R, Zhao L, Bai Y T, Zhang G Z, Wu L, Yao J Q 2018 Appl. Opt. 57 3154
Google Scholar
[8] Ding S H, Zhang X Y, Wang Q P, Jia P, Zhang C, Liu B 2006 Opt. Commun. 267 480
Google Scholar
[9] Smetanin S N, Doroshenko M E, Ivleva L I, Jelínek M, V. Kubeček, Jelínková H 2014 Appl. Phys. B 117 225
Google Scholar
[10] Ding S H, Zhang X Y, Wang Q P, Zhang J, Wang S M, Liu Y R, Zhang X H 2007 J. Phys. D 40 2736
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Google Scholar
[12] Smetanin S N, Jelínek M, Kubeček V 2017 Appl. Phys. B 123 203
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[14] Grasiuk A Z, Kurbasov S V, Losev L L 2004 Opt. Commun. 240 239
Google Scholar
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Google Scholar
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[17] Wang C, Cong Z H, Qin Z G, Zhang X Y, Wei W, Wang W T, Zhang Y G, Zhang H J, Yu H H 2014 Opt. Commun. 322 44
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[19] Smetanin S N, Jelínek M, Tereshchenko D P, Shukshin V E, Konyukhov M V, Papashvili A G, Voronina I S, Ivleva L I, Kubeček V 2020 Opt. Express 28 22919
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图 1 抽运通道和探测通道中的拉曼散射能级图 (a) 抽运通道的SSRS能级图; (b) 探测通道的CARS能级图; (c) 探测通道的SSRS能级图
Figure 1. Raman scattering energy levels in pump and probe channels: (a) SSRS in pump channel; (b) CARS in probe channel; (c) SSRS in probe channel.
图 2 G = 90, Wp = 0.2, rprobe取不同值时(a) ηa, (b) η1s和(c) η2s随ΔK的变化
Figure 2. (a) ηa, (b) η1s and (c) η2s versus ΔK for different rprobe with G = 90 and Wp = 0.2.
图 3 rprobe = 0.3, G = 90, Wp = 0.2时, 抽运光、探测光、一阶斯托克斯光和反斯托克斯光归一化光强随ζ的空间演化 (a) |ΔK| = 0; (b) |ΔK| = 4; (c) |ΔK| = 8
Figure 3. Plots of the spatial evolution of pump, probe, first Stokes, and anti-Stokes normalized intensities with rprobe = 0.3, G = 90 and Wp = 0.2: (a) |ΔK| = 0; (b) |ΔK| = 4; and (c) |ΔK| = 8.
图 4 rprobe = 0.39, G = 90, Wp = 0.2时, 抽运光、探测光、一阶斯托克斯光和反斯托克斯光归一化光强随ζ的空间演化 (a) |ΔK| = 0; (b) |ΔK| = 4; (c) |ΔK| = 8
Figure 4. Plots of the spatial evolution of pump, probe, first Stokes, and anti-Stokes normalized intensities with rprobe = 0.39, G = 90 and Wp = 0.2: (a) |ΔK| = 0; (b) |ΔK| = 4; and (c) |ΔK| = 8.
图 5 G = 90, |ΔK| = 0, Wp = 0.2时抽运光、探测光、一阶斯托克斯光、二阶斯托克斯光和反斯托克斯光的脉冲形状 (a) rprobe = 0.3; (b) rprobe = 0.39
Figure 5. Temporal profiles of the pump, probe, first Stokes, second Stokes and anti-Stokes pulses with G = 90, |ΔK| = 0 and Wp = 0.2: (a) rprobe = 0.3; (b) rprobe = 0.39.
图 6 |ΔK| = 0, Wp = 0.2, rprobe取不同值时(a) ηa, (b) η1 s和(c) η2 s随G的变化
Figure 6. (a) ηa, (b) η1s and (c) η2s versus G for different rprobe with |ΔK| = 0 and Wp = 0.2.
图 7 |ΔK| = 0, Wp = 0.2时, ropt和ηamax随G的变化
Figure 7. ropt and ηamax versus G with |ΔK| = 0 and Wp = 0.2
图 8 |ΔK| = 0, Wp = 0.2时抽运光、探测光、一阶斯托克斯光、二阶斯托克斯光和反斯托克斯光的脉冲形状 (a) ropt = 0.270, G = 60; (b) ropt = 0.373, G = 110; (c) ropt = 0.414, G = 160
Figure 8. Temporal profiles of the pump, probe, first Stokes, second Stokes, and anti-Stokes pulses with |ΔK |= 0 and Wp = 0.2: (a) ropt = 0.270, G = 60; (b) ropt = 0.373, G = 110; (c) ropt = 0.414, G = 160.
图 9 |ΔK| = 0, Wp = 0.2时, Gopt和ηamax随rprobe的变化
Figure 9. Gopt and ηamax versus rprobe with |ΔK| = 0 and Wp = 0.2
参数 值 参数 值 νa/νp 1.06 Ap/cm2 2.83 × 10–4 ν1s/νp 0.94 lR/cm 3.2 ν2s/νp 0.88 g/(cm·GW–1) 13 wp/ps 20 Δk 0 
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表 2 不同情况下反斯托克斯转化效率的理论值与实验数据的对比结果
Table 2. Comparisons of theoretical and experimental results of anti-Stokes conversion efficiency under different conditions.
抽运脉冲
能量/μJ探测脉冲
能量/μJG rprobe 实验
值/%理论
值/%30 25 206 0.45 2.80 2.54 30 2 118 0.063 1.88 1.86 26 12 140 0.32 3.50 4.13
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表 3 高斯近似时反斯托克斯转化效率的理论值
Table 3. Theoretical values of anti-Stokes conversion efficiency for Gaussian approximation.
抽运脉冲能量/μJ 探测脉冲能量/μJ $ \eta _{\rm{a}}^{\rm{g}}$/% 30 25 2.63 30 2 1.91 26 12 4.09
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[1] 孙瑛璐, 段延敏, 程梦瑶, 袁先漳, 张立, 张栋, 朱海永 2020 物理学报 69 124201
Google Scholar
Sun Y L, Duan Y M, Cheng M Y, Yuan X Z, Zhang L, Zhang D, Zhu H Y 2020 Acta Phys. Sin. 69 124201
Google Scholar
[2] 张蕴川, 樊莉, 魏晨飞, 顾晓敏, 任思贤 2018 物理学报 67 024206
Google Scholar
Zhang Y C, Fan L, Wei C F, Gu X M, Ren S X 2018 Acta Phys. Sin. 67 024206
Google Scholar
[3] Zhou Q Q, Shi S C, Chen S M, Duan Y M, Zhang X M, Guo J, Zhao B, Zhu H Y 2019 Chin. Phys. Lett. 36 014205
Google Scholar
[4] Sheng Q, Li R, Lee A J, Spence D J, Pask H M 2019 Opt. Express 27 8540
Google Scholar
[5] Wei L J, Chen M T, Zhu S Q, Dai S B, Yin H, Chen Z Q 2018 Laser Phys. Lett. 15 125001
Google Scholar
[6] Duan Y M, Sun Y L, Zhu H Y, Mao T W, Zhang L, Chen X 2020 Opt. Lett. 45 2564
Google Scholar
[7] Liu J, Ding X, Jiang P B, Sheng Q, Yu X Y, Sun B, Wang J B, Shi R, Zhao L, Bai Y T, Zhang G Z, Wu L, Yao J Q 2018 Appl. Opt. 57 3154
Google Scholar
[8] Ding S H, Zhang X Y, Wang Q P, Jia P, Zhang C, Liu B 2006 Opt. Commun. 267 480
Google Scholar
[9] Smetanin S N, Doroshenko M E, Ivleva L I, Jelínek M, V. Kubeček, Jelínková H 2014 Appl. Phys. B 117 225
Google Scholar
[10] Ding S H, Zhang X Y, Wang Q P, Zhang J, Wang S M, Liu Y R, Zhang X H 2007 J. Phys. D 40 2736
[11] Smetanin S N, Jelínek M, Tereshchenko D P, Kubeček V 2018 Opt. Express 26 22637
Google Scholar
[12] Smetanin S N, Jelínek M, Kubeček V 2017 Appl. Phys. B 123 203
[13] Vermeulen N, Debaes C, Fotiadi A A, Panajotov K, Thienpont H 2006 IEEE J. Quantum Electron. 42 1144
Google Scholar
[14] Grasiuk A Z, Kurbasov S V, Losev L L 2004 Opt. Commun. 240 239
Google Scholar
[15] Mildren R P, Coutts D W, Spence D J 2009 Opt. Express 17 810
Google Scholar
[16] Wang C, Zhang X Y, Wang Q P, Cong Z H, Liu Z J, Wei W, Wang W T, Wu Z G, Zhang Y G, Li L, Chen X H, Li P, Zhang H J, Ding S H 2013 Opt. Express 21 26014
Google Scholar
[17] Wang C, Cong Z H, Qin Z G, Zhang X Y, Wei W, Wang W T, Zhang Y G, Zhang H J, Yu H H 2014 Opt. Commun. 322 44
Google Scholar
[18] Wei W, Zhang X Y, Wang Q P, Wang C, Cong Z H, Chen X H, Liu Z J, Wang W T, Wu Z G, Ding S H, Tu C Y, Li Y F, Cheng W Y 2014 Appl. Phys. B 116 561
[19] Smetanin S N, Jelínek M, Tereshchenko D P, Shukshin V E, Konyukhov M V, Papashvili A G, Voronina I S, Ivleva L I, Kubeček V 2020 Opt. Express 28 22919
Google Scholar
[20] Shen Y R, Bloembergen N 1965 Phys. Rev. 137 1787
Google Scholar
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