1.School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China 2.Key Laboratory of Opto-Electronic Information Science and Technology of Jiangxi Province, Nanchang Hangkong University, Nanchang 330063, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 41776111, 61865013), the National Key R&D Program of China (Grant No. 2018YFE0115700), and the Defense Industrial Technology Development Program of China (Grant No. JCKY2019401D002)
Received Date:16 February 2021
Accepted Date:14 March 2021
Available Online:07 June 2021
Published Online:05 August 2021
Abstract:Stimulated Brillouin scattering (SBS) is a typical inelastic scattering effect generated by the interaction between intense incident laser and the acoustic wave field in medium and has always been an active research topic in nonlinear optics. The SBS can be used as a novel LIDAR technology for active optical remote sensing of temperature and sound speed structure in ocean. Although, the threshold value and gain property of SBS at normal temperature are studied, none of the threshold values and gain coefficients of SBS at different temperatures, pressures and attenuation coefficients has been investigated in detail. Further, neither the relation between threshold value and water pressure nor the relation between gain coefficient and water pressure is clear now, and little work has been reported. The theoretical and experimental studies of the influence of water parameters on the threshold value and gain coefficient of SBS are still scanty. In this paper, the effects of temperature, pressure and attenuation coefficient of water on threshold value and gain coefficient of SBS are studied theoretically and experimentally. Theoretically, the variations of threshold value and gain coefficient of SBS with temperature, pressure and attenuation coefficient are analyzed by the average attenuation coefficient method based on the distributed noise model (DNM) and coupled wave equations. The temporal waveforms of Stokes-, pump- and transmission-beam at different water parameters are obtained by using the DNM. Experimentally, a temperature-pressure controlled simulator is designed to obtain the threshold values and gain coefficients of SBS in water at different temperatures, pressures and attenuation coefficients through measuring the change of attenuation coefficient of laser pulses. The results indicate that (i) the threshold value of SBS increases with pressure increasing at the same temperature and decreases with temperature increasing at the same pressure; (ii) the threshold value is positively correlated with the attenuation coefficient at the same temperature and pressure; (iii) the gain coefficient of SBS increases with temperature increasing at the same pressure and decreases with pressure increasing at the same temperature. We also find that the temperature and attenuation coefficient have greater effect on threshold value and gain coefficient of SBS than the water pressure. The studied results are of great significance in realizing the ocean remote sensing by SBS lidar. Keywords:stimulated Brillouin scattering/ threshold value/ gain coefficient/ water parameters
SBS的噪声起振模型主要包括边界式噪声注入模型[14]、分布式噪声模型[15,16]、自发Brillouin散射噪声源模型[17]等. 为了解SBS产生过程中泵浦光、透射光及布里渊散射光能量的变化情况, 徐德[18]采用分布式噪声模型分析了非聚焦泵浦下SBS的产生, 在此基础上, 我们采用该方法对不同能量密度下泵浦光、Stokes光和透射光的波形进行了仿真, 仿真结果如图2所示. 图 2 激光器泵浦能量分别为60, 70, 80 mJ时, 泵浦光、Stokes光和透射光的波形 Figure2. Temporal waveforms of pump, Stokes and transmission laser beams at the pump energy of 60, 70, 80 mJ.
图6所示为不同温度、压强和衰减系数下的SBS阈值的实验测量结果. 可以看出, 温度一定时, SBS阈值随着压强的增大而增大; 当温度和压强恒定时, 水的衰减系数越大, SBS阈值越高; 同一压强下, 温度越高, SBS阈值越小. 图 6 不同水体参数下SBS阈值的实验测量结果 (a) $\alpha =0.25\;{\mathrm{m}}^{-1}$; (b) T = 25 ℃ Figure6. Experimental measured values of threshold value of SBS in water at different water parameters: (a) $\alpha =0.25\;{\mathrm{m}}^{-1}$, (b) T = 25 ℃.
图7为不同温度、压强和衰减系数下SBS阈值的理论仿真与实验测量结果的比较. 可以看出, SBS理论计算所得阈值与实验测量阈值具有相同的变化趋势, 但数值上有一定差异, 这主要是因为理论仿真考虑的是理想瞬态SBS的情况, 而实验中产生的SBS既不属于理想稳态SBS又不属于理想瞬态SBS, 实验测量值为偏向于瞬态SBS情况. 同时, 理论仿真仅考虑布里渊散射现象的产生, 然而实验测量过程中, 也将发生其他非线性效应, 进而导致实验值与理论值具有一定差异. 图 7 不同水体参数下SBS阈值的实验测量与理论仿真结果对比 (a)相同衰减系数、不同温度; (b)相同温度、不同衰减系数; (c)相同压强和衰减系数、不同温度 Figure7. Comparison of experimental measurements with theoretical simulations of SBS threshold at different water parameters: (a) Different temperatures at the same attenuation coefficient; (b) different attenuation coefficients at the same temperature; (c) different temperatures at the same pressure and attenuation coefficient.
根据(4)式及实验测量的阈值, 可得到不同温度和压强下SBS增益, 如图8(a)和图8(b)所示. 图8(c)和图8(d)给出了由SBS增益公式理论仿真所得的压强为0—10 MPa, 温度为5—30 ℃时的SBS增益. 将实验测量结果与理论仿真进行对比可以看出, 温度恒定时, 随着压强的增大, SBS增益将逐渐减小; 压强恒定时, 随着温度的增高, SBS增益将逐渐增大. 比较实验测量值与理论仿真值可知, 温度对SBS增益的影响大于压强对SBS增益的影响. 这主要是因为温度对水的声速和黏滞系数的影响较大, 而压强为0—10 MPa时, 其对水的黏滞系数影响较小, 可以忽略不计. 图 8 不同温度及压强下SBS增益的理论仿真与实验测量结果 (a), (b)实验值; (c), (d)理论值 Figure8. Comparison of experimental measurements with theoretical simulations of gain coefficient in water at different temperatures and pressures: (a), (b) Experimental values; (c), (d) theoretical values.
图 1 布里渊散射的产生过程
图 2 激光器泵浦能量分别为60, 70, 80 mJ时, 泵浦光、Stokes光和透射光的波形
图 3 不同温度、压强和衰减系数下泵浦光和Stokes光的波形
图 4 水中SBS阈值随水体参数的变化 (a) 25 ℃, 稳态阈值; (b) 25 ℃, 瞬态阈值; (c) 0 MPa, 稳态阈值; (d) 0 MPa, 瞬态阈值; (e) 0.25 m–1, 稳态阈值; (f) 0.25 m–1, 瞬态阈值
图 5 泵浦光在水中的衰减系数 (a) 25 ℃, 2 MPa; (b) 25 ℃, 4 MPa
图 6 不同水体参数下SBS阈值的实验测量结果 (a) 
图 7 不同水体参数下SBS阈值的实验测量与理论仿真结果对比 (a)相同衰减系数、不同温度; (b)相同温度、不同衰减系数; (c)相同压强和衰减系数、不同温度
图 8 不同温度及压强下SBS增益的理论仿真与实验测量结果 (a), (b)实验值; (c), (d)理论值