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Abstract
Effects of temperature and pressure on the threshold value of stimulated Brillouin scattering (SBS) in seawater were analyzed theoretically and experimentally. Theoretically, the change of threshold value of SBS versus the ocean depth was simulated based on the International Thermodynamic Equation of Seawater-2010 (TEOS-10) and the World Ocean Atlas 2013 (WOA13). Experimentally, an ocean temperature and pressure simulator (OTPS) was designed to measure the threshold value of SBS through simulating the changes of temperature and pressure of seawater in 0∼1000 meters. The theoretical and experimental results exhibit that the threshold value of SBS decreases with the increase of temperature at the same seawater pressure and increases with the increase of pressure at the same seawater temperature. The results imply that the SBS process is more likely to occur in upper seawater of lower-latitude areas. The theoretical and experimental results are helpful for remote sensing in ocean using the SBS LIDAR.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Accurate remote sensing of the temperature, salinity and sound speed structures of the ocean is of major importance to the understanding of the physical and biological behavior of the ocean [1,2]. There currently exist several different ways can be used to obtain the temperature, salinity and sound speed information in the ocean, e.g. buoys, CTD instruments, or satellite sensing. However, these techniques do not allow the rapid, accurate, and real-time range-resolved monitoring. Therefore, a flexible, cost efficient, and real-time remote sensing technique is highly desirable.
As an alternative approach, Brillouin scattering can be used as a novel LIDAR technique for active optical remote sensing of ocean, and it has long been recognized as potential method to measure the sound speed, temperature, and salinity in the upper ocean. Several studies have demonstrated the potential accuracy of Brillouin-LIDAR measurements of temperature and sound speed in the ocean by measuring the frequency shift and linewidth of the backscattered Brillouin scattering spectra [3–9]. There are two alternative techniques for constructing Brillouin-LIDAR system: spontaneous Brillouin scattering and stimulated Brillouin scattering (SBS). In 1990, Leonard and Sweeney made a comparison of spontaneous and stimulated Brillouin scattering used for measuring water temperature [10]. They analyzed the advantages and disadvantages of the two kinds of techniques. Compared with spontaneous-Brillouin LIDAR, SBS LIDAR has the advantages of optical phase conjugation (OPC) and high signal-to-noise ratio (SNR). It is significative in increasing the detection depth and in improving the depth resolution of the measurement. However, when the powerful laser enters the water, large amounts of energy could be consumed by exciting the SBS process so that the detected depth is greatly limited. In order to improve the LIDAR system so that it can maintain the advantages of SBS and avoid its disadvantages simultaneously, our group have proposed a new lidar system based on the SBS technique [11–15]. The improved SBS LIDAR system has been used to determine water parameters and detect submerged object.
The major limitation of the stimulated vs spontaneous Brillouin technique is that it needs a powerful laser source to meet the threshold value condition for exciting the signal. When the powerful laser beam gets into the water, the threshold value of SBS is given by [16,17]:
where, ${g_B}$ is the Brillouin gain coefficient of medium,$\alpha$ is the linear attenuation coefficient and ${\tau _B}$ is the phonon life-time, c is the light velocity in medium. For a given incident laser wavelength, the gain coefficient and the phonon lifetime of Brillouin scattering depend on the water parameters such as temperature, salinity and refractive index. The change of pressure may affect the attenuation coefficient of the high energy laser as it transmits in water. We have discussed the influence of water temperature on the threshold value of SBS in our previous works [16,18]. The existing reports merely analyze the influence of a certain parameter on the threshold value of SBS in isolation. However, in the real ocean circumstance, the temperature, salinity, and pressure of seawater change with increasing ocean depth. For a SBS LIDAR, investigations on the influence of various seawater parameters on threshold value of SBS are extremely important for remote sensing at different ocean depths. Although, the threshold value of SBS in pure water has been studied [17,19], the threshold value of SBS in seawater of different depths has not yet been investigated in detail. Further, the relationships between temperature and pressure of seawater and the threshold value of SBS are not clear.The purpose of the present work is to investigate the threshold value of SBS at different ocean depths, especially in the upper ocean mixed layer. The investigated results provide reference standard for remote sensing of ocean that how much threshold intensity is required at different ocean depths to excite the SBS signal. The final goal of our work is to develop a SBS LIDAR technique that allows remote measurements of temperature, salinity or sound velocity profiles of sea water.
2. Theoretical analysis
According to Eq. (1), it is known that the threshold value of SBS is directly related to the gain coefficient ${g_B}$ and phonon life-time ${\tau _B}$. The gain coefficient of SBS can be expressed as [20–22]:
where, ${\omega _S}$ is the frequency of the Stokes component in SBS, ${\gamma _e}$ is electrostrictive coefficient of medium, ${\rho _0}$ and n are the density and the refractive index of medium respectively, ${\upsilon _S}$ is the sound speed in medium. The phonon life-time ${\tau _B}$ is defined as: here, $\eta$ is the viscosity of medium. For water, the variation of temperature has severe influence on the viscosity. With the decrease of temperature of water, the value of the viscosity will become larger [23], which results in the decrease of phonon life-time. Therefore, the gain coefficient will decrease and the threshold value will increase when the water temperature decreases.For a given incident laser wavelength $\lambda$, the Brillouin frequency shift ${\nu _B}$ can be expressed as [4]:
The dependence of the refractive index on wavelength, temperature, salinity, and pressure is given by the empirical equation as published by Seaver [24]:
The equation for the dependence of sound speed on salinity, temperature, and pressure can be expressed by using Gibbs function as [25,26]:
where, ${g_p}$ and ${g_T}$ represents the first-order partial derivative of Gibbs function g with respect to p and T, and ${g_{pp}}$ and ${g_{TT}}$ represents the second-order derivative of g with respect to p and T.Assuming that only the parameters of temperature, salinity and pressure of seawater are taken into account, the seawater density can be expressed as [25,27]:
where ${\rho _0}$ is the reciprocal of The specific enthalpy of seawater: The specific enthalpy of seawater can be directly obtained by using the 25 terms density formula fitted by McDougall [28]. The water pressure in dependence of the depth is well known, it can be obtained by using the geopotential and the database of WOA13 [25,29,30]. Therefore, the threshold value of SBS at different ocean depths can be obtained by using Eqs. (1)∼(8).Based on the theory mentioned above, the temperature and salinity data of East China Sea (N27.5°, E127.5°) were selected from the World Ocean Atlas 2013 (WOA13) as an example for predicting the threshold value of SBS. Figure 1 shows the relationship between sea pressure and depth, we can see that the pressure increases linearly with the increase of the ocean depth. The vertical distribution curves of the temperature and salinity are shown in Fig. 2. It can be seen that the seawater temperature drops from 25 to 4 degrees Celsius with the increase of the ocean depth from 0 to 1000 meters, and the salinity of seawater varies from 34.3‰ to 34.9‰.
The changes of the refractive index and the sound speed of seawater versus the ocean depth can also be simulated, as shown in Fig. 3. The simulation results indicate that the refractive index of seawater increases with the increase of ocean depth, and the sound speed decreases with the increase of ocean depth from 0 to 1000 meters. Also based on Eq. (4), the frequency shift of SBS in seawater can be obtained, the results are shown in Fig. 4. The frequency shift of SBS decreases with the increase of ocean depth, dropping from ∼7.74 GHz to ∼7.49 GHz when the ocean depth increases from 0 to 1000 meters.
Figure 5 gives the change of gain coefficient with the change of ocean depth. We can see that the gain coefficient drops from ∼1.4 cm/GW to ∼0.7 cm/GW when the ocean depth increases from 0 to 1000 meters. The threshold value shown in Fig. 5 is obtained by using the given parameters in experimental measurement, for example, the average attenuation coefficient is ∼0.26 cm-1, the temperature is stabilized to values between 5 and 25 ◦C. Because the change of salinity in 0-1000 meters is very small, a fixed salinity value of 34.6 ‰ is selected for calculating and measuring. The result shows that the threshold value of SBS increases from ∼15 MW/cm2 to ∼30 MW/cm2 with the increases of ocean depth from 0 to 1000 meters.
3. Experimental measurement
In order to verify the theoretical computation results, an experimental system was designed to measure the threshold value of SBS in seawater by simulating the changes of temperature and pressure of seawater in 0∼1000 meters. The experimental setup comprises the light source, an ocean temperature and pressure simulator (OTPS) and a detector system, as shown in Fig. 6. The light source is an injection-seeded and Q-switched Nd: YAG pulse laser operating at 532 nm after through an amplifier and a second harmonic generator (SHG). The light source holds the following parameters: repetition frequency is 10 Hz, pulse duration is 8 ns, beam diameter is 17 mm, divergence angle is 0.45 mrad. The linewidth of single-longitudinal mode with 90 MHz and multi-longitudinal mode with 30 GHz can be obtained by switching on or off a seed laser, respectively. The OTPS system consists of a pressure chamber (1 meter in length) and four hydraulic pumps, in which the maximum water pressure is 10 MPa (100 dbar). The water temperature can be stabilized to values between 4 and 40 ◦C. The pressure sensor and thermocouple are installed to measure the water pressure and temperature in the pressure chamber.
Fig. 6. (a) Schematic of the experimental setup, (b) Pressure chamber. λ/2: half-wave plate, λ/4: quarter-wave plate, PBS: polarization beam splitter, PM1 and PM2: power meters, OW: Optical window.
In Fig. 6(a), the output beam of laser with the vertical polarization passes through the λ/2 plate, PBS, λ/4 plate in turn and then enters the pressure chamber of OTPS system. Here, the polarization control system (λ/2, PBS, and λ/4 plates) is used to manipulate the polarization of incident beams for avoiding the influence of backscattered light on the laser. The energy of incident laser and transmitted laser is measured by power meters PM1 and PM2 (Coherent Fieldmate), respectively. The threshold value of SBS can be measured by the point of the deviation of the value of the attenuation coefficients of wide- and narrow-linewidth lasers, the measured process is described in detail in our previous works [16,19]. When a wide-linewidth laser is used, the attenuation coefficient of water will be a constant. But when a narrow-linewidth laser is used, the narrow-band SBS process will be excited, which consumes a large amount of laser energy, resulting in the attenuation coefficient increasing with the increase of the pumped laser energy. Therefore, the threshold value of SBS can be determined by measuring the attenuation coefficients of wide- and narrow-linewidth lasers. The deviation point between the curve of the attenuation coefficient versus the pump laser intensity measured using the narrow-linewidth laser and that measured with the wide-linewidth laser corresponds to the threshold value.
According to the simulated results shown in Fig. 1 and Fig. 2, the seawater with the salinity of 34.6 ‰ was prepared by dissolving sea salt (Sigma-Aldrich) in distilled water, the water temperature was stabilized to the values between 5 and 25 ◦C, and the pressure was set between 0 and 10 MPa. Figure 7 shows the measured attenuation coefficients by using single- and multi-longitudinal mode laser pulses, respectively, at the same temperature and different pressures of seawater. Based on the measured results, the threshold value can be determined by fitting the experimental data. The threshold value is 28.79 and 35.93 MW/cm2, corresponding to output pulse energy of 0.52 and 0.65 J/Pulse, respectively. This means that the threshold value of SBS increases with the increase of pressure.
Fig. 7. Measured attenuation coefficients using single- and multi-longitudinal mode laser pulses, respectively, at different pressures: (a) 2 MPa and (b) 10 MPa. The seawater temperature is 25 °C.
Figure 8 shows the changes in the threshold value of SBS with the change of temperature and pressure of seawater, respectively. It can be seen that the threshold value decreases with the increase of water temperature at the same water pressure but increases with the increase of water pressure at the same water temperature. Besides, we can see that temperature has a greater effect on the threshold value than the pressure. The reason may be that, the threshold value depends on the Brillouin gain coefficient and the life time of the phonons, as shown in Eq. (1). With the increase of water temperature, both of the Brillouin gain coefficient and the life time of the phonons will become larger, and result in the decrease of threshold value [18,22,23]. However, compared with the temperature, the pressure has a smaller effect on the density and refractive index of seawater. The lower of the water temperature, the smaller of the effect of pressure on the threshold value. The threshold value varies from 27.69 to 51.11 MW/cm2, corresponding to pulse energy from 0.50 to 0.93 J/Pulse. Compared with the result shown in Fig. 5, the measured threshold values are greater than the theoretical values.
Fig. 8. Changes of threshold value at different temperatures and pressures. (a) Threshold value vs. temperature, (b) Threshold value vs. pressure.
In order to show more visually the relationship between the threshold value and temperature and pressure in seawater, Fig. 9 gives the two-dimensional (2D) contour distribution of experimental data. It can be seen that the threshold value increases with the increase of pressure and the decrease of temperature, the maximum threshold value is distributed in the region of the lowest temperature and the maximum pressure. This phenomenon implies that the SBS process is more likely to occur in upper seawater of lower-latitude areas.
It is necessary to state that we cannot simulate the real ocean environment through the OTPS system, so there are some deviations between the measured results and theoretical calculations. In addition, during the analysis we assume that the attenuation coefficient of seawater is a constant, but in fact, the attenuation coefficient of seawater could also change in different areas. The larger the attenuation coefficient, the higher the threshold value of SBS. Here, the experimental results provide a qualitative analysis and logical judgement through comparison with the theoretical simulation.
4. Conclusion
We theoretically analyze the threshold value of SBS in different ocean depths depending on TEOS-10 and the ocean database of 0∼1000 m obtained from World Ocean Atlas 2013 (WOA13). The temperature and salinity data of the East China Sea (N27.5°, E127.5°) were selected from the World Ocean Atlas 2013 (WOA13) as an example for predicting the threshold value of SBS. The theoretical result shows that the threshold value of SBS increases with the increases of ocean depth. To verify the theoretical computation results, an experimental measurement system based on an ocean temperature and pressure simulator was designed to simulate the changes of temperature and pressure of seawater in 0∼1000 meters. The theoretical and experimental results indicate that the threshold value increases with the increase of pressure and the decrease of temperature.
Funding
National Natural Science Foundation of China (41666004, 41776111, 61865013); Defense Industrial Technology Development Program (JCKY2019401D002); Natural Science Foundation of Jiangxi Province (20171BAB202039); Distinguished Young Fund of Jiangxi Province (20171BCB23053).
Disclosures
The authors declare no conflicts of interest.
References
1. D. Leonard and B. Caputo, “Raman Remote Sensing Of The Ocean Mixed-Layer Depth,” Opt. Eng. 22(3), 223288 (1983). [CrossRef]
2. G. D. Hickman, J. M. Harding, M. Carnes, A. Pressman, G. W. Kattawar, and E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sensing of Environment 36(3), 165–178 (1991). [CrossRef]
3. J. G. Hirschberg, J. D. Byrne, A. W. Wouters, and G. C. Boynton, “Speed of sound and temperature in the ocean by Brillouin scattering,” Appl. Opt. 23(15), 2624–2628 (1984). [CrossRef]
4. E. S. Fry, Y. Emery, X. Quan, and J. W. Katz, “Accuracy limitations on Brillouin lidar measurements of temperature and sound speed in the ocean,” Appl. Opt. 36(27), 6887–6894 (1997). [CrossRef]
5. K. Schorstein, A. Popescu, M. Gobel, and T. Walther, “Remote water temperature measurements based on Brillouin scattering with a frequency doubled pulsed Yb : doped fiber amplifier,” Sensors 8(9), 5820–5831 (2008). [CrossRef]
6. K. Schorstein, E. S. Fry, and T. Walther, “Depth-resolved temperature measurements of water using the Brillouin lidar technique,” Appl. Phys. B 97(4), 931–934 (2009). [CrossRef]
7. A. Popescu, K. Schorstein, and T. Walther, “A novel approach to a Brillouin–LIDAR for remote sensing of the ocean temperature,” Appl. Phys. B 79(8), 955–961 (2004). [CrossRef]
8. A. Rudolf and T. Walther, “Laboratory demonstration of a Brillouin lidar to remotely measure temperature profiles of the ocean,” Opt. Eng. 53(5), 051407 (2014). [CrossRef]
9. D. Liu, J. Xu, R. Li, R. Dai, and W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203(3-6), 335–340 (2002). [CrossRef]
10. A. D. A. Leonard and H. E. Sweeney, “Comparison of stimulated and spontaneous laser-radar methods for the remote sensing of ocean physical properties,” Proceedings of SPIE - The International Society for Optical Engineering, 568–582 (1990).
11. J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86(1), 177–179 (2006). [CrossRef]
12. J. Shi, M. Ouyang, W. Gong, S. Li, and D. Liu, “A Brillouin lidar system using F–P etalon and ICCD for remote sensing of the ocean,” Appl. Phys. B 90(3-4), 569–571 (2008). [CrossRef]
13. J. Shi, H. Wang, J. Qian, and X. He, “Investigations on thermal-transfer characteristics of water based on stimulated Brillouin scattering,” Opt. Commun. 363, 21–25 (2016). [CrossRef]
14. D. Yuan, J. Xu, Z. Liu, S. Hao, J. Shi, N. Luo, S. Li, J. Liu, S. Wan, and X. He, “High resolution stimulated Brillouin scattering lidar using Galilean focusing system for detecting submerged objects,” Opt. Commun. 427, 27–32 (2018). [CrossRef]
15. Y. Yao, Q. J. Niu, and K. Liang, “Measurement error analysis of Brillouin lidar system using F-P etalon and ICCD,” Opt. Commun. 375, 58–62 (2016). [CrossRef]
16. J. Shi, Y. Tang, H. Wei, L. Zhang, D. Zhang, J. Shi, W. Gong, X. He, K. Yang, and D. Liu, “Temperature dependence of threshold and gain coefficient of stimulated Brillouin scattering in water,” Appl. Phys. B 108(4), 717–720 (2012). [CrossRef]
17. J. Shi, X. Chen, M. Ouyang, J. Liu, and D. Liu, “Theoretical investigation on the threshold value of stimulated Brillouin scattering in terms of laser intensity,” Appl. Phys. B 95(4), 657–660 (2009). [CrossRef]
18. X. He, Y. Tang, J. Shi, J. Liu, W. Cheng, and X. Mo, “Investigation of the influence of temperature on threshold value and pulse duration of stimulated Brillouin scattering in liquid water,” J. Mod. Opt. 59(16), 1410–1414 (2012). [CrossRef]
19. J. Bai, J. Shi, M. Ouyang, X. Chen, W. Gong, H. Jing, J. Liu, and D. Liu, “Method for measuring the threshold value of stimulated Brillouin scattering in water,” Opt. Lett. 33(13), 1539–1541 (2008). [CrossRef]
20. R. W. Boyd, “Chapter 9 - Stimulated Brillouin and Stimulated Rayleigh Scattering,” in Nonlinear Optics (Third Edition) (Academic, 2008), 429–471.
21. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42(9), 5514–5521 (1990). [CrossRef]
22. M. J. Damzen, V. I. Vlad, V. Babin, and A. Mocofanescu, Stimulated Brillouin scattering : fundamentals and applications (Institute of Physics Publishing, 2003).
23. J. F. Xu, X. B. Ren, W. P. Gong, R. Dai, and D. H. Liu, “Measurement of the bulk viscosity of liquid by Brillouin scattering,” Appl. Opt. 42(33), 6704–6709 (2003). [CrossRef]
24. R. C. Millard and G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep-Sea Res., Part A 37(12), 1909–1926 (1990). [CrossRef]
25. P. Ioc, “Th international thermodynamic equation of seawater-2010: Calculation and use of thermodynamic properties,” (Intergovernmental Oceanographic Commission, 2010).
26. L. Hu, X. Zhang, and M. J. Perry, “Light scattering by pure seawater: Effect of pressure,” Deep Sea Res., Part I 146, 103–109 (2019). [CrossRef]
27. F. Roquet, G. Madec, T. J. Mcdougall, and P. M. Barker, “Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard,” Ocean Modelling 90, 29–43 (2015). [CrossRef]
28. T. J. McDougall and P. M. Barker, “Getting started with TEOS-10 and the Gibbs Seawater (GSW)Oceanographic Toolbox,” SCOR/IAPSO WG 127, 1–28 (2011).
29. D. Johnson, Regional Climatology of the East Asian Seas: An Introduction (2015).
30. D. Johnson, “Dataset: East Asian Seas Regional Climatology,” (2015).
