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π相移光纤光栅因具有较短的有效光栅传感长度, 近年来成为了超声传感领域的研究热点. 本研究旨在探究π相移光纤光栅作为水听器应用时对超声波的指向性特性. 选取π相移光纤光栅作为超声传感单元, 先基于分层介质的声传播理论计算出水中超声波入射时光纤纤芯的应变, 再运用基于光学耦合模方程的传递矩阵法计算反射光谱得到光波长偏移. 将角度-频率空间分为三个区域, 计算了声波频率在1—10 MHz时不同角度下的应变结果和光波长偏移响应特性, 并开展了实验研究. 结果表明, 理论和实验结果具有较高的一致性, π相移光纤光栅在超声波垂直光纤入射时响应最大, 随声波入射方向与光纤法向间夹角的增加, π相移光纤光栅的声响应先急剧下降, 后在水中直达声波和光纤中导波叠加时出现极大值. 此外, π相移光纤光栅的声响应随声波频率增加而降低. 本研究对π相移光纤光栅在超声传感中的实际应用具有重要意义.
${\text{π }}$ -phase-shifted fiber Bragg grating with a short effective sensing length becomes one of research hotspots in ultrasonic sensing, because light undergoes strong localization centered at its phase shift position. To investigate the directional sensing characteristics of${\text{π }}$ -phase-shifted fiber Bragg grating as hydrophone, the theory of sound propagation in layered media is used to calculate the strain of fiber core, then the transfer matrix method based on the coupled-mode theory in optics is used to calculate the shift of central wavelength in optical reflection spectrum. Results of strain and wavelength shift under obliquely incident ultrasonic from 1－10 MHz are divided into A area, B area, and C area, and analyzed by numerical calculation and simulation calculation. Axial strain and elasto-optical strain change the grating period and effective refractive index by the mechanical effect and elasto-optical effect, respectively, thereby resulting in wavelength shift. In A area (frequency below 5 MHz, incident angle below$15^\circ $ ), the axial strain nearly equals zero, thus elasto-optical effect plays a predominant role in wavelength shift. The maximal response occurs at vertical incidence, and then obviously declines with angle increasing. The maximum is essentially unchanged with grating length. In B area and C area (angle above$15^\circ $ ), both mechanical effect and elasto-optical effect contribute to wavelength shift. In B area (frequency below 5 MHz), the amplitude of strain is the largest in three areas. A peak of wavelength shift appears at the same angle of the peak of strain, where exists the interference of the guided wave in fiber with the direct ultrasonic wave form water. The peak amplitude of wavelength shift decreases with grating length increasing. In C area (frequency below 5 MHz), the amplitude of strain is larger than in A area, but the wavelength shift is smaller, which is correlated to its higher axial wave number. Comparing the results in three areas, it is clear that the wavelength shift is larger at lower frequency and at vertical incidence. Experiments on 3 MHz and 5 MHz are then performed with a π-phase-shifted fiber Bragg grating. The experimental result accords well with the theoretical result. The research is important in practically using the${\text{π }}$ -phase-shifted fiber Bragg grating in ultrasonic sensing.-
Keywords:
- π-phase-shifted fiber Bragg grating /
- ultrasonic sensing /
- directivity
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图 1 (a) 声波入射示意图; (b)坐标示意图
Fig. 1. (a) Diagram of an obliquely incident ultrasonic wave at PS-FBG; (b) coordinates.
图 2 (a)三层结构的有限元仿真模型; (b)
$\alpha = 0^\circ $ 时的入射声场; (c)$\alpha = 20^\circ $ 时的入射声场Fig. 2. (a) Simulation model of the three-layer structure; (b) incident sound field when
$\alpha = 0^\circ $ ; (c) incident sound field when$\alpha = 20^\circ $ .
图 3 纤芯应变计算结果 (a), (b)分别是数值计算的轴向应变和弹光应变; (c), (d) 分别是有限元仿真计算的轴向应变和弹光应变
Fig. 3. Calculations of strain in fiber core: (a), (b) The numerical results of axial strain and elasto-optical strain, respectively; (c), (d) the simulation results of axial strain and elasto-optical strain, respectively.
图 4 不同区域应变数值计算结果 (a) A区域,
$\alpha = 0^\circ $ ; (b) B区域,$\alpha = 20^\circ $ ; (c) C区域,$\alpha = 20^\circ $ Fig. 4. Numerical results of different area: (a) area A,
$\alpha = 0^\circ $ ; (b) area B,$\alpha = 20^\circ $ ; (c) area C,$\alpha = 20^\circ $ .
图 5 光纤中导波和水中直达声波的干涉示意图
Fig. 5. Interference of guided wave in fiber and direct ultrasonic wave in water.
图 6 波长偏移结果 (a) 超声波频率为3 MHz; (b) 超声波频率为5 MHz; (c) 超声波频率为9 MHz
Fig. 6. Results of wavelength shift at the ultrasonic wave frequency of (a) 3 MHz, (b) 5 MHz, (c) 9 MHz.
图 7 实验系统 (a)系统示意图; (b)实验测量示意图
Fig. 7. Sensing system: (a) Schematic diagram; (b) experimental measurement
图 8 理论计算和实验测量的波长偏移结果 (a) 超声波频率为3 MHz; (b) 超声波频率为5 MHz
Fig. 8. Results of wavelength shift by numerical calculation and experiment measurement at the ultrasonic wave frequency of (a) 3 MHz and (b) 5 MHz.
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[1] Majumder M, Gangopadhyay T K, Chakraborty A K, Dasgupta K, Bhattacharya D K 2008 Sens. Actuator A: Phys. 147 150
Google Scholar
[2] Wu Q, Okabe Y, Yu F 2018 Sensors 18 3395
Google Scholar
[3] Roriz P, Frazão O, Lobo-Ribeiro A B, Santos J L, Simões J A 2013 J. Biomed. Opt. 18 50903
Google Scholar
[4] 王力, 王永杰, 于非, 李芳 2021 激光与光电子学进展 58 1306014
Google Scholar
Wang L, Wang Y J, Yu F, Li F 2021 Laser. Optoelectron. Prog. 58 1306014
Google Scholar
[5] Tosi D 2017 Sensors. 17 2368
Google Scholar
[6] Minardo A, Cusano A, Bernini R, Zeni L, Giordano M 2005 IEEE T. Ultrason., Ferr. 52 304
Google Scholar
[7] Rosenthal A, Razansky D, Ntziachristos V 2011 Opt. Lett. 36 1833
Google Scholar
[8] Takeda N, Okabe Y, Kuwahara J, Kojima S, Ogisu T 2005 Compos. Sci. Technol. 65 2575
Google Scholar
[9] Gatti D, Galzerano G, Janner D, Longhi S, Laporta P 2008 Opt. Express 16 1945
Google Scholar
[10] Rosenthal A, Caballero M Á A, Kellnberger S, Razansky D, Ntziachristos V 2012 Opt. Lett. 37 3174
Google Scholar
[11] Guo J, Xue S, Zhao Q, Yang C 2014 Opt. Express 22 19573
Google Scholar
[12] Wu Q, Okabe Y, Saito K, Yu F 2014 Sensors 14 1094
Google Scholar
[13] Wu Q, Okabe Y 2014 J. Intell. Mater. Syst. Struct. 25 640
Google Scholar
[14] Guo J, Yang C 2015 IEEE Photon. Technol. Lett. 27 848
Google Scholar
[15] Meng L J, Yi J G, Tan X, Li C 2017 IEICE Electron. Express. 14 20170259
Google Scholar
[16] Foster S B, Cranch G A, Harrison J, Tikhomirov A E, Miller G A 2017 J. Light. Technol. 35 3514
Google Scholar
[17] Jiang Y, Liu C, Li D, Yang D, Zhao J 2018 Meas. Sci. Technol. 29 045101
Google Scholar
[18] Srivastava D, Tiwari U, Das B 2018 Opt. Commun. 410 88
Google Scholar
[19] Wu Q, Wang R, Lan W, Zhang H, Zhai H 2021 Advanced Sensor Systems and Applications XI Nantong, China , October 10–12, 2021 p26
[20] Fomitchov P, Krishnaswamy S 2003 Opt. Eng. 42 956
Google Scholar
[21] Liu T, Han M 2012 IEEE Sensors. J. 12 2368
Google Scholar
[22] Wu D, Marchi G, Rus J, Hopf B, Drexler P, Roths J 2018 German Acoustic Conference 2018 Muenchen, German, March 29, 2018 p978
[23] Veres I A, Burgholzer P, Berer T, Rosenthal A, Wissmeyer G, Ntziachristos V 2014 J. Acoust. Soc. Am. 135 1853
Google Scholar
[24] Nagy P B 1995 J. Acoust. Soc. Am. 98 454
Google Scholar
[25] Ahmad F 2001 J. Acoust. Soc. Am. 109 886
Google Scholar
[26] Honarvar F, Sinclair A N 1996 J. Acoust. Soc. Am. 100 57
Google Scholar
[27] Rokhlin S I, Wang L 2002 J. Acoust. Soc. Am. 112 822
Google Scholar
[28] Huang W, Wang Y J, Rokhlin S I 1996 J. Acoust. Soc. Am. 99 2742
Google Scholar
[29] Erdogan T 1997 J. Light. Technol. 15 1277
Google Scholar
[30] Yamada M, Sakuda K 1987 Appl. Opt. 26 3474
Google Scholar
[31] Thurston R N 1978 J. Acoust. Soc. Am. 64 1
Google Scholar
[32] Jarzynski J 2001 Opt. Eng. 40 2115
Google Scholar
[33] 江毅, 陈淑芬 2004 光学学报 24 11
Google Scholar
Jiang Y, Chen S F 2004 Acta Opt. Sin. 24 11
Google Scholar
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