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${\text{π }}$ -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
[1] Majumder M, Gangopadhyay T K, Chakraborty A K, Dasgupta K, Bhattacharya D K 2008 Sens. Actuator A: Phys. 147 150
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图 1 (a) 声波入射示意图; (b)坐标示意图
Figure 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Figure 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
Figure 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 $ Figure 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
Figure 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
Figure 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
Figure 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
Figure 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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