Abstract

Although experimental advances in the implementation and characterization of fiber speckle sensor have been reported, a suitable model to interpret the speckle-pattern variation under perturbation is desirable but very challenging to be developed due to the various factors influencing the speckle pattern. In this work, a new methodology based on the finite element method (FEM) for modeling and optimizing fiber specklegram sensors (FSSs) is proposed. The numerical method allows computational visualization and quantification, in near field, of changes of a step multi-mode fiber (SMMF) specklegram, due to the application of a uniformly distributed force line (UDFL). In turn, the local modifications of the fiber speckle produce changes in the optical power captured by a step single-mode fiber (SSMF) located just at the output end of the SMMF, causing a filtering effect that explains the operation of the FSSs. For each external force, the stress distribution and the propagations modes supported by the SMMF are calculated numerically by means of FEM. Then, those modes are vectorially superposed to reconstruct each perturbed fiber specklegram. Finally, the performance of the sensing mechanism is evaluated for different radius of the filtering SSMF and force-gauges, what evidences design criteria for these kinds of measuring systems. Results are in agreement with those theoretical and experimental ones previously reported.

© 2016 Optical Society of America

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References

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2016 (1)

2015 (1)

2014 (1)

J. L. Camas-Anzueto, A. E. Aguilar-Castillejos, J. H. Castañón-González, M. C. Lujpán-Hidalgo, H. R. Hernández-León, and R. Mota-Grajales, “Fiber sensor based on Lophine sensitive layer for nitrate detection in drinking water,” Opt. Lasers Eng. 60, 38–43 (2014).
[Crossref]

2013 (3)

L. Rodriguez, M. Lomer, A. Cobo, and J. M. López, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sens. Actuators A Phys. 203, 341–345 (2013).
[Crossref]

N. D. Gómez and J. A. Gómez, “Effects of the speckle size on non-holographic fiber specklegram sensors,” Opt. Lasers Eng. 51(11), 1291–1295 (2013).
[Crossref]

A. Hoyos, N. D. Gómez, and J. A. Gómez, “Fiber specklegram sensors (FSS) for measuring high frequency mechanical perturbations,” Proc. SPIE 8785, 8785BH (2013).

2012 (3)

J. A. Gómez and A. Salazar, “Self-correlation fiber specklegram sensor by using volume characteristics of speckle patterns,” Opt. Lasers Eng. 50(5), 812–815 (2012).
[Crossref]

C. K. Suzuki, Y. T. Wu, and E. Fujiwara, “Vibration-based specklegram fiber sensor for measurement of properties of liquids,” Opt. Lasers Eng. 50(12), 1726–1730 (2012).
[Crossref]

Y. Fan, G. Wu, W. Wei, Y. Yuan, F. Lin, and X. Wu, “Fiber-optic bend sensor using LP21 mode operation,” Opt. Express 20(24), 26127–26134 (2012).
[Crossref] [PubMed]

2011 (3)

P. Torres, V. H. Aristizabal, and M. V. Andres, “Modeling of photonic crystal fibers from the scalar wave equation with a purely transverse linearly polarized vector potential,” J. Opt. Soc. Am. 28(4), 787–791 (2011).
[Crossref]

J. A. Gómez, H. Lorduy, and G. A. Salazar, “Improvement of the dynamic range of a fiber specklegram sensor based on volume speckle recording in photorefractive materials,” Opt. Lasers Eng. 49(3), 473–480 (2011).
[Crossref]

J. A. Gómez, H. Lorduy, and G. A. Salazar, “Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials,” Opt. Commun. 284(4), 1008–1014 (2011).
[Crossref]

2008 (1)

2007 (2)

2006 (3)

V. H. Aristizabal, F. J. Vélez, and P. Torres, “Analysis of photonic crystal fibers: Scalar solution and polarization correction,” Opt. Express 14(24), 11848–11854 (2006).
[Crossref] [PubMed]

Z. Zhang and F. Ansari, “Fiber-optic laser speckle-intensity crack sensor for embedment in concrete,” Sens. Actuators A Phys. 126(1), 107–111 (2006).
[Crossref]

F. J. Velez, V. H. Aristizabal, and P. Torres, “Numerical model and analysis of optical fiber with internal electrodes,” Revista Colombiana de Física 38(1), 173–176 (2006).

2005 (1)

2003 (1)

B. Wang, H. Chuanyong, R. Guo, and F. T. S. Yu, “A novel chemical sensor using inner product multimode fiber speckle fields,” Proc. SPIE 5206, 299 (2003).
[Crossref]

1996 (1)

1995 (1)

1994 (2)

F. T. S. Yu, S. Yin, J. Zhang, and R. Guo, “Application of a fiber-speckle hologram to fiber sensing,” Appl. Opt. 33(22), 5202–5203 (1994).
[Crossref] [PubMed]

K. Fischer, J. Müller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12(1), 163–169 (1994).
[Crossref]

1993 (1)

1991 (1)

1988 (1)

A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficient in single-mode optical fiber,” J. Lightwave Technol. 6(1), 17–20 (1988).
[Crossref]

Aguilar-Castillejos, A. E.

J. L. Camas-Anzueto, A. E. Aguilar-Castillejos, J. H. Castañón-González, M. C. Lujpán-Hidalgo, H. R. Hernández-León, and R. Mota-Grajales, “Fiber sensor based on Lophine sensitive layer for nitrate detection in drinking water,” Opt. Lasers Eng. 60, 38–43 (2014).
[Crossref]

Andres, M. V.

P. Torres, V. H. Aristizabal, and M. V. Andres, “Modeling of photonic crystal fibers from the scalar wave equation with a purely transverse linearly polarized vector potential,” J. Opt. Soc. Am. 28(4), 787–791 (2011).
[Crossref]

Ansari, F.

Z. Zhang and F. Ansari, “Fiber-optic laser speckle-intensity crack sensor for embedment in concrete,” Sens. Actuators A Phys. 126(1), 107–111 (2006).
[Crossref]

Aristizabal, V. H.

P. Torres, V. H. Aristizabal, and M. V. Andres, “Modeling of photonic crystal fibers from the scalar wave equation with a purely transverse linearly polarized vector potential,” J. Opt. Soc. Am. 28(4), 787–791 (2011).
[Crossref]

F. J. Velez, V. H. Aristizabal, and P. Torres, “Numerical model and analysis of optical fiber with internal electrodes,” Revista Colombiana de Física 38(1), 173–176 (2006).

V. H. Aristizabal, F. J. Vélez, and P. Torres, “Analysis of photonic crystal fibers: Scalar solution and polarization correction,” Opt. Express 14(24), 11848–11854 (2006).
[Crossref] [PubMed]

Bertholds, A.

A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficient in single-mode optical fiber,” J. Lightwave Technol. 6(1), 17–20 (1988).
[Crossref]

Cai, H.

Camas-Anzueto, J. L.

J. L. Camas-Anzueto, A. E. Aguilar-Castillejos, J. H. Castañón-González, M. C. Lujpán-Hidalgo, H. R. Hernández-León, and R. Mota-Grajales, “Fiber sensor based on Lophine sensitive layer for nitrate detection in drinking water,” Opt. Lasers Eng. 60, 38–43 (2014).
[Crossref]

Castañón-González, J. H.

J. L. Camas-Anzueto, A. E. Aguilar-Castillejos, J. H. Castañón-González, M. C. Lujpán-Hidalgo, H. R. Hernández-León, and R. Mota-Grajales, “Fiber sensor based on Lophine sensitive layer for nitrate detection in drinking water,” Opt. Lasers Eng. 60, 38–43 (2014).
[Crossref]

Chuanyong, H.

B. Wang, H. Chuanyong, R. Guo, and F. T. S. Yu, “A novel chemical sensor using inner product multimode fiber speckle fields,” Proc. SPIE 5206, 299 (2003).
[Crossref]

Cobo, A.

L. Rodriguez, M. Lomer, A. Cobo, and J. M. López, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sens. Actuators A Phys. 203, 341–345 (2013).
[Crossref]

Dandliker, R.

A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficient in single-mode optical fiber,” J. Lightwave Technol. 6(1), 17–20 (1988).
[Crossref]

Fan, Y.

Fang, Z.

Fischer, K.

K. Fischer, J. Müller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12(1), 163–169 (1994).
[Crossref]

Fujiwara, E.

C. K. Suzuki, Y. T. Wu, and E. Fujiwara, “Vibration-based specklegram fiber sensor for measurement of properties of liquids,” Opt. Lasers Eng. 50(12), 1726–1730 (2012).
[Crossref]

Gafsi, R.

Geng, J.

Gómez, J. A.

N. D. Gómez and J. A. Gómez, “Effects of the speckle size on non-holographic fiber specklegram sensors,” Opt. Lasers Eng. 51(11), 1291–1295 (2013).
[Crossref]

A. Hoyos, N. D. Gómez, and J. A. Gómez, “Fiber specklegram sensors (FSS) for measuring high frequency mechanical perturbations,” Proc. SPIE 8785, 8785BH (2013).

J. A. Gómez and A. Salazar, “Self-correlation fiber specklegram sensor by using volume characteristics of speckle patterns,” Opt. Lasers Eng. 50(5), 812–815 (2012).
[Crossref]

J. A. Gómez, H. Lorduy, and G. A. Salazar, “Improvement of the dynamic range of a fiber specklegram sensor based on volume speckle recording in photorefractive materials,” Opt. Lasers Eng. 49(3), 473–480 (2011).
[Crossref]

J. A. Gómez, H. Lorduy, and G. A. Salazar, “Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials,” Opt. Commun. 284(4), 1008–1014 (2011).
[Crossref]

Gómez, N. D.

A. Hoyos, N. D. Gómez, and J. A. Gómez, “Fiber specklegram sensors (FSS) for measuring high frequency mechanical perturbations,” Proc. SPIE 8785, 8785BH (2013).

N. D. Gómez and J. A. Gómez, “Effects of the speckle size on non-holographic fiber specklegram sensors,” Opt. Lasers Eng. 51(11), 1291–1295 (2013).
[Crossref]

Guo, R.

B. Wang, H. Chuanyong, R. Guo, and F. T. S. Yu, “A novel chemical sensor using inner product multimode fiber speckle fields,” Proc. SPIE 5206, 299 (2003).
[Crossref]

F. T. S. Yu, S. Yin, J. Zhang, and R. Guo, “Application of a fiber-speckle hologram to fiber sensing,” Appl. Opt. 33(22), 5202–5203 (1994).
[Crossref] [PubMed]

Hernández-León, H. R.

J. L. Camas-Anzueto, A. E. Aguilar-Castillejos, J. H. Castañón-González, M. C. Lujpán-Hidalgo, H. R. Hernández-León, and R. Mota-Grajales, “Fiber sensor based on Lophine sensitive layer for nitrate detection in drinking water,” Opt. Lasers Eng. 60, 38–43 (2014).
[Crossref]

Hoffmann, R.

K. Fischer, J. Müller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12(1), 163–169 (1994).
[Crossref]

Hoyos, A.

A. Hoyos, N. D. Gómez, and J. A. Gómez, “Fiber specklegram sensors (FSS) for measuring high frequency mechanical perturbations,” Proc. SPIE 8785, 8785BH (2013).

Koshiba, M.

Labarrère, M.

Lecoy, P.

Li, J.

Lin, F.

Liu, Y.

Lomer, M.

L. Rodriguez-Cobo, M. Lomer, and J. M. Lopez-Higuera, “Fiber Specklegram-Multiplexed Sensor,” J. Lightwave Technol. 33(12), 2591–2597 (2015).
[Crossref]

L. Rodriguez, M. Lomer, A. Cobo, and J. M. López, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sens. Actuators A Phys. 203, 341–345 (2013).
[Crossref]

López, J. M.

L. Rodriguez, M. Lomer, A. Cobo, and J. M. López, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sens. Actuators A Phys. 203, 341–345 (2013).
[Crossref]

Lopez-Higuera, J. M.

Lorduy, H.

J. A. Gómez, H. Lorduy, and G. A. Salazar, “Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials,” Opt. Commun. 284(4), 1008–1014 (2011).
[Crossref]

J. A. Gómez, H. Lorduy, and G. A. Salazar, “Improvement of the dynamic range of a fiber specklegram sensor based on volume speckle recording in photorefractive materials,” Opt. Lasers Eng. 49(3), 473–480 (2011).
[Crossref]

Lujpán-Hidalgo, M. C.

J. L. Camas-Anzueto, A. E. Aguilar-Castillejos, J. H. Castañón-González, M. C. Lujpán-Hidalgo, H. R. Hernández-León, and R. Mota-Grajales, “Fiber sensor based on Lophine sensitive layer for nitrate detection in drinking water,” Opt. Lasers Eng. 60, 38–43 (2014).
[Crossref]

Malki, A.

Marin, E.

Meunier, J. P.

Michel, L.

Mota-Grajales, R.

J. L. Camas-Anzueto, A. E. Aguilar-Castillejos, J. H. Castañón-González, M. C. Lujpán-Hidalgo, H. R. Hernández-León, and R. Mota-Grajales, “Fiber sensor based on Lophine sensitive layer for nitrate detection in drinking water,” Opt. Lasers Eng. 60, 38–43 (2014).
[Crossref]

Müller, J.

K. Fischer, J. Müller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12(1), 163–169 (1994).
[Crossref]

Qian, S.

Qu, R.

Rodriguez, L.

L. Rodriguez, M. Lomer, A. Cobo, and J. M. López, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sens. Actuators A Phys. 203, 341–345 (2013).
[Crossref]

Rodriguez-Cobo, L.

Ruffin, P. B.

Saitoh, K.

Salazar, A.

J. A. Gómez and A. Salazar, “Self-correlation fiber specklegram sensor by using volume characteristics of speckle patterns,” Opt. Lasers Eng. 50(5), 812–815 (2012).
[Crossref]

Salazar, G. A.

J. A. Gómez, H. Lorduy, and G. A. Salazar, “Improvement of the dynamic range of a fiber specklegram sensor based on volume speckle recording in photorefractive materials,” Opt. Lasers Eng. 49(3), 473–480 (2011).
[Crossref]

J. A. Gómez, H. Lorduy, and G. A. Salazar, “Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials,” Opt. Commun. 284(4), 1008–1014 (2011).
[Crossref]

Salle, D.

K. Fischer, J. Müller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12(1), 163–169 (1994).
[Crossref]

Su, L.

Suzuki, C. K.

C. K. Suzuki, Y. T. Wu, and E. Fujiwara, “Vibration-based specklegram fiber sensor for measurement of properties of liquids,” Opt. Lasers Eng. 50(12), 1726–1730 (2012).
[Crossref]

Torres, P.

P. Torres, V. H. Aristizabal, and M. V. Andres, “Modeling of photonic crystal fibers from the scalar wave equation with a purely transverse linearly polarized vector potential,” J. Opt. Soc. Am. 28(4), 787–791 (2011).
[Crossref]

F. J. Velez, V. H. Aristizabal, and P. Torres, “Numerical model and analysis of optical fiber with internal electrodes,” Revista Colombiana de Física 38(1), 173–176 (2006).

V. H. Aristizabal, F. J. Vélez, and P. Torres, “Analysis of photonic crystal fibers: Scalar solution and polarization correction,” Opt. Express 14(24), 11848–11854 (2006).
[Crossref] [PubMed]

Uang, C.-M.

Velez, F. J.

F. J. Velez, V. H. Aristizabal, and P. Torres, “Numerical model and analysis of optical fiber with internal electrodes,” Revista Colombiana de Física 38(1), 173–176 (2006).

Vélez, F. J.

Wang, B.

B. Wang, H. Chuanyong, R. Guo, and F. T. S. Yu, “A novel chemical sensor using inner product multimode fiber speckle fields,” Proc. SPIE 5206, 299 (2003).
[Crossref]

Wang, Y.

Wasse, F.

K. Fischer, J. Müller, R. Hoffmann, F. Wasse, and D. Salle, “Elastooptical properties of SiON layers in an integrated optical interferometer used as a pressure sensor,” J. Lightwave Technol. 12(1), 163–169 (1994).
[Crossref]

Wei, L.

Wei, W.

Wen, M.

Wu, G.

Wu, S.

Wu, X.

Wu, Y. T.

C. K. Suzuki, Y. T. Wu, and E. Fujiwara, “Vibration-based specklegram fiber sensor for measurement of properties of liquids,” Opt. Lasers Eng. 50(12), 1726–1730 (2012).
[Crossref]

Xu, Y.

Yin, S.

Yu, F. T.

Yu, F. T. S.

Yuan, Y.

Zhang, J.

Zhang, Z.

Z. Zhang and F. Ansari, “Fiber-optic laser speckle-intensity crack sensor for embedment in concrete,” Sens. Actuators A Phys. 126(1), 107–111 (2006).
[Crossref]

Zhong, L.

Appl. Opt. (8)

S. Wu, S. Yin, and F. T. S. Yu, “Sensing with fiber specklegrams,” Appl. Opt. 30(31), 4468–4470 (1991).
[Crossref] [PubMed]

F. T. Yu, M. Wen, S. Yin, and C.-M. Uang, “Submicrometer displacement sensing using inner-product multimode fiber speckle fields,” Appl. Opt. 32(25), 4685–4689 (1993).
[Crossref] [PubMed]

F. T. S. Yu, S. Yin, J. Zhang, and R. Guo, “Application of a fiber-speckle hologram to fiber sensing,” Appl. Opt. 33(22), 5202–5203 (1994).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

(a) SMMF under a UDFL, (b) FEM element grid and (c) description of an element and its nodes.

Fig. 2
Fig. 2

SMMF under an UDFL. (a) change in x and (b) y of the refractive index, and (c) Von Mises-principal stresses distribution in cross section for F =1.0 N/ mm   y ^ .

Fig. 3
Fig. 3

Electric field distribution for the first 20 modes of propagation calculated by FEM for F=1N in the SMMF at 1630 nm.

Fig. 4
Fig. 4

Vector superposition of the electric field for (a) the first 10 modes, (b) the first 20 modes, (c) the first 50 modes and (d) all modes supported by SMMF (104 modes approximately) for F=1N .

Fig. 5
Fig. 5

Simulated speckle patterns for F=1N in the SMMF at (a) 632.8nm, (b) 1064nm, (c) 1630nm and (d) 2940nm. The circles indicate the detection windows (filtering fiber) of diameter: 2, 4, 8, 16, 32 and 62.5 μm, thus illustrating the captured power of each window.

Fig. 6
Fig. 6

Snapshots of the simulated speckle patterns in the SMMF at 1630 nm for various values of F gauge .

Fig. 7
Fig. 7

Sensitivity and linearity of the sensor for different calibration points at 1630 nm with a filtering SSMF of 14μm of diameter.

Fig. 8
Fig. 8

Sensitivity and linearity of the sensor for different diameters of filtering SSMF at 1630 nm for calibration forces of: (a) 5.0 N/mm and (b) 9.0 N/mm.

Tables (2)

Tables Icon

Table 1 Properties of the SMMF Used in the Simulation with NA = 0.12

Tables Icon

Table 2 Ratio Between D13.58μm at 1630μm and the Core Diameter of the Filtering Fibers d.

Equations (20)

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Δ B ij =Δ( 1/ n ij 2 )= P ijkl S kl .
Δ n ij = n ij n 0 I ij n 0 3 2 P ijkl S kl ,
S kl = 1 Y [ ( 1+ν ) σ kl ν δ kl σ mm ],
Δ n i = n i n 0 n 0 3 2 P ik S k ,
S k = 1 Y [ ( 1+ν ) σ k ν σ mm ],
Δ n i C ik σ k ,
[ Δ n 1 Δ n 2 Δ n 3 ] n 0 3 2 [ P 11 P 12 P 12 P 12 P 11 P 12 P 12 P 12 P 11 ][ S 1 S 2 S 3 ]=[ C 1 C 2 C 2 C 2 C 1 C 2 C 2 C 2 C 1 ][ σ 1 σ 2 σ 3 ],
[ S 1 S 2 S 3 ]= 1 Y [ 1 ν ν ν 1 ν ν ν 1 ][ σ 1 σ 2 σ 3 ],
C 1 = n 0 3 2Y ( P 11 2ν P 12 ), C 2 = n 0 3 2Y ( ν P 11 +( 1ν ) P 12 ).
n 1 n 0 n 0 3 2 ( P 11 S 1 + P 12 S 2 ), n 2 n 0 n 0 3 2 ( P 12 S 1 + P 11 S 2 ), n 3 n 0 n 0 3 2 ( P 12 S 1 + P 12 S 2 ).
n 1 = n 0 C 1 σ 1 C 2 ( σ 2 + σ 3 ) n 0 ( C 1 +ν C 2 ) σ 1 C 2 ( 1+ν ) σ 2 , n 2 = n 0 C 1 σ 2 C 2 ( σ 3 + σ 1 ) n 0 C 2 ( 1+ν ) σ 1 ( C 1 +ν C 2 ) σ 2 , n 3 = n 0 C 1 σ 3 C 2 ( σ 1 + σ 2 ) n 0 ( C 1 ν+ C 2 ) σ 1 ( C 1 ν+ C 2 ) σ 2 .
σ ji,j =0,
S ij,km + S km,ij S ik,jm S jm,ik =0,
T i ( n ^ ) = T i 0( n ^ ) ,or u i = u i 0 onΓ,
n 0co 2 ( λ[ μm ] )=1+ 0.6961663 λ 2 λ 2 ( 0.0684043 ) 2 + 0.4079426 λ 2 λ 2 ( 0.1162414 ) 2 + 0.8974794 λ 2 λ 2 ( 9.896161 ) 2 ,
σ VM = 1 2 [ ( σ 1 σ 2 ) 2 + ( σ 1 σ 3 ) 2 + ( σ 2 σ 3 ) 2 ] .
×× E k 0 2 n 2 E =0,
n=[ n 1 0 0 0 n 2 0 0 0 n 3 ].
P= A IdA,
P P e = 1 2 c ε 0 n 0core | E e | 2 A e ,

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