Abstract

The sensitivity of an optical fiber microsensor based on inter-modal interference can be considerably improved by tapering a short extension of the multimode fiber. In the case of Graded Index fibers with a parabolic refractive index profile, a meridional ray exhibits a sinusoidal path. When these fibers are tapered, the period of the propagated beam decrease down-taper and increase up-taper. We take advantage of this modulation –along with the enhanced overlap between the evanescent field and the external medium– to substantially increase the sensitivity of these devices by tuning the sensor’s maximum sensitivity wavelength. Moreover, the extension of this device is reduced by one order of magnitude, making it more propitious for reduced space applications. Numerical and experimental results demonstrate the success and feasibility of this approach.

© 2014 Optical Society of America

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References

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    [Crossref]
  2. J. Villatoro, D. Monzón-Hernández, and E. Mejía, “Fabrication and modeling of uniform-waist single-mode tapered optical fiber sensors,” Appl. Opt. 42, 2278–2283 (2003).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  5. C. R. Biazoli, S. Silva, M. A. R. Franco, O. Frazão, and C. M. B. Cordeiro, “Multimode interference tapered fiber refractive index sensors,” Appl. Opt. 51, 5941–5945 (2012).
    [Crossref] [PubMed]
  6. F. Beltrán-Mejía, J. H. Osório, C. R. Biazoli, and C. M. B. Cordeiro, “D-microfibers,” J. Lightwave Technol. 31, 2756–2761 (2013).
    [Crossref]
  7. P. Wang, G. Brambilla, M. Ding, Y. Semenova, Q. Wu, and G. Farrell, “Investigation of single-mode–multimode–single-mode and single-mode–tapered-multimode–single-mode fiber structures and their application for refractive index sensing,” J. Opt. Soc. Am. B 28, 1180–1186 (2011).
    [Crossref]
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  10. Comsol Multiphysics, Burlington, MA, USA (2014). Version 4.4.
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    [Crossref]
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    [Crossref]
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    [Crossref]

2013 (1)

2012 (1)

2011 (2)

2009 (1)

2007 (1)

2003 (2)

J. Villatoro, D. Monzón-Hernández, and E. Mejía, “Fabrication and modeling of uniform-waist single-mode tapered optical fiber sensors,” Appl. Opt. 42, 2278–2283 (2003).
[Crossref] [PubMed]

A. Kumar, R. K. Varshney, and P. Sharma, “Transmission characteristics of SMS fiber optic sensor structures,” Optics Communications 219, 215–219 (2003).
[Crossref]

2000 (1)

1992 (1)

T. Birks and Y. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[Crossref]

1965 (1)

H. Kogelnik, “On the propagation of gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt 4, 1562–1569 (1965).
[Crossref]

Beltrán-Mejía, F.

Biazoli, C. R.

Birks, T.

T. Birks and Y. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[Crossref]

Brambilla, G.

Chan, T. H.

H. Y. Tam, S. Y. Liu, B. O. Guan, W. H. Chung, T. H. Chan, and L. K. Cheng, “Fiber bragg grating sensors for structural and railway applications,” in “Advanced Sensor Systems and Applications II,” 5634, 85–97 (2005).
[Crossref]

Cheng, L. K.

H. Y. Tam, S. Y. Liu, B. O. Guan, W. H. Chung, T. H. Chan, and L. K. Cheng, “Fiber bragg grating sensors for structural and railway applications,” in “Advanced Sensor Systems and Applications II,” 5634, 85–97 (2005).
[Crossref]

Chung, W. H.

H. Y. Tam, S. Y. Liu, B. O. Guan, W. H. Chung, T. H. Chan, and L. K. Cheng, “Fiber bragg grating sensors for structural and railway applications,” in “Advanced Sensor Systems and Applications II,” 5634, 85–97 (2005).
[Crossref]

Cordeiro, C. M. B.

Ding, M.

Farrell, G.

Franco, M. A. R.

Frazão, O.

Ghatak, A.

A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University Press, 1998), chap. 9.
[Crossref]

Guan, B. O.

H. Y. Tam, S. Y. Liu, B. O. Guan, W. H. Chung, T. H. Chan, and L. K. Cheng, “Fiber bragg grating sensors for structural and railway applications,” in “Advanced Sensor Systems and Applications II,” 5634, 85–97 (2005).
[Crossref]

Guenther, R. D.

R. D. Guenther, Modern Optics (Wiley, 1990), chap. 5.

Kogelnik, H.

H. Kogelnik, “On the propagation of gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt 4, 1562–1569 (1965).
[Crossref]

Kumar, A.

Kumar, Y. P.

Kuroo, S.-I.

Li, Y.

T. Birks and Y. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[Crossref]

Liu, S. Y.

H. Y. Tam, S. Y. Liu, B. O. Guan, W. H. Chung, T. H. Chan, and L. K. Cheng, “Fiber bragg grating sensors for structural and railway applications,” in “Advanced Sensor Systems and Applications II,” 5634, 85–97 (2005).
[Crossref]

Liu, Y.

Lorenser, D.

Marin, E.

Mejía, E.

Meunier, J.-P.

Monzón-Hernández, D.

Osório, J. H.

Pillai, R. S.

Sampson, D. D.

Semenova, Y.

Sharma, P.

A. Kumar, R. K. Varshney, and P. Sharma, “Transmission characteristics of SMS fiber optic sensor structures,” Optics Communications 219, 215–219 (2003).
[Crossref]

Shiraishi, K.

Silva, S.

Tam, H. Y.

H. Y. Tam, S. Y. Liu, B. O. Guan, W. H. Chung, T. H. Chan, and L. K. Cheng, “Fiber bragg grating sensors for structural and railway applications,” in “Advanced Sensor Systems and Applications II,” 5634, 85–97 (2005).
[Crossref]

Thyagarajan, K.

A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University Press, 1998), chap. 9.
[Crossref]

Tripathi, S. M.

Varshney, R. K.

Villatoro, J.

Wang, P.

Wei, L.

Wu, Q.

Appl. Opt (1)

H. Kogelnik, “On the propagation of gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt 4, 1562–1569 (1965).
[Crossref]

Appl. Opt. (3)

J. Lightwave Technol. (4)

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Optics Communications (1)

A. Kumar, R. K. Varshney, and P. Sharma, “Transmission characteristics of SMS fiber optic sensor structures,” Optics Communications 219, 215–219 (2003).
[Crossref]

Other (4)

H. Y. Tam, S. Y. Liu, B. O. Guan, W. H. Chung, T. H. Chan, and L. K. Cheng, “Fiber bragg grating sensors for structural and railway applications,” in “Advanced Sensor Systems and Applications II,” 5634, 85–97 (2005).
[Crossref]

R. D. Guenther, Modern Optics (Wiley, 1990), chap. 5.

Comsol Multiphysics, Burlington, MA, USA (2014). Version 4.4.

A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University Press, 1998), chap. 9.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) Scheme of a conventional SMS sensor of length L and (b) a tapered SMS sensor as proposed here, with a waist of length Lw and diameter Dw.
Fig. 2
Fig. 2 Numerical results for the fractional modal power of the first two lower order modes using different misalignment values at the splice between the singlemode fiber and the GRIN fiber. As shown in the legend box, bluish and reddish solid lines represent the modal amplitude for LP01 and LP02 respectively. All results obtained using a Finite Element software [10].
Fig. 3
Fig. 3 (a) Free Spectral Range (FSR) as a function of λ̄ for a constant length. Marks represent experimental values when using Newport FS-V (green dots) and Corning SMF-28 (red crosses) as input single-mode fibers. Further experimental details as explained in Sec. 5. (b) FSR as a function of the multimode fiber’s length L for a fixed wavelength. Both graphs are for a conventional SMS sensor while the solid blue line represent an analytical approximation as explained for Eq. (2).
Fig. 4
Fig. 4 (a) Ray trajectories for a GRIN fiber using different input angles. Dashed lines represent an homogeneous GRIN fiber with core radius a0 = 40μm and Ag = 200μm, as in [12]. Solid lines represent the same GRIN fiber but with an exponentially decaying taper profile. The black arrows show the different periods for rays propagating on the tapered and untapered versions of the GRIN fiber. (b and c) Color-coded electric field amplitude for 1.5 mm long slices of a tapered GRIN fiber simulated using RSoft’s Beamprop software. Plot (b) is for the homogeneous region, while (c) is for the tapered region of the taper as illustrated by the scheme at right. By choosing the appropriate fiber parameters and the same taper profile, similar results were obtained in comparison with the ray trajectories at left.
Fig. 5
Fig. 5 (a) Dependence of β1β2 as a function of wavelength for a tapered GRIN fiber (normalized data). (b) Critical wavelength for different outer diameters. For both figures, different colors represent different cladding diameters for the tapered fiber as shown in the legend box. All the results are for an outer refractive index n = 1.39 RIU obtained using a Finite Element software [10].
Fig. 6
Fig. 6 (a) Propagation constant difference for the two lower-order modes LP01 and LP02 at the tapered GRIN fiber as a function of wavelength. It can be seen that an SMS sensor will only be sensitive to external refractive index variations (different colored disks) when using tapers thinner than Dw ⩽ 20μm. (b) Zoom of the previous plot around the critical wavelength for Dw = 15μm. A small shift of the maximum toward lower wavelengths can be observed when the external refractive index increases. (c) An almost linear behavior is observed for the critical wavelengths as the outer refractive index varies. All results obtained using a Finite Element software [10].
Fig. 7
Fig. 7 (a) Comparison between the output intensity spectrum for a conventional SMS sensor (red) made with a 3 m long GRIN fiber and a tapered GRIN fiber (blue) whose total length is shorter than 1 m (a uniform waist length Lw = 15mm, plus two transition regions of ≈ 30mm long). Inset shows the numerical results for cos(ΔβL)2 as a function of wavelength. (b) Peak shift as a function of the outer refractive index difference. Inset shows the spectra used to obtain a sensitivity of 3842 nm/RIU. For all graphs, the taper transition region of the GRIN fiber has an exponential form similar as in Fig. 1(b).

Equations (11)

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a i = ψ S ψ i * d A ,
P ( λ ) = | a 1 2 + a 2 2 e j ( β 1 β 2 ) L + + a i 2 e j ( β 1 β i ) L + | 2 .
FSR π q L ( λ λ 0 ) .
n ( r ) = n 0 ( 1 A g 2 r 2 ) , r < a
d 2 r d z 2 + 2 r Δ a 2 = 0 ,
r ( z ) = C 1 cos ( z / A g ) + C 2 sin ( z / A g ) ,
T = 2 π A g .
( r γ ) = ( sin ( z / A g ) A g cos ( z / A g ) 1 A g cos ( z / A g ) sin ( z / A g ) ) ( r 0 γ 0 ) .
Δ ϕ = ϕ λ Δ λ + ϕ n Δ n .
Δ λ Δ n = ( Δ ϕ Δ n ϕ n ) ( ϕ λ ) 1
Δ n = ( d n 0 / d T ) Δ T ,

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