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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26714–26720
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Bending effect on modal interference in a fiber taper and sensitivity enhancement for refractive index measurement

Li-Peng Sun, Jie Li, Yanzhen Tan, Shuai Gao, Long Jin, and Bai-Ou Guan  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26714-26720 (2013)
http://dx.doi.org/10.1364/OE.21.026714


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Abstract

We demonstrate the bending effect of microfiber on interference fringes in a compact taper-based modal interferometer and sensitivity for refractive index (RI) measurement. For the bend curvature ranging from 0 to 0.283 mm−1, the measured RI sensitivity distinctively increases from 342.5 nm/RIU (refractive-index unit) to 1192.7nm/RIU around RI = 1.333 and from 3847.1 nm/RIU to 11006.0 nm/RIU around RI = 1.430, respectively. Theoretical analysis reveals that such enhancement is determined by the dispersion property of the intermodal index rather than other parameters, such as the variation of the straightforward evanescent field. The magnitude of sensitivity varies as a function of the microfiber bend curvature. Approaching a critical curvature (the intermodal-index dispersion factor approaches zero), the sensitivity is significantly enhanced, exhibiting great potential in RI sensing areas.

© 2013 Optical Society of America

1. Introduction

2. Bending effect on fringes of a single taper-based modal interferometer

As shown in Fig. 1(a), the light beam is partially coupled into the HE11 and HE12 modes at the incident transition and experiences different effective indices in the microfiber. The interference is given by recombination of the modes at the output transition, with the resultant phase difference Φ:
Φ=(2π/λ)ΔnL
(1)
where Δn = neff1neff2 represents the intermodal index with neff1 and neff2 the effective indices for the HE11 and HE12 modes, respectively, L is the interaction length of the modes, and λ is the wavelength. The transmittance is approximately given by T = cos2(Φ/2). The transmission maxima occur at the points when Φ equals an even number of π and the minima occur at the points when Φ equals an odd number of π. The effective indices shown in Eq. (1) can be solved using the wave equation [13

13. G. Brambilla, “Optical fibre nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010). [CrossRef]

], given that the refractive index profile is known. We adopt a local mode model as has been demonstrated in conventional slab waveguides or fibers [18

18. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. A 66(3), 216–220 (1976). [CrossRef]

] for the mode analysis at the microfiber bend. When a mode travels over the bend, the local group velocity along the phase fronts of the mode decreases on the inside while increases on the outside of the bend to maintain a constant angular velocity. As shown in Fig. 1(b), the equivalent index profile along the cross section of a bent microfiber is approximately expressed as
n=n1+2xξ
(2)
where n is the real index profile in the microfiber bend, x is perpendicular to the microfiber axis, and ξ = 1/R is the bend curvature with R the bend radius as shown in Fig. 1(a). From Eq. (2), the index rises on the outside but drops on the inside of the waveguide bend compared to the original value. Figure 1(c) shows a picture of a fabricated structure.

Figure 2(a)
Fig. 2 (a) Measured (solid curves) and modeled (dashed curves) transmission spectra of the interferometer at curvatures: ① ξ = 0 mm−1 and ② ξ = 0.15mm−1, respectively. Inset shows the profile of the fabricated taper-based interferometer. (b) Measured (points) and modeled (solid curves) dip wavelengths in respect of bend curvature.
plots transmission spectra of our taper-based interferometer with ① ξ = 0 and ② 0.15mm−1, respectively, by the use of a broadband light source (BBS) and an optical spectrum analyzer (OSA). The taper profile is also provided as an inset of the figure. The total taper length is around 16.9mm and the transition length is around 3.2mm. A strong interference pattern is observed. The typical insertion loss is ~2.0dB and the maximum extinction ratio is higher than 20dB in Fig. 2(a). We fix the two ends of the taper with two fiber holders and bend the microfiber by changing the positions of the holders, as shown in Fig. 1(a). Strictly speaking, when the structure is bent, the bend is made along the whole structure. But because the microfiber has a much smaller size than the untapered fiber, the bend is mainly in the microfiber rather than other areas. During the microfiber bending, the spectral dips blueshift and the spacing of dips becomes large accordingly, as detailed in Fig. 2(b). For example, for the curvature changing from 0 to 0.15 mm−1, the dip wavelength blueshifts from 1510.8nm to 1418.9nm with a range of ~91.9 nm and simultaneously, the dip spacing slightly increases from 44.6nm to 51.9nm around wavelength 1500nm.

The mode characteristics can be calculated by considering a scaled-down UVS-INT fiber model with the help of a full-vector finite element method [19

19. M. Koshiba and Y. Tsuji, “Curvillinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18(5), 737–743 (2000). [CrossRef]

]. This model has a diameter ratio between the core and the cladding of 6.1μm/125μm, a core-cladding index contrast of 0.0125, a silica fiber diameter of 20μm, and an interaction length of modes with 10.5mm, respectively. Note that although a UVS-INT fiber contains an inner cladding which is used to heighten the photosensitivity of the fiber, it has been ignored in our calculation due to same index to the outer cladding. The material dispersion of the fused silica [20

20. M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009).

] in the cladding is taken into account. By substituting the effective indices of the modes into Eq. (1), the transmission is calculated and plotted in Figs. 2(a) and 2(b). The calculation shows good agreement with the experimental values. Investigation shows that bending the microfiber increases the intermodal index Δn and thus shifts the wavelength of the interferometer. The variation of wavelength, on the other side, alters the Δn value in Eq. (1) due to the dispersion characteristic of Δn. Normally, Δn becomes large with an increase of wavelength. To understand the behavior of wavelength shift, we take small variations of curvature and wavelength, i.e., δξ and δλ, from Eq. (1) and obtain the phase change δΦ = (2π/λ2)L[λ(∂Δn/∂ξ)⋅δξГδλ], where Г = Δnλ⋅∂Δn/∂λ represents the dispersion factor of the intermodal index. Analysis shows ∂Δn/∂ξ > 0 and Г < 0 within the wavelength region of Fig. 2 and thereby the condition of δΦ = 0 and δξ >0 produces δλ < 0. With an increase of curvature, the wavelength should blueshift to obtain a small Δn and to keep the phase Φ fixed, consistent to the observation in Fig. 2.The small discrepancy between the experimental and theoretical results is mainly attributed to the existence of nonuniform bend in the microfiber along the interaction length of modes.

3. Sensitivity enhancement for refractive index measurement

A variation of external RI can produce different changes to the dissimilar mode indices, leading to a modification of the intermodal index. To further understand the RI sensitivity, the spectral responsivity on external RI can be achieved by taking a small variation of nex from Eq. (1) for Φ to be considered unchanged. After several mathematical treatments, we obtain
S=dλdnex=λΓΔnnex
(3)
From Eq. (3), the determinative parameters of S are the wavelength λ, the RI-induced variation of intermodal index ∂Δn/∂nex, and the dispersion factor Г. An increase of nex can normally generate a larger index increment for the HE12 mode than that for the HE11 mode, producing ∂Δn/∂nex<0. Simultaneously, we have Г < 0 since the group velocity of the HE11 mode is larger than the HE12 mode within the wavelength region shown in Fig. 3. Thereby a positive S is enabled, corresponding to a redshift of wavelength with an increase of external RI, as demonstrated in Fig. 3. According to Eq. (3), an extremely high sensitivity is achieved in case of Γ ~0. The effect of Г on the RI sensitivity is similar to that of the group birefringence in a polarization interferometer [16

16. J. Li, L.-P. Sun, S. Gao, Z. Quan, Y.-L. Chang, Y. Ran, L. Jin, and B.-O. Guan, “Ultrasensitive refractive-index sensors based on rectangular silica microfibers,” Opt. Lett. 36(18), 3593–3595 (2011). [CrossRef] [PubMed]

]. However the polarization interferometer is based on the use of a highly-birefringent microfiber. Generally, the fiber size should be thin sufficiently to produce a large phase birefringence for the RI measurement [16

16. J. Li, L.-P. Sun, S. Gao, Z. Quan, Y.-L. Chang, Y. Ran, L. Jin, and B.-O. Guan, “Ultrasensitive refractive-index sensors based on rectangular silica microfibers,” Opt. Lett. 36(18), 3593–3595 (2011). [CrossRef] [PubMed]

]. The present structure, however, allows interference of the modes with different mode orders, which can exhibit the advantages of simplicity, robustness, and ease of fabrication. Moreover, bending the microfiber can alter the dispersion factor Г and thus change the RI sensitivity from Eq. (3). We conduct a numerical simulation by taking into account the material dispersion of aqueous liquid [21

21. K. F. Palmer and D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am. 64(8), 1107–1110 (1974). [CrossRef]

] using a full-vector finite element method [19

19. M. Koshiba and Y. Tsuji, “Curvillinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18(5), 737–743 (2000). [CrossRef]

]. As shown in Fig. 3(b), the calculated results can agree with the experimental values very well. From Eq. (3), the calculated sensitivities are S ’ = 415.38 nm/RIU, 454.84 nm/RIU, 573.97 nm/RIU, 1035.80 nm/RIU, respectively, around nex = 1.333 and S ’ = 4797.54 nm/RIU, 5389.38 nm/RIU, 6944.23 nm/RIU, 9940.13nm/RIU, respectively, around nex = 1.430, at dips of A~D, respectively. At dip E, the sensitivity is S ’ = 813.28 nm/RIU around nex = 1.333.

To further understand the effect of bending microfiber on the magnitude of sensitivity, Fig. 4(a)
Fig. 4 (a) Modeled sensitivity as a function of bend curvature at wavelength 1350nm. The experimental points are also marked. (b) Dependence of the critical curvature on the fiber diameter at wavelength 1350nm and the wavelength at fiber diameter 20μm, respectively.
models the sensitivity as a function of the bend curvature at a wavelength of 1350 nm. The experimental points are marked as comparison. Other than the redshift at ξ < 0.365 mm−1, the increasing of external RI can induce a blueshift of wavelength at ξ > 0.365 mm−1. Close to the critical curvature of ξ = 0.365 mm−1 (Γ approaches zero), the sensitivity is enhanced significantly. Moreover, Fig. 4(b) plots the calculated critical curvature as a function of the microfiber diameter at wavelength 1350nm and the wavelength at microfiber diameter 20μm, respectively. A larger microfiber diameter or a shorter wavelength is readier to produce the smaller critical curvature, of which the study is useful for design and optimization of the device in real-world applications. Note that the sensitivity shown in Eq. (2) is achieved at a specific wavelength point. Considering a spectral width in a dip, the infinite sensitivity cannot be achieved in practice.

4. Conclusion

Acknowledgments

This work is supported by the National Natural Science Foundation of China (61225023, 61177074, 11004085, and 11104117), the Project of Science and Technology New Star of Zhujiang in Guangzhou city (2012J2200062), the Research Fund for the Doctoral Program of Higher Education of China (20114401110006), and the Guangdong Natural Science Foundation (S2013030013302).

References and links

1.

B. H. Lee and J. Nishii, “Dependence of fringe spacing on the grating separation in a long-period fiber grating pair,” Appl. Opt. 38(16), 3450–3459 (1999). [CrossRef] [PubMed]

2.

G. Laffont and P. Ferdinand, “Tilted short-period fibre-Bragg-grating-induced coupling to cladding modes for accurate refractometry,” Meas. Sci. Technol. 12(7), 765–770 (2001). [CrossRef]

3.

B. Li, L. Jiang, S. Wang, L. Zhou, H. Xiao, and H. L. Tsai, “Ultra-abrupt tapered fiber Mach-Zehnder interferometer sensors,” Sensors (Basel) 11(12), 5729–5739 (2011). [CrossRef] [PubMed]

4.

Z. B. Tian and S. S. Yam, “In-line abrupt taper optical fiber Mach–Zehnder interferometric strain sensor,” IEEE Photon. Technol. Lett. 21(3), 161–163 (2009). [CrossRef]

5.

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18(21), 2239–2241 (2006). [CrossRef]

6.

T. Wei, X. Lan, and H. Xiao, “Fiber inline core–cladding-mode Mach–Zehnder interferometer fabricated by two-point CO2 laser irradiations,” IEEE Photon. Technol. Lett. 21(10), 669–671 (2009). [CrossRef]

7.

J. Yang, L. Jiang, S. Wang, B. Li, M. Wang, H. Xiao, Y. Lu, and H. Tsai, “High sensitivity of taper-based Mach-Zehnder interferometer embedded in a thinned optical fiber for refractive index sensing,” Appl. Opt. 50(28), 5503–5507 (2011). [CrossRef] [PubMed]

8.

M. Zibaii, O. Frazao, H. Latifi, and P. A. S. Jorge, “Controlling the sensitivity of refractive index measurement using a tapered fiber loop mirror,” IEEE Photon. Technol. Lett. 23(17), 1219–1221 (2011). [CrossRef]

9.

Z. B. Tian, S. S. Yam, and H. P. Loock, “Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber,” Opt. Lett. 33(10), 1105–1107 (2008). [CrossRef] [PubMed]

10.

G. Salceda-Delgado, D. Monzon-Hernandez, A. Martinez-Rios, G. A. Cardenas-Sevilla, and J. Villatoro, “Optical microfiber mode interferometer for temperature-independent refractometric sensing,” Opt. Lett. 37(11), 1974–1976 (2012). [CrossRef] [PubMed]

11.

C. Zhong, C. Shen, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, and J. Wang, “Temperature-insensitive optical fiber two-dimensional micrometric displacement sensor based on an in-line Mach–Zehnder interferometer,” J. Opt. Soc. Am. B 29(5), 1136–1140 (2012). [CrossRef]

12.

H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?id=132856. [CrossRef] [PubMed]

13.

G. Brambilla, “Optical fibre nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010). [CrossRef]

14.

H. Xuan, W. Jin, and M. Zhang, “CO2 laser induced long period gratings in optical microfibers,” Opt. Express 17(24), 21882–21890 (2009). [CrossRef] [PubMed]

15.

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: A Review,” Sensors (Basel) 12(12), 8861–8876 (2012). [CrossRef] [PubMed]

16.

J. Li, L.-P. Sun, S. Gao, Z. Quan, Y.-L. Chang, Y. Ran, L. Jin, and B.-O. Guan, “Ultrasensitive refractive-index sensors based on rectangular silica microfibers,” Opt. Lett. 36(18), 3593–3595 (2011). [CrossRef] [PubMed]

17.

D. T. Cassidy, D. C. Johnson, and K. O. Hill, “Wavelength-dependent transmission of monomode optical fiber tapers,” Appl. Opt. 24(7), 945–950 (1985). [CrossRef] [PubMed]

18.

D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. A 66(3), 216–220 (1976). [CrossRef]

19.

M. Koshiba and Y. Tsuji, “Curvillinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18(5), 737–743 (2000). [CrossRef]

20.

M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009).

21.

K. F. Palmer and D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am. 64(8), 1107–1110 (1974). [CrossRef]

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(230.1150) Optical devices : All-optical devices
(230.3990) Optical devices : Micro-optical devices
(260.3160) Physical optics : Interference

ToC Category:
Sensors

History
Original Manuscript: September 3, 2013
Revised Manuscript: October 20, 2013
Manuscript Accepted: October 23, 2013
Published: October 29, 2013

Citation
Li-Peng Sun, Jie Li, Yanzhen Tan, Shuai Gao, Long Jin, and Bai-Ou Guan, "Bending effect on modal interference in a fiber taper and sensitivity enhancement for refractive index measurement," Opt. Express 21, 26714-26720 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26714


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References

  1. B. H. Lee and J. Nishii, “Dependence of fringe spacing on the grating separation in a long-period fiber grating pair,” Appl. Opt.38(16), 3450–3459 (1999). [CrossRef] [PubMed]
  2. G. Laffont and P. Ferdinand, “Tilted short-period fibre-Bragg-grating-induced coupling to cladding modes for accurate refractometry,” Meas. Sci. Technol.12(7), 765–770 (2001). [CrossRef]
  3. B. Li, L. Jiang, S. Wang, L. Zhou, H. Xiao, and H. L. Tsai, “Ultra-abrupt tapered fiber Mach-Zehnder interferometer sensors,” Sensors (Basel)11(12), 5729–5739 (2011). [CrossRef] [PubMed]
  4. Z. B. Tian and S. S. Yam, “In-line abrupt taper optical fiber Mach–Zehnder interferometric strain sensor,” IEEE Photon. Technol. Lett.21(3), 161–163 (2009). [CrossRef]
  5. K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett.18(21), 2239–2241 (2006). [CrossRef]
  6. T. Wei, X. Lan, and H. Xiao, “Fiber inline core–cladding-mode Mach–Zehnder interferometer fabricated by two-point CO2 laser irradiations,” IEEE Photon. Technol. Lett.21(10), 669–671 (2009). [CrossRef]
  7. J. Yang, L. Jiang, S. Wang, B. Li, M. Wang, H. Xiao, Y. Lu, and H. Tsai, “High sensitivity of taper-based Mach-Zehnder interferometer embedded in a thinned optical fiber for refractive index sensing,” Appl. Opt.50(28), 5503–5507 (2011). [CrossRef] [PubMed]
  8. M. Zibaii, O. Frazao, H. Latifi, and P. A. S. Jorge, “Controlling the sensitivity of refractive index measurement using a tapered fiber loop mirror,” IEEE Photon. Technol. Lett.23(17), 1219–1221 (2011). [CrossRef]
  9. Z. B. Tian, S. S. Yam, and H. P. Loock, “Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber,” Opt. Lett.33(10), 1105–1107 (2008). [CrossRef] [PubMed]
  10. G. Salceda-Delgado, D. Monzon-Hernandez, A. Martinez-Rios, G. A. Cardenas-Sevilla, and J. Villatoro, “Optical microfiber mode interferometer for temperature-independent refractometric sensing,” Opt. Lett.37(11), 1974–1976 (2012). [CrossRef] [PubMed]
  11. C. Zhong, C. Shen, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, and J. Wang, “Temperature-insensitive optical fiber two-dimensional micrometric displacement sensor based on an in-line Mach–Zehnder interferometer,” J. Opt. Soc. Am. B29(5), 1136–1140 (2012). [CrossRef]
  12. H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express15(9), 5711–5720 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?id=132856 . [CrossRef] [PubMed]
  13. G. Brambilla, “Optical fibre nanowires and microwires: a review,” J. Opt.12(4), 043001 (2010). [CrossRef]
  14. H. Xuan, W. Jin, and M. Zhang, “CO2 laser induced long period gratings in optical microfibers,” Opt. Express17(24), 21882–21890 (2009). [CrossRef] [PubMed]
  15. J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: A Review,” Sensors (Basel)12(12), 8861–8876 (2012). [CrossRef] [PubMed]
  16. J. Li, L.-P. Sun, S. Gao, Z. Quan, Y.-L. Chang, Y. Ran, L. Jin, and B.-O. Guan, “Ultrasensitive refractive-index sensors based on rectangular silica microfibers,” Opt. Lett.36(18), 3593–3595 (2011). [CrossRef] [PubMed]
  17. D. T. Cassidy, D. C. Johnson, and K. O. Hill, “Wavelength-dependent transmission of monomode optical fiber tapers,” Appl. Opt.24(7), 945–950 (1985). [CrossRef] [PubMed]
  18. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. A66(3), 216–220 (1976). [CrossRef]
  19. M. Koshiba and Y. Tsuji, “Curvillinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol.18(5), 737–743 (2000). [CrossRef]
  20. M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009).
  21. K. F. Palmer and D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am.64(8), 1107–1110 (1974). [CrossRef]

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