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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 9996–10009
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Highly sensitive in-fiber interferometric refractometer with temperature and axial strain compensation

Jeremie Harris, Ping Lu, Hugo Larocque, Yanping Xu, Liang Chen, and Xiaoyi Bao  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 9996-10009 (2013)
http://dx.doi.org/10.1364/OE.21.009996


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Abstract

A novel fiber-optic refractometer is proposed and demonstrated to achieve temperature- and axial strain-compensated refractive index measurement using highly sensitive outer-cladding modes in a tapered bend-insensitive fiber based Mach-Zehnder interferometer. Peak wavelength shifts associated with different spatial frequency peaks are calibrated to obtain a wavelength-related character matrix λMRI,T,ε for simultaneous measurement of multiple environmental variables. A phase-related character matrix ΦMRI,T,ε is also acquired by direct determination of refractive index, temperature, and axial strain induced phase shifts of the corresponding sensing modes.

© 2013 OSA

1. Introduction

2. Operation principle

The bend-insensitive fiber (ClearCurve, Corning) consists of a germanium-doped silica core and pure-silica cladding, having a structure similar to a standard single-mode fiber, except that numerous nano-scale gas filled voids are embedded in the cladding [30

30. M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” J. Lightwave Technol. 27(3), 376–382 (2009). [CrossRef]

]. Figure 1(a)
Fig. 1 (a) A SEM cross-sectional image of the bend-insensitive fiber etched with 5% hydrofluoric acid solution for 2 minutes; (b) A schematic illustration of the tapered bend-insensitive fiber based Mach-Zehnder interferometer under various external disturbances with an inset of the abrupt taper picture.
shows a Scanning Electron Microscopy (SEM) picture of the BIF cross-section where a narrow layer of randomly distributed air holes divides the cladding region into the inner-cladding and outer-cladding sub-regions. The proposed in-fiber interferometric sensor consists of a length of the BIF onto which a pair of abrupt tapers is fabricated, with the plastic coating between tapers removed to create a multi-parameter sensing zone, as shown in Fig. 1(b). The pristine BIF is designed to confine the energy in the fiber core region via reflection at the low-index trench and thus reduce its bending loss. Fiber tapering can drive the concentrated energy to propagate in the outer-cladding region of the modified BIF. Input light travels in the fundamental mode of the BIF until it reaches the first taper, where its energy is partially coupled to a number of cladding modes, while a large portion of the energy remains in the fundamental mode, which continues to propagate with negligible optical loss along the middle coating stripped section. Upon reaching the second taper, much of the cladding mode energy is coupled back to the fundamental mode, so that the device constitutes a tapered bend-insensitive fiber based Mach-Zehnder interferometer. The excited cladding modes may be classified into two categories, namely the inner-cladding modes (IC) and outer-cladding modes (OC), according to their respective mode field patterns. The former are characterized by mode-field distribution within the inner-cladding region due to total internal reflection made possible by the presence of the depressed-index trench, and the latter by mode-field sandwiched in the outer-cladding region between the depressed-index trench and the environmental air media.

The optical path length (OPL) difference between the fundamental mode of LP01 and a given cladding mode of LPij propagating through an interferometer of length L at operation wavelength λ leads to a phase difference given by
ΔΦij=Φ01Φij=2πLλ(neff01neffij)=2πΔneffijLλ,
(1)
where ∆nijeff represents the difference between the effective refractive indices of the two modes. When the phase difference between the core mode of LP01 and a cladding mode of LPij is equal to 2, an interference maximum is observed in the transmission spectrum, for which the m-order peak wavelength is located at

λmij=ΔneffijLm.
(2)

The intensity of the core and cladding modes interference spectrum is thus expressed by

I=I01+ijIij+2ijI01Iijcos(2πΔneffijLλ).
(3)

Since O(∆nijeff) ≈10−3, L = 10−1 m, and O(λ) ≈10−6 m, then O(∆nijeffL/λ) ≈102. Thus the optical path length difference ∆OPL = ∆nijeffL between the core and cladding modes is large enough that ∆nijeffL >> λ and m >> 1, the separation between successive maxima in the interference spectrum may be approximated to
Δλij=λm1ijλmijλ02ΔneffijL,
(4)
where λ0 is the center wavelength in the wavelength span. The interference between the fundamental mode and a particular outer-cladding mode of LPij will therefore result in an oscillating interference pattern with a period of ∆λij corresponding to intensity peak at a spatial frequency ξij which can be expressed as

ξij=1ΔλijΔneffijLλ02.
(5)

The demodulation method of the multiplexed signal of a tapered bend-insensitive fiber based Mach-Zehnder interferometer is depicted in Fig. 2
Fig. 2 Flow chart of the demodulation algorithm for an interference spectrum between the fundamental mode and multiple cladding modes.
. The Fast Fourier Transform (FFT) of the interference spectrum is first performed, showing multiple peaks in the spatial frequency domain of the received signal that correspond to different groups of cladding modes. The application of a narrow band-pass filter with a rectangle window function to the original interference spectrum allowed individual spatial frequency components to be isolated and transformed back to the wavelength domain, where their phase information is extracted in the form of filtered interference spectra accordingly. Since the measured spectrum is only for a limited wavelength range, the FFT makes an implicit assumption that the spectrum is repetitive outside the measured interval. Thus in the filtered interference spectra, a low-frequency sinusoidal envelope due to the presumed repeating spectral properties is always superimposed on a high-frequency sinusoidal signal corresponding to a specific cladding mode. In this way, each peak in the FFT spectrum could be calibrated separately for its filtered spectral shift response to different environmental parameters such as refractive index, temperature, and axial strain. A second calibration is achieved by directly considering phase responses of multiple peaks in the FFT spectrum to provide another means of carrying out temperature- and axial strain-compensated refractive index measurement. As changes occur in environmental parameters, the difference in the effective refractive indices between the core mode and one specific cladding mode, ∆neff, will change correspondingly to (∆neff + δ(∆neff)), and lead to a peak wavelength shift δλ in the position of the m-order peak of each spatial frequency component originally at λ to a new position λ' in the interference spectrum. The peak wavelength shift δλ and an associated phase shift δΦ can be expressed using Eqs. (6.1)-(6.2). It is obvious that the peak wavelength and phase will shift in opposite directions with changing environmental parameters.

δλ=δ(ΔneffLm)=(δ(Δneff)Δneff)λ,
(6.1)
δΦ=δ(2πλ02ξλ)=2πξδλ.
(6.2)

The spectral shifts accompanying changes in concentrations of external solutions may be explained by considering that an increase in external refractive index causes a corresponding increase δ(∆neff,RI) in the effective refractive index of the cladding modes, while leaving the core mode essentially unaffected. Thus the interference peak wavelength blueshift and the corresponding phase redshift due to an increase in the external refractive index is

δλ=(δ(Δneff,RI)Δneff)λ,
(7.1)
δΦ=2πLδ(Δneff,RI)λ.
(7.2)

Temperature changes also produce peak wavelength shifts in the spectral interference between the fundamental mode and the cladding modes, since the thermo-optic coefficient of the germanium-doped silica core is greater than that of the pure silica cladding. As a result, the effective refractive index of the core will increase more rapidly than cladding modes by an amount δ(∆neff,T). Therefore the interference peak wavelength redshift and the corresponding phase blueshift with increasing surrounding temperature are given by

δλ=(δ(Δneff,T)Δneff)λ,
(8.1)
δΦ=2πLδ(Δneff,T)λ.
(8.2)

An axial strain ε applied on the fiber will cause an increase δL in the interferometer length, along with a change δ(∆neff,ε) in the refractive index difference between the core and cladding modes induced by the photo-elastic effect and waveguide geometry effect. This also results in relocation of a given interference maximum from λ to λ' with
δλ=(δLL+δ(Δneff,ε)Δneff,ε)λ,
(9.1)
The peak wavelength shift is induced by changes in both the fiber interferometer length (first term) and the effective refractive index difference (second term). The second term is contributed by the longitudinal stress induced photoelastic effect and the fiber geometry modification due to a change in the fiber diameter. Provided that the fiber is elastic and mechanically homogeneous, the increasing fiber length will decrease the fiber diameter, and the difference in the effective refractive index between the fundamental mode and cladding modes will be altered due to the change in the fiber transverse index profile. Therefore interference peak wavelength blueshifts and redshifts are both possible, depending upon the sign of δ(∆neff,ε) and the relative magnitudes of δL/L and δ(∆neff,ε)/∆neff,ε. The corresponding phase shift can be expressed by

δΦ=2π(Δneff,εδL+Lδ(Δneff,ε))λ.
(9.2)

3. Experimental methods

The abrupt tapers were created on the bend-insensitive fiber using a fusion splicer (Ericsson, FA995) with a custom taper fabrication program. An optical micrograph of the taper with a waist diameter of 50 µm and a length of 700 µm is shown in the inset of Fig. 1(b). The in-fiber Mach-Zehnder interferometer was constructed by fabricating two identical tapers separated by a distance L = 10.0 cm along the BIF. A 50:50 fiber coupler was used to combine outputs from L- and C-band erbium-doped fiber amplifiers. The resultant signal was sent to the input end of the BIF interferometer, which was in turn connected to an optical spectrum analyzer (Agilent, 86142A) with a wavelength resolution of 0.06 nm, from which a transmission spectrum comprising 10,000 data points over a spectral range of 1520 nm to 1610 nm could be observed and recorded. During the refractive index calibration procedure, the peak wavelength and phase shifts associated with the spatial frequencies under consideration were determined by submerging the tapered bend-insensitive fiber in a series of solutions consisting of varying concentrations of glycerol solution at a constant 20.0 °C. The percent by weight of glycerol in these solutions could be used to determine the solution refractive index. Temperature calibration was achieved by mounting the fiber interferometer in an oven with temperature resolution of 0.1 °C. Strain measurements were carried out by suspending the fiber interferometer horizontally between a motorized translational platform and a stationary platform, each end of the fiber being fixed to their respective positions with super glue. The motorized platform was driven to move along the axis of the BIF-MZI so as to stretch the fiber longitudinally by sequential strain increases of 200 microstrain, while the relative zero-strain was determined as the fiber was stretched to a particular pre-strain state.

Figure 3(a)
Fig. 3 (a) Transmission spectrum of the BIF-MZI suspended in air at 24.6 °C with zero-strain; (b) FFT spectrum of the BIF-MZI with an inset of the simulated mode field patterns of the fundamental mode, IC mode, OC-1 mode, the OC-2 mode, the OC-3 mode, and OC-4 mode respectively.
shows a typical interference spectrum for the case of the BIF-MZI suspended in air at 24.6 °C with zero-strain. Figure 3(b) shows a corresponding FFT spectrum where distinct peaks at spatial frequencies of 0, 0.0444 nm−1, 0.0888 nm−1, 0.1333 nm−1, 0.1555 nm−1 and 0.1777 nm−1 are visible. The differences between the effective refractive indices of the core mode and specific cladding-modes are calculated using the spatial frequencies of the respective FFT peaks in Fig. 3(b) according to Eq. (5). Then a finite element analysis using COMSOL Multiphysics is carried out to simulate the effective mode indices and mode field patterns of both the fundamental mode and different cladding modes. When the simulated effective index difference between the fundamental mode and one cladding mode matches the calculated result of one particular FFT peak, its mode field pattern is obtained with the result presented in the inset of Fig. 3(b). The simulation results clearly show that the indicated peaks correspond to the fundamental mode LP01 (0 nm−1), inner cladding mode IC (0.0444 nm−1), and groups of outer-cladding modes, hereafter referred to as the OC-1 (0.0888 nm−1), OC-2 (0.1333 nm−1), OC-3 (0.1777 nm−1) and OC-4 (0.1555 nm−1) modes, respectively. It is noted that the spatial frequency peak with highest intensity corresponding to the OC-4 mode is located between the OC-2 mode and the OC-3 mode, which may tend to cause crosstalk problem and exhibit poor linearity under changes in external refractive index, temperature, and axial strain. It is clear that the optical fields of all these outer-cladding modes are effectively confined to the outer-cladding region due to the presence of the depressed-index trench which is treated as a pure air layer in a simplified structural model with custom mesh parameters over the geometry. However the higher-order outer-cladding mode (OC-3) has a greater number of intensity nodes along the radial direction than the lower-order outer-cladding mode (OC-1). Furthermore, the optical field intensity of the higher-order outer-cladding mode is pushed radially toward the depressed-index trench. Therefore the OC-3 mode has a smaller effective index and larger effective index difference from the fundamental mode and consequently higher spatial frequency than those of the OC-1 mode with an optical field concentrated closer to the cladding-environment boundary, as indicated by Eq. (5).

Figure 4(a)
Fig. 4 (a) Filtered transmission spectra of the BIF-MZI corresponding to isolated spatial frequency components; (b) Spatial frequency dependent phase spectrum of the BIF-MZI.
presents the filtered interference spectra corresponding to extracted 0.0888 nm−1, 0.1333 nm−1, and 0.1777 nm−1 spatial frequency components obtained from Fig. 3. According to Eq. (4) and (5), the peak wavelength separation is the reciprocal of the spatial frequency. Thus the higher-order outer-cladding mode (OC-3) with a larger spatial frequency has shorter wavelength spacing than the lower-order outer-cladding mode (OC-1). A plot of the phase spectrum in the spatial frequency domain is shown in Fig. 4(b), where the normalized phase in the range of 0 to 2π was computed using the Fourier transform method at each spatial frequency.

4. Experimental results and discussion

The OC1-, OC2-, and OC3-modes indicated in Fig. 3(b), corresponding to the FFT peaks at 0.0888 nm−1, 0.1333 nm−1 and 0.1777 nm−1, were selected for simultaneous refractive index, temperature, and axial strain sensing based on the consistency of their responses to each of the environmental parameters investigated in the experiment. Both the peak wavelength and the phase responses associated with individual outer-cladding modes were studied. Figure 5
Fig. 5 Transmission spectra of the BIF-MZI submerged in solutions of 10% and 25% glycerol at 20.0 °C with zero-strain.
shows the transmission spectra of the BIF-MZI submerged in solutions of 10% and 25% glycerol at 20.0 °C with zero-strain.

Figure 6
Fig. 6 Filtered transmission spectra of the BIF-MZI in solutions of 10% and 25% glycerol corresponding to different groups of outer-cladding modes of (a) the OC-1 mode, (b) the OC-2 mode, and (c) the OC-3 mode.
presents overlays of filtered frequency components obtained by submerging the BIF-MZI in 10% and 25% glycerol with the OC-1, OC-2, and OC-3 modes shown in Fig. 6(a)-6(c), respectively. The expected spectral blueshifts are clearly visible for different outer-cladding modes, and the magnitude of the peak wavelength shifts are seen to differ from one mode to the next. Figure 7
Fig. 7 Spatial frequency dependent phase spectra of the BIF-MZI in solutions of 10% and 25% glycerol.
shows the spatial frequency dependent phase spectra of the BIF-MZI in solutions of 10% and 25% glycerol, along with the isolated 0.0888 nm−1, 0.1333 nm−1 and 0.1777 nm−1 spatial frequency components. All three spatial frequency components were found to experience the expected phase redshifts, and associated peak wavelength shifts, in opposing directions.

4. Conclusion

Acknowledgments

The research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants and Canada Research Chairs (CRC) Program. Ping Lu would like to acknowledge the Province of Ontario Ministry of Research and Innovation and the University of Ottawa for the financial support of the Vision 2020 Postdoctoral Fellowship.

References and links

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2.

P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett. 30(11), 1273–1275 (2005). [CrossRef] [PubMed]

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Q. Wang and G. Farrell, “All-fiber multimode-interference-based refractometer sensor: proposal and design,” Opt. Lett. 31(3), 317–319 (2006). [CrossRef] [PubMed]

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M. C. Phan Huy, G. Laffont, V. Dewynter, P. Ferdinand, P. Roy, J.-L. Auguste, D. Pagnoux, W. Blanc, and B. Dussardier, “Three-hole microstructured optical fiber for efficient fiber Bragg grating refractometer,” Opt. Lett. 32(16), 2390–2392 (2007). [CrossRef] [PubMed]

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C. Caucheteur, M. Wuilpart, C. Chen, P. Mégret, and J. Albert, “Quasi-distributed refractometer using tilted Bragg gratings and time domain reflectometry,” Opt. Express 16(22), 17882–17890 (2008). [CrossRef] [PubMed]

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T. Guo, H.-Y. Tam, P. A. Krug, and J. Albert, “Reflective tilted fiber Bragg grating refractometer based on strong cladding to core recoupling,” Opt. Express 17(7), 5736–5742 (2009). [CrossRef] [PubMed]

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K. Zhou, Z. Yan, L. Zhang, and I. Bennion, “Refractometer based on fiber Bragg grating Fabry-Pérot cavity embedded with a narrow microchannel,” Opt. Express 19(12), 11769–11779 (2011). [CrossRef] [PubMed]

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J. Wo, G. Wang, Y. Cui, Q. Sun, R. Liang, P. P. Shum, and D. Liu, “Refractive index sensor using microfiber-based Mach-Zehnder interferometer,” Opt. Lett. 37(1), 67–69 (2012). [CrossRef] [PubMed]

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O. Frazão, L. A. Ferreira, and F. M. Araújo, “Applications of fiber optic grating technology to multi-parameter measurement,” Fiber Integr. Opt. 24(3–4), 227–244 (2005).

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Y.-J. Rao, Y.-P. Wang, Z.-L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21(5), 1320–1327 (2003). [CrossRef]

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R. Yang, Y.-S. Yu, C. Chen, Y. Xue, X.-L. Zhang, J.-C. Guo, C. Wang, F. Zhu, B.-L. Zhang, Q.-D. Chen, and H.-B. Sun, “S-tapered fiber sensors for highly sensitive measurement of refractive index and axial strain,” J. Lightwave Technol. 30(19), 3126–3132 (2012). [CrossRef]

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M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” J. Lightwave Technol. 27(3), 376–382 (2009). [CrossRef]

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OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(060.4005) Fiber optics and optical communications : Microstructured fibers

ToC Category:
Sensors

History
Original Manuscript: February 19, 2013
Revised Manuscript: March 30, 2013
Manuscript Accepted: April 5, 2013
Published: April 15, 2013

Citation
Jeremie Harris, Ping Lu, Hugo Larocque, Yanping Xu, Liang Chen, and Xiaoyi Bao, "Highly sensitive in-fiber interferometric refractometer with temperature and axial strain compensation," Opt. Express 21, 9996-10009 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9996


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References

  1. S. Singh, “Refractive index measurement and its applications,” Phys. Scr.65(2), 167–180 (2002). [CrossRef]
  2. P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett.30(11), 1273–1275 (2005). [CrossRef] [PubMed]
  3. Q. Wang and G. Farrell, “All-fiber multimode-interference-based refractometer sensor: proposal and design,” Opt. Lett.31(3), 317–319 (2006). [CrossRef] [PubMed]
  4. M. C. Phan Huy, G. Laffont, V. Dewynter, P. Ferdinand, P. Roy, J.-L. Auguste, D. Pagnoux, W. Blanc, and B. Dussardier, “Three-hole microstructured optical fiber for efficient fiber Bragg grating refractometer,” Opt. Lett.32(16), 2390–2392 (2007). [CrossRef] [PubMed]
  5. C. Caucheteur, M. Wuilpart, C. Chen, P. Mégret, and J. Albert, “Quasi-distributed refractometer using tilted Bragg gratings and time domain reflectometry,” Opt. Express16(22), 17882–17890 (2008). [CrossRef] [PubMed]
  6. T. Guo, H.-Y. Tam, P. A. Krug, and J. Albert, “Reflective tilted fiber Bragg grating refractometer based on strong cladding to core recoupling,” Opt. Express17(7), 5736–5742 (2009). [CrossRef] [PubMed]
  7. O. Frazão, T. Martynkien, J. M. Baptista, J. L. Santos, W. Urbanczyk, and J. Wojcik, “Optical refractometer based on a birefringent Bragg grating written in an H-shaped fiber,” Opt. Lett.34(1), 76–78 (2009). [CrossRef] [PubMed]
  8. M. Han, F. W. Guo, and Y. F. Lu, “Optical fiber refractometer based on cladding-mode Bragg grating,” Opt. Lett.35(3), 399–401 (2010). [CrossRef] [PubMed]
  9. Q. Wu, Y. Semenova, P. Wang, and G. Farrell, “High sensitivity SMS fiber structure based refractometer--analysis and experiment,” Opt. Express19(9), 7937–7944 (2011). [CrossRef] [PubMed]
  10. K. Zhou, Z. Yan, L. Zhang, and I. Bennion, “Refractometer based on fiber Bragg grating Fabry-Pérot cavity embedded with a narrow microchannel,” Opt. Express19(12), 11769–11779 (2011). [CrossRef] [PubMed]
  11. J. Wo, G. Wang, Y. Cui, Q. Sun, R. Liang, P. P. Shum, and D. Liu, “Refractive index sensor using microfiber-based Mach-Zehnder interferometer,” Opt. Lett.37(1), 67–69 (2012). [CrossRef] [PubMed]
  12. O. Frazão, L. A. Ferreira, and F. M. Araújo, “Applications of fiber optic grating technology to multi-parameter measurement,” Fiber Integr. Opt.24(3–4), 227–244 (2005).
  13. Y.-J. Rao, Y.-P. Wang, Z.-L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol.21(5), 1320–1327 (2003). [CrossRef]
  14. R. Yang, Y.-S. Yu, C. Chen, Y. Xue, X.-L. Zhang, J.-C. Guo, C. Wang, F. Zhu, B.-L. Zhang, Q.-D. Chen, and H.-B. Sun, “S-tapered fiber sensors for highly sensitive measurement of refractive index and axial strain,” J. Lightwave Technol.30(19), 3126–3132 (2012). [CrossRef]
  15. P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett.94(13), 131110 (2009). [CrossRef]
  16. D. J. J. Hu, J. L. Lim, M. Jiang, Y. Wang, F. Luan, P. P. Shum, H. Wei, and W. Tong, “Long period grating cascaded to photonic crystal fiber modal interferometer for simultaneous measurement of temperature and refractive index,” Opt. Lett.37(12), 2283–2285 (2012). [CrossRef] [PubMed]
  17. H.-J. Kim, O.-J. Kwon, S. B. Lee, and Y.-G. Han, “Polarization-dependent refractometer for discrimination of temperature and ambient refractive index,” Opt. Lett.37(11), 1802–1804 (2012). [CrossRef] [PubMed]
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