Abstract

In this paper, temperature compensated microfiber Bragg grating (mFBG) is realized by use of a liquid with a negative thermo-optic coefficient. The effects of grating elongation and the index change of silica glass are compensated by refractive index change of the liquid through evanescent-field interaction. A reduced thermal sensitivity of 0.67 pm/°C is achieved, which is 1/15 in magnitude of the uncompensated counterparts. Further theoretical analysis demonstrates that temperature insensitivity can be obtained with different combinations of microfiber diameter and the refractive index/thermal optic coefficient of the employed liquid. The proposed method is promising due to the compactness and high flexibility of the device.

© 2012 OSA

1. Introduction

Fiber Bragg grating (FBG) is one of the most important photonic elements in fiber optic communication and sensing systems. Temperature compensation for FBGs have been investigated in the past years, for the requirement of minimizing the temperature/strain cross sensitivity for accurate measurement for FBG sensors, and the implementation of a highly environmentally stable optical filters in fiber communications. Temperature insensitivity has been achieved by bonding or embedding a FBG into a material with negative thermal expansion coefficients [13] or two materials with different thermal-expansion coefficients [4, 5]. Complex mechanic structures, e. g., a lever configuration [6], have also been proposed. In these approaches, a thermally induced compressive stress over the grating is created due to the difference in thermal expansion, which effectively compensates the expansion of the grating. Alternatively, liquids and liquid crystals with negative thermo-optic coefficients can be used to alter the temperature sensitivity through the interaction with the mode field. This has been first implemented by using a liquid-core fiber with gratings inscribed in the fiber cladding [7]. Recently, microstructured optical fibers with holy cladding have also been used for temperature compensation for FBGs by filling selected liquid into the air holes [8, 9]. However, the fabrication of the fibers is expensive and the requirement of geometrical precision is high. Furthermore, the connection between single-mode fibers and these specialty fibers could introduce considerable insertion loss.

Microfibers, optical fibers with micron-scaled diameters, have received great interest due to the exceptional advantages including compact sizes, highly flexible structures, and low transmission loss with extreme bends [10, 11]. The tapered microfibers present natural compatibility to conventional single mode fibers. The minimal insertion loss can be less than 0.1 dB for an adiabatic tapered microfiber. In addition, the interaction between the light and surrounding medium is possible due to the strong evanescent field [12, 13]. The modal properties, including the propagation constants and transverse mode profiles can be significantly modified by immersing the microfiber into a selected liquid. Consequently, tunable photonic devices and refractive-index (RI) sensors for potential biomedical applications can be implemented. In this paper, temperature compensation of Bragg gratings in microfibers is demonstrated by immersing the grating into a liquid with a negative thermo-optic coefficient. The effects of grating elongation and index change of silica can be compensated due to the evanescent-field interaction between the light and the liquid. The Bragg wavelength shifts by only 30 pm when the temperature changes from 15 to 60 °C for the mFBG with the optimal diameter. The corresponding sensitivity is 0.67 pm/°C, which is 1/15 of that of the uncompensated grating. Further theoretical analysis demonstrates that the temperature insensitivity can be realized with different liquids and matched microfiber diameters. The proposed method is promising for sensing and communication applications due to the compact structure and high flexibility.

2. Principle

The Bragg wavelength λB of a mFBG immersed into a liquid can be expressed by the well-known phase-matching condition

λB=2neffΛ
where neff is the effective index of the fundamental mode and Λ is grating pitch. The temperature sensitivity can be expressed by
dλBdT=λB(α+β)
where α=1ΛdΛdT denotes the thermal expansion coefficient of silica glass, which measures the effect of grating elongation, and β=1neffdneffdT is the effective thermal-optic coefficient, which represents the influence of temperature on the modal properties of the microfiber. The influence of transverse thermal expansion of the microfiber is ignored in this paper. For the waveguide structure composed by the silica “core” and liquid “cladding”, whose material indexes are nsi and nliq, respectively, the wavelength-temperature dependence can be extended as
dλBdT=λB(α+1neff(dneffdnsiηsi+dneffdnliqηliq))
where ηsi=dnsidT and ηliq=dnliqdTare the thermal-optic coefficients of silica and the employed liquid, respectively. The dependence of the fundamental-mode index on material index dneffdnsi and dneffdnliq and the thermal expansion coefficient α and ηsi are all positive. Consequently, it is possible to achieve temperature insensitivity, i. e., dλBdT=0, by using a liquid with a negative thermal-optic coefficient ηliq. Note that the contrast between dneffdnsi and dneffdnliqis critical for the compensation, which is determined by the transverse index profile of the silica-liquid waveguide. The microfiber diameter needs to be optimized to reach a balance between the contribution of grating elongation/index change of silica and the effect of the liquid.

3. Experimental result

The microfibers are fabricated by tapering standard single-mode fibers by means of the heat-and-draw method. The heat source is a 2 mm wide flame generated by the burning of butane. The heat source scans along fiber length back and forth while stretching the fiber with two computer-controlled linear stages. The geometrical parameters, including the microfiber diameter and waist length, are mainly determined by the moving speed and range of the linear stages. The moving speeds of the stages and the heat source have been optimized to minimize the transmission loss. The lengths of the uniform region and transition region of the fiber taper are 3 cm and 3.5 cm, respectively.

Bragg gratings are inscribed into the microfibers by use of a 193 nm ArF excimer laser and a phase mask [14]. The repetition rate is 200 Hz and the single pulse energy is 3 mJ. The grating pitch is 1089.21 nm. The grating length is 3 mm, which is determined by the 193 nm laser beam dimension. The calculated exposure dosage is estimated as 7.2 kJ. The growth of grating is monitored by use of a SLED light source and an optical spectrum analyzer (OSA), with a resolution of 0.05 nm.

The employed liquid for temperature compensation is ethanol with a purity of 99.8%. Its refractive index of the liquid at 20 °C is nliq = 1.36048 and the thermo-optic coefficient is ηliq = dnliq/dT = −4 × 10−4. Bragg grating is inscribed in a microfiber with a diameter of D = 5.2 μm, which has been optimized in advance to achieve temperature insensitivity. The measured temperature sensitivity of the uncompensated grating is 10 pm/°C. The microfiber is then immersed into the liquid and the reflection spectrum is measured under different temperatures. Figure 1(a) shows the measured reflection spectra at 15 and 60 °C, respectively. The reflection peak blue-shifts by only 30 pm and the spectral profile hardly changes. The weaker reflection band at the short wavelength side is a result of unapodized longitudinal profile of the index modulation. The spectral quality can be improved by enhancing the coupling strength as described in [15] and creating an apodized index modulation. Figure 1(b) shows the measured Bragg wavelength as a function of temperature. The temperature sensitivity is −0.67 pm/°C for the compensated mFBG and it is 1/15 in magnitude of the uncompensated counterparts. For comparison, the measured temperature responses for two mFBGs with different diameters are also shown in Fig. 1(b). The 10.2-μm mFBG presents a temperature sensitivity of 8.73 pm/°C, which is close to the uncompensated grating. In contrast, the 4-μm mFBG presents a sensitivity of −9.68 pm/°C, suggesting that the temperature sensitivity has been over-compensated.

 

Fig. 1 (a) Measured reflection spectra of the immersed mFBG with a diameter of 5.2 µm measured at 15°C and 60°C, respectively; (b) Measured wavelength shifts as a function of temperature for the immersed mFBGs with different diameters. The curves are linear fits for individual responses.

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4. Discussion

The above experimental result suggests that the temperature sensitivity of the immersed mFBG is largely determined by the microfiber diameter for a given liquid. To better understand the result, detailed theoretical analysis is carried out. Figure 2 shows the calculated fundamental-mode profiles for microfibers with diameters of 4.0μm, 5.2μm and 10.2μm, respectively, calculated by use of a mode solver based on finite-element-method (FEM). The 10.2-μm microfiber presents a tight confinement of the fundamental mode. The evanescent field is very weak and the liquid can hardly affect the modal property of the silica microfiber, corresponding to a small amplitude of dneffdnliqin Eq. (3). In contrast, the 4-μm microfiber presents a considerable portion of mode energy in the form of evanescent field in liquid, which effectively increases the value of dneffdnliq in contrast with dneffdnsi. As a result, a negative temperature sensitivity can be observed due to the strong interaction between light and the liquid.

 

Fig. 2 Calculated transverse energy distribution of microfibers along the fiber diameter, (a) D = 4µm; (b) D = 5.2µm; (c) D = 10.2µm.

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Figure 3 shows the calculated and measured temperature sensitivities for the mFBGs immersed in the ethanol as a function of fiber diameter. The sensitivity is then obtained based on the phase-matching condition. The thermal expansion coefficient and thermal optic coefficient of silica are α = 5 × 10−7/°C and ηsi = 6 × 10−6/°C, respectively. In the calculation, these coefficients are considered invariant with temperature and the modal dispersion is ignored. The optimal microfiber diameter is Dopt = 5.3 μm to obtain temperature insensitivity. The measured result is in good agreement with the calculated curve. When the diameter is down to about 2 μm, the temperature sensitivity can be as high as −100 pm/°C, as a result of much stronger evanescent-field interaction, which indicates that the proposed method can also be used to greatly enhance the temperature sensitivity. However, the reflection peak of mFBG with such small diameter is difficult to observe due to the low transverse overlap between the mode energy and the grating region.

 

Fig. 3 Calculated and measured temperature sensitivity as a function of microfiber diameter for the mFBG immersed in ethanol.

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According to Eq. (3), the compensation capability of the liquid can be enhanced by two means: (1) using a liquid with larger ηliq; (2) enhancing the evanescent-field interaction, i. e., increasing dneffdnliq in contrast with dneffdnsi, which can be realized by decreasing microfiber diameter or using liquid with a RI closer to silica. As a result, temperature insensitivity can be obtained with different combinations of D, nliq and ηliq. Figure 4 shows the calculated optimal fiber diameters Dopt to achieve temperature sensitivity as a function of ηliq for different nliq. The optimal diameters are obtained by plotting the sensitivity-diameter curves as shown in Fig. 3 for individual nliq and ηliq. The curves represent the individual combinations of D, nliq and ηliq which can result in temperature insensitivity. The upper and lower regions of the individual curves correspond to positive and negative temperature sensitivities, respectively.

 

Fig. 4 Calculated optimal diameters for temperature insensitivity as a function of the thermal-optic coefficient of liquid for different liquid refractive indexes.

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5. Conclusion

In conclusion, we have presented temperature-compensated mFBGs by immersing them into a liquid with a negative thermo-optic coefficient. The temperature insensitivity can be obtained due to the evanescent-field interaction between light and liquid. In our experiment, the temperature sensitivity has been reduced to its 1/15 for a 5.2-μm microfiber by immersing it into ethanol with a purity of 99.8%. The theoretical analysis suggests that temperature compensation for mFBGs can be achieved by using different liquids, by optimizing the fiber diameter. The proposed method can meet the requirement on stability in dense wavelength-division-multiplexing system and dispersion compensation. In addition, the FBGs in microfibers have presented advanced sensing characteristics for mechanic measurands, e. g., hydrostatic pressure [16]. The proposed technique can effectively reduce the temperature cross sensitivity, which greatly benefit precise measurement.

Acknowledgments

This work was supported by National Natural Science Foundation of China (11104117 and 61177074), the Research Fund for the Doctoral Program of Higher Education (Grant No. 20114401110006), and the Fundamental Research Funds for the Central Universities (21609102).

References and links

1. R. Kashyap, S. Hornung, M. H. Reeve, and S. A. Cassidy, “Temperature de-sensitization of delay in optical fibres for sensor applications,” Electron. Lett. 19(24), 1039–1040 (1983). [CrossRef]  

2. D. L. Weidman, G. H. Beall, K. C. Chyung, G. L. Francis, R. A. Modavis, and R. M. Morena, “A novel negative expansion substrate material for athermalizing fiber Bragg,” in 22nd European Conference on Optical Communication- ECOC'96, Oslo, Norway, September 15–19, 1996.

3. T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett. 33(5), 417–419 (1997). [CrossRef]  

4. R. Kashyap, Fibre Bragg Gratings, 2nd ed. (Academic Press, 2009),Chap. 10.

5. G. W. Yoffe, P. A. Krug, F. Ouellette, and D. A. Thorncraft, “Passive temperature-compensating package for optical fiber gratings,” Appl. Opt. 34(30), 6859–6861 (1995). [CrossRef]   [PubMed]  

6. G. W. Yoffe, P. A. Krug, F. Ouelette, and D. Thorncraft, “Temperature-compensated optical-fiber Bragg gratings,” in Optical Fiber Communications Conference, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), paper WI4.

7. R. Kashyap, D. Williams, and R. P. Smith, “Novel liquid and liquid crystal cored optical fibre Bragg gratings,” in Optical Society of America Topical meeting on Photosensitivity and Quadratic Nonlinearity in Glass Waveguides: Fundamentals and Applications, Williamsburg, USA, (ISBN 1 55752517 X), Opt. Soc. America, pp 25–7, 26–28 October 1997.

8. M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J. 8(7), 1073–1078 (2008). [CrossRef]  

9. N. Mothe and D. Pagnoux, M. CV. Phan Huy, G. Dewinter, Laffont, and P. Ferdinand, “Thermal wavelength stabilization of Bragg gratings photowritten in hole-filled microstructured optical fibers,” Opt. Express 16(23), 19018–19033 (2008). [CrossRef]   [PubMed]  

10. L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004). [CrossRef]   [PubMed]  

11. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef]   [PubMed]  

12. L. M. Tong and M. Sumetsky, Subwavelength and Nanometer Diameter Optical Fibers (Zhe Jiang University Press, Zhe Jiang, 2009), Chap. 1.

13. J. Bures and R. Ghosh, “Power density of the evanescent field in the vicinity of a tapered fiber,” J. Opt. Soc. Am. A 16(8), 1992–1996 (1999). [CrossRef]  

14. Y. Ran, Y. N. Tan, L. P. Sun, S. Gao, J. Li, L. Jin, and B. O. Guan, “193 nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011). [CrossRef]   [PubMed]  

15. Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J. 4(1), 181–186 (2012). [CrossRef]  

16. K. M. Chung, Z. Y. Liu, C. Lu, and H. Y. Tam, “Highly sensitive compact force sensor based on microfiber Bragg grating,” IEEE Photon. Technol. Lett. 24(8), 700–702 (2012). [CrossRef]  

References

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  1. R. Kashyap, S. Hornung, M. H. Reeve, and S. A. Cassidy, “Temperature de-sensitization of delay in optical fibres for sensor applications,” Electron. Lett.19(24), 1039–1040 (1983).
    [CrossRef]
  2. D. L. Weidman, G. H. Beall, K. C. Chyung, G. L. Francis, R. A. Modavis, and R. M. Morena, “A novel negative expansion substrate material for athermalizing fiber Bragg,” in 22nd European Conference on Optical Communication- ECOC'96, Oslo, Norway, September 15–19, 1996.
  3. T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett.33(5), 417–419 (1997).
    [CrossRef]
  4. R. Kashyap, Fibre Bragg Gratings, 2nd ed. (Academic Press, 2009),Chap. 10.
  5. G. W. Yoffe, P. A. Krug, F. Ouellette, and D. A. Thorncraft, “Passive temperature-compensating package for optical fiber gratings,” Appl. Opt.34(30), 6859–6861 (1995).
    [CrossRef] [PubMed]
  6. G. W. Yoffe, P. A. Krug, F. Ouelette, and D. Thorncraft, “Temperature-compensated optical-fiber Bragg gratings,” in Optical Fiber Communications Conference, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), paper WI4.
  7. R. Kashyap, D. Williams, and R. P. Smith, “Novel liquid and liquid crystal cored optical fibre Bragg gratings,” in Optical Society of America Topical meeting on Photosensitivity and Quadratic Nonlinearity in Glass Waveguides: Fundamentals and Applications, Williamsburg, USA, (ISBN 1 55752517 X), Opt. Soc. America, pp 25–7, 26–28 October 1997.
  8. M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
    [CrossRef]
  9. N. Mothe and D. Pagnoux, M. CV. Phan Huy, G. Dewinter, Laffont, and P. Ferdinand, “Thermal wavelength stabilization of Bragg gratings photowritten in hole-filled microstructured optical fibers,” Opt. Express16(23), 19018–19033 (2008).
    [CrossRef] [PubMed]
  10. L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express12(6), 1025–1035 (2004).
    [CrossRef] [PubMed]
  11. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
    [CrossRef] [PubMed]
  12. L. M. Tong and M. Sumetsky, Subwavelength and Nanometer Diameter Optical Fibers (Zhe Jiang University Press, Zhe Jiang, 2009), Chap. 1.
  13. J. Bures and R. Ghosh, “Power density of the evanescent field in the vicinity of a tapered fiber,” J. Opt. Soc. Am. A16(8), 1992–1996 (1999).
    [CrossRef]
  14. Y. Ran, Y. N. Tan, L. P. Sun, S. Gao, J. Li, L. Jin, and B. O. Guan, “193 nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express19(19), 18577–18583 (2011).
    [CrossRef] [PubMed]
  15. Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
    [CrossRef]
  16. K. M. Chung, Z. Y. Liu, C. Lu, and H. Y. Tam, “Highly sensitive compact force sensor based on microfiber Bragg grating,” IEEE Photon. Technol. Lett.24(8), 700–702 (2012).
    [CrossRef]

2012 (2)

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
[CrossRef]

K. M. Chung, Z. Y. Liu, C. Lu, and H. Y. Tam, “Highly sensitive compact force sensor based on microfiber Bragg grating,” IEEE Photon. Technol. Lett.24(8), 700–702 (2012).
[CrossRef]

2011 (1)

2008 (2)

2004 (1)

2003 (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

1999 (1)

1997 (1)

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett.33(5), 417–419 (1997).
[CrossRef]

1995 (1)

1983 (1)

R. Kashyap, S. Hornung, M. H. Reeve, and S. A. Cassidy, “Temperature de-sensitization of delay in optical fibres for sensor applications,” Electron. Lett.19(24), 1039–1040 (1983).
[CrossRef]

Ashcom, J. B.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Blanc, W.

M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
[CrossRef]

Bures, J.

Cassidy, S. A.

R. Kashyap, S. Hornung, M. H. Reeve, and S. A. Cassidy, “Temperature de-sensitization of delay in optical fibres for sensor applications,” Electron. Lett.19(24), 1039–1040 (1983).
[CrossRef]

Chung, K. M.

K. M. Chung, Z. Y. Liu, C. Lu, and H. Y. Tam, “Highly sensitive compact force sensor based on microfiber Bragg grating,” IEEE Photon. Technol. Lett.24(8), 700–702 (2012).
[CrossRef]

Dewinter, G.

Dewynter, V.

M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
[CrossRef]

Dussardier, B.

M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
[CrossRef]

Ferdinand, P.

N. Mothe and D. Pagnoux, M. CV. Phan Huy, G. Dewinter, Laffont, and P. Ferdinand, “Thermal wavelength stabilization of Bragg gratings photowritten in hole-filled microstructured optical fibers,” Opt. Express16(23), 19018–19033 (2008).
[CrossRef] [PubMed]

M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
[CrossRef]

Gao, S.

Gattass, R. R.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Ghosh, R.

Guan, B. O.

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
[CrossRef]

Y. Ran, Y. N. Tan, L. P. Sun, S. Gao, J. Li, L. Jin, and B. O. Guan, “193 nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express19(19), 18577–18583 (2011).
[CrossRef] [PubMed]

Hattori, Y.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett.33(5), 417–419 (1997).
[CrossRef]

He, S. L.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Hornung, S.

R. Kashyap, S. Hornung, M. H. Reeve, and S. A. Cassidy, “Temperature de-sensitization of delay in optical fibres for sensor applications,” Electron. Lett.19(24), 1039–1040 (1983).
[CrossRef]

Huy, M. C. P.

M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
[CrossRef]

Inoue, A.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett.33(5), 417–419 (1997).
[CrossRef]

Iwashima, T.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett.33(5), 417–419 (1997).
[CrossRef]

Jin, L.

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
[CrossRef]

Y. Ran, Y. N. Tan, L. P. Sun, S. Gao, J. Li, L. Jin, and B. O. Guan, “193 nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express19(19), 18577–18583 (2011).
[CrossRef] [PubMed]

Kashyap, R.

R. Kashyap, S. Hornung, M. H. Reeve, and S. A. Cassidy, “Temperature de-sensitization of delay in optical fibres for sensor applications,” Electron. Lett.19(24), 1039–1040 (1983).
[CrossRef]

Krug, P. A.

Laffont,

Laffont, G.

M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
[CrossRef]

Li, J.

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
[CrossRef]

Y. Ran, Y. N. Tan, L. P. Sun, S. Gao, J. Li, L. Jin, and B. O. Guan, “193 nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express19(19), 18577–18583 (2011).
[CrossRef] [PubMed]

Liu, Z. Y.

K. M. Chung, Z. Y. Liu, C. Lu, and H. Y. Tam, “Highly sensitive compact force sensor based on microfiber Bragg grating,” IEEE Photon. Technol. Lett.24(8), 700–702 (2012).
[CrossRef]

Lou, J. Y.

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express12(6), 1025–1035 (2004).
[CrossRef] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Lu, C.

K. M. Chung, Z. Y. Liu, C. Lu, and H. Y. Tam, “Highly sensitive compact force sensor based on microfiber Bragg grating,” IEEE Photon. Technol. Lett.24(8), 700–702 (2012).
[CrossRef]

Maxwell, I.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express12(6), 1025–1035 (2004).
[CrossRef] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Mothe, N.

Nishimura, M.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett.33(5), 417–419 (1997).
[CrossRef]

Ouellette, F.

Pagnoux, D.

N. Mothe and D. Pagnoux, M. CV. Phan Huy, G. Dewinter, Laffont, and P. Ferdinand, “Thermal wavelength stabilization of Bragg gratings photowritten in hole-filled microstructured optical fibers,” Opt. Express16(23), 19018–19033 (2008).
[CrossRef] [PubMed]

M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
[CrossRef]

Phan Huy, V.

Ran, Y.

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
[CrossRef]

Y. Ran, Y. N. Tan, L. P. Sun, S. Gao, J. Li, L. Jin, and B. O. Guan, “193 nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express19(19), 18577–18583 (2011).
[CrossRef] [PubMed]

Reeve, M. H.

R. Kashyap, S. Hornung, M. H. Reeve, and S. A. Cassidy, “Temperature de-sensitization of delay in optical fibres for sensor applications,” Electron. Lett.19(24), 1039–1040 (1983).
[CrossRef]

Shen, M. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Shigematsu, M.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett.33(5), 417–419 (1997).
[CrossRef]

Sun, L. P.

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
[CrossRef]

Y. Ran, Y. N. Tan, L. P. Sun, S. Gao, J. Li, L. Jin, and B. O. Guan, “193 nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express19(19), 18577–18583 (2011).
[CrossRef] [PubMed]

Tam, H. Y.

K. M. Chung, Z. Y. Liu, C. Lu, and H. Y. Tam, “Highly sensitive compact force sensor based on microfiber Bragg grating,” IEEE Photon. Technol. Lett.24(8), 700–702 (2012).
[CrossRef]

Tan, Y. N.

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
[CrossRef]

Y. Ran, Y. N. Tan, L. P. Sun, S. Gao, J. Li, L. Jin, and B. O. Guan, “193 nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express19(19), 18577–18583 (2011).
[CrossRef] [PubMed]

Thorncraft, D. A.

Tong, L. M.

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express12(6), 1025–1035 (2004).
[CrossRef] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Yoffe, G. W.

Appl. Opt. (1)

Electron. Lett. (2)

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, “Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes,” Electron. Lett.33(5), 417–419 (1997).
[CrossRef]

R. Kashyap, S. Hornung, M. H. Reeve, and S. A. Cassidy, “Temperature de-sensitization of delay in optical fibres for sensor applications,” Electron. Lett.19(24), 1039–1040 (1983).
[CrossRef]

IEEE Photon. J. (1)

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet-inscription of Bragg gratings in microfibers,” IEEE Photon. J.4(1), 181–186 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. M. Chung, Z. Y. Liu, C. Lu, and H. Y. Tam, “Highly sensitive compact force sensor based on microfiber Bragg grating,” IEEE Photon. Technol. Lett.24(8), 700–702 (2012).
[CrossRef]

IEEE Sens. J. (1)

M. C. P. Huy, G. Laffont, V. Dewynter, P. Ferdinand, D. Pagnoux, B. Dussardier, and W. Blanc, “Passive temperature-compensating technique for microstructured fiber Bragg gratings,” IEEE Sens. J.8(7), 1073–1078 (2008).
[CrossRef]

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

Nature (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Other (5)

L. M. Tong and M. Sumetsky, Subwavelength and Nanometer Diameter Optical Fibers (Zhe Jiang University Press, Zhe Jiang, 2009), Chap. 1.

D. L. Weidman, G. H. Beall, K. C. Chyung, G. L. Francis, R. A. Modavis, and R. M. Morena, “A novel negative expansion substrate material for athermalizing fiber Bragg,” in 22nd European Conference on Optical Communication- ECOC'96, Oslo, Norway, September 15–19, 1996.

R. Kashyap, Fibre Bragg Gratings, 2nd ed. (Academic Press, 2009),Chap. 10.

G. W. Yoffe, P. A. Krug, F. Ouelette, and D. Thorncraft, “Temperature-compensated optical-fiber Bragg gratings,” in Optical Fiber Communications Conference, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, 1995), paper WI4.

R. Kashyap, D. Williams, and R. P. Smith, “Novel liquid and liquid crystal cored optical fibre Bragg gratings,” in Optical Society of America Topical meeting on Photosensitivity and Quadratic Nonlinearity in Glass Waveguides: Fundamentals and Applications, Williamsburg, USA, (ISBN 1 55752517 X), Opt. Soc. America, pp 25–7, 26–28 October 1997.

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Figures (4)

Fig. 1
Fig. 1

(a) Measured reflection spectra of the immersed mFBG with a diameter of 5.2 µm measured at 15°C and 60°C, respectively; (b) Measured wavelength shifts as a function of temperature for the immersed mFBGs with different diameters. The curves are linear fits for individual responses.

Fig. 2
Fig. 2

Calculated transverse energy distribution of microfibers along the fiber diameter, (a) D = 4µm; (b) D = 5.2µm; (c) D = 10.2µm.

Fig. 3
Fig. 3

Calculated and measured temperature sensitivity as a function of microfiber diameter for the mFBG immersed in ethanol.

Fig. 4
Fig. 4

Calculated optimal diameters for temperature insensitivity as a function of the thermal-optic coefficient of liquid for different liquid refractive indexes.

Equations (3)

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λ B =2 n eff Λ
d λ B dT = λ B ( α+β )
d λ B dT = λ B ( α+ 1 n eff ( d n eff d n si η si + d n eff d n liq η liq ) )

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