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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 19 — Sep. 12, 2011
  • pp: 18452–18457
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Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe

Jun-long Kou, Sun-jie Qiu, Fei Xu, and Yan-qing Lu  »View Author Affiliations


Optics Express, Vol. 19, Issue 19, pp. 18452-18457 (2011)
http://dx.doi.org/10.1364/OE.19.018452


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Abstract

We experimentally demonstrate an all-silica first-order fiber Bragg grating (FBG) for high temperature sensing by focused ion beam (FIB) machining in a fiber probe tapered to a point. This 61-period FBG is compact (~36.6 μm long and ~6.5 μm in diameter) with 200-nm-deep shallow grooves. We have tested the sensor from room temperature to around 500 °C and it shows a temperature sensitivity of nearly 20 pm/°C near the resonant wavelength of 1550 nm. This kind of sensor takes up little space because of its unique geometry and small size and may be integrated in devices that work in harsh environment or for detecting small objects.

© 2011 OSA

1. Introduction

Over the last two decades, optical sensors based on fiber gratings, including fiber Bragg gratings (FBGs) and long-period gratings (LPGs), have attracted much attention due to their widespread applications in various physical or chemical parameter measurements such as refractive index, strain and temperature. Standard fiber gratings fabricated by exposing photosensitive fibers to an intense ultraviolet interference pattern can be normally used for measuring relatively low temperature below 200 °C. Various fabrication methods such as CO2 laser irradiation [1

1. Y. P. Wang, “Review of long period fiber gratings written by CO2 laser,” J. Appl. Phys. 108(8), 081101 (2010). [CrossRef]

,2

2. 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]

], femtosecond laser exposure [3

3. Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, “Fabrication of long-period fiber gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett. 24(10), 646–648 (1999). [CrossRef] [PubMed]

,4

4. L. B. Fu, G. D. Marshall, J. A. Bolger, P. Steinvurzel, E. C. Magi, M. J. Withford, and B. J. Eggleton, “Femtosecond laser writing Bragg gratings in pure silica photonic crystal fibres,” Electron. Lett. 41(11), 638–640 (2005). [CrossRef]

] and etched corrugations [5

5. C. Y. Lin and L. A. Wang, “A wavelength- and loss-tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13(4), 332–334 (2001). [CrossRef]

,6

6. T. L. Lowder, K. H. Smith, B. L. Ipson, A. R. Hawkins, R. H. Selfridge, and S. M. Schultz, “High-temperature sensing using surface relief fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17(9), 1926–1928 (2005). [CrossRef]

], have been demonstrated to write gratings for high temperature sensing in different types of optical fibers [7

7. G. Brambilla, V. Pruneri, L. Reekie, C. Contardi, D. Milanese, and M. Ferraris, “Bragg gratings in ternary SiO2:SnO2:Na2O optical glass fibers,” Opt. Lett. 25(16), 1153–1155 (2000). [CrossRef] [PubMed]

]. However, these gratings fabricated in thick fibers have weak index modulation and the grating lengths are at least several millimeters, which greatly limit the size of sensor heads. One alternative solution is to write short and strong grating in a micrometer-order-diameter microfiber. Several kinds of techniques on fabrication microfiber gratings have been proposed, for example, wrapping a microfiber on a microstructured rod [8

8. F. Xu, G. Brambilla, J. Feng, and Y.-Q. Lu, “A microfiber Bragg grating based on a microstructured rod: a proposal,” IEEE Photon. Technol. Lett. 22(4), 218–220 (2010). [CrossRef]

,9

9. J.-l. Kou, Z.-d. Huang, G. Zhu, F. Xu, and Y.-q. Lu, “Wave guiding properties and sensitivity of D-shaped optical fiber microwire devices,” Appl. Phys. B 102(3), 615–619 (2011). [CrossRef]

], using CO2 lasers [10

10. 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]

] and femtosecond lasers [11

11. H. Xuan, W. Jin, and S. Liu, “Long-period gratings in wavelength-scale microfibers,” Opt. Lett. 35(1), 85–87 (2010). [CrossRef] [PubMed]

,12

12. A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41(4), 176–178 (2005). [CrossRef]

]. The former can be used to realize compact FBG but it needs extra polymer coating which is not suitable for high temperature sensing. The latter can only be used to write LPG or long high-order FBG which means that the grating length is still long.

In this letter, we experimentally demonstrate a compact all-silica deeply-corrugated first-order-FBG for high-temperature sensing by focused ion beam (FIB) machining in a tapered non-photosensitive single-mode-fiber probe with a sharp profile. FIB technology is perfect for micro-machining and nano-fabrication due to its small and controllable spot size and high beam current density. It has been successfully used to directly micromachine micro-cavities [13

13. J. L. Kou, J. Feng, Q. J. Wang, F. Xu, and Y. Q. Lu, “Microfiber-probe-based ultrasmall interferometric sensor,” Opt. Lett. 35(13), 2308–2310 (2010). [CrossRef] [PubMed]

,14

14. J. L. Kou, J. Feng, L. Ye, F. Xu, and Y. Q. Lu, “Miniaturized fiber taper reflective interferometer for high temperature measurement,” Opt. Express 18(13), 14245–14250 (2010). [CrossRef] [PubMed]

] or to modify the tip geometry in a subwavelength fiber [15

15. F. Renna, D. Cox, and G. Brambilla, “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers,” Opt. Express 17(9), 7658–7663 (2009). [CrossRef] [PubMed]

]. Here, we directly carve periodic grooves on a sharp micrometer scale tapered fiber probe (TFP), which is around 6.5 μm in diameter. The groove period is 600 nm for the first order resonance. The groove depth is 0.2 μm and the total grating length is 36.6 μm. The all-silica TFP grating (TFPG) has a temperature sensitivity of ~20 pm/°C with a reflection peak-to-trough ratio of > 10 dB. Its extremely small size, all fiber connection, high sensitivity and especially unique structure offer possible potentials for fast-response high temperature sensing, particularly in small object, e.g. bubbles.

2. Fabrication of the TFPG

As in a planar corrugated Bragg grating, the Bragg wavelength of the grating is expressed by λB = 2neffΛ, where neff is the mode effective refractive index in the equivalent unperturbed geometry, and Λ is the period. The mode field and neff in the equivalent unperturbed waveguide geometry can be derived from the perturbed (straight) geometry using the method developed by W. Streifer [16

16. W. Streifer, D. Scifres, and R. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975). [CrossRef]

,17

17. W. Streifer and A. Hardy, “Analysis of two-dimensional waveguides with misaligned or curved gratings,” IEEE J. Quantum Electron. 14(12), 935–943 (1978). [CrossRef]

]. Figure 2
Fig. 2 The cross-sections of (a) an un-etched fiber, (b) an etched fiber and (c) an equivalent unperturbed geometry, respectively. hg is the groove height and heff is effective height.
shows the cross-sections of an un-etched fiber, an etched fiber and the equivalent unperturbed geometry with this method, which shifts the boundary between air and silica to compensate for the different geometry [16

16. W. Streifer, D. Scifres, and R. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975). [CrossRef]

,17

17. W. Streifer and A. Hardy, “Analysis of two-dimensional waveguides with misaligned or curved gratings,” IEEE J. Quantum Electron. 14(12), 935–943 (1978). [CrossRef]

], respectively. The effective groove height heff of the equivalent unperturbed geometry satisfies:
{(1τ)(θgsinθgcosθg)=θeffsinθeffcosθeffθg=arccos{(rhg)/r}θeff=arccos{(rheff)/r}
(1)
where τ is the grating duty cycle, hg is the groove height and r is the fiber radius, respectively. In our device, r = 3.25 μm, τ = 0.5 and hg = 0.2 μm. We find heff = 0.125 μm by solving Eq. (1) and neff = 1.433 by utilizing a finite element analysis. Thus, the Bragg wavelength is 1720 nm for the fundamental mode. It is different with the following experimental results (~1550 nm). The possible reason is that higher order mode is excited in the multi-mode fiber taper because the higher order mode has more overlap with the side corrugated surface. Moreover, the grating is nearly liner chirped because the taper is nonuniform. It agrees well with the following experimental results. The chirp can be cancelled if we use uniform tapered fiber.

3. Experiments and discussions

For most of these applications the required operational temperature only needs to be as high as 400 °C [18

18. M. L. Åslund, J. Canning, M. Stevenson, and K. Cook, “Thermal stabilization of Type I fiber Bragg gratings for operation up to 600 ° C,” Opt. Lett. 35(4), 586–588 (2010). [CrossRef] [PubMed]

]. So we characterize the thermal response of the TFPG from room temperature (21 °C) to 440 °C which can meet conventional applications. The TFPG is heated up in a micro-furnace and the temperature is measured by a thermocouple (TES-1310, Type K, TES Electrical Electronic Corp.). The spectrum and temperature are recorded when both of them are stable for several minutes.

The resonant spectra of the TFPG at different temperatures (21 °C, 124 °C, 187 °C and 440°C) are shown in Fig. 3
Fig. 3 Reflection spectra of the TFPG in air at different temperatures.
. The Bragg wavelength is ~1550 nm, with excited higher order mode as deduced from our theoretical calculation. The spectra indicate an extinction ratio of ~11 dB at the Bragg wavelength which is achieved with a 36.6 μm long Bragg grating and is similar with or even better than some other long length fiber gratings, enough for sensing applications.

The temperature sensitivity ST is defined as the resonant wavelength shift divided by the corresponding temperature change. ST depends on temperature through the thermo-optics and/or thermal expansion effect [19

19. H. Y. Choi, K. S. Park, S. J. Park, U. C. Paek, B. H. Lee, and E. S. Choi, “Miniature fiber-optic high temperature sensor based on a hybrid structured Fabry-Perot interferometer,” Opt. Lett. 33(21), 2455–2457 (2008). [CrossRef] [PubMed]

]:
ST=dλrdT=2(σTΛneffnsilica+rΛαTneffr+ΛαTneff)
(2)
where σT (1.4 × 10−5 /°C) is the thermo-optics coefficient and αT (5.5 × 10−7 /°C) is the thermal expansion coefficient. Temperature change influences three items: temperature-induced index variation, taper volume variation and temperature-induced grating length variation. According to our calculations, thermal expansion effect [the second and third part of Eq. (2)] contributes little to the total sensitivity (< 6%), mainly due to the low thermal expansion coefficient of silica. The first one is about 15 ~25 pm/°C and dominates in temperature sensing. Moreover, in the first part of Eq. (2), neff/nsilicais nearly 1 and does not change much with the microfiber diameter, which means that the most efficient method to increase temperature sensitivity is to use fiber with higher thermo-optics coefficient.

The resolution of a sensor is limited by several practical terms, e.g. the width of reflection peak, detection method, spectral variation and intrinsic sensor noise. For our devices, the bandwidth of the reflection peak (several nm) and the OSA resolution are the main issues. The reflection peak bandwidth can be narrowed by fabricating the grating with more periods in a more uniform taper region. On the other hand, we can use a power meter accompanied by a tunable laser with higher resolution which will give a more precise peak value.

The reproducibility and stability of a geometric-modulated grating depend on the geometric stability. The experimental results in [6

6. T. L. Lowder, K. H. Smith, B. L. Ipson, A. R. Hawkins, R. H. Selfridge, and S. M. Schultz, “High-temperature sensing using surface relief fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17(9), 1926–1928 (2005). [CrossRef]

] show a good reproducibility and stability by heating and cooling it between room temperature to 1000 °C. Our grating has the same working mechanism thus it can be stable and keep good reproducibility before the material melts and the structure is destroyed.

4. Discussions and Conclusions

Conventional FBG is fabricated by writing variation of refractive index into the core of Ge-doped silica fiber using UV light by phase mask. The index modulation is very weak and is unstable when temperature is high. Compared with the standard FBG grating, the main advantages of our proposed grating are the compact size, stable geometric modulation, and flexible fabrication technique without the limitation of fiber material.

First, the standard FBG is usually up to centimeters in length [20

20. S. Ju, P. R. Watekar, and W.-T. Han, “Enhanced sensitivity of the FBG temperature sensor based on the PbO-GeO2-SiO2 glass optical fiber,” J. Lightwave Technol. 28(18), 2697–2700 (2010). [CrossRef]

] which is much longer than our FIB-milled one. Device with long length is usually much difficult to handle and move in air or fluid and it is often easy to be influenced by other effect, e.g., bending, strain and vibration. However, our FIB-milled FBG in a tapered fiber tip is much compact (~36.6 μm long located in ~6.5 μm in diameter) which may be useful in detecting ultra-tiny object, e.g. bubbles.

Second, the common FBG fabricated by UV light usually cannot serve in environment with temperature above 200 °C, because the index modulation will degrade after long-time exposure in high temperature environment. However, FIB-machined grating is different because the index modulation results from the corrugations on the fiber tip surface. It means that the grating can be very stable if the fiber material (silica) does not melt and the corrugations will not be destroyed.

Third, we emphasize on the method (i.e. FIB) of fabricating the grating. The FIB milling can be extended to micromachining fibers made of different materials such as sapphire whose melting point can be well above 2000 °C [21

21. J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high temperature sensing with sapphire fiber air gap-based extrinsic Fabry-Perot interferometers,” Opt. Lett. 35(5), 619–621 (2010). [CrossRef] [PubMed]

], which means that it is possible to realize an ultra-high temperature sensor.

In summary, we experimentally demonstrate an all-silica FBG for high-temperature sensing by FIB machining in a tapered fiber probe with a sharp profile. The grating is relatively short (only 36.6 μm) with shallow corrugations in a fiber taper with diameter around 6.5 μm. The calibration of the sensor is carried out from room temperature to around 500 °C and shows a temperature sensitivity of ~20 pm/°C. The resonance at the Bragg wavelength is achieved with as few as 61-period and 200-nm-deep corrugations on the taper surface. All these performance are better than or similar with other fiber gratings with much bigger size or length. Its advantages of compact size, high sensitivity, easy interrogation, simple fabrication and unique geometry offer great possible prospects for developing novel high temperature sensors for small space.

Acknowledgments

This work is supported by National 973 program under contract No. 2010CB327803, 2012CB921803 and 2011CBA00200, NSFC program No. 11074117 and 60977039. The authors also acknowledge the support from the Priority Academic Program Development of Jiangsu (PAPD) and the Fundamental Research Funds for the Central Universities.

References and links

1.

Y. P. Wang, “Review of long period fiber gratings written by CO2 laser,” J. Appl. Phys. 108(8), 081101 (2010). [CrossRef]

2.

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]

3.

Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, “Fabrication of long-period fiber gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett. 24(10), 646–648 (1999). [CrossRef] [PubMed]

4.

L. B. Fu, G. D. Marshall, J. A. Bolger, P. Steinvurzel, E. C. Magi, M. J. Withford, and B. J. Eggleton, “Femtosecond laser writing Bragg gratings in pure silica photonic crystal fibres,” Electron. Lett. 41(11), 638–640 (2005). [CrossRef]

5.

C. Y. Lin and L. A. Wang, “A wavelength- and loss-tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13(4), 332–334 (2001). [CrossRef]

6.

T. L. Lowder, K. H. Smith, B. L. Ipson, A. R. Hawkins, R. H. Selfridge, and S. M. Schultz, “High-temperature sensing using surface relief fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17(9), 1926–1928 (2005). [CrossRef]

7.

G. Brambilla, V. Pruneri, L. Reekie, C. Contardi, D. Milanese, and M. Ferraris, “Bragg gratings in ternary SiO2:SnO2:Na2O optical glass fibers,” Opt. Lett. 25(16), 1153–1155 (2000). [CrossRef] [PubMed]

8.

F. Xu, G. Brambilla, J. Feng, and Y.-Q. Lu, “A microfiber Bragg grating based on a microstructured rod: a proposal,” IEEE Photon. Technol. Lett. 22(4), 218–220 (2010). [CrossRef]

9.

J.-l. Kou, Z.-d. Huang, G. Zhu, F. Xu, and Y.-q. Lu, “Wave guiding properties and sensitivity of D-shaped optical fiber microwire devices,” Appl. Phys. B 102(3), 615–619 (2011). [CrossRef]

10.

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]

11.

H. Xuan, W. Jin, and S. Liu, “Long-period gratings in wavelength-scale microfibers,” Opt. Lett. 35(1), 85–87 (2010). [CrossRef] [PubMed]

12.

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41(4), 176–178 (2005). [CrossRef]

13.

J. L. Kou, J. Feng, Q. J. Wang, F. Xu, and Y. Q. Lu, “Microfiber-probe-based ultrasmall interferometric sensor,” Opt. Lett. 35(13), 2308–2310 (2010). [CrossRef] [PubMed]

14.

J. L. Kou, J. Feng, L. Ye, F. Xu, and Y. Q. Lu, “Miniaturized fiber taper reflective interferometer for high temperature measurement,” Opt. Express 18(13), 14245–14250 (2010). [CrossRef] [PubMed]

15.

F. Renna, D. Cox, and G. Brambilla, “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers,” Opt. Express 17(9), 7658–7663 (2009). [CrossRef] [PubMed]

16.

W. Streifer, D. Scifres, and R. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975). [CrossRef]

17.

W. Streifer and A. Hardy, “Analysis of two-dimensional waveguides with misaligned or curved gratings,” IEEE J. Quantum Electron. 14(12), 935–943 (1978). [CrossRef]

18.

M. L. Åslund, J. Canning, M. Stevenson, and K. Cook, “Thermal stabilization of Type I fiber Bragg gratings for operation up to 600 ° C,” Opt. Lett. 35(4), 586–588 (2010). [CrossRef] [PubMed]

19.

H. Y. Choi, K. S. Park, S. J. Park, U. C. Paek, B. H. Lee, and E. S. Choi, “Miniature fiber-optic high temperature sensor based on a hybrid structured Fabry-Perot interferometer,” Opt. Lett. 33(21), 2455–2457 (2008). [CrossRef] [PubMed]

20.

S. Ju, P. R. Watekar, and W.-T. Han, “Enhanced sensitivity of the FBG temperature sensor based on the PbO-GeO2-SiO2 glass optical fiber,” J. Lightwave Technol. 28(18), 2697–2700 (2010). [CrossRef]

21.

J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high temperature sensing with sapphire fiber air gap-based extrinsic Fabry-Perot interferometers,” Opt. Lett. 35(5), 619–621 (2010). [CrossRef] [PubMed]

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(120.6780) Instrumentation, measurement, and metrology : Temperature

ToC Category:
Sensors

History
Original Manuscript: July 12, 2011
Revised Manuscript: August 7, 2011
Manuscript Accepted: August 22, 2011
Published: September 6, 2011

Citation
Jun-long Kou, Sun-jie Qiu, Fei Xu, and Yan-qing Lu, "Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe," Opt. Express 19, 18452-18457 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18452


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References

  1. Y. P. Wang, “Review of long period fiber gratings written by CO2 laser,” J. Appl. Phys.108(8), 081101 (2010). [CrossRef]
  2. 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]
  3. Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, “Fabrication of long-period fiber gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett.24(10), 646–648 (1999). [CrossRef] [PubMed]
  4. L. B. Fu, G. D. Marshall, J. A. Bolger, P. Steinvurzel, E. C. Magi, M. J. Withford, and B. J. Eggleton, “Femtosecond laser writing Bragg gratings in pure silica photonic crystal fibres,” Electron. Lett.41(11), 638–640 (2005). [CrossRef]
  5. C. Y. Lin and L. A. Wang, “A wavelength- and loss-tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett.13(4), 332–334 (2001). [CrossRef]
  6. T. L. Lowder, K. H. Smith, B. L. Ipson, A. R. Hawkins, R. H. Selfridge, and S. M. Schultz, “High-temperature sensing using surface relief fiber Bragg gratings,” IEEE Photon. Technol. Lett.17(9), 1926–1928 (2005). [CrossRef]
  7. G. Brambilla, V. Pruneri, L. Reekie, C. Contardi, D. Milanese, and M. Ferraris, “Bragg gratings in ternary SiO2:SnO2:Na2O optical glass fibers,” Opt. Lett.25(16), 1153–1155 (2000). [CrossRef] [PubMed]
  8. F. Xu, G. Brambilla, J. Feng, and Y.-Q. Lu, “A microfiber Bragg grating based on a microstructured rod: a proposal,” IEEE Photon. Technol. Lett.22(4), 218–220 (2010). [CrossRef]
  9. J.-l. Kou, Z.-d. Huang, G. Zhu, F. Xu, and Y.-q. Lu, “Wave guiding properties and sensitivity of D-shaped optical fiber microwire devices,” Appl. Phys. B102(3), 615–619 (2011). [CrossRef]
  10. H. Xuan, W. Jin, and M. Zhang, “CO2 laser induced long period gratings in optical microfibers,” Opt. Express17(24), 21882–21890 (2009). [CrossRef] [PubMed]
  11. H. Xuan, W. Jin, and S. Liu, “Long-period gratings in wavelength-scale microfibers,” Opt. Lett.35(1), 85–87 (2010). [CrossRef] [PubMed]
  12. A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett.41(4), 176–178 (2005). [CrossRef]
  13. J. L. Kou, J. Feng, Q. J. Wang, F. Xu, and Y. Q. Lu, “Microfiber-probe-based ultrasmall interferometric sensor,” Opt. Lett.35(13), 2308–2310 (2010). [CrossRef] [PubMed]
  14. J. L. Kou, J. Feng, L. Ye, F. Xu, and Y. Q. Lu, “Miniaturized fiber taper reflective interferometer for high temperature measurement,” Opt. Express18(13), 14245–14250 (2010). [CrossRef] [PubMed]
  15. F. Renna, D. Cox, and G. Brambilla, “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers,” Opt. Express17(9), 7658–7663 (2009). [CrossRef] [PubMed]
  16. W. Streifer, D. Scifres, and R. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron.11(11), 867–873 (1975). [CrossRef]
  17. W. Streifer and A. Hardy, “Analysis of two-dimensional waveguides with misaligned or curved gratings,” IEEE J. Quantum Electron.14(12), 935–943 (1978). [CrossRef]
  18. M. L. Åslund, J. Canning, M. Stevenson, and K. Cook, “Thermal stabilization of Type I fiber Bragg gratings for operation up to 600 ° C,” Opt. Lett.35(4), 586–588 (2010). [CrossRef] [PubMed]
  19. H. Y. Choi, K. S. Park, S. J. Park, U. C. Paek, B. H. Lee, and E. S. Choi, “Miniature fiber-optic high temperature sensor based on a hybrid structured Fabry-Perot interferometer,” Opt. Lett.33(21), 2455–2457 (2008). [CrossRef] [PubMed]
  20. S. Ju, P. R. Watekar, and W.-T. Han, “Enhanced sensitivity of the FBG temperature sensor based on the PbO-GeO2-SiO2 glass optical fiber,” J. Lightwave Technol.28(18), 2697–2700 (2010). [CrossRef]
  21. J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high temperature sensing with sapphire fiber air gap-based extrinsic Fabry-Perot interferometers,” Opt. Lett.35(5), 619–621 (2010). [CrossRef] [PubMed]

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