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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 5 — Feb. 27, 2012
  • pp: 5402–5408
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A microfiber coupler tip thermometer

Ming Ding, Pengfei Wang, and Gilberto Brambilla  »View Author Affiliations


Optics Express, Vol. 20, Issue 5, pp. 5402-5408 (2012)
http://dx.doi.org/10.1364/OE.20.005402


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Abstract

A compact thermometer based on a broadband microfiber coupler tip is demonstrated. This sensor can measure a broad temperature interval ranging from room temperature to 1283 °C with sub-200 µm spatial resolution. An average sensitivity of 11.96 pm/°C was achieved for a coupler tip with ~2.5 µm diameter. This is the highest temperature measured with a silica optical fiber device.

© 2012 OSA

1. Introduction

Temperature monitoring is vital for many applications in harsh environments, such as the oil and gas industries, power generation, or engine turbines. Because of their immunity to electromagnetic interference and possibility to work in contact with explosives, the use of optical fibers for temperature monitoring has been widely investigated [1

1. Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8(4), 355–375 (1997). [CrossRef]

4

4. 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]

]. Among optical fiber devices, fiber Bragg gratings (FBGs) [1

1. Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8(4), 355–375 (1997). [CrossRef]

,5

5. D. Grobnic, S. J. Mihailov, C. W. Smelser, and H. Ding, “Sapphire fiber Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett. 16(11), 2505–2507 (2004). [CrossRef]

12

12. Y. Li, M. Yang, D. N. Wang, J. Lu, T. Sun, and K. T. Grattan, “Fiber Bragg gratings with enhanced thermal stability by residual stress relaxation,” Opt. Express 17(22), 19785–19790 (2009). [CrossRef] [PubMed]

] are possibly the most common tool used for temperature sensing. FBGs inscribed in telecom optical fibers can reach temperatures T as high as 800 °C [8

8. V. de Oliveira, M. Muller, and H. J. Kalinowski, “Bragg gratings in standard nonhydrogenated fibers for high-temperature sensing,” Appl. Opt. 50(25), E55–E58 (2011). [CrossRef]

]. Silica optical fibers have been shown to be capable to measure temperatures in excess of 1000 °C [10

10. D. Barrera, V. Finazzi, J. Villatoro, S. Sales, and V. Pruneri, “Packaged optical sensors based on regenerated fiber Bragg gratings for high temperature application,” IEEE Sens. J. 12(1), 107–112 (2012). [CrossRef]

12

12. Y. Li, M. Yang, D. N. Wang, J. Lu, T. Sun, and K. T. Grattan, “Fiber Bragg gratings with enhanced thermal stability by residual stress relaxation,” Opt. Express 17(22), 19785–19790 (2009). [CrossRef] [PubMed]

], but they require specialty fibers and/or a long manufacturing process which includes hydrogen loading, a cumbersome grating writing equipment working with toxic gases and a relatively long post fabrication annealing. In addition to a relatively complex and expensive process, FBGs exhibit a big size (diameter d~125 µm and length L~1 cm) which restricts their application for high resolution measurements.

2. Microfiber coupler thermometer fabrication

The MFCT thermometer was manufactured by cutting a MFC (Fig. 1(a)) with a ceramic cleaver into two equal parts at the center of the minimum waist region. A MFC comprises two conical transition regions, a central uniform waist region and four input/output ports: light injected from ports P1 or P2 exits MFC from ports P3 and P4. In the MFCT, light launched from port P1 is partially reflected by the flat surface of the tip and can be measured at port P2. In these experiments, a low-loss MFC was fabricated from two standard telecom optical fibers (SMF-28, Corning, NY, USA) using the microheater brushing technique [20

20. G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, “Compound-glass optical nanowires,” Electron. Lett. 41(7), 400–402 (2005). [CrossRef]

]. The lengths of tapered and uniform waist regions were ~25 mm and ~6 mm, respectively. Figure 2(a)
Fig. 2 (a) SEM images of the MFCT. Single microfiber diameter and uniform region length are ~2.5 µm and ~3 mm, respectively; (b) MFCT reflection spectrum at room temperature.
shows the scanning electron microscope (SEM) image of the MFCT: the minimum diameter and length of the uniform waist region were ~2.5 µm and ~3 mm. The MFCT spectral characterization was carried out connecting a supercontinuum (SC) source (Fianium Ltd, Southampton, U.K.), with emission over the wavelengths range 450-1800 nm, to port P1 and an optical spectrum analyzer (OSA) (AQ6317, Yokogawa, Japan) to port P2. The reflection spectrum at room temperature is presented in Fig. 2(b) and shows the multipeak pattern of optical fiber couplers. On the contrary of conventional fused couplers made from telecom singlemode optical fibers, the pattern is not limited to the 1250-1750 nm range, but covers the whole investigated wavelength range 700-1700 nm.

A long wavelength modulation is superimposed to the coupler spectrum and it is due to difference of coupling coefficient for x and y polarizations.

3. Temperature dependence of the MFCT

The MFC output can be predicted by assuming that power exchange at the output ports occurs as a result of the interference between the lowest-order symmetric and antisymmetric modes of the waveguide formed by the whole of the cross section of the fused region. From Fig. 2(a), the MFCT can be assumed to be a “weakly fused” coupler, approximated by two touching cylindrical waveguides (the Fig. 3
Fig. 3 The output power from port P2 at 26 °C, 471 °C and 828 °C. Inset: MCFT cross section in the “weakly fusing” approximation.
inset shows a schematic of coupler cross section in this approximation). Since the original fiber cores have a negligible size, they can be ignored and the coupling coefficients Cxand Cy for the x and y polarization are given by [21

21. F. P. Payne, C. D. Hussey, and M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett. 21(13), 561–563 (1985). [CrossRef]

]:
Cx=23/2(n12n02)1/2U2(2n12V+1)n13a(π)V7/2
(1)
Cy=23/2(n12n02)1/2U2(2n12V1)n13a(π)V7/2
(2)
where n1and n0are the refractive indices of silica and air, ais the diameter of one of the microfibers, U=2.405and V=[(2πa)/λ](n12n02)1/2.

In the MFCT, light launched from port P1 is reflected by the tip and the power emerging from P2 is proportional to P4 in Eq. (3):

P2=(n1n0n1+n0)2P4
(4)

Equations (1-4) show that the output power depends on the wavelength λ and on three factors (refractive index n1, coupling length L and coupler radial size 2a), which are temperature dependent.

The temperature dependence of the MFCT output spectrum was evaluated assuming the refractive index of silica at λ~1530 nm at T = 26 °C, 471 °C and 828 °C to be 1.44444, 1.44961 and 1.45352 [22

22. J. H. Wray and J. T. Neu, “Refractive index of several glasses as a function of wavelength and temperature,” J. Opt. Soc. Am. 59(6), 774–776 (1969). [CrossRef]

], respectively. The diameter of each microfiber in the uniform region and the length of the uniform region (2.5 µm and 3 mm, respectively) were assumed to expand with an average coefficient 5.5 × 10−7 °C−1. Figure 3 shows the output power variation at three different temperatures. The resonance peak shifts 15.5 nm when T is increased from 26 °C to 828 °C, with an average responsivity of 19.3 pm/ °C.

4. MFCT Characterization

4.1. Responsivity

Sensor characterization was carried out using the same microheater (NTT-AT, Tokyo, Japan) used to fabricate the MFC, as it can reach temperatures in excess of 1700 °C. The MFCT was inserted to the microheater center (Fig. 4(a)
Fig. 4 (a) MFCT characterization set-up; (b) relation between the driver current and temperature; (c) reflection spectra of the peak at 1219 nm in Fig. 2(b) when the driver current increases from 0.4 A to 2.8 A by steps of 0.2 A.
) and the reflection spectra were recorded at different T. The microheater temperature was changed by increasing the current flowing into the microheater from 0.4 A to 2.8 A in steps of 0.2 A. Measurements were taken every 15 minutes to ensure a stable temperature. The microheater response was proposed in ref [23

23. C. Rodenburg, X. Lui, M. A. E. Jepson, S. A. Boden, and G. Brambilla, ““Surface morphology of silica nanowires at the nanometer scale,”J. Non-Cryst. Sol. 357, 3042–3045 (2011).

]. and it is reported in Fig. 4(b) to include small currents. Figure 4(c) shows the spectral shift of the peak at 1219 nm in Fig. 2(b) for increasing currents. When the driver current is increased, the temperature increases and the peak redshifts to long wavelengths, as predicted by simulations in Fig. 3.

The sensor responsivity (also called sensitivity) R is defined as the wavelength shift associated to a temperature change. In order to minimize the measurement error, spectra were fit with Lorentzian functions and the fit peak wavelength was used to calculate the wavelength shift. An average R~11.96 pm/°C was achieved in the temperature range ~247 °C to ~1283 °C, comparable to the value obtained for FBG thermometers at lower T [24

24. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]

, 25

25. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. Joseph Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997). [CrossRef]

]. The possible explanation for the difference between the theoretical calculation and experimental measurement could be the unperfected weakly fused coupler structure, the measured wavelength difference and the refractive index error. The sensor resolution was estimated to be ~0.836 °C for an OSA resolution of 0.01 nm. Better resolutions can be potentially achieved with more spectral data points for the Lorentzian fitting and/or better signal/noise (i.e. spectral averaging).

4.2. Repeatability

The MFCT thermometer repeatability was measured recording spectra for increasing and decreasing temperatures with an interval of one hour. The wavelength shift with the temperature is shown in Fig. 5
Fig. 5 Wavelength shift dependence on the microheater temperature. The red solid curve and the blue dash curve report measurements for decreasing and increasing temperatures, respectively.
: data from the two curves fit very well within 3 °C, showing that the MFCT thermometer has good repeatability.

4.3. 2D spatial resolution

In order to demonstrate the sensor high 2D spatial resolution, measurements were carried out as shown in Fig. 6(a)
Fig. 6 (a) Experimental set-up used to demonstrate the MFCT 2D spatial resolution; (b) sensor response when the MFCT was scanned along the tangential direction of the Ni-Cr wire at ~250 µm from the wire surface. The red solid and the blue dash curves are the experiment results and the curve expected from heat transfer equation, respectively.
. A Nickel-Chromium (Ni-Cr) wire with ~500 µm diameter was heated exploiting its Ohm effect. Spectra were recorded every 125 µm at a distance of ~250 µm from the Ni-Cr surface along the tangential direction: the peak shift of Lorentzian fitting spectra variation with the MFCT position is presented in Fig. 6(b), with the origin taken as the central axis of the wire. A sharp peak with a full width at half maximum (FWHM) of ~1150 µm was observed. FWHM is larger than the wire size as the temperature gradient becomes smaller for increasing distances from the heated wire, thus the FWHM is bound to increase for increasing distances from the wire.

A reasonably good fit between Eq. (5) theory and experimental data shown in Fig. 6(b) occurred for C1 = −284.7 and C2 = 1114.7, respectively. The small difference between two curves can be associated to the tip head movement, to the wire temperature fluctuations during the measurement and to the stage movement error. The measurement errors are shown with error bars.

5. Conclusions

In summary, a compact temperature sensor which uses a MFCT for high-T sensing with high 2D spatial resolution has been demonstrated. This device exploits the temperature dependence of intermodal coupling in the coupler uniform waist region. The thermometer had a responsivity of 11.96 pm/°C and an operational range exceeding 1200 °C (from room temperature to ~1283 °C). A measurement with a sub-200 µm 2D spatial resolution has also been demonstrated. Because of the small coupler cross section, the theoretical device resolution is limited by the Raleigh criterion, meaning that measurements with resolutions smaller than 5 µm can be possible. Since the MFCT is made from pure silica and silica softens at ~1680 °C, this device could potentially work at temperatures well in excess of 1283 °C, which is the highest temperature recorded so far with a device made from a conventional telecom optical fiber. MFCT offers several advantages, including compactness (few µm in diameter), high temperature measurement capabilities, high responsivity, high spatial resolution, easy connection with other fiberized optical components, simple fabrication and low cost. Since the measured temperature is the average temperature of the intermodal coupling region, high resolution 3D measurements could be made possible by reducing the length of the sensitive area. Moreover, although response time measurements have not been carried out, because of the reduced volume this device is expected to have a response time comparable/better than that observed in thermometers based on optical fiber gratings. The possibility to have high resolution T measurements could find useful applications in biology, medicine and material science.

Acknowledgments

GB gratefully acknowledges the Royal Society (UK) for his University Research Fellowship.

References and links

1.

Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8(4), 355–375 (1997). [CrossRef]

2.

K. T. V. Grattan, Z. Y. Zhang, T. Sun, Y. Shen, L. Tong, and Z. Ding, “Sapphire-ruby single-crystal fibre for application in high temperature optical fibre thermometers: studies at temperatures up to 1500 °C,” Meas. Sci. Technol. 12, 981–986 (2001).

3.

G. Coviello, V. Finazzi, J. Villatoro, and V. Pruneri, “Thermally stabilized PCF-based sensor for temperature measurements up to 1000 ° C,” Opt. Express 17(24), 21551–21559 (2009). [CrossRef] [PubMed]

4.

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]

5.

D. Grobnic, S. J. Mihailov, C. W. Smelser, and H. Ding, “Sapphire fiber Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett. 16(11), 2505–2507 (2004). [CrossRef]

6.

J. Feng, M. Ding, J.-L. Kou, F. Xu, and Y. Q. Lu, “An optical fiber tip micrograting thermometer,” IEEE Photonics J. 3(5), 810–814 (2011). [CrossRef]

7.

J. L. Kou, S. J. Qiu, F. Xu, and Y. Q. Lu, “Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe,” Opt. Express 19(19), 18452–18457 (2011). [CrossRef] [PubMed]

8.

V. de Oliveira, M. Muller, and H. J. Kalinowski, “Bragg gratings in standard nonhydrogenated fibers for high-temperature sensing,” Appl. Opt. 50(25), E55–E58 (2011). [CrossRef]

9.

G. Brambilla and H. Rutt, “Fiber Bragg gratings with enhanced thermal stability,” Appl. Phys. Lett. 80(18), 3259–3261 (2002). [CrossRef]

10.

D. Barrera, V. Finazzi, J. Villatoro, S. Sales, and V. Pruneri, “Packaged optical sensors based on regenerated fiber Bragg gratings for high temperature application,” IEEE Sens. J. 12(1), 107–112 (2012). [CrossRef]

11.

J. Canning, M. Stevenson, S. Bandyopadhyay, and K. Cook, “Extreme silica optical fibre gratings,” Sensors (Basel Switzerland) 8(10), 6448–6452 (2008). [CrossRef]

12.

Y. Li, M. Yang, D. N. Wang, J. Lu, T. Sun, and K. T. Grattan, “Fiber Bragg gratings with enhanced thermal stability by residual stress relaxation,” Opt. Express 17(22), 19785–19790 (2009). [CrossRef] [PubMed]

13.

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]

14.

C. Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol. 24(3), 1395–1402 (2006). [CrossRef]

15.

G. Brambilla, “Optical fibre nanotaper sensors,” Opt. Fiber Technol. 16(6), 331–342 (2010). [CrossRef]

16.

G. Brambilla, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical manipulation of microspheres along a subwavelength optical wire,” Opt. Lett. 32(20), 3041–3043 (2007). [CrossRef] [PubMed]

17.

Y. Jung, G. Brambilla, and D. J. Richardson, “Broadband single-mode operation of standard optical fibers by using a sub-wavelength optical wire filter,” Opt. Express 16(19), 14661–14667 (2008). [CrossRef] [PubMed]

18.

Y. Jung, G. Brambilla, and D. J. Richardson, “Optical microfiber coupler for broadband single-mode operation,” Opt. Express 17(7), 5273–5278 (2009). [CrossRef] [PubMed]

19.

H. Guo, F. Pang, X. Zeng, N. Chen, Z. Chen, and T. Wang, “Temperature sensor using an optical fiber coupler with a thin film,” Appl. Opt. 47(19), 3530–3534 (2008). [CrossRef] [PubMed]

20.

G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, “Compound-glass optical nanowires,” Electron. Lett. 41(7), 400–402 (2005). [CrossRef]

21.

F. P. Payne, C. D. Hussey, and M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett. 21(13), 561–563 (1985). [CrossRef]

22.

J. H. Wray and J. T. Neu, “Refractive index of several glasses as a function of wavelength and temperature,” J. Opt. Soc. Am. 59(6), 774–776 (1969). [CrossRef]

23.

C. Rodenburg, X. Lui, M. A. E. Jepson, S. A. Boden, and G. Brambilla, ““Surface morphology of silica nanowires at the nanometer scale,”J. Non-Cryst. Sol. 357, 3042–3045 (2011).

24.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]

25.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. Joseph Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997). [CrossRef]

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(060.2340) Fiber optics and optical communications : Fiber optics components
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(230.1150) Optical devices : All-optical devices

ToC Category:
Sensors

History
Original Manuscript: December 21, 2011
Revised Manuscript: February 6, 2012
Manuscript Accepted: February 14, 2012
Published: February 21, 2012

Citation
Ming Ding, Pengfei Wang, and Gilberto Brambilla, "A microfiber coupler tip thermometer," Opt. Express 20, 5402-5408 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5402


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References

  1. Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol.8(4), 355–375 (1997). [CrossRef]
  2. K. T. V. Grattan, Z. Y. Zhang, T. Sun, Y. Shen, L. Tong, and Z. Ding, “Sapphire-ruby single-crystal fibre for application in high temperature optical fibre thermometers: studies at temperatures up to 1500 °C,” Meas. Sci. Technol.12, 981–986 (2001).
  3. G. Coviello, V. Finazzi, J. Villatoro, and V. Pruneri, “Thermally stabilized PCF-based sensor for temperature measurements up to 1000 ° C,” Opt. Express17(24), 21551–21559 (2009). [CrossRef] [PubMed]
  4. 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]
  5. D. Grobnic, S. J. Mihailov, C. W. Smelser, and H. Ding, “Sapphire fiber Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett.16(11), 2505–2507 (2004). [CrossRef]
  6. J. Feng, M. Ding, J.-L. Kou, F. Xu, and Y. Q. Lu, “An optical fiber tip micrograting thermometer,” IEEE Photonics J.3(5), 810–814 (2011). [CrossRef]
  7. J. L. Kou, S. J. Qiu, F. Xu, and Y. Q. Lu, “Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe,” Opt. Express19(19), 18452–18457 (2011). [CrossRef] [PubMed]
  8. V. de Oliveira, M. Muller, and H. J. Kalinowski, “Bragg gratings in standard nonhydrogenated fibers for high-temperature sensing,” Appl. Opt.50(25), E55–E58 (2011). [CrossRef]
  9. G. Brambilla and H. Rutt, “Fiber Bragg gratings with enhanced thermal stability,” Appl. Phys. Lett.80(18), 3259–3261 (2002). [CrossRef]
  10. D. Barrera, V. Finazzi, J. Villatoro, S. Sales, and V. Pruneri, “Packaged optical sensors based on regenerated fiber Bragg gratings for high temperature application,” IEEE Sens. J.12(1), 107–112 (2012). [CrossRef]
  11. J. Canning, M. Stevenson, S. Bandyopadhyay, and K. Cook, “Extreme silica optical fibre gratings,” Sensors (Basel Switzerland)8(10), 6448–6452 (2008). [CrossRef]
  12. Y. Li, M. Yang, D. N. Wang, J. Lu, T. Sun, and K. T. Grattan, “Fiber Bragg gratings with enhanced thermal stability by residual stress relaxation,” Opt. Express17(22), 19785–19790 (2009). [CrossRef] [PubMed]
  13. 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]
  14. C. Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol.24(3), 1395–1402 (2006). [CrossRef]
  15. G. Brambilla, “Optical fibre nanotaper sensors,” Opt. Fiber Technol.16(6), 331–342 (2010). [CrossRef]
  16. G. Brambilla, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical manipulation of microspheres along a subwavelength optical wire,” Opt. Lett.32(20), 3041–3043 (2007). [CrossRef] [PubMed]
  17. Y. Jung, G. Brambilla, and D. J. Richardson, “Broadband single-mode operation of standard optical fibers by using a sub-wavelength optical wire filter,” Opt. Express16(19), 14661–14667 (2008). [CrossRef] [PubMed]
  18. Y. Jung, G. Brambilla, and D. J. Richardson, “Optical microfiber coupler for broadband single-mode operation,” Opt. Express17(7), 5273–5278 (2009). [CrossRef] [PubMed]
  19. H. Guo, F. Pang, X. Zeng, N. Chen, Z. Chen, and T. Wang, “Temperature sensor using an optical fiber coupler with a thin film,” Appl. Opt.47(19), 3530–3534 (2008). [CrossRef] [PubMed]
  20. G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, “Compound-glass optical nanowires,” Electron. Lett.41(7), 400–402 (2005). [CrossRef]
  21. F. P. Payne, C. D. Hussey, and M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett.21(13), 561–563 (1985). [CrossRef]
  22. J. H. Wray and J. T. Neu, “Refractive index of several glasses as a function of wavelength and temperature,” J. Opt. Soc. Am.59(6), 774–776 (1969). [CrossRef]
  23. C. Rodenburg, X. Lui, M. A. E. Jepson, S. A. Boden, and G. Brambilla, ““Surface morphology of silica nanowires at the nanometer scale,”J. Non-Cryst. Sol.357, 3042–3045 (2011).
  24. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997). [CrossRef]
  25. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. Joseph Friebele, “Fiber grating sensors,” J. Lightwave Technol.15(8), 1442–1463 (1997). [CrossRef]

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