Abstract

We use the phase mask method to investigate both experimentally and theoretically the temporal thermal response of Type II–IR fiber Bragg gratings inscribed by a femtosecond laser. A fast testing system is developed to measure the thermal response time by means of periodic CO2 laser irradiation, which creates a rapid temperature change environment. The temporal thermal response is found to be independent of the heat power and the heat direction, although the grating produced destroys the axial symmetry of the fiber. The measured values of the temporal thermal response are 230ms for heating and 275ms for cooling, which different from the simulation results obtained from a lumped system equation. The causes of such differences are investigated in detail.

© 2009 Optical Society of America

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  1. Y. H. Shen, J. Xia, T. Sun, and K. T. V. Grattan, “Photosensitive indium-doped germano-silica fiber for strong FBG with high temperature sustainability,” IEEE Photon. Technol. Lett. 16, 1319-1321 (2004).
    [CrossRef]
  2. Y. H. Shen, J. L. He, T. Sun, and K. T. V. Grattan, “High-temperature sustainability of strong fiber Bragg gratings written into Sb-Ge-codoped photosensitive fiber: decay mechanisms involved during annealing,” Opt. Lett. 29, 554-556 (2004).
    [CrossRef] [PubMed]
  3. C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13, 5377-5386 (2005).
    [CrossRef] [PubMed]
  4. E. Wikszak, J. Thomas, J. Burghoff, B. Ortac, J. Limpert, and S. Nolte, “Erbium fiber laser based on intracore femtosecond-written fiber Bragg grating,” Opt. Lett. 31, 2390-2392 (2006).
    [CrossRef] [PubMed]
  5. M. Bernier, D. Faucher, R. Vallée, A. Saliminia, G. Androz, Y. Sheng, and S. L. Chin, “Bragg gratings photoinduced in ZBLAN fibers by femtosecond pulses at 800 nm,” Opt. Lett. 32, 454-456 (2007).
    [CrossRef] [PubMed]
  6. D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
    [CrossRef]
  7. Y. H. Li, C. R. Liao, D. N. Wang, T. Sun, and K. T. V. Grattan, “Study of spectral and annealing properties of fiber Bragg gratings written in H2-free and H2-loaded fibers by use of femtosecond laser pulses,” Opt. Express 16, 21239-21247 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  9. C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Hydrogen loading for fiber grating writing with a femtosecond laser and a phase mask,” Opt. Lett. 29, 2127-2129 (2004).
    [CrossRef] [PubMed]
  10. D. Grobnic, C. W. Smelser, S. J. Mihailov, and R. B. Walker, “Long-term thermal stability tests at 1000 °C of silica fibre Bragg gratings made with ultrafast laser radiation,” Meas. Sci. Technol. 17, 1009-1013 (2006).
    [CrossRef]
  11. G. M. H. Flockhart, R. R. J. Maier, J. S. Barton, W. N. Macpherson, J. D. C. Jones, K. E. Chisholm, L. Zhang, I. Bennion, I. Read, and P. D. Foote, “Quadratic behavior of fiber Bragg grating temperature coefficients,” Appl. Opt. 43, 2744-2751 (2004).
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    [CrossRef] [PubMed]
  13. S. H. Cho, J. Park, B. Kim, and M. H. Kang, “Fabrication and analysis of chirped fiber Bragg gratings by thermal diffusion,” ETRI J. 26, 371-374 (2004).
    [CrossRef]
  14. Y. Wang and K. Vafai, “An experimental investigation of the thermal performance of an asymmetrical flat plate heat pipe,” Int. J. Heat Mass Transfer 43, 2657-2668(2000).
    [CrossRef]
  15. M. Sumetsky, Y. Dulashko, J. M. Fini, A. Hale, and D. J. DiGiovanni, “The microfiber loop resonator: theory, experiment, and application,” J. Lightwave Technol. 24, 242-250 (2006).
    [CrossRef]
  16. A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat tranfer modeling in CO2 laser processing of optical fibers,” Opt. Commun. 152, 324-328 (1998).
    [CrossRef]
  17. G. Rego, L. M. N. B. F. Santos, and B. Schröder, “Estimation of the fiber temperature during an arc-discharge,” Microwave Opt. Technol. Lett. 50, 2020-2025 (2008).
    [CrossRef]

2008

2007

M. Bernier, D. Faucher, R. Vallée, A. Saliminia, G. Androz, Y. Sheng, and S. L. Chin, “Bragg gratings photoinduced in ZBLAN fibers by femtosecond pulses at 800 nm,” Opt. Lett. 32, 454-456 (2007).
[CrossRef] [PubMed]

D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
[CrossRef]

2006

A. J. V. Wyk, P. L. Swart, and A. A. Chtcherbakov, “Fiber Bragg grating gas temperature sensor with fast response,” Meas. Sci. Technol. 17, 1113-1117 (2006).
[CrossRef]

D. Grobnic, C. W. Smelser, S. J. Mihailov, and R. B. Walker, “Long-term thermal stability tests at 1000 °C of silica fibre Bragg gratings made with ultrafast laser radiation,” Meas. Sci. Technol. 17, 1009-1013 (2006).
[CrossRef]

M. Sumetsky, Y. Dulashko, J. M. Fini, A. Hale, and D. J. DiGiovanni, “The microfiber loop resonator: theory, experiment, and application,” J. Lightwave Technol. 24, 242-250 (2006).
[CrossRef]

E. Wikszak, J. Thomas, J. Burghoff, B. Ortac, J. Limpert, and S. Nolte, “Erbium fiber laser based on intracore femtosecond-written fiber Bragg grating,” Opt. Lett. 31, 2390-2392 (2006).
[CrossRef] [PubMed]

2005

2004

2000

Y. Wang and K. Vafai, “An experimental investigation of the thermal performance of an asymmetrical flat plate heat pipe,” Int. J. Heat Mass Transfer 43, 2657-2668(2000).
[CrossRef]

1998

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat tranfer modeling in CO2 laser processing of optical fibers,” Opt. Commun. 152, 324-328 (1998).
[CrossRef]

Androz, G.

Barton, J. S.

Bennion, I.

Bernier, M.

Burghoff, J.

Chin, S. L.

Chisholm, K. E.

Cho, S. H.

S. H. Cho, J. Park, B. Kim, and M. H. Kang, “Fabrication and analysis of chirped fiber Bragg gratings by thermal diffusion,” ETRI J. 26, 371-374 (2004).
[CrossRef]

Chtcherbakov, A. A.

A. J. V. Wyk, P. L. Swart, and A. A. Chtcherbakov, “Fiber Bragg grating gas temperature sensor with fast response,” Meas. Sci. Technol. 17, 1113-1117 (2006).
[CrossRef]

Croteau, A.

D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
[CrossRef]

DiGiovanni, D. J.

Dulashko, Y.

Faucher, D.

Fini, J. M.

Flockhart, G. M. H.

Foote, P. D.

Grattan, K. T. V.

Grellier, A. J. C.

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat tranfer modeling in CO2 laser processing of optical fibers,” Opt. Commun. 152, 324-328 (1998).
[CrossRef]

Grobnic, D.

D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
[CrossRef]

D. Grobnic, C. W. Smelser, S. J. Mihailov, and R. B. Walker, “Long-term thermal stability tests at 1000 °C of silica fibre Bragg gratings made with ultrafast laser radiation,” Meas. Sci. Technol. 17, 1009-1013 (2006).
[CrossRef]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Hydrogen loading for fiber grating writing with a femtosecond laser and a phase mask,” Opt. Lett. 29, 2127-2129 (2004).
[CrossRef] [PubMed]

Hale, A.

He, J. L.

Jones, J. D. C.

Kang, M. H.

S. H. Cho, J. Park, B. Kim, and M. H. Kang, “Fabrication and analysis of chirped fiber Bragg gratings by thermal diffusion,” ETRI J. 26, 371-374 (2004).
[CrossRef]

Kim, B.

S. H. Cho, J. Park, B. Kim, and M. H. Kang, “Fabrication and analysis of chirped fiber Bragg gratings by thermal diffusion,” ETRI J. 26, 371-374 (2004).
[CrossRef]

Kunzler, W. M.

Lafond, C.

D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
[CrossRef]

Li, Y. H.

Liao, C. R.

Limpert, J.

Lowder, T. L.

Macpherson, W. N.

Maier, R. R. J.

Mihailov, S. J.

D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
[CrossRef]

D. Grobnic, C. W. Smelser, S. J. Mihailov, and R. B. Walker, “Long-term thermal stability tests at 1000 °C of silica fibre Bragg gratings made with ultrafast laser radiation,” Meas. Sci. Technol. 17, 1009-1013 (2006).
[CrossRef]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Hydrogen loading for fiber grating writing with a femtosecond laser and a phase mask,” Opt. Lett. 29, 2127-2129 (2004).
[CrossRef] [PubMed]

Newman, J. A.

Nolte, S.

Ortac, B.

Pannell, C. N.

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat tranfer modeling in CO2 laser processing of optical fibers,” Opt. Commun. 152, 324-328 (1998).
[CrossRef]

Park, J.

S. H. Cho, J. Park, B. Kim, and M. H. Kang, “Fabrication and analysis of chirped fiber Bragg gratings by thermal diffusion,” ETRI J. 26, 371-374 (2004).
[CrossRef]

Read, I.

Rego, G.

G. Rego, L. M. N. B. F. Santos, and B. Schröder, “Estimation of the fiber temperature during an arc-discharge,” Microwave Opt. Technol. Lett. 50, 2020-2025 (2008).
[CrossRef]

Saliminia, A.

Santos, L. M. N. B. F.

G. Rego, L. M. N. B. F. Santos, and B. Schröder, “Estimation of the fiber temperature during an arc-discharge,” Microwave Opt. Technol. Lett. 50, 2020-2025 (2008).
[CrossRef]

Schröder, B.

G. Rego, L. M. N. B. F. Santos, and B. Schröder, “Estimation of the fiber temperature during an arc-discharge,” Microwave Opt. Technol. Lett. 50, 2020-2025 (2008).
[CrossRef]

Schultz, S. M.

Selfridge, R. H.

Shen, Y. H.

Y. H. Shen, J. Xia, T. Sun, and K. T. V. Grattan, “Photosensitive indium-doped germano-silica fiber for strong FBG with high temperature sustainability,” IEEE Photon. Technol. Lett. 16, 1319-1321 (2004).
[CrossRef]

Y. H. Shen, J. L. He, T. Sun, and K. T. V. Grattan, “High-temperature sustainability of strong fiber Bragg gratings written into Sb-Ge-codoped photosensitive fiber: decay mechanisms involved during annealing,” Opt. Lett. 29, 554-556 (2004).
[CrossRef] [PubMed]

Sheng, Y.

Smelser, C. W.

D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
[CrossRef]

D. Grobnic, C. W. Smelser, S. J. Mihailov, and R. B. Walker, “Long-term thermal stability tests at 1000 °C of silica fibre Bragg gratings made with ultrafast laser radiation,” Meas. Sci. Technol. 17, 1009-1013 (2006).
[CrossRef]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13, 5377-5386 (2005).
[CrossRef] [PubMed]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Hydrogen loading for fiber grating writing with a femtosecond laser and a phase mask,” Opt. Lett. 29, 2127-2129 (2004).
[CrossRef] [PubMed]

Sumetsky, M.

Sun, T.

Swart, P. L.

A. J. V. Wyk, P. L. Swart, and A. A. Chtcherbakov, “Fiber Bragg grating gas temperature sensor with fast response,” Meas. Sci. Technol. 17, 1113-1117 (2006).
[CrossRef]

Thomas, J.

Vafai, K.

Y. Wang and K. Vafai, “An experimental investigation of the thermal performance of an asymmetrical flat plate heat pipe,” Int. J. Heat Mass Transfer 43, 2657-2668(2000).
[CrossRef]

Vallée, R.

Walker, R. B.

D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
[CrossRef]

D. Grobnic, C. W. Smelser, S. J. Mihailov, and R. B. Walker, “Long-term thermal stability tests at 1000 °C of silica fibre Bragg gratings made with ultrafast laser radiation,” Meas. Sci. Technol. 17, 1009-1013 (2006).
[CrossRef]

Wang, D. N.

Wang, Y.

Y. Wang and K. Vafai, “An experimental investigation of the thermal performance of an asymmetrical flat plate heat pipe,” Int. J. Heat Mass Transfer 43, 2657-2668(2000).
[CrossRef]

Wikszak, E.

Wyk, A. J. V.

A. J. V. Wyk, P. L. Swart, and A. A. Chtcherbakov, “Fiber Bragg grating gas temperature sensor with fast response,” Meas. Sci. Technol. 17, 1113-1117 (2006).
[CrossRef]

Xia, J.

Y. H. Shen, J. Xia, T. Sun, and K. T. V. Grattan, “Photosensitive indium-doped germano-silica fiber for strong FBG with high temperature sustainability,” IEEE Photon. Technol. Lett. 16, 1319-1321 (2004).
[CrossRef]

Young, J. D.

Zayer,

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat tranfer modeling in CO2 laser processing of optical fibers,” Opt. Commun. 152, 324-328 (1998).
[CrossRef]

Zhang, L.

Appl. Opt.

ETRI J.

S. H. Cho, J. Park, B. Kim, and M. H. Kang, “Fabrication and analysis of chirped fiber Bragg gratings by thermal diffusion,” ETRI J. 26, 371-374 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

Y. H. Shen, J. Xia, T. Sun, and K. T. V. Grattan, “Photosensitive indium-doped germano-silica fiber for strong FBG with high temperature sustainability,” IEEE Photon. Technol. Lett. 16, 1319-1321 (2004).
[CrossRef]

D. Grobnic, S. J. Mihailov, R. B. Walker, C. W. Smelser, C. Lafond, and A. Croteau, “Bragg gratings made with a femtosecond laser in heavily doped Er-Yb phosphate glass fiber,” IEEE Photon. Technol. Lett. 19, 943-945 (2007).
[CrossRef]

Int. J. Heat Mass Transfer

Y. Wang and K. Vafai, “An experimental investigation of the thermal performance of an asymmetrical flat plate heat pipe,” Int. J. Heat Mass Transfer 43, 2657-2668(2000).
[CrossRef]

J. Lightwave Technol.

Meas. Sci. Technol.

A. J. V. Wyk, P. L. Swart, and A. A. Chtcherbakov, “Fiber Bragg grating gas temperature sensor with fast response,” Meas. Sci. Technol. 17, 1113-1117 (2006).
[CrossRef]

D. Grobnic, C. W. Smelser, S. J. Mihailov, and R. B. Walker, “Long-term thermal stability tests at 1000 °C of silica fibre Bragg gratings made with ultrafast laser radiation,” Meas. Sci. Technol. 17, 1009-1013 (2006).
[CrossRef]

Microwave Opt. Technol. Lett.

G. Rego, L. M. N. B. F. Santos, and B. Schröder, “Estimation of the fiber temperature during an arc-discharge,” Microwave Opt. Technol. Lett. 50, 2020-2025 (2008).
[CrossRef]

Opt. Commun.

A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat tranfer modeling in CO2 laser processing of optical fibers,” Opt. Commun. 152, 324-328 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (10)

Fig. 1
Fig. 1

Reflection spectrum and morphology of a Type II–IR FBG fabricated with a femtosecond laser by the phase mask method.

Fig. 2
Fig. 2

Graph showing the change of λ Bragg as a function of temperature. The triangles represent the recorded data; the solid curve represents the quadratic fit.

Fig. 3
Fig. 3

Experimental setup of the FBG used for temporal thermal response measurements.

Fig. 4
Fig. 4

Typical response of the detected optical power (lower trace) with the incident CO 2 laser signal (upper trace). Laser is ON at the rising edge of the signal and OFF at the constant high level. The upper trace refers only to the frequency reference output waveform from the chopper drive, not to the actual laser power. The laser power modulation has a rectangular waveform.

Fig. 5
Fig. 5

Spectrum of the LPFG superimposed with the FBG at room temperature, 330 ° C , 415 ° C , and 460 ° C . Inset: relationship between the height of the FBG and the final temperature attained by the FBG.

Fig. 6
Fig. 6

Heating curve as a function of time for a Type II–IR FBG, which is heated by a CO 2 laser beam at different heights, thus attaining different final temperatures.

Fig. 7
Fig. 7

Cooling curves as a function of time of a Type II–IR FBG with different initial temperatures.

Fig. 8
Fig. 8

Temporal thermal response of a Type II–IR FBG as a function of the laser heating direction. The triangles represent the heating data; the squares represent the cooling data.

Fig. 9
Fig. 9

Simulated heating and cooling curves of a SMF-28 optical fiber heated at various laser powers.

Fig. 10
Fig. 10

Simulated heating and cooling curves of two different size optical fibers at the same heating power.

Equations (3)

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d T ( t ) d t = 1 τ ( T ( t ) T air ) + Ξ ( t ) , τ = c ρ V f A f h = c ρ r 2 h , Ξ ( t ) = q ( t ) c ρ ,
T ( 0 ) = T air ,
Ξ ( t ) = k A b r c ρ P ( t ) , P ( t ) = { P 0 t 30 , 0 < t 30 ms P 0 , 30 m s < t 2000 ms P 0 ( - t 30 + 203 3 ) , 2000 ms < t 2030 ms 0 , 2030 ms < t 4000 ms ,

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