Abstract

We present a new theoretical model for the broadband reflection spectra of etched FBGs which includes the effects of axial contraction and stress-induced index change. The reflection spectra of the etched FBGs with several different taper profiles are simulated based on the proposed model. In our observation, decaying exponential profile produces a broadband reflection spectrum with good uniformity over the range of 1540-1560 nm. An etched FBG with similar taper profile is fabricated and the experimental result shows good agreement with the theoretical model.

©2013 Optical Society of America

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References

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  1. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
    [Crossref]
  2. C. Li, N. Chen, Z. Chen, and T. Wang, “Fully distributed chirped FBG sensor and application in laser-induced interstitial thermotherapy,” Communications and Photonics Conference and Exhibition (ACP), 2009 Asia, vol.2009-Supplement, 1,6, 2–6 (2009).
  3. Y. Takubo and S. Yamashita, “High-speed dispersion-tuned wavelength-swept fiber laser using a reflective SOA and a chirped FBG,” Opt. Express 21(4), 5130–5139 (2013).
    [Crossref] [PubMed]
  4. K. C. Byron, K. Sugden, T. Bricheno, and I. Bennion, “Fabrication of chirped Bragg gratings in photosensitive fiber,” Electron. Lett. 29(18), 1659–1660 (1993).
    [Crossref]
  5. F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22(11), 831–833 (1997).
    [Crossref] [PubMed]
  6. C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008).
    [Crossref]
  7. J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002).
    [Crossref]
  8. J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004).
    [Crossref]
  9. N. Q. Ngo, S. Y. Li, R. T. Zheng, S. C. Tjin, and P. Shum, “Electrically tunable dispersion compensator with fixed center wavelength using fiber Bragg grating,” J. Lightwave Technol. 21(6), 1568–1575 (2003).
    [Crossref]
  10. J. L. Cruz, L. Dong, S. Barcelos, and L. Reekie, “Fiber Bragg gratings with various chirp profiles made in etched tapers,” Appl. Opt. 35(34), 6781–6787 (1996).
    [Crossref] [PubMed]
  11. L. Dong, J. L. Cruz, L. Reekie, and J. A. Tucknott, “Fabrication of chirped fiber gratings using etched tapers,” Electron. Lett. 31(11), 908–909 (1995).
    [Crossref]
  12. X. Dong, P. Shum, N. Ngo, C. Chan, J. Ng, and C. Zhao, “A largely tunable CFBG-based dispersion compensator with fixed center wavelength,” Opt. Express 11(22), 2970–2974 (2003).
    [Crossref] [PubMed]
  13. Z. Li, Z. Chen, V. K. S. Hsiao, J. Y. Tang, F. Zhao, and S. J. Jiang, “Optically tunable chirped fiber Bragg grating,” Opt. Express 20(10), 10827–10832 (2012).
    [Crossref] [PubMed]
  14. M. G. Sceats, G. R. Atkins, and S. B. Poole, “Photolytic index changes in optical fibers,” Annu. Rev. Mater. Sci. 23(1), 381–410 (1993).
    [Crossref]
  15. K. S. Lim, H. Z. Yang, W. Y. Chong, Y. K. Cheong, C. H. Lim, N. M. Ali, and H. Ahmad, “Axial contraction in etched optical fiber due to internal stress reduction,” Opt. Express 21(3), 2551–2562 (2013).
    [Crossref] [PubMed]
  16. A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005).
    [Crossref]
  17. W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
    [Crossref]
  18. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
    [Crossref]
  19. T. Erdogan, “Cladding-mode resonances in short-and long-period fiber grating filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997).
    [Crossref]

2013 (2)

2012 (1)

2008 (1)

C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008).
[Crossref]

2005 (2)

A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005).
[Crossref]

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

2004 (1)

J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004).
[Crossref]

2003 (2)

2002 (1)

J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002).
[Crossref]

1997 (4)

1996 (1)

1995 (1)

L. Dong, J. L. Cruz, L. Reekie, and J. A. Tucknott, “Fabrication of chirped fiber gratings using etched tapers,” Electron. Lett. 31(11), 908–909 (1995).
[Crossref]

1993 (2)

K. C. Byron, K. Sugden, T. Bricheno, and I. Bennion, “Fabrication of chirped Bragg gratings in photosensitive fiber,” Electron. Lett. 29(18), 1659–1660 (1993).
[Crossref]

M. G. Sceats, G. R. Atkins, and S. B. Poole, “Photolytic index changes in optical fibers,” Annu. Rev. Mater. Sci. 23(1), 381–410 (1993).
[Crossref]

Ahmad, H.

Ali, N. M.

Andres, M. V.

J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004).
[Crossref]

J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002).
[Crossref]

Atkins, G. R.

M. G. Sceats, G. R. Atkins, and S. B. Poole, “Photolytic index changes in optical fibers,” Annu. Rev. Mater. Sci. 23(1), 381–410 (1993).
[Crossref]

Barcelos, S.

Bennion, I.

K. C. Byron, K. Sugden, T. Bricheno, and I. Bennion, “Fabrication of chirped Bragg gratings in photosensitive fiber,” Electron. Lett. 29(18), 1659–1660 (1993).
[Crossref]

Bricheno, T.

K. C. Byron, K. Sugden, T. Bricheno, and I. Bennion, “Fabrication of chirped Bragg gratings in photosensitive fiber,” Electron. Lett. 29(18), 1659–1660 (1993).
[Crossref]

Byron, K. C.

K. C. Byron, K. Sugden, T. Bricheno, and I. Bennion, “Fabrication of chirped Bragg gratings in photosensitive fiber,” Electron. Lett. 29(18), 1659–1660 (1993).
[Crossref]

Chan, C.

Chen, Z.

Cheong, Y. K.

Chong, W. Y.

Chryssis, A. N.

A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005).
[Crossref]

Cruz, J. L.

J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002).
[Crossref]

J. L. Cruz, L. Dong, S. Barcelos, and L. Reekie, “Fiber Bragg gratings with various chirp profiles made in etched tapers,” Appl. Opt. 35(34), 6781–6787 (1996).
[Crossref] [PubMed]

L. Dong, J. L. Cruz, L. Reekie, and J. A. Tucknott, “Fabrication of chirped fiber gratings using etched tapers,” Electron. Lett. 31(11), 908–909 (1995).
[Crossref]

Cui, J.

C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008).
[Crossref]

Cui, Y.

C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008).
[Crossref]

Dagenais, M.

A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005).
[Crossref]

Diez, A.

J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004).
[Crossref]

J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002).
[Crossref]

Dong, L.

J. L. Cruz, L. Dong, S. Barcelos, and L. Reekie, “Fiber Bragg gratings with various chirp profiles made in etched tapers,” Appl. Opt. 35(34), 6781–6787 (1996).
[Crossref] [PubMed]

L. Dong, J. L. Cruz, L. Reekie, and J. A. Tucknott, “Fabrication of chirped fiber gratings using etched tapers,” Electron. Lett. 31(11), 908–909 (1995).
[Crossref]

Dong, X.

Erdogan, T.

Fonjallaz, P. Y.

J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004).
[Crossref]

Haus, H. A.

Heine, C.

Hill, K. O.

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

Hsiao, V. K. S.

Huang, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Jiang, S. J.

Kärtner, F. X.

Keller, U.

Lee, R. K.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Lee, S. B.

A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005).
[Crossref]

Lee, S. M.

A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005).
[Crossref]

Li, S. Y.

Li, Z.

Liang, W.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Lim, C. H.

Lim, K. S.

Lu, C.

C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008).
[Crossref]

Matuschek, N.

Meltz, G.

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

Mora, J.

J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004).
[Crossref]

J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002).
[Crossref]

Morf, R.

Ng, J.

Ngo, N.

Ngo, N. Q.

Poole, S. B.

M. G. Sceats, G. R. Atkins, and S. B. Poole, “Photolytic index changes in optical fibers,” Annu. Rev. Mater. Sci. 23(1), 381–410 (1993).
[Crossref]

Popov, M.

J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004).
[Crossref]

Reekie, L.

J. L. Cruz, L. Dong, S. Barcelos, and L. Reekie, “Fiber Bragg gratings with various chirp profiles made in etched tapers,” Appl. Opt. 35(34), 6781–6787 (1996).
[Crossref] [PubMed]

L. Dong, J. L. Cruz, L. Reekie, and J. A. Tucknott, “Fabrication of chirped fiber gratings using etched tapers,” Electron. Lett. 31(11), 908–909 (1995).
[Crossref]

Saini, S. S.

A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005).
[Crossref]

Sceats, M. G.

M. G. Sceats, G. R. Atkins, and S. B. Poole, “Photolytic index changes in optical fibers,” Annu. Rev. Mater. Sci. 23(1), 381–410 (1993).
[Crossref]

Scheuer, V.

Schibli, T.

Shum, P.

Sugden, K.

K. C. Byron, K. Sugden, T. Bricheno, and I. Bennion, “Fabrication of chirped Bragg gratings in photosensitive fiber,” Electron. Lett. 29(18), 1659–1660 (1993).
[Crossref]

Takubo, Y.

Tang, J. Y.

Tilsch, M.

Tjin, S. C.

Tschudi, T.

Tucknott, J. A.

L. Dong, J. L. Cruz, L. Reekie, and J. A. Tucknott, “Fabrication of chirped fiber gratings using etched tapers,” Electron. Lett. 31(11), 908–909 (1995).
[Crossref]

Villatoro, J.

J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002).
[Crossref]

Xu, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Yamashita, S.

Yang, H. Z.

Yariv, A.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Zhao, C.

Zhao, F.

Zheng, R. T.

Annu. Rev. Mater. Sci. (1)

M. G. Sceats, G. R. Atkins, and S. B. Poole, “Photolytic index changes in optical fibers,” Annu. Rev. Mater. Sci. 23(1), 381–410 (1993).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Electron. Lett. (2)

L. Dong, J. L. Cruz, L. Reekie, and J. A. Tucknott, “Fabrication of chirped fiber gratings using etched tapers,” Electron. Lett. 31(11), 908–909 (1995).
[Crossref]

K. C. Byron, K. Sugden, T. Bricheno, and I. Bennion, “Fabrication of chirped Bragg gratings in photosensitive fiber,” Electron. Lett. 29(18), 1659–1660 (1993).
[Crossref]

IEEE Photon. Technol. Lett. (2)

J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004).
[Crossref]

A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005).
[Crossref]

J. Lightwave Technol. (3)

N. Q. Ngo, S. Y. Li, R. T. Zheng, S. C. Tjin, and P. Shum, “Electrically tunable dispersion compensator with fixed center wavelength using fiber Bragg grating,” J. Lightwave Technol. 21(6), 1568–1575 (2003).
[Crossref]

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

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

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

Opt. Commun. (1)

J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002).
[Crossref]

Opt. Express (4)

Opt. Fiber Technol. (1)

C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008).
[Crossref]

Opt. Lett. (1)

Other (1)

C. Li, N. Chen, Z. Chen, and T. Wang, “Fully distributed chirped FBG sensor and application in laser-induced interstitial thermotherapy,” Communications and Photonics Conference and Exhibition (ACP), 2009 Asia, vol.2009-Supplement, 1,6, 2–6 (2009).

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Figures (5)

Fig. 1
Fig. 1

(a) The neff varied with the fiber radius ξ in various nam of ambient materials. (b) The ∆neff varied with the nam in different fiber radius.

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Fig. 2
Fig. 2

(a) Graph of radius profile and (b) neff variation along the etched FBG. (c) Reflection spectra of etched FBG of different taper profiles, simulated based on conventional model (dotted) and proposed model (solid).

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Fig. 3
Fig. 3

Microscope images of the (a) transition and (b) taper end of the etched FBG.

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Fig. 4
Fig. 4

The spectra of the FBG before etching (black), under etching in BOE solution (green) and after etching (red).

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Fig. 5
Fig. 5

Comparison between (a) experimental and (b) simulation results for the etched FBG in mediums of different RIs. The spectral bandwidth varies with different RI.

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Tables (1)

Tables Icon

Table 1 Bandwidth comparison between experimental and simulation results.

View Table

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

λ B (ξ, n am )=2 n eff (ξ, n am )Λ(ξ)
Δ n eff (ξ, n am )= n eff (ξ, n am )− n eff (b, n am )
Δ n ¯ (ξ)=− ( C 1 +3 C 2 ) 2 ( EβT 1+ν ){ ( 1− 2 γ+2 )( a 2 ξ 2 − a 2 b 2 ) ξ>a 1− a 2 b 2 ( 1− 2 γ+2 )−( 2 γ+2 ) ( ξ a ) γ ξ<a
Λ(ξ)= Λ 0 ( 1−ε(ξ) )
ε(ξ)=− βT 1+ν { ( 1− 2 γ+2 )( 1− a 2 b 2 )+ 2 γ+2 [ 1− ( ξ a ) γ ] 0≤ξ≤a ( b 2 ξ 2 −1 ) ( a b ) 2 ( 1− 2 γ+2 ) a<ξ≤b
κ=υπδn λ −1
σ(ξ)=2π λ −1 (δn+Δ n eff (ξ)+Δ n ¯ (ξ))
δ(ξ)= 2π n eff λ − π Λ 0 ( 1−ε(ξ) )
F i =( cosh( γ B Δz)−i σ ^ γ B sinh( γ B Δz) −i κ γ B sinh( γ B Δz) i κ γ B sinh( γ B Δz) cosh( γ B Δz)+i σ ^ γ B sinh( γ B Δz) )
( R M S M )= F M ⋅ F M−1 ⋯ F i ⋯ F 1 ( R 0 S 0 )=( f 11 f 12 f 21 f 22 )( R 0 S 0 )
Δλ= λ B (b, n am )[ ε( ξ min )−( 1−ε( ξ min ) )( Δ n eff ( ξ min )+Δ n ¯ ( ξ min ) n eff (b) ) ]

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