Abstract

We propose a semi-empirical model for the complete analysis (spectrum, bandwidth, and wavelength/phase shifts) of a temperature-tuned long-period fiber grating (LPFG) filter. By applying the multi-port lattice model to LPFGs, while deriving and utilizing the empirically determined temperature-dependence of core-to-cladding intermodal dispersions, we achieve a precise, practical means of spectrum analysis. Excellent agreement of the model with the experimental results was obtained over wide spectral ranges.

© 2008 Optical Society of America

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  1. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
    [Crossref]
  2. B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
    [Crossref]
  3. V. Grubsky and J. Feinberg, “Long-period fiber gratings with variable coupling for real-time sensing applications,” Opt. Lett. 25, 203–205 (2000).
    [Crossref]
  4. B. J. Eggleton, R. E. Slusher, J. B. Judkins, J. B. Stark, and A. M. Vengsarkar, “All-optical switching in long period fiber gratings,” Opt. Lett. 22, 883–885 (1997).
    [Crossref] [PubMed]
  5. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
    [Crossref] [PubMed]
  6. Y. Liu, J. A. Willims, L. Zhang, and I. Bennion, “Phase shifted and cascaded long period fiber gratings,” Opt. Commun. 164, 27–31 (1999).
    [Crossref]
  7. M. Harurnoto, M. Shigehara, and H. Suganurna, “Gain-flattening filter using long-period fiber gratings,” J. Lightwave Technol. 20, 1027–1033 (2002).
    [Crossref]
  8. X. Shu, T. Allsop, B. Gwandu, and L. Zhang, “High-temperature sensitivity of long-period gratings in B—Ge codoped fiber,” Photon. Technol. Lett. 13, 818–820 (2001).
    [Crossref]
  9. J. K. Bae, J. Bae, S. H. Kim, N. Park, and S. B. Lee, “Dynamic EDFA gain-flattening filter using two LPFGs with divided coil heaters,” Photon. Technol. Lett. 17, 1226–1228 (2005).
    [Crossref]
  10. J. Bae, J. Chun, and S. B. Lee, “Synthesis of long-period fiber gratings with the inverted Erbium gain spectrum using the multiport lattice filter model,” J. Lightwave Technol. 22, 1976–1986 (2004).
    [Crossref]
  11. J. Bae, J. K. Bae, S. H. Kim, S. B. Lee, and J. Chun, “Analysis for long period fiber gratings using thermal kernel function,” Opt. Exp. 12, 797–810 (2004).
    [Crossref]
  12. T. Erdogan, “Cladding-mode resonances in short- and long- period fiber grating filters,” J. Opt. Soc. Am. A 14, 1760–1773 (1997).
    [Crossref]
  13. K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, and R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” Proc. Optical Fiber Communication Conf. Dallas, TX, 347–348, (1997).
    [Crossref]
  14. G. P. Agrawal, Fiber-Optic Communications Systems (New York: Wiley, 1997), Chap. 2.

2005 (1)

J. K. Bae, J. Bae, S. H. Kim, N. Park, and S. B. Lee, “Dynamic EDFA gain-flattening filter using two LPFGs with divided coil heaters,” Photon. Technol. Lett. 17, 1226–1228 (2005).
[Crossref]

2004 (2)

J. Bae, J. K. Bae, S. H. Kim, S. B. Lee, and J. Chun, “Analysis for long period fiber gratings using thermal kernel function,” Opt. Exp. 12, 797–810 (2004).
[Crossref]

J. Bae, J. Chun, and S. B. Lee, “Synthesis of long-period fiber gratings with the inverted Erbium gain spectrum using the multiport lattice filter model,” J. Lightwave Technol. 22, 1976–1986 (2004).
[Crossref]

2002 (1)

2001 (1)

X. Shu, T. Allsop, B. Gwandu, and L. Zhang, “High-temperature sensitivity of long-period gratings in B—Ge codoped fiber,” Photon. Technol. Lett. 13, 818–820 (2001).
[Crossref]

2000 (1)

1999 (1)

Y. Liu, J. A. Willims, L. Zhang, and I. Bennion, “Phase shifted and cascaded long period fiber gratings,” Opt. Commun. 164, 27–31 (1999).
[Crossref]

1997 (3)

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

T. Erdogan, “Cladding-mode resonances in short- and long- period fiber grating filters,” J. Opt. Soc. Am. A 14, 1760–1773 (1997).
[Crossref]

B. J. Eggleton, R. E. Slusher, J. B. Judkins, J. B. Stark, and A. M. Vengsarkar, “All-optical switching in long period fiber gratings,” Opt. Lett. 22, 883–885 (1997).
[Crossref] [PubMed]

1996 (2)

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[Crossref] [PubMed]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communications Systems (New York: Wiley, 1997), Chap. 2.

Allsop, T.

X. Shu, T. Allsop, B. Gwandu, and L. Zhang, “High-temperature sensitivity of long-period gratings in B—Ge codoped fiber,” Photon. Technol. Lett. 13, 818–820 (2001).
[Crossref]

Bae, J.

J. K. Bae, J. Bae, S. H. Kim, N. Park, and S. B. Lee, “Dynamic EDFA gain-flattening filter using two LPFGs with divided coil heaters,” Photon. Technol. Lett. 17, 1226–1228 (2005).
[Crossref]

J. Bae, J. Chun, and S. B. Lee, “Synthesis of long-period fiber gratings with the inverted Erbium gain spectrum using the multiport lattice filter model,” J. Lightwave Technol. 22, 1976–1986 (2004).
[Crossref]

J. Bae, J. K. Bae, S. H. Kim, S. B. Lee, and J. Chun, “Analysis for long period fiber gratings using thermal kernel function,” Opt. Exp. 12, 797–810 (2004).
[Crossref]

Bae, J. K.

J. K. Bae, J. Bae, S. H. Kim, N. Park, and S. B. Lee, “Dynamic EDFA gain-flattening filter using two LPFGs with divided coil heaters,” Photon. Technol. Lett. 17, 1226–1228 (2005).
[Crossref]

J. Bae, J. K. Bae, S. H. Kim, S. B. Lee, and J. Chun, “Analysis for long period fiber gratings using thermal kernel function,” Opt. Exp. 12, 797–810 (2004).
[Crossref]

Bagratashvili, V. N.

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

Bennion, I.

Y. Liu, J. A. Willims, L. Zhang, and I. Bennion, “Phase shifted and cascaded long period fiber gratings,” Opt. Commun. 164, 27–31 (1999).
[Crossref]

Bergano, N. S.

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Chun, J.

J. Bae, J. K. Bae, S. H. Kim, S. B. Lee, and J. Chun, “Analysis for long period fiber gratings using thermal kernel function,” Opt. Exp. 12, 797–810 (2004).
[Crossref]

J. Bae, J. Chun, and S. B. Lee, “Synthesis of long-period fiber gratings with the inverted Erbium gain spectrum using the multiport lattice filter model,” J. Lightwave Technol. 22, 1976–1986 (2004).
[Crossref]

Davidson, C. R.

de Sandro, J. P.

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

Dong, L.

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

Eggleton, B. J.

Erdogan, T.

T. Erdogan, “Cladding-mode resonances in short- and long- period fiber grating filters,” J. Opt. Soc. Am. A 14, 1760–1773 (1997).
[Crossref]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Feinberg, J.

Grubsky, V.

Gwandu, B.

X. Shu, T. Allsop, B. Gwandu, and L. Zhang, “High-temperature sensitivity of long-period gratings in B—Ge codoped fiber,” Photon. Technol. Lett. 13, 818–820 (2001).
[Crossref]

Harurnoto, M.

Himeno, K.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, and R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” Proc. Optical Fiber Communication Conf. Dallas, TX, 347–348, (1997).
[Crossref]

Judkins, J. B.

Kim, S. H.

J. K. Bae, J. Bae, S. H. Kim, N. Park, and S. B. Lee, “Dynamic EDFA gain-flattening filter using two LPFGs with divided coil heaters,” Photon. Technol. Lett. 17, 1226–1228 (2005).
[Crossref]

J. Bae, J. K. Bae, S. H. Kim, S. B. Lee, and J. Chun, “Analysis for long period fiber gratings using thermal kernel function,” Opt. Exp. 12, 797–810 (2004).
[Crossref]

Laming, R. I.

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

Lee, S. B.

J. K. Bae, J. Bae, S. H. Kim, N. Park, and S. B. Lee, “Dynamic EDFA gain-flattening filter using two LPFGs with divided coil heaters,” Photon. Technol. Lett. 17, 1226–1228 (2005).
[Crossref]

J. Bae, J. Chun, and S. B. Lee, “Synthesis of long-period fiber gratings with the inverted Erbium gain spectrum using the multiport lattice filter model,” J. Lightwave Technol. 22, 1976–1986 (2004).
[Crossref]

J. Bae, J. K. Bae, S. H. Kim, S. B. Lee, and J. Chun, “Analysis for long period fiber gratings using thermal kernel function,” Opt. Exp. 12, 797–810 (2004).
[Crossref]

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[Crossref] [PubMed]

Liu, W. F.

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

Liu, Y.

Y. Liu, J. A. Willims, L. Zhang, and I. Bennion, “Phase shifted and cascaded long period fiber gratings,” Opt. Commun. 164, 27–31 (1999).
[Crossref]

Okude, S.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, and R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” Proc. Optical Fiber Communication Conf. Dallas, TX, 347–348, (1997).
[Crossref]

Ortega, B.

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

Park, N.

J. K. Bae, J. Bae, S. H. Kim, N. Park, and S. B. Lee, “Dynamic EDFA gain-flattening filter using two LPFGs with divided coil heaters,” Photon. Technol. Lett. 17, 1226–1228 (2005).
[Crossref]

Pedrazzani, J. R.

Reekie, L.

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

Sakai, T.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, and R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” Proc. Optical Fiber Communication Conf. Dallas, TX, 347–348, (1997).
[Crossref]

Shigehara, M.

Shima, K.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, and R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” Proc. Optical Fiber Communication Conf. Dallas, TX, 347–348, (1997).
[Crossref]

Shu, X.

X. Shu, T. Allsop, B. Gwandu, and L. Zhang, “High-temperature sensitivity of long-period gratings in B—Ge codoped fiber,” Photon. Technol. Lett. 13, 818–820 (2001).
[Crossref]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Slusher, R. E.

Stark, J. B.

Suganurna, H.

Tsypina, S. I.

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

Vengsarkar, A. M.

Wada, A.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, and R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” Proc. Optical Fiber Communication Conf. Dallas, TX, 347–348, (1997).
[Crossref]

Willims, J. A.

Y. Liu, J. A. Willims, L. Zhang, and I. Bennion, “Phase shifted and cascaded long period fiber gratings,” Opt. Commun. 164, 27–31 (1999).
[Crossref]

Yamauchi, R.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, and R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” Proc. Optical Fiber Communication Conf. Dallas, TX, 347–348, (1997).
[Crossref]

Zhang, L.

X. Shu, T. Allsop, B. Gwandu, and L. Zhang, “High-temperature sensitivity of long-period gratings in B—Ge codoped fiber,” Photon. Technol. Lett. 13, 818–820 (2001).
[Crossref]

Y. Liu, J. A. Willims, L. Zhang, and I. Bennion, “Phase shifted and cascaded long period fiber gratings,” Opt. Commun. 164, 27–31 (1999).
[Crossref]

J. Lightwave Technol. (3)

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

Opt. Commun. (1)

Y. Liu, J. A. Willims, L. Zhang, and I. Bennion, “Phase shifted and cascaded long period fiber gratings,” Opt. Commun. 164, 27–31 (1999).
[Crossref]

Opt. Exp. (1)

J. Bae, J. K. Bae, S. H. Kim, S. B. Lee, and J. Chun, “Analysis for long period fiber gratings using thermal kernel function,” Opt. Exp. 12, 797–810 (2004).
[Crossref]

Opt. Lett. (3)

Photon. Technol. Lett. (3)

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, “High-performance optical fiber polarizers based on long-period grating in birefringent optical fibers,” Photon. Technol. Lett. 9, 1370–1372 (1997).
[Crossref]

X. Shu, T. Allsop, B. Gwandu, and L. Zhang, “High-temperature sensitivity of long-period gratings in B—Ge codoped fiber,” Photon. Technol. Lett. 13, 818–820 (2001).
[Crossref]

J. K. Bae, J. Bae, S. H. Kim, N. Park, and S. B. Lee, “Dynamic EDFA gain-flattening filter using two LPFGs with divided coil heaters,” Photon. Technol. Lett. 17, 1226–1228 (2005).
[Crossref]

Other (2)

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, and R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” Proc. Optical Fiber Communication Conf. Dallas, TX, 347–348, (1997).
[Crossref]

G. P. Agrawal, Fiber-Optic Communications Systems (New York: Wiley, 1997), Chap. 2.

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Figures (9)

Fig. 1.
Fig. 1.

Intermodal dispersion Φ(λ,T) for 1st~7th cladding modes extrapolated from experimental data, utilizing phase matching condition [3] and resonance peak wavelength of each grating.

Fig. 2.
Fig. 2.

Experimentally obtained (a) difference of intermodal dispersion ΔΦ(λ,T-T 0) and (b) core-to-cladding refractive index difference Δ(nco-ncl) values at different temperatures (reference temperature=25°C, 80°C, 140°C), for 1st to 7th cladding modes.

Fig. 3.
Fig. 3.

Experimental setup for the verification of the semi-empirical model. Independently tunable divided coil heater array with LPFG.

Fig. 4.
Fig. 4.

cascaded LPFGs with same cladding modes(1450~1650nm range).

Fig. 5.
Fig. 5.

(a). measured/calculated spectra and (b). intermodal dispersion curve of 7th cladding mode for the concatenated LPFG with different grating periods.

Fig. 6.
Fig. 6.

Cascaded LPFGs with different cladding modes.

Fig. 7.
Fig. 7.

(a), (c), (e) Measured/calculated LPFG spectra and (b), (d), (f) variations of intermodal dispersion under various temperature distributions (inset).

Fig. 8.
Fig. 8.

LPFG unit for tunable EDFA gain equalization filter; cascaded LPFGs with different grating lengths and different grating periods.

Fig. 9.
Fig. 9.

LPFG based dynamic gain equalization filter ; Applied temperature distributions (a, c, e) and their LPFG spectra (b, d, f).

Equations (13)

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κ ( λ , T ) = 2 π · σ λ · C ( λ , T ) 2 π · σ λ · C ( λ )
δ ( λ , T ) = 1 2 ( β ( 0 ) β ( p ) 2 π Λ ) = 1 2 ( Φ ( λ , T ) 2 π Λ )
= 1 2 ( Φ ( λ , T 0 ) + Δ Φ ( λ , T T 0 ) 2 π Λ ) δ 0 ( λ , T 0 ) + Δ Φ ( λ , T T 0 ) 2
Δ Φ ( λ , T T 0 ) = 2 π λ ( Δ n eff ( 0 ) ( λ , T T 0 ) Δ n eff ( p ) ( λ , T T 0 ) )
b = n eff ( 0 ) n cl n co n cl ( 1.1428 0.9960 V ) 2
V = 2 π a λ · n co 2 n cl 2
Δ Φ = 2 π λ ( Δ n eff ( 0 ) Δ n eff ( p ) ) = 2 π λ [ Δ b ( n co n cl ) + b Δ ( n co n cl ) + Δ n cl Δ n eff ( p ) ]
Δ V = 2 π a λ · n co Δ n co n cl Δ n cl n co 2 n cl 2 V · Δ ( n co n cl ) 2 ( n co n cl ) n co n cl
Δ b = 2 · ( 1.1428 0.9960 V ) · 0.9960 V 2 · Δ V = [ 1.1428 · 0.9960 V ( 0.9960 V ) 2 ] · Δ ( n co n cl ) ( n co n cl )
Δ Φ ( λ , T T 0 ) 2 π λ · ( 1.1428 2 1.1428 · 0.9960 2.405 · λ cutoff , T 0 · λ ) · Δ ( n co n cl )
δ ( λ , T ) δ 0 ( λ , T 0 ) + π λ · ( 1.1428 2 1.1428 · 0.9960 2.405 · λ cutoff , T 0 · λ ) · Δ ( n co n cl )
δ 0 ( λ , T 0 ) + ( 4.103 λ 1.487 λ cutoff , 0 ) · α T · ( T T 0 )
[ E ( 0 ) ( L ) E ( 1 ) ( L ) E ( p 1 ) ( L ) E ( p ) ( L ) ] = Q · [ E ( 0 ) ( 0 ) E ( 1 ) ( 0 ) E ( p 1 ) ( 0 ) E ( p ) ( 0 ) ] , Q = M k ( T k ) · M k 1 ( T k 1 ) M 1 ( T 1 ) ,

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