Abstract

Narrow linewidth transmission filters in lossy materials based phase-shifted fiber Bragg gratings have been investigated experimentally and analytically. A novel matrix technique has been developed in calculation of the transmission loss and linewidth. The elements of the matrix simply consist of the coefficients of the coupled mode equations. Simulation shows a small fiber loss could result in a significant transmission loss, which has not been explained properly yet to our knowledge. For phase-shifted gratings in erbium-doped fibers, the absorption could result in over 20  dB loss at transmission wavelengths. Such an approach can also be used to analyze cladding modes, radiation mode, and complex structure gratings.

© 2007 Optical Society of America

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References

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2005

Y. C. Zhao, X. F. Xu, Y. Li, Z. Shao, and J. Y. Gao, "A novel method to realize multiwavelength with phase-shifted FBG inscribed in PMF," Laser Phys. Lett. 2, 493-497 (2005).
[CrossRef]

2003

W. C. Wang, M. Fisher, A. Yacoubian, and J. Menders, "Phase-shifted Bragg grating filters in polymer waveguides," IEEE Photon. Technol. Lett. 15, 548-550 (2003).
[CrossRef]

2000

W. Zhang, Y. C. Lai, J. A. R. Williams, C. Lu, L. Zhang, and I. Bennion, "A fiber grating DFB laser for generation of optical microwave signal," Opt. Laser Technol. 32, 369-371 (2000).
[CrossRef]

1999

1998

Y. Liu, S. B. Lee, and S. S. Choi, "Phase-shifted fiber Bragg grating transmission filters based on the Fabry-Perot effect," Opt. Soc. Korea 2, 30-33 (1998).
[CrossRef]

1997

L. Wei and J. W. Y. Lit, "Phase-shifted Bragg grating filters with symmetrical structures," J. Lightwave Technol. 15, 1405-1410 (1997).
[CrossRef]

1996

F. Bakhti and P. Sansonetti, "Wide bandwidth, low loss and highly rejective double phase-shifted UV-written fiber bandpass filter," Electron. Lett. 32, 581-582 (1996).
[CrossRef]

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugden, and N. J. Doran, "UV-written in-fiber Bragg gratings," Opt. Quantum Electron. 28, 93-135 (1996).
[CrossRef]

1994

G. P. Agrawal and S. Radic, "Simulation of amplifying phase-shifted fiber Bragg gratings by the method of single expression," Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

1990

1987

Appl. Opt.

Electron. Lett.

F. Bakhti and P. Sansonetti, "Wide bandwidth, low loss and highly rejective double phase-shifted UV-written fiber bandpass filter," Electron. Lett. 32, 581-582 (1996).
[CrossRef]

IEEE Photon. Technol. Lett.

W. C. Wang, M. Fisher, A. Yacoubian, and J. Menders, "Phase-shifted Bragg grating filters in polymer waveguides," IEEE Photon. Technol. Lett. 15, 548-550 (2003).
[CrossRef]

J. Lightwave Technol.

L. Wei and J. W. Y. Lit, "Phase-shifted Bragg grating filters with symmetrical structures," J. Lightwave Technol. 15, 1405-1410 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Laser Phys. Lett.

Y. C. Zhao, X. F. Xu, Y. Li, Z. Shao, and J. Y. Gao, "A novel method to realize multiwavelength with phase-shifted FBG inscribed in PMF," Laser Phys. Lett. 2, 493-497 (2005).
[CrossRef]

Opt. Laser Technol.

W. Zhang, Y. C. Lai, J. A. R. Williams, C. Lu, L. Zhang, and I. Bennion, "A fiber grating DFB laser for generation of optical microwave signal," Opt. Laser Technol. 32, 369-371 (2000).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugden, and N. J. Doran, "UV-written in-fiber Bragg gratings," Opt. Quantum Electron. 28, 93-135 (1996).
[CrossRef]

Opt. Soc. Korea

Y. Liu, S. B. Lee, and S. S. Choi, "Phase-shifted fiber Bragg grating transmission filters based on the Fabry-Perot effect," Opt. Soc. Korea 2, 30-33 (1998).
[CrossRef]

Photon. Technol. Lett.

G. P. Agrawal and S. Radic, "Simulation of amplifying phase-shifted fiber Bragg gratings by the method of single expression," Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

Other

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

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Figures (2)

Fig. 1
Fig. 1

Reflection and transmission spectra of FBGs (Dash curve, simulation; solid curves, experiment). (a) Uniform structure FBGs with parameters of κ L = 3.0 , L = 30   mm . (b) Apodized FBGs ( κ L = 8.36 , L = 30   mm ).

Fig. 2
Fig. 2

Transmission spectra of phase-shifted FBGs: solid curve, experiment; dash curve, simulation. (a) Phase-shifted FBGs in B∕Ge-doped photosensitive fibers, showing 2.5   dB loss at the transmission peak ( κ L = 5.7 , L = 40   mm , α = 0.5 m 1 ). (b) Phase-shifted FBGs in erbium-doped fibers showing over 20 loss at the transmission peak ( κ L = 6.6 , L = 40   mm , α = 10 m 1 ).

Equations (10)

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d y i ( z ) d z = j = 1 N a i j ( z ) y j ( z ) ( i = 1 , 2 , 3 , … ,  N ) ,
[ y 1 ( L ) y 2 ( L ) y N ( L ) ] = M [ y 1 ( 0 ) y 2 ( 0 ) y N ( 0 ) ] ,
M = k = 1 Q [ 1 + a 11 Δ z a 12 Δ z a 1 N Δ z a 21 Δ z 1 + a 22 Δ z a 2 N Δ z a N 1 Δ z a N 2 Δ z 1 + a N N Δ z ] .
y 1 ( 0 ) = 1 y k ( L ) = 0 ( k = 2 , 3 , … ,  N ) .
[ y 1 ( L ) y 2 ( 0 ) y N ( 0 ) ] = [ 1 M 12 M 13 M 1 N 0 M 22 M 23 M 2 N 0 M N 2 M N 3 M N N ] 1 × [ M 11 M 21 M N 1 ] .
d A ( z ) d z = j κ ( z ) e ( α j 2 δ ) z B ( z ) ,
d B ( z ) d z = ± j κ ( z ) e ( α + j 2 δ ) z A ( z ) ,
M = k = 1 Q [ 1 j κ ( z i ) e ( α j 2 δ ) z k Δ z ± j κ ( z i ) e ( α + j 2 δ ) z k Δ z 1 ] ,
[ t r ] = [ 1 M 12 0 M 22 ] 1 [ M 11 M 21 ] ,
exp [ 6 ( z L / 2 L / 2 ) 2 ]

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