Abstract

Influence of cladding-mode coupling losses on the spectrum of multi-channel fiber Bragg grating (FBG) has been numerically investigated on the basis of the extended coupled-mode equations. It has been shown that there exists a reflection slope in the spectrum of both the intra- and inter-channels due to the existences of the cladding modes. This slope could be larger than 1 dB when the induced index change is about 3×10-3, which makes the channels considerably asymmetric. For comparison, a 39-channel linearly chirped FBG with a channel spacing of 0.8 nm and a chromatic dispersion of -850 ps/nm has been designed and fabricated. The experimental results show good agreement with the numerical ones. Finally, one method to pre-compensate the reflection slope within the intra-channels has been proposed and successfully demonstrated.

© 2005 Optical Society of America

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References

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Electron. Lett.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 30, 899-901(1995).
[CrossRef]

Eur. Conf. Optical Communication

K.-M. Feng, S. Lee, R. Khosravani, S. S. Havstad, and J. E. Rothenberg, “45 ITU-100 channels dispersion compensation using cascaded full C-band sampled FBGs for transmission over 640-Km SMF,” Eur. Conf. Optical Communication, Paper Mo3.2.5 (2003).

IEEE J. Lightwave Technol.

H. Li, Y. Sheng, Y. Li, J. E. Rothenberg, “Phased-only sampled fiber Bragg gratings for high channel counts chromatic dispersion compensation,” IEEE J. Lightwave Technol. 21, 2074-2083 (2003).
[CrossRef]

IEEE J. Quantum Electron.

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

IEEE Photon. Technol. Lett.

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, “Split of phase shifts in a phase mask for fiber Bragg gratings,” IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[CrossRef]

L. Dong, L. Reekie, J. L. Cruz, J. E. Caplen, J. P. de Sandro, and D. N. Payne, “Optical fibers with depressed claddings for suppression of coupling into cladding modes in fiber Bragg gratings,” IEEE Photon. Technol. Lett. 9, 64-66 (1997).
[CrossRef]

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311(2002).
[CrossRef]

IEEE Photonics Tech. Lett.

Y. W. Song, S. M. R. Motaghian Nezam, D. Starodubov, J. E.. Rothenberg, Z. Pan, H. Li, R. Wilcox, J. Popelek, R. Caldwell, V. Grubsky and A. E. Willner, “Tunable interchannel broad-band dispersion-slope compensation for 10-Gb/s WDM systems using a nonchannelized third-order chirped FBG,” IEEE Photonics Tech. Lett. 15, 144-146 (2003).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Quantum Electron.

S. J. Hewlett, J. D. Love, G. Meltz, T. J. Bailey, and W. W. Morey, “Coupling characteristics of photo-induced Bragg gratings in Depressed-and matched-cladding fibre” Opt. Quantum Electron. 28, 1641-1654 (1996).
[CrossRef]

Tech. Dig. OFC Conf.

Y. Painchaud, A. Mailoux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Tech. Dig. Optical Fiber Communication Conf., Paper THAA5 (2002).

Other

V. Finazzi and M. Zervas, “Cladding mode losses in chirped fibre Bragg gratings,” Proc. OSA Technical BGPP, Paper BThB4-1 (2001).

T. Taru, S. Ishikawa, and A. Inoue, “Suppression of cladding-mode coupling loss in fiber Bragg grating by precise control of photosensitive profiles in an optical fiber,” Proc. OSA Technical BGPP, Paper BThC11 (2001).

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Figures (8)

Fig. 1.
Fig. 1.

Calculated results for the effective indices and the normalized coupling coefficients for the least 35 cladding modes. (a) Dependence of the effective index on wavelength, and (b) dependence of the normalized coupling coefficients on wavelength.

Fig. 2.
Fig. 2.

Design results for a 39-channel linearly chirped FBG without considering the cladding-mode effects. (a) Reflection spectrum, (b) reflection and group delay spectra within the central channel.

Fig. 3.
Fig. 3.

Calculated results for the reflection spectrum of a 39-channel linearly chirped FBG, where Δn 1 is 1.6×10-4, and the coupling coefficients for each cladding modes are the ones as shown in Fig. 2. (a) Reflection spectrum for all 39-channel, (b) part of the spectrum at the shortest wavelength side, (c) part of the spectrum at the middle region of 39-channel, and (d) part of the spectrum at the longest wavelength side.

Fig. 4.
Fig. 4.

Transmission spectrum for a one-channel linearly chirped FBG, where Δn 1 is 1.6×10-4 and the coupling coefficients for the core-cladding modes are the ones shown in Fig. 2.

Fig. 5.
Fig. 5.

Principle of the pre-compensated apodization.

Fig. 6.
Fig. 6.

Calculated results for the reflection spectrum of a 39-channel with using the pre-compensated apodization. (a) Reflection spectrum for all 39-channel, (b) part of the spectrum at the shortest wavelength side, (c) part of the spectrum at the middle region of 39-channel, and (d) part of the spectrum at the longest wavelength side.

Fig. 7.
Fig. 7.

Measured results for a fabricated 39-channel linearly chirped FBG without pre-compensation apodization. (a) Reflection spectrum for all 39-channel, (b) part of the spectrum at the shortest wavelength side, (c) part of the spectrum at the middle region of 39-channel, and (d) part of the spectrum at the longest wavelength side.

Fig. 8.
Fig. 8.

Measured results for a fabricated 39-channel linearly chirped FBG with pre-compensation apodization. (a) Reflection spectrum for all 39-channel, (b) part of the spectrum at the shortest wavelength side, (c) part of the spectrum at the middle region of 39-channel, and (d) part of the spectrum at the longest wavelength side.

Tables (1)

Tables Icon

Table 1. Some specifications for the gratings shown in Fig. 7 and Fig. 8.

Equations (10)

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Δ n ( z ) = R e { ( Δ n 1 ( z ) 2 ) · exp ( i ( 2 π z Λ + ϕ g ( z ) ) ) · s ( z ) } ,
s ( z ) = m = s m exp ( i 2 m π z P ) ,
d A c o d z = i B c o m = M M S m ( κ c o c o 2 ) exp { i ( 2 Δ β c o c o z ϕ g ( z ) 2 m π z P ) } ,
+ i ν = 1 N m = M M S m ( κ ν c l c o 2 ) B ν c l exp { i ( 2 Δ β ν c l c o z ϕ g ( z ) 2 m π z P ) }
d B c o d z = i A c o m = M M S m ( κ c o c o 2 ) exp { i ( 2 Δ β c o c o z ϕ g ( z ) 2 m π z P ) } ,
d B ν cl d z = i A c o m = M M S m ( κ ν cl co 2 ) exp { i ( 2 Δ β ν cl co z ϕ g ( z ) 2 m π z P ) } , ν = 1 , 2 , 3 , , N ,
{ A co ( z = L 2 ) = 1 B co ( z = L 2 ) = 0 B ν cl ( z = L 2 ) = 0 ν = 1 , 2 , 3 , N ,
{ T ( λ ) = A co ( L 2 , λ ) A co ( L 2 , λ ) 2 R ( λ ) = B co ( L 2 , λ ) A co ( L 2 , λ ) 2 .
κ co co = ω ε 0 n 1 2 0 2 π d φ 0 a 1 Δ n 1 E co ( r , φ ) 2 r d r ,
κ ν cl co = ω ε 0 n 1 2 0 2 π d φ 0 a 1 Δ n 1 E ν cl ( r , φ ) E co ( r , φ ) * r d r ,

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