Abstract

We provide a full analysis of the distortion effects produced by the first and second order in-band dispersion of fiber Bragg grating based optical demultiplexers over analogue SCM (Sub Carrier Multiplexed) signals. Optical bandwidth utilization ranges for Dense WDM network are calculated considering different SCM system cases of frequency extension and modulation conditions.

© 2002 Optical Society of America

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References

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  1. B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997).
    [CrossRef]
  2. G. NyKolak, B.J. Eggleton, G. Lenz, and T.A. Strasser, “Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,” IEEE Photonics Technol. Lett. 10, 1319–1321, (1998).
    [CrossRef]
  3. J Capmany, D. Pastor, and B. Ortega, “RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,” Electron. Lett. 35, 2220–2221, (1999).
    [CrossRef]
  4. L.R. Chen, “Relative Intensity noise enhancement due to out-of-band dispersion in cascaded fiber Bragg Gratings,” Optics Communications 184, 157–160, (2000).
    [CrossRef]
  5. D. Pastor, A. Martinez, J. Capmany, and B. Ortega, “Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,” IEEE Photonics Technol. Lett. 14, 567–569, (2002).
    [CrossRef]
  6. S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990).
    [CrossRef]
  7. D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996).
    [CrossRef]
  8. M. Ibsen and M.N. Zervas, “99,9% reflectivity dispersion-less square-filter fiber bragg grating for high speed DWDM networks,” Conf. Opt. Fiber. Comm., Baltimore, OSA Tech. Dig. Paper PD21, (2000)

2002 (1)

D. Pastor, A. Martinez, J. Capmany, and B. Ortega, “Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,” IEEE Photonics Technol. Lett. 14, 567–569, (2002).
[CrossRef]

2000 (1)

L.R. Chen, “Relative Intensity noise enhancement due to out-of-band dispersion in cascaded fiber Bragg Gratings,” Optics Communications 184, 157–160, (2000).
[CrossRef]

1999 (1)

J Capmany, D. Pastor, and B. Ortega, “RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,” Electron. Lett. 35, 2220–2221, (1999).
[CrossRef]

1998 (1)

G. NyKolak, B.J. Eggleton, G. Lenz, and T.A. Strasser, “Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,” IEEE Photonics Technol. Lett. 10, 1319–1321, (1998).
[CrossRef]

1997 (1)

B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997).
[CrossRef]

1996 (1)

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

1990 (1)

S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990).
[CrossRef]

Capmany, J

J Capmany, D. Pastor, and B. Ortega, “RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,” Electron. Lett. 35, 2220–2221, (1999).
[CrossRef]

Capmany, J.

D. Pastor, A. Martinez, J. Capmany, and B. Ortega, “Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,” IEEE Photonics Technol. Lett. 14, 567–569, (2002).
[CrossRef]

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Charles, S. Ih.

S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990).
[CrossRef]

Chen, L.R.

L.R. Chen, “Relative Intensity noise enhancement due to out-of-band dispersion in cascaded fiber Bragg Gratings,” Optics Communications 184, 157–160, (2000).
[CrossRef]

Eggleton, B.J.

G. NyKolak, B.J. Eggleton, G. Lenz, and T.A. Strasser, “Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,” IEEE Photonics Technol. Lett. 10, 1319–1321, (1998).
[CrossRef]

B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997).
[CrossRef]

Gu, Wanyi

S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990).
[CrossRef]

Ibsen, M.

M. Ibsen and M.N. Zervas, “99,9% reflectivity dispersion-less square-filter fiber bragg grating for high speed DWDM networks,” Conf. Opt. Fiber. Comm., Baltimore, OSA Tech. Dig. Paper PD21, (2000)

Lenz, G.

G. NyKolak, B.J. Eggleton, G. Lenz, and T.A. Strasser, “Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,” IEEE Photonics Technol. Lett. 10, 1319–1321, (1998).
[CrossRef]

B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997).
[CrossRef]

Litchinitser, N.

B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997).
[CrossRef]

Marti, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Martinez, A.

D. Pastor, A. Martinez, J. Capmany, and B. Ortega, “Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,” IEEE Photonics Technol. Lett. 14, 567–569, (2002).
[CrossRef]

NyKolak, G.

G. NyKolak, B.J. Eggleton, G. Lenz, and T.A. Strasser, “Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,” IEEE Photonics Technol. Lett. 10, 1319–1321, (1998).
[CrossRef]

Ortega, B.

D. Pastor, A. Martinez, J. Capmany, and B. Ortega, “Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,” IEEE Photonics Technol. Lett. 14, 567–569, (2002).
[CrossRef]

J Capmany, D. Pastor, and B. Ortega, “RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,” Electron. Lett. 35, 2220–2221, (1999).
[CrossRef]

Ortega, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Pastor, D.

D. Pastor, A. Martinez, J. Capmany, and B. Ortega, “Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,” IEEE Photonics Technol. Lett. 14, 567–569, (2002).
[CrossRef]

J Capmany, D. Pastor, and B. Ortega, “RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,” Electron. Lett. 35, 2220–2221, (1999).
[CrossRef]

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Patterson, D.B.

B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997).
[CrossRef]

Slusher, R. E.

B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997).
[CrossRef]

Strasser, T.A.

G. NyKolak, B.J. Eggleton, G. Lenz, and T.A. Strasser, “Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,” IEEE Photonics Technol. Lett. 10, 1319–1321, (1998).
[CrossRef]

Tatay, V.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Zervas, M.N.

M. Ibsen and M.N. Zervas, “99,9% reflectivity dispersion-less square-filter fiber bragg grating for high speed DWDM networks,” Conf. Opt. Fiber. Comm., Baltimore, OSA Tech. Dig. Paper PD21, (2000)

Electron. Lett. (1)

J Capmany, D. Pastor, and B. Ortega, “RIN induced by out-of-band dispersion in fiber Bragg Grating based Add-Drop multiplexers,” Electron. Lett. 35, 2220–2221, (1999).
[CrossRef]

IEEE J. Selected Areas in Commun. (1)

S. Ih. Charles and Wanyi Gu, “Fiber Induced Distortion in a Sub Carrier Multiplexing Ligthwave System,” IEEE J. Selected Areas in Commun. 8, 1296–1303, (1990).
[CrossRef]

IEEE Journal of Lightwave Technol. (1)

D. Pastor, J. Capmany, D. Ortega, V. Tatay, and J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” IEEE Journal of Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

IEEE Photonics Technol. Lett. (3)

D. Pastor, A. Martinez, J. Capmany, and B. Ortega, “Impact of Fiber Bragg Grating based OADM outband dispersion in DWDM-SCM systems,” IEEE Photonics Technol. Lett. 14, 567–569, (2002).
[CrossRef]

B.J. Eggleton, G. Lenz, N. Litchinitser, D.B. Patterson, and R. E. Slusher, “Implications pf Fiber Grating Dispersion of WDM Communication Systems,” IEEE Photonics Technol. Lett. 9, 1403–1405, (1997).
[CrossRef]

G. NyKolak, B.J. Eggleton, G. Lenz, and T.A. Strasser, “Dispersion Penalty Measurements of Narrow Fiber Bragg Gratings at 10 Gb/s,” IEEE Photonics Technol. Lett. 10, 1319–1321, (1998).
[CrossRef]

Optics Communications (1)

L.R. Chen, “Relative Intensity noise enhancement due to out-of-band dispersion in cascaded fiber Bragg Gratings,” Optics Communications 184, 157–160, (2000).
[CrossRef]

Other (1)

M. Ibsen and M.N. Zervas, “99,9% reflectivity dispersion-less square-filter fiber bragg grating for high speed DWDM networks,” Conf. Opt. Fiber. Comm., Baltimore, OSA Tech. Dig. Paper PD21, (2000)

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Figures (5)

Fig 1.
Fig 1.

First order dispersion of the apodized UFBG inside the band. 3dB optical bandwidth of 25 GHz. (1) Cosine apodization profile with C=1.2 ([7]), (2) Hiperbolic tangent apodization profile with α=1.75 y β=2 ([7]) and (3) hamming apodization profile with H = 0.8 ([7]). Lg is the grating length that in this case is Lg = 1.168 cm.

Fig. 2.
Fig. 2.

Second order dispersion of the apodised UFBG. Same conditions of Fig. 1.

Fig. 3.
Fig. 3.

IM2(f1 + f2)/C2 and IM3(2f2 - f1)/C2 versus the detuning parameter y for different channel spacing, ΔυC =100, 50 , 25 GHz (3dB optical bandwidths are 50GHz (Lg=0.584 cm), 25GHz (Lg=1.168 cm) and 12.5GHz (Lg=2.336 cm) respectively). Hiperbolic tangent apodization profile with α=1.75 and Β=2, 100 MHz for the common frequency. mi =0.05 and mf =0.2 indexes (directed modulated systems). Results from analitical expressions (3) (continuous line) and numerical simulation (dots).

Fig. 4.
Fig. 4.

IM2/C2 and IM3/C2 terms versus the common frequency. ITU spacing of AυC=50GHz (AυB=25GHz), Hiperbolic tangent apodization profiles with α=1.75 and β=2 , and y = 0 (centre of the FBG). Indexes of modulation mf = 0.2 (continuous line), mf = 0.05 (dashed line) and mf = 0 (dotted line), all traces mi = 0.05.

Fig. 5.
Fig. 5.

Free of distortion optical bandwidth (BWfd) versus the common frequency for IM2 and HD terms (continuous line) and IM3 terms (dashed line). Hiperbolic tangent apodization profiles with α=1.75 y β=2, Intensity modulation indexes mi = 2 , 4 , 8, 16 % . (a) Low/Medium chirped modulation mf = mi , (b)High chirped modulation mf = 4mi .

Equations (13)

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e ( t ) = [ 2 ( 1 + m i cos ( W m ) ) ] 1 / 2 cos ( w o t + m f sin ( w m t ) )
I ( t ) = C o + k = 1 { C ck cos [ k ( w m t φ 1 ) ] + C sk sin [ k ( w m t φ 1 ) ] } = C o + k = 1 C k cos [ k ( w m t φ 1 + ϕ k ) ]
C o = a o 2 + ( 1 / 2 ) i = 1 ( a i 2 + b i 2 )
C ck = 2 a o a k cos [ k 2 φ 2 ] cos [ k 3 φ 3 ] 2 a 0 b k sin [ k 2 φ 2 ] sin [ k 3 φ 3 ] +
+ ( 1 / 2 ) k 1 i = 1 ( a i a k i b i b k i ) cos [ ( k 2 2 ik ) φ 2 ] cos [ ( k 3 3 ik 2 + 3 ik 3 ) φ 3 ] +
+ i = 1 ( a i a i + k + b i b i + k ) cos [ ( k 2 + 2 ik ) φ 2 ] cos [ ( k 3 + 3 ik 2 + 3 ki 2 ) φ 3 ]
k 1 i = 1 a i b k i sin [ ( k 2 + 2 ik ) φ 2 ] sin [ ( k 3 3 ik 2 + 3 ki 2 ) φ 3 ]
i = 1 ( a i b i + k + b i a i + k ) sin [ ( k 2 + 2 ik ) φ 2 ] sin [ ( k 3 + 3 ik 2 + 3 ki 2 ) φ 3 ]
C sk = 2 a o a k cos [ k 2 φ 2 ] sin [ k 3 φ 3 ] + 2 a 0 b k sin [ k 2 φ 2 ] cos [ k 3 φ 3 ] +
+ ( 1 / 2 ) k 1 i = 1 ( a i a k i b i b k i ) cos [ ( k 2 2 ik ) φ 2 ] sin [ ( k 3 3 ik 2 + 3 ik 2 ) φ 3 ] +
+ i = 1 ( a i a i + k + b i b i + k ) cos [ ( k 2 + 2 ik ) φ 2 ] sin [ ( k 3 + 3 ik 2 + 3 ki 2 ) φ 3 ] +
+ k 1 i = 1 a i b k i sin [ ( k 2 2 ik ) φ 2 ] cos [ ( k 3 3 ik 2 + 3 ki 2 ) φ 3 ] +
+ i = 1 ( a i b i + k + b i a i + k ) sin [ ( k 2 + 2 ik ) φ 2 ] cos [ ( k 3 + 3 ik 2 + 3 ki 2 ) φ 3 ]

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