Abstract

The method to design the incoherent pump power spectrum described with a set of piece-wise continuous functions (PWCFs) for the distributed fiber Raman amplifier (DFRA) is presented. The pump power spectrum is divided into a number of sub-bands, in which each sub-band is described with a polynomial. The power spectral density function (PSDF) is the absolute value of the set of PWCFs, in which the polynomial coefficients are optimized with the least-square minimization method for reducing the signal gain ripple. Two 100-km TW-Reach DFRAs using backward pumping and bidirectional pumping respectively are taken as examples. The numerical results show that the gain ripple of less than 0.02 dB over 70-nm bandwidth can be achieved. The spectral characteristics of the optimized PSDF for the ultra-low gain ripple are investigated. The optimized PSDF can be synthesized with multiple incoherent pumps. The synthesis examples using the multiple Gaussian incoherent pumps are shown, in which the gain ripples are increased to 0.3 dB due to the discrepancy between the optimized PSDF and the synthesized PSDF. The gain ripples can be reduced to 0.05 dB by further optimizing the parameters of the multiple Gaussian incoherent pumps.

© 2006 Optical Society of America

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  1. A. Yariv, "Signal-to-noise considerations in fiber links with periodic or distributed optical amplification," Opt. Lett. 15, 1064-1066 (1990).
    [CrossRef] [PubMed]
  2. H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
    [CrossRef]
  3. M. Islam, "Raman amplifiers for telecommunications," IEEE J. Sel. Top. Quantum Electron. 8, 548-559 (2002).
    [CrossRef]
  4. V. Perlin and G. Winful, "On distributed Raman amplification for ultrabroad-band long-haul WDM systems," J. Lightwave Technol. 20, 409-416 (2002).
    [CrossRef]
  5. J. Bromage, "Raman amplification for fiber communication systems," J. Lightwave Technol. 22, 79-93 (2004).
    [CrossRef]
  6. D. Vakhshoori, M. Azimi, P. Chen, B. Han, M. Jiang, L. Knopp, C. Lu, Y. Shen, G. Rodes, S. Vote, P. Wang, and X. Zhu, "Raman amplification using high-power incoherent semiconductor pump sources," OFC 2003, Paper PD47.
  7. T. Zhang, X. Zhang, and G. Zhang, "Distributed fiber Raman amplifiers with incoherent pumping," IEEE Photon. Technol. Lett. 17, 1175-1177 (2005).
    [CrossRef]
  8. B. Han, X. Zhang, G. Zhang, Z. Lu and G. Yang, "Composite broad-band fiber Raman amplifiers using incoherent pumping," Opt. Express 13, 6023-6032 (2005).
    [CrossRef] [PubMed]
  9. E. Lichtman, R. Waarts, and A. Friesem, "Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fiber," J. Lightwave Technol. 7, 171-1174 (1989).
    [CrossRef]
  10. X. Zhou, M. Birk, and S. Woodward, "Pump-noise induced FWM effect and its reduction in a distributed Raman fiber amplifiers," IEEE Photon. Technol. Lett. 14, 1686-1688 (2002).
    [CrossRef]
  11. T. Kung, C. Chang, J. Dung, and S. Chi, "Four-wave mixing between pump and signal in a distributed Raman amplifier," J. Lightwave Technol. 21, 1164 - 1170 (2003).
    [CrossRef]
  12. J. Bouteiller, L. Leng, and C. Headley, "Pump-pump four-wave mixing in distributed Raman amplified systems," J. Lightwave Technol.,  22, 723 - 732 (2004).
    [CrossRef]
  13. S. Sugliani, G. Sacchi, G. Bolognini, S. Faralli, and F. Pasquale, "Effective suppression of penalties induced by parametric nonlinear interaction in distributed Raman amplifiers based on NZ-DS fibers," IEEE Photon. Technol. Lett. 16, 81-83 (2004).
    [CrossRef]
  14. I. Mandelbaum and M. Bolshtyansky, "Raman amplifier model in singlemode optical fiber," IEEE Photon. Technol. Lett. 15, 1704-1706 (2003).
    [CrossRef]
  15. S. Wen, T.-Y. Wang, and S. Chi, "Self-consistent pump depletion method to design optical transmission systems amplified by bidirectional Raman pumps," Int. J. Nonlinear Opt. Phys. 1, 595-608 (1992).
    [CrossRef]
  16. J. Moré, B. Garbow, and K. Hillstrom, User Guide for MINPACK-1, Argonne National Laboratory Report ANL-80-74, Argonne, Illinois, 1980.

2005

T. Zhang, X. Zhang, and G. Zhang, "Distributed fiber Raman amplifiers with incoherent pumping," IEEE Photon. Technol. Lett. 17, 1175-1177 (2005).
[CrossRef]

B. Han, X. Zhang, G. Zhang, Z. Lu and G. Yang, "Composite broad-band fiber Raman amplifiers using incoherent pumping," Opt. Express 13, 6023-6032 (2005).
[CrossRef] [PubMed]

2004

J. Bromage, "Raman amplification for fiber communication systems," J. Lightwave Technol. 22, 79-93 (2004).
[CrossRef]

J. Bouteiller, L. Leng, and C. Headley, "Pump-pump four-wave mixing in distributed Raman amplified systems," J. Lightwave Technol.,  22, 723 - 732 (2004).
[CrossRef]

S. Sugliani, G. Sacchi, G. Bolognini, S. Faralli, and F. Pasquale, "Effective suppression of penalties induced by parametric nonlinear interaction in distributed Raman amplifiers based on NZ-DS fibers," IEEE Photon. Technol. Lett. 16, 81-83 (2004).
[CrossRef]

2003

I. Mandelbaum and M. Bolshtyansky, "Raman amplifier model in singlemode optical fiber," IEEE Photon. Technol. Lett. 15, 1704-1706 (2003).
[CrossRef]

T. Kung, C. Chang, J. Dung, and S. Chi, "Four-wave mixing between pump and signal in a distributed Raman amplifier," J. Lightwave Technol. 21, 1164 - 1170 (2003).
[CrossRef]

2002

X. Zhou, M. Birk, and S. Woodward, "Pump-noise induced FWM effect and its reduction in a distributed Raman fiber amplifiers," IEEE Photon. Technol. Lett. 14, 1686-1688 (2002).
[CrossRef]

M. Islam, "Raman amplifiers for telecommunications," IEEE J. Sel. Top. Quantum Electron. 8, 548-559 (2002).
[CrossRef]

V. Perlin and G. Winful, "On distributed Raman amplification for ultrabroad-band long-haul WDM systems," J. Lightwave Technol. 20, 409-416 (2002).
[CrossRef]

2000

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

1992

S. Wen, T.-Y. Wang, and S. Chi, "Self-consistent pump depletion method to design optical transmission systems amplified by bidirectional Raman pumps," Int. J. Nonlinear Opt. Phys. 1, 595-608 (1992).
[CrossRef]

1990

1989

E. Lichtman, R. Waarts, and A. Friesem, "Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fiber," J. Lightwave Technol. 7, 171-1174 (1989).
[CrossRef]

Birk, M.

X. Zhou, M. Birk, and S. Woodward, "Pump-noise induced FWM effect and its reduction in a distributed Raman fiber amplifiers," IEEE Photon. Technol. Lett. 14, 1686-1688 (2002).
[CrossRef]

Bolognini, G.

S. Sugliani, G. Sacchi, G. Bolognini, S. Faralli, and F. Pasquale, "Effective suppression of penalties induced by parametric nonlinear interaction in distributed Raman amplifiers based on NZ-DS fibers," IEEE Photon. Technol. Lett. 16, 81-83 (2004).
[CrossRef]

Bolshtyansky, M.

I. Mandelbaum and M. Bolshtyansky, "Raman amplifier model in singlemode optical fiber," IEEE Photon. Technol. Lett. 15, 1704-1706 (2003).
[CrossRef]

Bouteiller, J.

Bromage, J.

Chang, C.

Chi, S.

T. Kung, C. Chang, J. Dung, and S. Chi, "Four-wave mixing between pump and signal in a distributed Raman amplifier," J. Lightwave Technol. 21, 1164 - 1170 (2003).
[CrossRef]

S. Wen, T.-Y. Wang, and S. Chi, "Self-consistent pump depletion method to design optical transmission systems amplified by bidirectional Raman pumps," Int. J. Nonlinear Opt. Phys. 1, 595-608 (1992).
[CrossRef]

Dung, J.

Faralli, S.

S. Sugliani, G. Sacchi, G. Bolognini, S. Faralli, and F. Pasquale, "Effective suppression of penalties induced by parametric nonlinear interaction in distributed Raman amplifiers based on NZ-DS fibers," IEEE Photon. Technol. Lett. 16, 81-83 (2004).
[CrossRef]

Friesem, A.

E. Lichtman, R. Waarts, and A. Friesem, "Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fiber," J. Lightwave Technol. 7, 171-1174 (1989).
[CrossRef]

Han, B.

Headley, C.

Islam, M.

M. Islam, "Raman amplifiers for telecommunications," IEEE J. Sel. Top. Quantum Electron. 8, 548-559 (2002).
[CrossRef]

Iwatsuki, K.

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

Kani, J.

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

Kung, T.

Leng, L.

Lichtman, E.

E. Lichtman, R. Waarts, and A. Friesem, "Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fiber," J. Lightwave Technol. 7, 171-1174 (1989).
[CrossRef]

Lu, Z.

Mandelbaum, I.

I. Mandelbaum and M. Bolshtyansky, "Raman amplifier model in singlemode optical fiber," IEEE Photon. Technol. Lett. 15, 1704-1706 (2003).
[CrossRef]

Masuda, H.

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

Pasquale, F.

S. Sugliani, G. Sacchi, G. Bolognini, S. Faralli, and F. Pasquale, "Effective suppression of penalties induced by parametric nonlinear interaction in distributed Raman amplifiers based on NZ-DS fibers," IEEE Photon. Technol. Lett. 16, 81-83 (2004).
[CrossRef]

Perlin, V.

Sacchi, G.

S. Sugliani, G. Sacchi, G. Bolognini, S. Faralli, and F. Pasquale, "Effective suppression of penalties induced by parametric nonlinear interaction in distributed Raman amplifiers based on NZ-DS fibers," IEEE Photon. Technol. Lett. 16, 81-83 (2004).
[CrossRef]

Sugliani, S.

S. Sugliani, G. Sacchi, G. Bolognini, S. Faralli, and F. Pasquale, "Effective suppression of penalties induced by parametric nonlinear interaction in distributed Raman amplifiers based on NZ-DS fibers," IEEE Photon. Technol. Lett. 16, 81-83 (2004).
[CrossRef]

Sumida, M.

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

Suzuki, H.

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

Tada, Y.

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

Takachio, N.

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

Waarts, R.

E. Lichtman, R. Waarts, and A. Friesem, "Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fiber," J. Lightwave Technol. 7, 171-1174 (1989).
[CrossRef]

Wang, T.-Y.

S. Wen, T.-Y. Wang, and S. Chi, "Self-consistent pump depletion method to design optical transmission systems amplified by bidirectional Raman pumps," Int. J. Nonlinear Opt. Phys. 1, 595-608 (1992).
[CrossRef]

Wen, S.

S. Wen, T.-Y. Wang, and S. Chi, "Self-consistent pump depletion method to design optical transmission systems amplified by bidirectional Raman pumps," Int. J. Nonlinear Opt. Phys. 1, 595-608 (1992).
[CrossRef]

Winful, G.

Woodward, S.

X. Zhou, M. Birk, and S. Woodward, "Pump-noise induced FWM effect and its reduction in a distributed Raman fiber amplifiers," IEEE Photon. Technol. Lett. 14, 1686-1688 (2002).
[CrossRef]

Yang, G.

Yariv, A.

Zhang, G.

T. Zhang, X. Zhang, and G. Zhang, "Distributed fiber Raman amplifiers with incoherent pumping," IEEE Photon. Technol. Lett. 17, 1175-1177 (2005).
[CrossRef]

B. Han, X. Zhang, G. Zhang, Z. Lu and G. Yang, "Composite broad-band fiber Raman amplifiers using incoherent pumping," Opt. Express 13, 6023-6032 (2005).
[CrossRef] [PubMed]

Zhang, T.

T. Zhang, X. Zhang, and G. Zhang, "Distributed fiber Raman amplifiers with incoherent pumping," IEEE Photon. Technol. Lett. 17, 1175-1177 (2005).
[CrossRef]

Zhang, X.

T. Zhang, X. Zhang, and G. Zhang, "Distributed fiber Raman amplifiers with incoherent pumping," IEEE Photon. Technol. Lett. 17, 1175-1177 (2005).
[CrossRef]

B. Han, X. Zhang, G. Zhang, Z. Lu and G. Yang, "Composite broad-band fiber Raman amplifiers using incoherent pumping," Opt. Express 13, 6023-6032 (2005).
[CrossRef] [PubMed]

Zhou, X.

X. Zhou, M. Birk, and S. Woodward, "Pump-noise induced FWM effect and its reduction in a distributed Raman fiber amplifiers," IEEE Photon. Technol. Lett. 14, 1686-1688 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Islam, "Raman amplifiers for telecommunications," IEEE J. Sel. Top. Quantum Electron. 8, 548-559 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

H. Suzuki, J. Kani, H. Masuda, N. Takachio, K. Iwatsuki, Y. Tada, and M. Sumida, "1-Tb/s (100 × 10 Gb/s) super-dense WDM Transmission with 25-GHz channel spacing in the zero-dispersion region employing distributed Raman amplification technology," IEEE Photon. Technol. Lett. 12, 903-905 (2000).
[CrossRef]

T. Zhang, X. Zhang, and G. Zhang, "Distributed fiber Raman amplifiers with incoherent pumping," IEEE Photon. Technol. Lett. 17, 1175-1177 (2005).
[CrossRef]

S. Sugliani, G. Sacchi, G. Bolognini, S. Faralli, and F. Pasquale, "Effective suppression of penalties induced by parametric nonlinear interaction in distributed Raman amplifiers based on NZ-DS fibers," IEEE Photon. Technol. Lett. 16, 81-83 (2004).
[CrossRef]

I. Mandelbaum and M. Bolshtyansky, "Raman amplifier model in singlemode optical fiber," IEEE Photon. Technol. Lett. 15, 1704-1706 (2003).
[CrossRef]

X. Zhou, M. Birk, and S. Woodward, "Pump-noise induced FWM effect and its reduction in a distributed Raman fiber amplifiers," IEEE Photon. Technol. Lett. 14, 1686-1688 (2002).
[CrossRef]

Int. J. Nonlinear Opt. Phys.

S. Wen, T.-Y. Wang, and S. Chi, "Self-consistent pump depletion method to design optical transmission systems amplified by bidirectional Raman pumps," Int. J. Nonlinear Opt. Phys. 1, 595-608 (1992).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Opt. Lett.

Other

D. Vakhshoori, M. Azimi, P. Chen, B. Han, M. Jiang, L. Knopp, C. Lu, Y. Shen, G. Rodes, S. Vote, P. Wang, and X. Zhu, "Raman amplification using high-power incoherent semiconductor pump sources," OFC 2003, Paper PD47.

J. Moré, B. Garbow, and K. Hillstrom, User Guide for MINPACK-1, Argonne National Laboratory Report ANL-80-74, Argonne, Illinois, 1980.

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Figures (5)

Fig. 1.
Fig. 1.

Optimized pump power spectral density functions (PSDFs), (b) gains, (c) effective noise figures, and (d) output forward ASEN PSDFs for the DFRAs using backward pumping, in which the numbers of sub-bands (N) are shown in the figures. The gains, effective noise figures, and output forward ASEN PSDF for the case using the four optimized Gaussian incoherent pumps given in the Table 1 are also shown.

Fig. 2.
Fig. 2.

(a) Optimized pump power spectral density functions (PSDFs), (b) gains, (c) effective noise figures, and (d) output forward ASEN PSDFs for the DFRAs using bidirectional pumping, in which the numbers of sub-bands (N) are shown in the figures. The gains, effective noise figures, and output forward ASEN PSDF for the case using the five optimized Gaussian incoherent pumps given in the Table 2 are also shown.

Fig. 3.
Fig. 3.

Evolutions of the forward ASEN PSDs at 1530 nm and 1600 nm for the DFRA using the optimized pump power spectral density functions (PSDFs) shown in the Fig. 2(a).

Fig. 4.
Fig. 4.

Synthesized pump power spectral density function (PSDF) with four Gaussian incoherent pumps for the case of N= 9 shown in the Fig. 1(a), where the original pump PSDF is shown for comparison. The optimized PSDF with four Gaussian incoherent pumps is also shown in which their parameters are given in the Table 1.

Fig. 5.
Fig. 5.

Synthesized power spectral density functions (PSDFs) with five Gaussian incoherent pumps for the case of N= 6 shown in the Fig. 2(a), where the original pump PSDFs are shown for comparison. The optimized PSDFs with five Gaussian incoherent pumps are also shown in which their parameters are given in the Table 2.

Tables (2)

Tables Icon

Table 1: Parameters of the four optimized Gaussian incoherent pumps for the DFRA using backward pumping.

Tables Icon

Table 2: Parameters of the five optimized Gaussian incoherent pumps for the DFRA using bidirectional pumping.

Equations (17)

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

f i ( v ) = j = 0 M a ij ( v v i = 1 ) j , v i 1 v v i ,
f N ( v ) = j = 0 M a Nj ( v v N ) j , v N 1 v v N .
f i ( v i ) = f i + 1 ( v i ) ,
f ' i ( v i ) = f ' i + 1 ( v i ) ,
f 0 ( v 0 ) = 0 ,
f N ( v N ) = 0 ,
f ' o ( v 0 ) = 0 ,
f ' N ( v N ) = 0 ,
p i ( v ) = f i ( v ) , v i 1 v v i .
U = N ( M 1 ) 2 .
h ( A ) = k = 1 N s ( G k ( A ) G k T ) 2 , N A N S ,
A = ( a 12 , a 13 , , a 1 M , a 22 , a 23 , , a 2 M , , a ( N 2 ) 2 , a ( N 2 ) 3 , , a ( N 2 ) M , a ( N 2 ) 3 , a ( N 2 ) 4 , , a ( N 2 ) M , a N 3 , a N 4 , , a N M ) .
a i 0 = j = 0 M a ( i 1 ) j Δ v i 1 i ,
a i 1 = j = 1 M j a ( i 1 ) j Δ v i 1 j 1 ,
a i 2 = 1 2 Δ v i ( Δ v i Δ v k ) [ 2 ( a k 0 a i 0 ) + j = 1 j 2 M ( 2 j ) a k j Δ v k j j = 1 j 2 M ( 2 Δ v i j Δ v k ) a i j Δ v i j 1 ] ,
E N F = 1 G on off ( 1 + P ASE + h v Δ v ) ,
P G ( v ) = P p exp [ 4 ln ( 2 ) ( v v c Δ v W ) 2 ] ,

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