Abstract

In this paper, a novel frequency domain model to compute the pump to signal relative intensity noise (RIN) transfer in multi-pump Raman fiber amplifiers (RFAs) is proposed. The analytical expressions for RFAs with single pump and single signal channel are derived as a specific case of the model. The formulas exactly agree with the published results both for the co-pumped and counter-pumped RFAs. Afterwards, the pump to signal RIN transfer in multi-pump RFAs is studied numerically with thorough discussions.

© 2006 Optical Society of America

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References

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  1. S. Namiki and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Top.Quantum Electron. l 7, 3-16 (2001).
  2. C. R. S. Fludger, V. Handerek, and R. J. Mears, "Pump to Signal RIN Transfer in Raman Fiber Amplifiers," IEEE, J. Lightwave Technol. 19, 1140-1148 (2001).
    [CrossRef]
  3. M. D. Mermelstein, C. Headley, and J.-C. Bouteillier, "RIN transfer analysis in pump depletion regime for Raman fiber amplifiers," Electron. Lett. 38, 403-405, (2002).
    [CrossRef]
  4. Bruno Bristiel, Shifeng Jiang, Philippe Gallion, and Erwan Pincemin, "New Model of Noise Figure and RIN Transfer in Fiber Raman Amplifiers," IEEE Photon. Technol. Lett. 18, 980-982 (2006).
    [CrossRef]
  5. X. Zhou, C. Lu, P. Shum, and TH. Cheng, "A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).
    [CrossRef]
  6. M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
    [CrossRef]
  7. V.E Perlin, H.G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers," IEEE, J. lightwave technol. 20, 250 - 254 (2002).
    [CrossRef]
  8. V.E. Perlin, H.G. Winful, "On distributed raman amplification for ultrabroad-band long-haul wdm systems," IEEE, J. lightwave technol. 20, 409-417 (2002).
    [CrossRef]
  9. Jaehyoung Park, Pilhan Kim, Jonghan Park, H. Lee, and Namkyoo Park, "Closed Integral form expansion of Raman equation for efficient gain optimization Process," IEEE Photon. Tech. Lett. 16, 1649 - 1651 (2004).
    [CrossRef]
  10. Jian Chen, Xueming Liu, Chao Lu, Yixin Wang, and Zhaohui Li, "Design of Multistage Gain-Flattened Fiber Raman Amplifiers," IEEE, J. lightwave technol. 24, 935-944 (2006).
    [CrossRef]
  11. M. Karásek and M. Menif, "Channel Addition/Removal Response in Raman Fiber Amplifiers: Modeling and Experimentation," IEEE J. Lightwave Technol. 20, 1680-1688 (2002).
    [CrossRef]
  12. G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, New York, 2001)
  13. C. Fludger, A. Maroney, N. Jolley, and R. Mears, "An analysis of the improvements in OSNR from distributed Raman amplifiers using modern transmission fibers," in Optical Fiber Communication Conference Technical Digest (Optical Society of America, 2000) 100-102.

2006 (2)

Bruno Bristiel, Shifeng Jiang, Philippe Gallion, and Erwan Pincemin, "New Model of Noise Figure and RIN Transfer in Fiber Raman Amplifiers," IEEE Photon. Technol. Lett. 18, 980-982 (2006).
[CrossRef]

Jian Chen, Xueming Liu, Chao Lu, Yixin Wang, and Zhaohui Li, "Design of Multistage Gain-Flattened Fiber Raman Amplifiers," IEEE, J. lightwave technol. 24, 935-944 (2006).
[CrossRef]

2004 (1)

Jaehyoung Park, Pilhan Kim, Jonghan Park, H. Lee, and Namkyoo Park, "Closed Integral form expansion of Raman equation for efficient gain optimization Process," IEEE Photon. Tech. Lett. 16, 1649 - 1651 (2004).
[CrossRef]

2002 (4)

M. Karásek and M. Menif, "Channel Addition/Removal Response in Raman Fiber Amplifiers: Modeling and Experimentation," IEEE J. Lightwave Technol. 20, 1680-1688 (2002).
[CrossRef]

V.E Perlin, H.G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers," IEEE, J. lightwave technol. 20, 250 - 254 (2002).
[CrossRef]

V.E. Perlin, H.G. Winful, "On distributed raman amplification for ultrabroad-band long-haul wdm systems," IEEE, J. lightwave technol. 20, 409-417 (2002).
[CrossRef]

M. D. Mermelstein, C. Headley, and J.-C. Bouteillier, "RIN transfer analysis in pump depletion regime for Raman fiber amplifiers," Electron. Lett. 38, 403-405, (2002).
[CrossRef]

2001 (4)

C. R. S. Fludger, V. Handerek, and R. J. Mears, "Pump to Signal RIN Transfer in Raman Fiber Amplifiers," IEEE, J. Lightwave Technol. 19, 1140-1148 (2001).
[CrossRef]

X. Zhou, C. Lu, P. Shum, and TH. Cheng, "A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).
[CrossRef]

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
[CrossRef]

S. Namiki and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Top.Quantum Electron. l 7, 3-16 (2001).

Bouteillier, J.-C.

M. D. Mermelstein, C. Headley, and J.-C. Bouteillier, "RIN transfer analysis in pump depletion regime for Raman fiber amplifiers," Electron. Lett. 38, 403-405, (2002).
[CrossRef]

Chen, J.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
[CrossRef]

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
[CrossRef]

Cheng, TH.

X. Zhou, C. Lu, P. Shum, and TH. Cheng, "A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).
[CrossRef]

Emori, Y.

S. Namiki and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Top.Quantum Electron. l 7, 3-16 (2001).

Fludger, C. R. S.

Handerek, V.

Headley, C.

M. D. Mermelstein, C. Headley, and J.-C. Bouteillier, "RIN transfer analysis in pump depletion regime for Raman fiber amplifiers," Electron. Lett. 38, 403-405, (2002).
[CrossRef]

Jiang, W.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
[CrossRef]

Karásek, M.

M. Karásek and M. Menif, "Channel Addition/Removal Response in Raman Fiber Amplifiers: Modeling and Experimentation," IEEE J. Lightwave Technol. 20, 1680-1688 (2002).
[CrossRef]

Li, J.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
[CrossRef]

Li, X.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
[CrossRef]

Lu, C.

X. Zhou, C. Lu, P. Shum, and TH. Cheng, "A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).
[CrossRef]

Mears, R. J.

Menif, M.

M. Karásek and M. Menif, "Channel Addition/Removal Response in Raman Fiber Amplifiers: Modeling and Experimentation," IEEE J. Lightwave Technol. 20, 1680-1688 (2002).
[CrossRef]

Mermelstein, M. D.

M. D. Mermelstein, C. Headley, and J.-C. Bouteillier, "RIN transfer analysis in pump depletion regime for Raman fiber amplifiers," Electron. Lett. 38, 403-405, (2002).
[CrossRef]

Namiki, S.

S. Namiki and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Top.Quantum Electron. l 7, 3-16 (2001).

Perlin, V.E

Perlin, V.E.

Shum, P.

X. Zhou, C. Lu, P. Shum, and TH. Cheng, "A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).
[CrossRef]

Winful, H.G.

Yan, M.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
[CrossRef]

Zhou, X.

X. Zhou, C. Lu, P. Shum, and TH. Cheng, "A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).
[CrossRef]

Electron. Lett. (1)

M. D. Mermelstein, C. Headley, and J.-C. Bouteillier, "RIN transfer analysis in pump depletion regime for Raman fiber amplifiers," Electron. Lett. 38, 403-405, (2002).
[CrossRef]

IEEE J. Lightwave Technol. (1)

M. Karásek and M. Menif, "Channel Addition/Removal Response in Raman Fiber Amplifiers: Modeling and Experimentation," IEEE J. Lightwave Technol. 20, 1680-1688 (2002).
[CrossRef]

IEEE Photon. Tech. Lett. (1)

Jaehyoung Park, Pilhan Kim, Jonghan Park, H. Lee, and Namkyoo Park, "Closed Integral form expansion of Raman equation for efficient gain optimization Process," IEEE Photon. Tech. Lett. 16, 1649 - 1651 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

Bruno Bristiel, Shifeng Jiang, Philippe Gallion, and Erwan Pincemin, "New Model of Noise Figure and RIN Transfer in Fiber Raman Amplifiers," IEEE Photon. Technol. Lett. 18, 980-982 (2006).
[CrossRef]

X. Zhou, C. Lu, P. Shum, and TH. Cheng, "A Simplified Model and Optimal Design of a Multiwavelength Backward-Pumped Fiber Raman Amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).
[CrossRef]

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol. Lett. 13, 948-950 (2001).
[CrossRef]

J. Lightwave Technol. (1)

Quantum Electron. l (1)

S. Namiki and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Top.Quantum Electron. l 7, 3-16 (2001).

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, New York, 2001)

C. Fludger, A. Maroney, N. Jolley, and R. Mears, "An analysis of the improvements in OSNR from distributed Raman amplifiers using modern transmission fibers," in Optical Fiber Communication Conference Technical Digest (Optical Society of America, 2000) 100-102.

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Figures (10)

Fig. 1.
Fig. 1.

Net gain spectrum of the co-pumped 50km RFA

Fig. 2.
Fig. 2.

RIN transfer of the co-pumped 50km RFA from pump 1 to different signal channels

Fig. 3.
Fig. 3.

RIN transfer of the co-pumped 50km RFA at 1530nm

Fig. 4.
Fig. 4.

RIN transfer of the co-pumped 50km RFA at 1561nm

Fig. 5.
Fig. 5.

RIN transfer of the co-pumped 50km RFA at 1594nm

Fig. 6.
Fig. 6.

net gain spectrum of the co-pumped 50km RFA

Fig. 7.
Fig. 7.

RIN transfer of the counter-pumped 50km RFA from pump 1 to different signal channels

Fig. 8.
Fig. 8.

RIN transfer of the counter-pumped 50km RFA at 1530nm

Fig. 9.
Fig. 9.

RIN transfer of the counter-pumped 50km RFA at 1561nm

Fig. 10.
Fig. 10.

RIN transfer of the counter-pumped 50km RFA at 1594nm

Equations (33)

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s ( i ) P i z + 1 v g , i P i t = j = 1 , j i n + m g ( ν i , ν j ) P i P j α i P i
i = 1 . . . . . . n + m
g ( ν i , ν j ) = { g r ( ν i ν j ) 2 A eff ( ν i > ν j ) ( ν j ν i ) g r ( ν j ν i ) 2 A eff ( ν i < ν j )
s ( i ) Δ P i ( z , t ) z + 1 v g , i Δ P i ( z , t ) t = j = 1 , j i n + m g ( ν i , ν j ) P i ( z ) Δ P j ( z , t )
+ j = 1 , j i n + m g ( ν i , ν j ) P j ( z ) Δ P i ( z , t ) α i Δ P i ( z , t )
i = 1 . . . . . . n + m
Δ P ( z , ω ) z = AΔP ( z , ω )
Δ P ( z , ω ) = ( Δ P 1 ( z , ω ) Δ P m ( z , ω ) )
A = ( s ( 1 ) ( j = 1 , j 1 m + n g ( ν 1 , ν j ) P j α 1 j ω v g 1 ) s ( 1 ) g ( ν 1 , ν m ) P 1 s ( n + m ) g ( ν n + m , ν 1 ) P n + m s ( n + m ) ( j = 1 , j n + m n + m g ( ν n + m , ν j ) P j α n + m j ω v g , m + n ) )
Δ P ( L , ω ) = M RIN Δ P ( 0 , ω )
M RIN = lim Δ z 0 k = 1 L Δ z ( I + A ( k Δ z ) Δ z )
[ Δ p p out Δ p s out ] = [ M 11 M 12 M 21 M 22 ] [ Δ p p in 0 ]
Δ p s out = M 21 M 11 1 Δ p p out
Δ P p ( z , ω ) z + j ω v g , p Δ P p ( z , ω ) = α p Δ P p ( z , ω )
Δ P s ( z , ω ) z + j ω v g , s Δ P s ( z , ω ) = g P p ( z ) Δ P s ( z , ω ) + g P s ( z ) Δ P p ( z , ω ) α s Δ P s ( z , ω )
P p ( z ) = P p 0 exp ( α p z )
P s ( z ) = P s 0 exp ( 0 z g P p 0 exp ( α p l ) α s d l )
Δ P p ( z , ω ) = exp [ [ j ω v g , p α p ] z ] Δ P p ( 0 , ω )
Δ P s ( z , ω ) z = [ j ω v g , s α s + g P p 0 exp ( α p z ) ] Δ P s ( z , ω )
+ g P s 0 exp [ 0 z g P p 0 exp ( α p l ) α s d l ] exp [ [ j ω v g , p + α p ] z ] Δ P p ( 0 , ω )
Δ P s ( L , ω ) = exp ( 0 L [ j ω v g , s α s + g P p 0 exp ( α p z ) ] d z )
* g P s 0 Δ P p ( 0 , ω ) 0 L exp ( ( ( j ω v g , p + α p ) + j ω v g , s z ) z ) d z
= g P s 0 Δ P p ( 0 , ω ) exp ( j ω v g , s L ) G v g , s ( 1 exp ( ( j 2 π f b v g , s α p ) L ) ) α p v g , s + j 2 π f b
G = exp [ 0 L g P p 0 exp ( α p l ) α s d l ] = g P p 0 L eff α s L
L eff = 1 exp ( α p L ) α p
b = j 2 π ( 1 v g , s v g , p )
j ω [ 1 v g , p + 1 v g , s ] = j 2 π f b v g , s
Δ P s ( L , ω ) P s ( L ) = Δ P s ( L , ω ) P s 0 G
= Δ P p ( 0 , ω ) P p 0 ln G L eff exp ( j ω v g , s L ) v g , s [ 1 exp [ ( j 2 π f b v g , s α p ) L ] ] α p v g , s + j 2 π f b
r s = Δ P s ( L , ω ) P s ( L ) 2
r p = Δ P p ( 0 , ω ) P p ( 0 ) 2
r s = r p ( ln G ) 2 [ v g , s L eff ] 2 ( α p v g , s ) 2 + ( 2 π f b ) 2
* [ 1 2 cos [ 2 π f b v g , s L ] exp ( α p L ) + exp ( 2 α p L ) ]

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