Abstract

An analytic expression for the variance of nonlinear phase noise that uses a first-order perturbation technique is obtained. The results show that for highly dispersive transmission systems, amplified spontaneous emission-induced phase noise due to self-phase modulation becomes much smaller than that for the systems with no dispersion.

© 2005 Optical Society of America

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References

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2005 (1)

2004 (1)

2003 (2)

A. G. Green, P. P. Mitra, and L. G.L. Wegener, Opt. Lett. 28, 2455 (2003).
[CrossRef] [PubMed]

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

2002 (1)

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

1994 (1)

A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
[CrossRef]

1990 (1)

Boivin, D.

Gnauck, A. H.

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

Goedgebuer, J.-P.

Gordon, J. P.

Green, A. G.

Hanna, M.

Kim, H.

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

Kumar, S.

Lacourt, P.-A.

McKinstrie, C. J.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

Mecozzi, A.

A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
[CrossRef]

Mitra, P. P.

Mollenauer, L. F.

Wegener, L. G.L.

Xie, C.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

Yang, D.

IEEE J. Sel. Top. Quantum Electron. (1)

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

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Figures (1)

Fig. 1
Fig. 1

Variance of phase noise. The solid curves and the plus signs show the analytical and numerical simulation results, including linear and nonlinear phase noise, respectively. The dashed line shows the analytical results including only linear phase noise.

Equations (26)

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i u z β 2 ( z ) 2 2 u t 2 = γ exp [ w ( z ) ] u 2 u + i R ( z , t ) ,
R ( z , t ) = n = 1 N a δ ( z n L ) δ u a ,
δ u a r ( t ) δ u a r ( t ) = δ u a i ( t ) δ u a i ( t ) = ρ 2 δ ( t t ) ,
ρ = n sp h f ( G 1 ) .
u 0 ( z , t ) = ( E π T ( z ) ) 1 2 exp { t 2 [ 1 + i C ( z ) ] 2 T 2 ( z ) + i θ ( z ) } ,
T ( z ) = T 0 4 + S 2 ( z ) T 0 , C ( z ) = S ( z ) T 0 2 ,
θ ( z ) = 1 2 tan 1 [ C ( z ) ] .
S ( z ) = 0 z β 2 ( s ) d s .
u ( z , t ) = u 0 ( z , t ) + γ u 1 ( z , t ) + γ 2 u 2 ( z , t ) + ,
u ( L tot , t ) = E T eff exp [ t 2 ( 2 T 0 2 ) ] { 1 + i γ E g ( 0 , t ) } ,
g ( z , t ) = T 0 2 T eff z L tot exp [ ω ( r ) Δ ( r ) t 2 ] d r [ T 0 4 + 3 S 2 ( r ) + 2 i T 0 2 S ( r ) ] 1 2 ,
Δ ( r ) = T 0 2 i S ( r ) T 0 2 [ T 0 2 + i 3 S ( r ) ] ,
ϕ nl ( t ) = tan 1 { γ E Re [ g ( 0 , t ) ] 1 γ E Im [ g ( 0 , t ) ] } γ E Re [ g ( 0 , t ) ] { 1 + γ E Im [ g ( 0 , t ) ] } .
δ ϕ nl , n ( t ) = γ Re [ g ( n L , t ) ] { 1 + 2 γ E Im [ g ( n L , t ) ] } δ E ,
g ( n L , t ) = ( N a n ) h ( t ) T eff ,
h ( t ) = T 0 2 0 L exp [ α 0 r Δ ( r ) t 2 ] d r [ T 0 4 + 3 S 2 ( r ) + 2 i T 0 2 S ( r ) ] 1 2 ,
δ ϕ nl , n ( t ) = γ ( N a n ) h r ( t ) T eff { 1 + 2 γ E ( N a n ) h i ( t ) T eff } δ E ,
d E d z = 2 Re [ R u 0 ] d t .
δ E = 2 Re [ δ u a ( t ) u 0 ( t , n L ) ] d t .
δ E 2 = 2 ρ E .
δ ϕ nl , n 2 = 2 ( N a n ) 2 γ 2 ρ E h r 2 ( 0 ) [ 1 + K ( N a n ) ] 2 T eff 2 ,
K = 2 γ E h i ( 0 ) T eff .
h r ( 0 ) = [ 1 exp ( α 0 L ) ] α 0 L eff , h i ( 0 ) = 0 ,
δ ϕ nl 2 = 2 γ 2 ρ E h r 2 ( 0 ) [ I 2 + K 2 I 4 + 2 K I 3 ] T eff 2 ,
I j = n = 1 N a n j ,
N a ρ 2 E .

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