Abstract

Phase modulation schemes are attracting much interest for use in ultra-fast optical communication systems because they are much less affected by fiber nonlinearities than conventional modulation formats. Semiconductor optical amplifiers (SOAs) can be used to amplify and process phase modulated signals. However, existing SOA nonlinear phase noise (NLPN) models are simplistic and, sometimes, inaccurate. It is, therefore, important to correctly model their behavior since NLPN is the main drawback in these applications. In this paper we show that a more accurate model can be used leading to simple nonlinear noise expressions at the SOA output of differential phase shift keying systems. To demonstrate the utility of this model, we have used it to calculate the optical signal to noise ratio penalties introduced by a power booster SOA and the first inline amplifier of a 40 Gb/s NRZ-DQPSK single channel link. The model parameters have been estimated from measurements taken of a commercial SOA.

© 2010 OSA

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References

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  1. M. J. Connelly, Semiconductor optical amplifiers, (Kluwer Academic Press, Boston, 2002).
  2. K. E. Zoiros, C. O’Riordan, and M. J. Connelly, “Semiconductor optical amplifier pattern effect suppression using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 22(4), 221–223 (2010).
    [CrossRef]
  3. E. Ciaramella, A. D’Errico, and V. Donzella, “Using semiconductor-optical amplifiers with constant envelope WDM signals,” IEEE J. Quantum Electron. 44(5), 403–409 (2008).
    [CrossRef]
  4. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmissions,” J. Lightwave Technol. 23(1), 115–130 (2005).
    [CrossRef]
  5. X. Wei and L. Zhang, “Analysis of the phase noise in saturated SOAs for DPSK applications,” IEEE J. Quantum Electron. 41(4), 554–561 (2005).
    [CrossRef]
  6. F. Vocondio, A. Ghazisaeidi, A. Bonini, and L. A. Rush, “Low-complexity compensation of SOA nonlinearity for single-channel PSK and OOK,” J. Lightwave Technol. 28(3), 277–288 (2010).
    [CrossRef]
  7. M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
    [CrossRef]
  8. M. J. Connelly, “Theoretical calculations of the carrier induced refractive index change in tensile-strained InGaAsP for use in 1550 nm semiconductor optical amplifiers,” Appl. Phys. Lett. 93(18), 181111 (2008).
    [CrossRef]
  9. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995), Chap. 2.
  10. A. Mecozzi, “Probability density functions of the nonlinear phase noise,” Opt. Lett. 29(7), 673–675 (2004).
    [CrossRef] [PubMed]
  11. G. P. Agrawal and N. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
    [CrossRef]
  12. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).
  13. M. J. Connelly, “Wide-band steady-state numerical model and parameter extraction of a tensile-strained bulk semiconductor optical amplifier,” IEEE J. Quantum Electron. 43(1), 47–56 (2007).
    [CrossRef]
  14. N. Costa, and A. Carataxo, Advances in Lasers and Electro Optics (INTECH, 2010), Chap. 19.
  15. X. Wei, X. Liu, and C. Xu, “Q-factor in numerical simulations of dpsk with optical delay line demodulation,” (2003), http://arXiv.org/abs/physics/0304002 .
  16. G. P. Agrawal, “Population pulsations and non-degenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5(1), 147–159 (1988).
    [CrossRef]

2010

K. E. Zoiros, C. O’Riordan, and M. J. Connelly, “Semiconductor optical amplifier pattern effect suppression using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 22(4), 221–223 (2010).
[CrossRef]

F. Vocondio, A. Ghazisaeidi, A. Bonini, and L. A. Rush, “Low-complexity compensation of SOA nonlinearity for single-channel PSK and OOK,” J. Lightwave Technol. 28(3), 277–288 (2010).
[CrossRef]

2008

E. Ciaramella, A. D’Errico, and V. Donzella, “Using semiconductor-optical amplifiers with constant envelope WDM signals,” IEEE J. Quantum Electron. 44(5), 403–409 (2008).
[CrossRef]

M. J. Connelly, “Theoretical calculations of the carrier induced refractive index change in tensile-strained InGaAsP for use in 1550 nm semiconductor optical amplifiers,” Appl. Phys. Lett. 93(18), 181111 (2008).
[CrossRef]

2007

M. J. Connelly, “Wide-band steady-state numerical model and parameter extraction of a tensile-strained bulk semiconductor optical amplifier,” IEEE J. Quantum Electron. 43(1), 47–56 (2007).
[CrossRef]

2005

X. Wei and L. Zhang, “Analysis of the phase noise in saturated SOAs for DPSK applications,” IEEE J. Quantum Electron. 41(4), 554–561 (2005).
[CrossRef]

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmissions,” J. Lightwave Technol. 23(1), 115–130 (2005).
[CrossRef]

2004

1998

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

1989

G. P. Agrawal and N. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[CrossRef]

1988

Agrawal, G. P.

G. P. Agrawal and N. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[CrossRef]

G. P. Agrawal, “Population pulsations and non-degenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5(1), 147–159 (1988).
[CrossRef]

Bonini, A.

Ciaramella, E.

E. Ciaramella, A. D’Errico, and V. Donzella, “Using semiconductor-optical amplifiers with constant envelope WDM signals,” IEEE J. Quantum Electron. 44(5), 403–409 (2008).
[CrossRef]

Connelly, M. J.

K. E. Zoiros, C. O’Riordan, and M. J. Connelly, “Semiconductor optical amplifier pattern effect suppression using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 22(4), 221–223 (2010).
[CrossRef]

M. J. Connelly, “Theoretical calculations of the carrier induced refractive index change in tensile-strained InGaAsP for use in 1550 nm semiconductor optical amplifiers,” Appl. Phys. Lett. 93(18), 181111 (2008).
[CrossRef]

M. J. Connelly, “Wide-band steady-state numerical model and parameter extraction of a tensile-strained bulk semiconductor optical amplifier,” IEEE J. Quantum Electron. 43(1), 47–56 (2007).
[CrossRef]

D’Errico, A.

E. Ciaramella, A. D’Errico, and V. Donzella, “Using semiconductor-optical amplifiers with constant envelope WDM signals,” IEEE J. Quantum Electron. 44(5), 403–409 (2008).
[CrossRef]

Donzella, V.

E. Ciaramella, A. D’Errico, and V. Donzella, “Using semiconductor-optical amplifiers with constant envelope WDM signals,” IEEE J. Quantum Electron. 44(5), 403–409 (2008).
[CrossRef]

Eisenstein, G.

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

Ghazisaeidi, A.

Gnauck, A. H.

Mecozzi, A.

O’Riordan, C.

K. E. Zoiros, C. O’Riordan, and M. J. Connelly, “Semiconductor optical amplifier pattern effect suppression using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 22(4), 221–223 (2010).
[CrossRef]

Olsson, N.

G. P. Agrawal and N. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[CrossRef]

Rush, L. A.

Shtaif, M.

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

Tromborg, B.

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

Vocondio, F.

Wei, X.

X. Wei and L. Zhang, “Analysis of the phase noise in saturated SOAs for DPSK applications,” IEEE J. Quantum Electron. 41(4), 554–561 (2005).
[CrossRef]

Winzer, P. J.

Zhang, L.

X. Wei and L. Zhang, “Analysis of the phase noise in saturated SOAs for DPSK applications,” IEEE J. Quantum Electron. 41(4), 554–561 (2005).
[CrossRef]

Zoiros, K. E.

K. E. Zoiros, C. O’Riordan, and M. J. Connelly, “Semiconductor optical amplifier pattern effect suppression using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 22(4), 221–223 (2010).
[CrossRef]

Appl. Phys. Lett.

M. J. Connelly, “Theoretical calculations of the carrier induced refractive index change in tensile-strained InGaAsP for use in 1550 nm semiconductor optical amplifiers,” Appl. Phys. Lett. 93(18), 181111 (2008).
[CrossRef]

IEEE J. Quantum Electron.

G. P. Agrawal and N. Olsson, “Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[CrossRef]

E. Ciaramella, A. D’Errico, and V. Donzella, “Using semiconductor-optical amplifiers with constant envelope WDM signals,” IEEE J. Quantum Electron. 44(5), 403–409 (2008).
[CrossRef]

M. Shtaif, B. Tromborg, and G. Eisenstein, “Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions,” IEEE J. Quantum Electron. 34(5), 869–878 (1998).
[CrossRef]

M. J. Connelly, “Wide-band steady-state numerical model and parameter extraction of a tensile-strained bulk semiconductor optical amplifier,” IEEE J. Quantum Electron. 43(1), 47–56 (2007).
[CrossRef]

X. Wei and L. Zhang, “Analysis of the phase noise in saturated SOAs for DPSK applications,” IEEE J. Quantum Electron. 41(4), 554–561 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

K. E. Zoiros, C. O’Riordan, and M. J. Connelly, “Semiconductor optical amplifier pattern effect suppression using a birefringent fiber loop,” IEEE Photon. Technol. Lett. 22(4), 221–223 (2010).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Lett.

Other

N. Costa, and A. Carataxo, Advances in Lasers and Electro Optics (INTECH, 2010), Chap. 19.

X. Wei, X. Liu, and C. Xu, “Q-factor in numerical simulations of dpsk with optical delay line demodulation,” (2003), http://arXiv.org/abs/physics/0304002 .

M. J. Connelly, Semiconductor optical amplifiers, (Kluwer Academic Press, Boston, 2002).

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

L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995), Chap. 2.

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Figures (11)

Fig. 1
Fig. 1

Normalized power distribution along the SOA. The normalized input powers are 0.001 (blue line), 0.01 (redline), 0.1 (green line) and 0.5 (magenta line).

Fig. 2
Fig. 2

Saturated gain coefficient distribution along the SOA. The normalized input powers are 0.001 (blue line), 0.01 (red line), 0.1 (green line) and 0.5 (magenta line).

Fig. 3
Fig. 3

Spectral power density of the RIN noise components. The normalized input power is 0.1. The input RIN is assumed to be equal to 0.

Fig. 4
Fig. 4

Spectral power density of the phase noise components. The normalized input power is 0.1. The input phase noise is assumed to be equal to 0.

Fig. 5
Fig. 5

Spectral power density of the total phase for r = 0.4737 (blue) and r = 0.5211 (red). Their Lorentzian approximations are plotted in green. The normalized input power is 0.1.

Fig. 6
Fig. 6

Phase noise standard deviation for input powers ranging from 0.01 to 0.1.

Fig. 7
Fig. 7

Simulated NRZ-DQPSK single channel link.

Fig. 8
Fig. 8

OSNR at the output of the power-booster and the in-line amplifier as a function of α. The other parameters take their nominal values.

Fig. 9
Fig. 9

OSNR at the output of the power-booster and the in-line amplifier as a function of τ. The other parameters take their nominal values.

Fig. 10
Fig. 10

OSNR at the output of the power-booster and the in-line amplifier as a function of τ. The other parameters take their nominal values.

Fig. 11
Fig. 11

OSNR at the output of the power-booster and the in-line amplifier as a function of the normalized input power.

Tables (2)

Tables Icon

Table 1 SOA model parameters. go is the unsaturated gain coefficient, G0 the total gain, ξ the current source noise parameter, α the linewidth enhancement factor, τ the carrier lifetime, Psat the saturation power, L the cavity length, γsc the scattering loss coefficient and r = γsc/ go.

Tables Icon

Table 2 A, B and C constant values for Fig. 3(a).

Equations (28)

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ϕ o u t ( t ) = ϕ i n ( t ) + α 2 0 L g s ( z ) d z
z ( δ ρ ρ S ) = g S ρ S 2 1 + ρ S 2 + i ω τ δ ρ ρ S + N ρ ( ω , z )
δ ϕ z = α g S ρ S 2 1 + ρ S 2 + i ω τ δ ρ ρ S + N ϕ ( ω , z )
N ρ ( ω , z ) = 1 2 τ 1 + ρ + s 2 i ω τ F g ( ω , z ) + 1 2 [ f ( ω , z ) ρ s e i ϕ s + f * ( ω , z ) ρ s e i ϕ s ]
N ϕ ( ω , z ) = α 2 τ 1 + ρ + s 2 i ω τ F g ( ω , z ) + 1 2 i [ f ( ω , z ) ρ s e i ϕ s f * ( ω , z ) ρ s e i ϕ s ]
f * ( t , z ) f ( t ' , z ' ) = ω 0 P s a t g s n s p δ ( t t ' ) δ ( z z ' )
f ( t , z ) f ( t ' , z ' ) = f * ( t , z ) f * ( t ' , z ' ) = 0
F g ( t , z ) F g ( t ' , z ' ) = a τ A c [ ξ g 0 + g s + a N t ( 1 + ξ ) + g s ρ s 2 ( 2 n s p 1 ) ] δ ( t t ' ) δ ( z z ' )
F g ( t , z ) f ( t ' , z ' ) = a ρ s e i ϕ s g s n s p A c δ ( t t ' ) δ ( z z ' )
E z = 1 2 [ g S ( 1 i α ) γ S C ] E
g t = g o g S τ g S | E | 2 τ
E = ρ S ( z ) exp [ i ϕ S ( z ) ]
R 0 c ( ω ) = | H ( 0 ) | 2 R I N  ( ω , z = 0 )
R s p c ( ω ) = ω 0 P s a t 0 L | H ( z ) | 2 2 g s n s p ρ s 2 d z
R g c ( ω ) = ω 0 P s a t 0 L | H ( z ) | 2 ξ g 0 + g s + a N t ( 1 + ξ ) + g s ρ s 2 ( 2 n s p 1 ) ( 1 + ρ s 2 ) 2 + ( ω τ ) 2 d z
R g , s p c ( ω ) = 2 ω 0 P s a t 0 L | H ( z ) | 2 2 ( 1 + ρ s 2 ) 2 g s n s p ( 1 + ρ s 2 ) 2 + ( ω τ ) 2 d z
φ 0 c ( ω ) = S δ ϕ ( ω , z = 0 ) + α 2 G 4 | H ( 0 ) 1 | 2 R I N c ( ω , z = 0 ) 2 α ρ s ( 0 ) Re [ ( H ( 0 ) 1 ) S δ ϕ , δ ρ ( ω , z = 0 ) ]
φ s p c ( ω ) = ω 0 4 P s a t 0 L ( α 2 | H ( z ) 1 | 2 + 1 ) 2 g s n s p ρ s 2 d z
φ g c ( ω ) = ω 0 4 P s a t 0 L α 2 | H ( z ) | 2 ξ g 0 + g s + a N t ( 1 + ξ ) + g s ρ s 2 ( 2 n s p 1 ) ( 1 + ρ s 2 ) 2 + ( ω τ ) 2 d z
φ g , s p c ( ω ) = ω 0 P s a t 0 L Re  [ H ( z ) ( 1 H * ( z ) ) 1 + ρ s 2 + i ω τ ] α 2 g s n s p d z
R I N c = R 0 c + R s p c + R g c + R g , s p c
S δ ϕ c = φ 0 c + φ s p c + φ g c + φ g , s p c
H ~ ( z ) = [ 1 r ( 1 + ρ s 2 ) 1 + ρ s 2 + i ω τ ] 1 1 + i ω τ r
H ( z ) = H ~ ( L ) H ~ ( z )
S δ ϕ c = A B 1 + ( ω / Δ ω l ) 2 + B R E C ( ω / 2 C )
R Δ ϕ Δ ϕ = A B 2 Δ ω l exp ( Δ ω l | τ | ) + 2 B C 2 π S i n c ( C τ π )
σ δ ϕ 2 = ( A B ) Δ ω l 2 + 2 B C 2 π
O S N R = 10 L o g 10 π 2 8 σ δ ϕ 2

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