Abstract

The nature of how a chirped Gaussian pulse is affected in the system with both polarization mode dispersion (PMD) and polarization-dependent loss (PDL) is analyzed. We develop a mathematical description and verify the results through numerical simulation. The delay of a chirped Gaussian pulse depends not only on the group delay characteristic of the transmission system but also on the chirp of the pulse itself. The delay also depends on the magnitude profile of the frequency response of the system. Therefore, the effective PMD for a chirped Gaussian pulse is related to both the PMD and PDL in the transmission system. The results show that the effective PMD may deteriorate when a PDL exists.

© 2004 Optical Society of America

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References

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  1. B. Huttner, C. Geiser, and N. Gisin, �??Polarization-induced distortions in optical fiber networks with polarization-mode dispersion and polarization-dependent losses,�?? IEEE J. Sel. Top. Quantum Electron. 6, 317-329 (2000).
    [CrossRef]
  2. N. Gisin and B. Huttner, �??Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers,�?? Opt. Commun. 142, 119-125 (1997).
    [CrossRef]
  3. P. Lu, L. Chen, and X. Bao, �??Polarization mode dispersion and polarization dependent loss for a pulse in single-mode fibers,�?? J. Lightwave Technol. 19, 856-860 (2001).
    [CrossRef]
  4. W. Shieh, �??Principal states of polarization for an optical pulse,�?? IEEE Photon. Technol. Lett. 11, 677�??679 (1999).
    [CrossRef]
  5. B. L. Heffner, �??Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,�?? IEEE Photon. Technol. Lett. 4, 1066�??1069 (1992).
    [CrossRef]

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

B. Huttner, C. Geiser, and N. Gisin, �??Polarization-induced distortions in optical fiber networks with polarization-mode dispersion and polarization-dependent losses,�?? IEEE J. Sel. Top. Quantum Electron. 6, 317-329 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

W. Shieh, �??Principal states of polarization for an optical pulse,�?? IEEE Photon. Technol. Lett. 11, 677�??679 (1999).
[CrossRef]

B. L. Heffner, �??Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,�?? IEEE Photon. Technol. Lett. 4, 1066�??1069 (1992).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (1)

N. Gisin and B. Huttner, �??Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers,�?? Opt. Commun. 142, 119-125 (1997).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

The dependence of the effective PMD on chirping when PDL2=8 dB, PMD1=10 ps. Solid curve: chirp-free, dotted curve: chirp =2, dashed curve: chirp =4, dash-dot curve: chirp =7, asterisk symbol: chirp =8, square symbol: chirp =10. triangle symbol: chirp-free pulse with the pulse width of 50/501/2 ps. The relative angle is the angle between the PMD and the PDL elements.

Fig. 2.
Fig. 2.

(a) Magnitude of the frequency response with maximum and minimum delay for a chirp parameter of 7. Pulse width =50ps, PMD1=10 ps, PDL2=8 dB. Solid curve: maximum delay, dashed curve: minimum delay. (b) Spectrum of the output pulse with maximum and minimum delay for a chirp parameter of 7. Pulse width =50ps, PMD1=10 ps, PDL2=8 dB. Solid curve: maximum delay, dashed curve: minimum delay.

Fig. 3.
Fig. 3.

Amplitude of pulses with maximum and minimum delay for different chirp parameters. Pulse width=50ps, PMD1=10 ps. Solid curves: chirp-free, PDL2=0 dB, dotted curves: chirp =0, PDL2=8 dB, dashed curves: chirp =7, PDL2=8 dB.

Fig. 4.
Fig. 4.

States corresponding to the maximum and the minimum delay in the Poincare sphere when the chirp parameter and PDL value are different. Squares : PDL2=0 dB, PMD1=10 ps, chirp =0, diamonds : PDL2=8 dB, PMD1=10 ps, chirp =0, circles : PDL2=8 dB, PMD1=10 ps, chirp =7.

Equations (27)

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H ( ω ) = H m ( ω ) exp ( j ω t 0 ) .
y ( t ) = exp [ ( 1 + j C ) ( t t 0 + j α ) 2 2 T 0 2 ]
= exp { [ ( t t 0 ) 2 α 2 2 C α ( t t 0 ) ] 2 T 0 2 }
= exp { [ ( t t 0 α C ) 2 α 2 ( α C ) 2 ] 2 T 0 2 } .
< t > = ψ out * ( t ) t ψ out ( t ) dt ψ out * ( t ) ψ out ( t ) dt
= H * ( ω ) Ψ in * ( ω ) j [ H ( ω ) Ψ in ( ω ) ] d ω H ( ω ) Ψ in ( ω ) 2 d ω ,
< t > = H m ( ω ) exp ( j ϕ H ) exp [ ( 1 + j C ) T 0 2 ω 2 2 ( 1 + C 2 ) ] j
× { H m ( ω ) exp ( j ϕ H ) exp [ ( 1 j C ) T 0 2 ω 2 2 ( 1 + C 2 ) ] } d ω H ( ω ) Ψ in ( ω ) 2 d ω ,
H m ( ω ) exp [ T 0 2 ω 2 ( 1 + C 2 ) ] j [ H m ( ω ) + j ϕ H H m ( ω ) ( 1 j C ) T 0 2 ω H m ( ω ) ( 1 + C 2 ) ] d ω .
H m 2 ( ω ) exp [ T 0 2 ω 2 ( 1 + C 2 ) ] [ ϕ H C T 0 2 ω ( 1 + C 2 ) ] d ω .
C T 0 2 1 + C 2 H m 2 ( ω ) exp [ T 0 2 ω 2 ( 1 + C 2 ) ] ω d ω
= C exp [ T 0 2 ω 2 ( 1 + C 2 ) ] H m 2 { ln [ H m ( ω ) ] } d ω .
< t > = { H m 2 ( ω ) exp [ T 0 2 ω 2 ( 1 + C 2 ) ] ϕ H d ω
C exp [ T 0 2 ω 2 ( 1 + C 2 ) ] H m 2 { ln [ H m ( ω ) ] } d ω } H ( ω ) Ψ in ( ω ) 2 d ω
{ H m 2 ( ω ) exp [ T 0 2 ω 2 ( 1 + C 2 ) ] } H ( ω ) Ψ in ( ω ) 2 d ω
= { H ( ω ) Ψ in ( ω ) 2 } H ( ω ) Ψ in ( ω ) 2 d ω .
H 1 m ( ω ) = ρ 1 + ( T ( ω ) φ ̂ in ) , H 2 m ( ω ) = ρ 2 + ( T ( ω ) φ ̂ in ) ,
H m ( ω ) = T ( ω ) φ ̂ in ,
P out ( ω ) = H 1 m 2 Ψ in ( ω ) 2 + H 2 m 2 Ψ in ( ω ) 2 .
C [ Ψ in ( ω ) 2 H 1 m 2 { ln [ H 1 m ( ω ) ] } + Ψ in ( ω ) 2 H 2 m 2 { ln [ H 2 m ( ω ) ] } ] P out ( ω ) d ω
= C ( H 1 m H 1 m + H 2 m H 2 m ) [ Ψ in ( ω ) 2 P out ( ω ) d ω ] .
C ( H 1 m H 1 m + H 2 m H 2 m ) [ Ψ in ( ω ) 2 P out ( ω ) d ω ]
= C H m H m [ Ψ in ( ω ) 2 P out ( ω ) d ω ]
= C { ln [ H m ( ω ) ] } [ H m 2 Ψ in ( ω ) 2 P out ( ω ) d ω ] .
C { ln [ H m ( ω ) ] } [ P out ( ω ) P out ( ω ) d ω ] .
t = [ ψ out + ( t ) t ψ out ( t ) dt ] E out = [ Ψ out + ( ω ) j Ψ out ( ω ) d ω ] E out = ( φ ̂ + P 1 φ ̂ ) E out ,
P 1 = j [ T + ( ω ) T ( ω ) Ψ in ( ω ) 2 + T + ( ω ) T ( ω ) Ψ in ( ω ) Ψ in * ( ω ) ] d ω

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