Abstract

We develop new expressions for power fading and average power fading that are induced by first-order polarization mode dispersion, polarization-dependent chromatic dispersion, chromatic dispersion, and chirp under both (i) carrier suppressed modulation and (ii) odd-order optical sideband and carrier suppression. Experimental results show the effectiveness of the theoretical analysis. Further, based on the expressions, we propose a technique for optically compensating the polarization mode dispersion-induced power fading in carrier suppressed modulation.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. R. Hui, B. Zhu, R. Huang, C. Allen, K. Demarest, and D. Richards, "10-Gb/s SCM fibers system using optical SSB modulation," IEEE Photon. Technol. Lett. 13, 896-898 (2001).
    [CrossRef]
  2. C. D. Poole and T. E. Darcie, "Distortion related to polarization mode dispersion in analog lightwave systems," J. Lightwave Technol. 11, 1749-1759 (1993).
    [CrossRef]
  3. P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. P. Von der Weild, F. Prieto, and C. W. Zimmer, "Second-order polarization mode dispersion impact on analog and digital transmissions," J. Lightwave Technol. 16, 757-771 (1998).
    [CrossRef]
  4. C. D. Poole and R. E. Wagner, "Phenomenological approach to polarization dispersion in long single mode fibres," Electron. Lett. 22, 1029-12301986.
    [CrossRef]
  5. G. Ning, S. Aditya, P. Shum, H. Dong, C. Q. Wu, and Y. D. Gong, "New approach to determine the effects of polarization mode dispersion and chromatic dispersion on pulse and RF signals," J. Opt. Soc. Am. A 23, 117-123 (2006).
    [CrossRef]
  6. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  7. C. D. Poole and David L. Favin, "Polarization mode dispersion measurements based on transmission spectra through a polarizer," J. Lightwave Technol. 12, 917-929 (1994).
    [CrossRef]
  8. H. F. Haunstein, H. M. Kallert, and H. Kogelink, "Fast PMD penalty measurement using polarization scrambling," in Optical Fiber Communications Conference (OFC) 2002, Vol. 70 of Trends in OSA Optics and Photonics Series (Optical Society of America, 2002), paper WQ6, pp. 305-306.
    [CrossRef]
  9. G. H. Qi, J. P. Yao, J. Seregelyi, S. Paquet, and C. Belisle, "Generation and distribution of a wide-band continuously tunable millimeter-wave signal with an optical external modulation technique," IEEE Trans. Microwave Theory Tech. 53, 10, 3090-3097 (2005).
    [CrossRef]
  10. C. Yu, Q. Yu, Z. Pan, A. B. Sahin, and A. E. Willner, "Optical compensation of PMD-induced power fading for single sideband subcarrier-multiplexed systems," in Optical Fiber Communications Conference (OFC) 2002, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 304-305.
    [CrossRef]

2006 (1)

2005 (1)

G. H. Qi, J. P. Yao, J. Seregelyi, S. Paquet, and C. Belisle, "Generation and distribution of a wide-band continuously tunable millimeter-wave signal with an optical external modulation technique," IEEE Trans. Microwave Theory Tech. 53, 10, 3090-3097 (2005).
[CrossRef]

2001 (1)

R. Hui, B. Zhu, R. Huang, C. Allen, K. Demarest, and D. Richards, "10-Gb/s SCM fibers system using optical SSB modulation," IEEE Photon. Technol. Lett. 13, 896-898 (2001).
[CrossRef]

1998 (1)

1994 (1)

C. D. Poole and David L. Favin, "Polarization mode dispersion measurements based on transmission spectra through a polarizer," J. Lightwave Technol. 12, 917-929 (1994).
[CrossRef]

1993 (1)

C. D. Poole and T. E. Darcie, "Distortion related to polarization mode dispersion in analog lightwave systems," J. Lightwave Technol. 11, 1749-1759 (1993).
[CrossRef]

1986 (1)

C. D. Poole and R. E. Wagner, "Phenomenological approach to polarization dispersion in long single mode fibres," Electron. Lett. 22, 1029-12301986.
[CrossRef]

Electron. Lett. (1)

C. D. Poole and R. E. Wagner, "Phenomenological approach to polarization dispersion in long single mode fibres," Electron. Lett. 22, 1029-12301986.
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. Hui, B. Zhu, R. Huang, C. Allen, K. Demarest, and D. Richards, "10-Gb/s SCM fibers system using optical SSB modulation," IEEE Photon. Technol. Lett. 13, 896-898 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

G. H. Qi, J. P. Yao, J. Seregelyi, S. Paquet, and C. Belisle, "Generation and distribution of a wide-band continuously tunable millimeter-wave signal with an optical external modulation technique," IEEE Trans. Microwave Theory Tech. 53, 10, 3090-3097 (2005).
[CrossRef]

J. Lightwave Technol. (3)

C. D. Poole and David L. Favin, "Polarization mode dispersion measurements based on transmission spectra through a polarizer," J. Lightwave Technol. 12, 917-929 (1994).
[CrossRef]

C. D. Poole and T. E. Darcie, "Distortion related to polarization mode dispersion in analog lightwave systems," J. Lightwave Technol. 11, 1749-1759 (1993).
[CrossRef]

P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. P. Von der Weild, F. Prieto, and C. W. Zimmer, "Second-order polarization mode dispersion impact on analog and digital transmissions," J. Lightwave Technol. 16, 757-771 (1998).
[CrossRef]

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

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

H. F. Haunstein, H. M. Kallert, and H. Kogelink, "Fast PMD penalty measurement using polarization scrambling," in Optical Fiber Communications Conference (OFC) 2002, Vol. 70 of Trends in OSA Optics and Photonics Series (Optical Society of America, 2002), paper WQ6, pp. 305-306.
[CrossRef]

C. Yu, Q. Yu, Z. Pan, A. B. Sahin, and A. E. Willner, "Optical compensation of PMD-induced power fading for single sideband subcarrier-multiplexed systems," in Optical Fiber Communications Conference (OFC) 2002, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 304-305.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Experimental setup to demonstrate power fading due to PMD and CD, and optically compensating the PMD-induced power fading in carrier suppressed modulation.

Fig. 2
Fig. 2

Optical output spectrum for carrier suppression modulation.

Fig. 3
Fig. 3

RF output spectrum with 300 MHz span.

Fig. 4
Fig. 4

Variation in output RF power with different values of CD.

Fig. 5
Fig. 5

Power fading due to the worst case ( 2 α = π 2 ) and the average case with the polarization scrambler.

Fig. 6
Fig. 6

Relative output RF power with or without PMD compensation in the worst case ( 2 α = π 2 ) .

Equations (29)

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

d S o ( ω ) d ω = τ × S o ( ω ) .
S o ( ω ) = Ω cos ( 2 α ) + [ S o ( ω 0 ) Ω cos ( 2 α ) ] cos ( Δ τ Δ ω Δ τ 1 Δ ω 2 ) + B sin ( 2 α ) sin ( Δ τ Δ ω Δ τ 1 Δ ω 2 ) .
e ( ω ) = cos ( α ) exp ( j ϕ + ) e Ω + + sin ( α ) exp ( j ϕ ) e Ω ,
e ( ω ) = cos ( α ) exp [ j ( Δ τ Δ ω Δ τ 1 Δ ω 2 ) 2 ] e Ω + + sin ( α ) exp [ j ( Δ τ Δ ω + Δ τ 1 Δ ω 2 ) 2 ] e Ω .
β ( ω ) = β 0 + β 1 ( ω ω 0 ) + 1 2 β 2 ( ω ω 0 ) 2 + ,
β m = ( m β ω m ) ω = ω 0 .
Φ Ω ± = ( β 2 L ω m 2 2 ) ,
f ( t ) = cos [ m cos ( ω m t ) + θ 2 ] cos ( ω 0 t ) ,
f ( t ) = J 0 ( m 2 ) cos ( θ 2 ) cos ( ω 0 t ) J 1 ( m 2 ) sin ( θ 2 ) { cos [ ( ω 0 ω m ) t ] + cos [ ( ω 0 + ω m ) t ] } J 2 ( m 2 ) cos ( θ 2 ) { cos [ ( ω 0 2 ω m ) t ] + cos [ ( ω 0 + 2 ω m ) t ] } J 3 ( m 2 ) sin ( θ 2 ) { cos [ ( ω 0 3 ω m ) t ] + cos [ ( ω 0 + 3 ω m ) t ] } + .
f ( t ) = J 1 ( m 2 ) { cos [ ( ω 0 ω m ) t ] + cos [ ( ω 0 + ω m ) t ] } J 3 ( m 2 ) { cos [ ( ω 0 3 ω m ) t ] + cos [ ( ω 0 + 3 ω m ) t ] } + .
f ( t ) = [ m 4 cos ( ω 0 + ω m ) t + m 4 cos ( ω 0 ω m ) t ] .
f ( t ) = [ m ( 1 + ϵ j ) 4 cos ( ω 0 + ω m ) t + m ( 1 + ϵ j ) 4 cos ( ω 0 ω m ) t ] ,
f Ω + ( t ) = M cos ( α ) 2 π + F ( ω ω 0 ) exp { j [ ( Δ τ Δ ω 2 ) ( Δ τ 1 Δ ω 2 2 ) ( β 2 L Δ ω 2 2 ) ] } e j ( ω ω 0 ) t d ω ,
f Ω ( t ) = M sin ( α ) 2 π + F ( ω ω 0 ) exp { j [ ( Δ τ Δ ω 2 ) ( Δ τ 1 Δ ω 2 2 ) + ( β 2 L Δ ω 2 2 ) ] } e j ( ω ω 0 ) t d ω ,
f ( t ) = f Ω + ( t ) e Ω + + f Ω ( t ) e Ω .
f Ω + ( t ) = cos ( α ) M P i { m 1 + ϵ 2 4 cos [ ( ω 0 + ω m ) t + ( Δ τ ω m 2 ) ( Δ τ 1 ω m 2 2 ) ( β 2 L ω m 2 2 ) arctan ( ϵ ) ] + m 1 + ϵ 2 4 cos [ ( ω 0 ω m ) t ( Δ τ ω m 2 ) ( Δ τ 1 ω m 2 2 ) ( β 2 L ω m 2 2 ) arctan ( ϵ ) ] } ,
f Ω ( t ) = sin ( α ) M P i { m 1 + ϵ 2 4 cos [ ( ω 0 + ω m ) t ( Δ τ ω m 2 ) + ( Δ τ 1 ω m 2 2 ) ( β 2 L ω m 2 2 ) arctan ( ϵ ) ] + m 1 + ϵ 2 4 cos [ ( ω 0 ω m ) t + ( Δ τ ω m 2 ) ( ω 0 ω m ) t + ( Δ τ ω m 2 ) ] } .
I ( t ) = f ( t ) 2 = f ( t ) f * ( t ) = f Ω + ( t ) 2 + f Ω ( t ) 2 .
I ( t ) = [ cos ( α ) ] 2 R M 2 P i { m 2 4 { cos [ ω m ( t + Δ τ 2 ) ] } 2 } + [ sin ( α ) ] 2 R M 2 P i { m 2 4 { cos [ ω m ( t Δ τ 2 ) ] } 2 } .
P ( ω m ) = P 0 { 1 [ sin ( 2 α ) ] 2 [ sin ( Δ τ ω m ) ] 2 } ,
P ( ω m ) = P 0 { 1 [ sin ( 2 α ) ] 2 [ sin ( 2 π Δ τ f m ) ] 2 } .
f x = x 1 x 2 ( 0 x 1 ) .
P ( f m ) = P 0 { 1 2 3 [ sin ( 2 π Δ τ f m ) ] 2 } .
P ( f m ) = P 0 { 1 3 4 [ sin ( 2 π Δ τ f m ) ] 2 }
f ( t ) = J 2 ( m 2 ) { cos [ ( ω 0 2 ω m ) t ] + cos [ ( ω 0 + 2 ω m ) t ] } J 4 ( m 2 ) { cos [ ( ω 0 4 ω m ) t ] + cos [ ( ω 0 + 4 ω m ) t ] } + .
f ( t ) = J 2 ( m 2 ) cos ( θ 2 ) { cos [ ( ω 0 2 ω m ) t ] + cos [ ( ω 0 + 2 ω m ) t ] } ,
P ( ω m ) = P 0 { 1 [ sin ( 2 α ) ] 2 [ sin ( 4 π Δ τ f m ) ] 2 } .
P ( f m ) = P 0 { 1 2 3 [ sin ( 4 π Δ τ f m ) ] 2 } .
P ( f m ) = P 0 { 1 3 4 [ sin ( 4 π Δ τ f m ) ] 2 } .

Metrics