Abstract

We investigate the effect of cross-phase modulation in wavelength-division-multiplexed polarization-modulation lightwave systems. Analytical expression for the Q factor penalty in terms of signal power, the number of channels, and other parameters are derived. The theory is compared with numerical experiments.

© 2004 Optical Society of America

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References

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  1. S. Benedetto, R. Gaudino, P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Commun. 13, 531–542 (1995).
    [CrossRef]
  2. S. Betti, G. De Marchis, E. Iannone, “A novel direct-detection optical transmission system based on polarization modulation,” Microwave Opt. Technol. Lett. 5, 367–369 (1992).
    [CrossRef]
  3. B. C. Collings, L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12, 1582–1584 (2000).
    [CrossRef]
  4. E. Iannone, F. Matera, A. Mecozzi, M. Settembre, “Performance evaluation of very long span direct detection intensity and polarization modulated systems,” IEEE J. Lightwave Technol. 14, 261–272 (1996).
    [CrossRef]
  5. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).
  6. E. Iannone, F. Matera, A. Mecozzi, M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).
  7. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1991).
  8. D. Marcuse, “Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,” J. Lightwave Technol. 8, 1816–1823 (1990).
    [CrossRef]
  9. M. Zitelli, “Optolink software user documentation,” http://www.tel-con.com .
  10. A. O. Dal Forno, A. Paradisi, R. Passy, J. P. von der Weid, “Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 12, 296–298 (2000).
    [CrossRef]

2000 (2)

B. C. Collings, L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12, 1582–1584 (2000).
[CrossRef]

A. O. Dal Forno, A. Paradisi, R. Passy, J. P. von der Weid, “Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 12, 296–298 (2000).
[CrossRef]

1996 (1)

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, “Performance evaluation of very long span direct detection intensity and polarization modulated systems,” IEEE J. Lightwave Technol. 14, 261–272 (1996).
[CrossRef]

1995 (1)

S. Benedetto, R. Gaudino, P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Commun. 13, 531–542 (1995).
[CrossRef]

1992 (1)

S. Betti, G. De Marchis, E. Iannone, “A novel direct-detection optical transmission system based on polarization modulation,” Microwave Opt. Technol. Lett. 5, 367–369 (1992).
[CrossRef]

1990 (1)

D. Marcuse, “Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,” J. Lightwave Technol. 8, 1816–1823 (1990).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

Benedetto, S.

S. Benedetto, R. Gaudino, P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Commun. 13, 531–542 (1995).
[CrossRef]

Betti, S.

S. Betti, G. De Marchis, E. Iannone, “A novel direct-detection optical transmission system based on polarization modulation,” Microwave Opt. Technol. Lett. 5, 367–369 (1992).
[CrossRef]

Boivin, L.

B. C. Collings, L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12, 1582–1584 (2000).
[CrossRef]

Collings, B. C.

B. C. Collings, L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12, 1582–1584 (2000).
[CrossRef]

Dal Forno, A. O.

A. O. Dal Forno, A. Paradisi, R. Passy, J. P. von der Weid, “Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 12, 296–298 (2000).
[CrossRef]

De Marchis, G.

S. Betti, G. De Marchis, E. Iannone, “A novel direct-detection optical transmission system based on polarization modulation,” Microwave Opt. Technol. Lett. 5, 367–369 (1992).
[CrossRef]

Gaudino, R.

S. Benedetto, R. Gaudino, P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Commun. 13, 531–542 (1995).
[CrossRef]

Iannone, E.

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, “Performance evaluation of very long span direct detection intensity and polarization modulated systems,” IEEE J. Lightwave Technol. 14, 261–272 (1996).
[CrossRef]

S. Betti, G. De Marchis, E. Iannone, “A novel direct-detection optical transmission system based on polarization modulation,” Microwave Opt. Technol. Lett. 5, 367–369 (1992).
[CrossRef]

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Marcuse, D.

D. Marcuse, “Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,” J. Lightwave Technol. 8, 1816–1823 (1990).
[CrossRef]

Matera, F.

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, “Performance evaluation of very long span direct detection intensity and polarization modulated systems,” IEEE J. Lightwave Technol. 14, 261–272 (1996).
[CrossRef]

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Mecozzi, A.

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, “Performance evaluation of very long span direct detection intensity and polarization modulated systems,” IEEE J. Lightwave Technol. 14, 261–272 (1996).
[CrossRef]

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1991).

Paradisi, A.

A. O. Dal Forno, A. Paradisi, R. Passy, J. P. von der Weid, “Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 12, 296–298 (2000).
[CrossRef]

Passy, R.

A. O. Dal Forno, A. Paradisi, R. Passy, J. P. von der Weid, “Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 12, 296–298 (2000).
[CrossRef]

Poggiolini, P.

S. Benedetto, R. Gaudino, P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Commun. 13, 531–542 (1995).
[CrossRef]

Settembre, M.

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, “Performance evaluation of very long span direct detection intensity and polarization modulated systems,” IEEE J. Lightwave Technol. 14, 261–272 (1996).
[CrossRef]

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

von der Weid, J. P.

A. O. Dal Forno, A. Paradisi, R. Passy, J. P. von der Weid, “Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 12, 296–298 (2000).
[CrossRef]

IEEE J. Lightwave Technol. (1)

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, “Performance evaluation of very long span direct detection intensity and polarization modulated systems,” IEEE J. Lightwave Technol. 14, 261–272 (1996).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

S. Benedetto, R. Gaudino, P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Commun. 13, 531–542 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

B. C. Collings, L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12, 1582–1584 (2000).
[CrossRef]

A. O. Dal Forno, A. Paradisi, R. Passy, J. P. von der Weid, “Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers,” IEEE Photon. Technol. Lett. 12, 296–298 (2000).
[CrossRef]

J. Lightwave Technol. (1)

D. Marcuse, “Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers,” J. Lightwave Technol. 8, 1816–1823 (1990).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

S. Betti, G. De Marchis, E. Iannone, “A novel direct-detection optical transmission system based on polarization modulation,” Microwave Opt. Technol. Lett. 5, 367–369 (1992).
[CrossRef]

Other (4)

M. Zitelli, “Optolink software user documentation,” http://www.tel-con.com .

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

E. Iannone, F. Matera, A. Mecozzi, M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1991).

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Figures (2)

Fig. 1
Fig. 1

Effect of ASE noise on a received four-point constellation in PS (a square). Optical signal-to-noise ratio in the example is 21.5 dB over a 0.2-nm bandwidth.

Fig. 2
Fig. 2

(a) Typical received eye diagram (the electrical signal at the differential photodetector) obtained in the simulation and the definitions for the Q-factor evaluation (σAS + σXPM = σ1 + σ0; see text). (b) Penalty in the Q factor for an increasing number of channels and for different average powers per channel P m . o, P m = -4 dBm; +, P m = -2 dBm; x, P m = 0 dBm; *, P m = 2 dBm. The continuous lines are the corresponding penalties evaluated after Eq. (10) by use of the maximum peak power in the link for P (given by P = P m + 4.54 dB for our system).

Equations (10)

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

izEx,y+iβx,ytEx,y-β22 t2Ex,y-i β36 t3Ex,y+i α2 Ex,y+γ|Ex,y|2+23 |Ey,x|2Ex,y=0,
dφx,ydz=γPx,y+23 Py,x+n=1Nc 2Px,yn+23 Py,xnexp-αz.
ΔφSPM=γ3 PLeffs10
ΔφXPM=43 γPLeffn=1Nc s1n n=1, 2,, Nc,
Sb=R1-ϕR2-θR1ΔφR2θR1ϕSa,
σc,NL2=σc,SPM2+σc,XPM2,σc,SPM2=P236γPLc,eff2,σc,XPM2=4P227 NcγPLc,eff2,
σNL2NLσc,XPM2427 γ2P4NcLc,effLampl,eff,
Q=I1-I02NAσAS+σXPMpXPMQ0.
σAS=2σnrP=2NsphνG-1BP1/2,
pXPM=1+γNcP327Lc,effLampl,effσnr21/2-1.

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