Abstract

In this paper, optimum detection threshold for minimum bit error rate (BER) due to four-wave mixing is calculated taking the probability distribution of power depletion as binomial and considering nonuniform channel spacing. Nondegenerate four-wave mixing has been assumed for the worst-case analysis. The effects of the number of interfering channels, receiver noise, and input power on the BER in the presence of four-wave mixing are studied. The optimum detection threshold for minimum BER is studied as a function of the number of channels. This optimum threshold significantly deviates from the conventional threshold in the Gaussian distribution approximation as the channel number increases beyond three.

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References

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  1. C. S. Murthy and M. Gurusamy, WDM Optical Networks. Upper Saddle River, NJ: Pearson Education, 2004.
  2. B. Mukherjee, “WDM optical communication networks: Progress and challenges,” IEEE J. Sel. Areas Commun., vol.  18, pp. 1810–1824, 2000.
    [CrossRef]
  3. F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol., vol.  13, pp. 889–897, 1995.
    [CrossRef]
  4. N. R. Das and S. Sarkar, “Probability of power depletion due to SRS cross-talk and optimum detection threshold in a WDM receiver,” IEEE J. Quantum Electron., vol.  47, pp. 424–430, 2011.
    [CrossRef]
  5. Y. London and D. Sadot, “Nonlinear effects mitigation in coherent optical OFDM system in presence of high peak power,” J. Lightwave Technol., vol.  29, pp. 3275–3281, 2011.
    [CrossRef]
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    [CrossRef]
  9. J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “Optical parametric oscillator based on four-wave mixing in microstructure fiber,” Opt. Lett., vol.  27, pp. 1675–1677, 2002.
    [CrossRef]
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    [CrossRef]
  11. J. Liang and K. Iwashita, “FWM compensation in DPSK transmission by reducing detectors with digital coherent detection using backward propagation,” Int. J. Inf. Electron. Eng., vol.  1, pp. 99–104, 2011.
  12. K. K. Y. Wong, G. W. Lu, and L. K. Chen, “Experimental studies of the WDM signal crosstalk in two-pump fiber optical parametric amplifiers,” Opt. Commun., vol.  270, pp. 429–432, 2007.
    [CrossRef]
  13. I. Neokosmidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “New techniques for the suppression of the four-wave mixing-induced distortion in nonzero dispersion fiber WDM systems,” J. Lightwave Technol., vol.  23, pp. 1137–1144, 2005.
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    [CrossRef]
  17. D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev., vol.  126, pp. 1977–1979, 1962.
    [CrossRef]
  18. R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol., vol.  13, pp. 841–849, 1995.
    [CrossRef]
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2011 (3)

N. R. Das and S. Sarkar, “Probability of power depletion due to SRS cross-talk and optimum detection threshold in a WDM receiver,” IEEE J. Quantum Electron., vol.  47, pp. 424–430, 2011.
[CrossRef]

Y. London and D. Sadot, “Nonlinear effects mitigation in coherent optical OFDM system in presence of high peak power,” J. Lightwave Technol., vol.  29, pp. 3275–3281, 2011.
[CrossRef]

J. Liang and K. Iwashita, “FWM compensation in DPSK transmission by reducing detectors with digital coherent detection using backward propagation,” Int. J. Inf. Electron. Eng., vol.  1, pp. 99–104, 2011.

2009 (1)

2007 (1)

K. K. Y. Wong, G. W. Lu, and L. K. Chen, “Experimental studies of the WDM signal crosstalk in two-pump fiber optical parametric amplifiers,” Opt. Commun., vol.  270, pp. 429–432, 2007.
[CrossRef]

2005 (1)

2004 (2)

2002 (1)

2000 (1)

B. Mukherjee, “WDM optical communication networks: Progress and challenges,” IEEE J. Sel. Areas Commun., vol.  18, pp. 1810–1824, 2000.
[CrossRef]

1995 (2)

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol., vol.  13, pp. 889–897, 1995.
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol., vol.  13, pp. 841–849, 1995.
[CrossRef]

1994 (1)

K. Inoue, “Tunable and selective wavelength conversion using fibre four-wave mixing with two pump lights,” IEEE Photon. Technol. Lett., vol.  6, pp. 1451–1453, 1994.
[CrossRef]

1980 (1)

K. Washio, K. Inove, and S. Kishida, “Efficient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber,” Electron. Lett., vol.  16, pp. 650–660, 1980.
[CrossRef]

1978 (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol.  49, pp. 5098–5106, 1978.
[CrossRef]

1962 (1)

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev., vol.  126, pp. 1977–1979, 1962.
[CrossRef]

Agrawal, G. P.

Chen, D.

Chen, L. K.

K. K. Y. Wong, G. W. Lu, and L. K. Chen, “Experimental studies of the WDM signal crosstalk in two-pump fiber optical parametric amplifiers,” Opt. Commun., vol.  270, pp. 429–432, 2007.
[CrossRef]

Chipouras, A.

Chraplyvy, A. R.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol., vol.  13, pp. 889–897, 1995.
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol., vol.  13, pp. 841–849, 1995.
[CrossRef]

Das, N. R.

N. R. Das and S. Sarkar, “Probability of power depletion due to SRS cross-talk and optimum detection threshold in a WDM receiver,” IEEE J. Quantum Electron., vol.  47, pp. 424–430, 2011.
[CrossRef]

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol., vol.  13, pp. 841–849, 1995.
[CrossRef]

Fiorentino, M.

Forghieri, F.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol., vol.  13, pp. 889–897, 1995.
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol., vol.  13, pp. 841–849, 1995.
[CrossRef]

Gnauck, A. H.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol., vol.  13, pp. 841–849, 1995.
[CrossRef]

Gurusamy, M.

C. S. Murthy and M. Gurusamy, WDM Optical Networks. Upper Saddle River, NJ: Pearson Education, 2004.

Hill, K. O.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol.  49, pp. 5098–5106, 1978.
[CrossRef]

Inoue, K.

K. Inoue, “Tunable and selective wavelength conversion using fibre four-wave mixing with two pump lights,” IEEE Photon. Technol. Lett., vol.  6, pp. 1451–1453, 1994.
[CrossRef]

Inove, K.

K. Washio, K. Inove, and S. Kishida, “Efficient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber,” Electron. Lett., vol.  16, pp. 650–660, 1980.
[CrossRef]

Iwashita, K.

J. Liang and K. Iwashita, “FWM compensation in DPSK transmission by reducing detectors with digital coherent detection using backward propagation,” Int. J. Inf. Electron. Eng., vol.  1, pp. 99–104, 2011.

Johnson, D. C.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol.  49, pp. 5098–5106, 1978.
[CrossRef]

Kahn, J. M.

Kamalakis, T.

Kawasaki, B. S.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol.  49, pp. 5098–5106, 1978.
[CrossRef]

Kishida, S.

K. Washio, K. Inove, and S. Kishida, “Efficient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber,” Electron. Lett., vol.  16, pp. 650–660, 1980.
[CrossRef]

Kleinman, D. A.

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev., vol.  126, pp. 1977–1979, 1962.
[CrossRef]

Kumar, P.

Liang, J.

J. Liang and K. Iwashita, “FWM compensation in DPSK transmission by reducing detectors with digital coherent detection using backward propagation,” Int. J. Inf. Electron. Eng., vol.  1, pp. 99–104, 2011.

Lin, Q.

London, Y.

Lu, G. W.

K. K. Y. Wong, G. W. Lu, and L. K. Chen, “Experimental studies of the WDM signal crosstalk in two-pump fiber optical parametric amplifiers,” Opt. Commun., vol.  270, pp. 429–432, 2007.
[CrossRef]

MacDonald, R. I.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol.  49, pp. 5098–5106, 1978.
[CrossRef]

Mukherjee, B.

B. Mukherjee, “WDM optical communication networks: Progress and challenges,” IEEE J. Sel. Areas Commun., vol.  18, pp. 1810–1824, 2000.
[CrossRef]

Murthy, C. S.

C. S. Murthy and M. Gurusamy, WDM Optical Networks. Upper Saddle River, NJ: Pearson Education, 2004.

Neokosmidis, I.

Papoulis, A.

A. Papoulis, Probability, Random Variable, and Stochastic Processes. New York: McGraw-Hill, 1984.

Sadot, D.

Sarkar, S.

N. R. Das and S. Sarkar, “Probability of power depletion due to SRS cross-talk and optimum detection threshold in a WDM receiver,” IEEE J. Quantum Electron., vol.  47, pp. 424–430, 2011.
[CrossRef]

Sharping, J. E.

Sphicopoulos, T.

Tkach, R. W.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol., vol.  13, pp. 889–897, 1995.
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high-speed WDM systems,” J. Lightwave Technol., vol.  13, pp. 841–849, 1995.
[CrossRef]

Wang, J.

Washio, K.

K. Washio, K. Inove, and S. Kishida, “Efficient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber,” Electron. Lett., vol.  16, pp. 650–660, 1980.
[CrossRef]

Windeler, R. S.

Wong, K. K. Y.

K. K. Y. Wong, G. W. Lu, and L. K. Chen, “Experimental studies of the WDM signal crosstalk in two-pump fiber optical parametric amplifiers,” Opt. Commun., vol.  270, pp. 429–432, 2007.
[CrossRef]

Xu, X.

Yao, Y.

Zhao, X.

Electron. Lett. (1)

K. Washio, K. Inove, and S. Kishida, “Efficient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber,” Electron. Lett., vol.  16, pp. 650–660, 1980.
[CrossRef]

IEEE J. Quantum Electron. (1)

N. R. Das and S. Sarkar, “Probability of power depletion due to SRS cross-talk and optimum detection threshold in a WDM receiver,” IEEE J. Quantum Electron., vol.  47, pp. 424–430, 2011.
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

B. Mukherjee, “WDM optical communication networks: Progress and challenges,” IEEE J. Sel. Areas Commun., vol.  18, pp. 1810–1824, 2000.
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Inoue, “Tunable and selective wavelength conversion using fibre four-wave mixing with two pump lights,” IEEE Photon. Technol. Lett., vol.  6, pp. 1451–1453, 1994.
[CrossRef]

Int. J. Inf. Electron. Eng. (1)

J. Liang and K. Iwashita, “FWM compensation in DPSK transmission by reducing detectors with digital coherent detection using backward propagation,” Int. J. Inf. Electron. Eng., vol.  1, pp. 99–104, 2011.

J. Appl. Phys. (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode optical fibers,” J. Appl. Phys., vol.  49, pp. 5098–5106, 1978.
[CrossRef]

J. Lightwave Technol. (6)

Opt. Commun. (1)

K. K. Y. Wong, G. W. Lu, and L. K. Chen, “Experimental studies of the WDM signal crosstalk in two-pump fiber optical parametric amplifiers,” Opt. Commun., vol.  270, pp. 429–432, 2007.
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev., vol.  126, pp. 1977–1979, 1962.
[CrossRef]

Other (3)

A. Papoulis, Probability, Random Variable, and Stochastic Processes. New York: McGraw-Hill, 1984.

C. S. Murthy and M. Gurusamy, WDM Optical Networks. Upper Saddle River, NJ: Pearson Education, 2004.

G. P. Agrawal, Nonlinear Fiber Optics. New York: Academic, 1995.

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Figures (7)

Fig. 1.
Fig. 1.

Probability distribution versus depletion for different numbers of channels.

Fig. 2.
Fig. 2.

BER versus input power in a WDM system in the presence of FWM cross talk. (a) Verification with experimental data (symbols) taken from literature [12] for N=4. (b) For different numbers of channels (N) at a fixed σ0=1.4mA. Here F=6, χ(3)=6×1014m3/W, Aeff=5×1011m2, nr=1.2.

Fig. 3.
Fig. 3.

(a) BER versus input power in a WDM system in the presence of FWM cross talk for different σ0 taking N=4. (b) BER versus thermal noise for different input power at a fixed σ0=1.4mA. Here F=6, χ(3)=6×1014m3/w, Aeff=5×1011m2, nr=1.2.

Fig. 4.
Fig. 4.

BER due to FWM cross talk versus channel number N for different input power (in pump channel) P0 at σ0=1.4mA. Horizontal lines indicate absence of four-wave mixing.

Fig. 5.
Fig. 5.

Power penalty versus input power for different numbers of channels at σ0=1.4mA.

Fig. 6.
Fig. 6.

(a) Variation of BER due to FWM cross talk with respect to d for different channel numbers (N), assuming Ip=0.04A. (b) Variation of optimum detection threshold (dopt) with the channel numbers (N) for three different values of Ip: 0.03 A, 0.035 A, and 0.04 A. Here, σ0=1.4mA.

Fig. 7.
Fig. 7.

Variation of BER due to FWM cross talk with the threshold of detection (d) (A) for different input powers (in pump channel) P0. Here, number of channels (N)=4 and σ0=1.4mA.

Tables (1)

Tables Icon

TABLE I Optimum Threshold for Minimum BER in a WDM System in Presence of FWM Cross Talk (σ0=1.4mA)

Equations (24)

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

ddzEn(z)=12αEn(z)+i2πωnnrc(Fχ(3))×Ej*(z)Ek(z)El(z)exp(iβnz),
Ej(z)=Ejexp(12αziβjz),
Em(z)=Emexp(12αziβmz12D),
ddzEn(z)=12αEn(z)+K×P3/2exp(3α2z)exp{i(βn+βjβkβl)z}exp(D),
K=16π2ωnnr2c2Aeff2(Fχ(3)),
D=(N2)PnPexp(αz),
ddzEn(z)=12αEn(z)+K×P3/2exp(3α2z)exp{i(βn+βjβkβl)z}×exp[(N2)PnPexp(αz)].
ddz{exp(α2z)En(z)}=K(N2)P×exp(αz)[P(N2)En2(z)exp(αz)],
PN2=a2andexp(α2z)En(z)=y,
12alog(a+yay)=KP(N2)1exp(αz)α
(N2)En2(z)Pexp(αz).
En(z)=P(N2)[exp{KP(N2)1exp(αz)α}exp{KP(N2)1exp(αz)α}exp{KP(N2)1exp(αz)α}+exp{KP(N2)1exp(αz)α}]exp(α2z).
D=[exp{KP(N2)1exp(αz)α}exp{KP(N2)1exp(αz)α}exp{KP(N2)1exp(αz)α}+exp{KP(N2)1exp(αz)α}]2.
Di=[exp{KPiLeff}exp{KPiLeff}exp{KPiLeff}+exp{KPiLeff}]2,i(0,1,,N2).
pD(i;N,12)=(N2)!i!(N2i)!(12)(N2).
Ep(t)=n=+anrectT(tnT)Ppexp(jωptjϕp(t)),
y(t)=n=+anrectT(tnT)Ip+ng(t),
pn1(y)=12πσ02exp{(yIp)22σ02},
Pe=12Pe0(d)+12DPe|1,D(d)pD(i;N,12),
Pe=14erfc(d2σ02)+14Dierfc{(Ipd)2σ02}×(N2)!i!(N2i)!(12)(N2).
Di=iPnPexp(αz)=[exp{KPiLeff}exp{KPiLeff}exp{KPiLeff}+exp{KPiLeff}]2.
PP=20log10[exp{KPiLeff}+exp{KPiLeff}exp{KPiLeff}exp{KPiLeff}],i(0,1,,N2).
dopt=2σ02ln[Dexp{(Ipdopt)22σ02}(N2)!i!(N2i)!(12)(N2)]1.
M=N22(N1).