Abstract

A technique to suppress optical nonlinearities is demonstrated using adaptive optical domain post distortion. The concept, rooted in electrical domain linearization, mitigates optical nonlinearities by generating sidebands that are equal but opposite in phase from the unwanted components. We model and experimentally demonstrate >20 dB extinction in four wave mixing by an adaptive phase controller and computer feedback loop.

© 2005 Optical Society of America

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References

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  1. M. Nazarathy, J. Berger, J. Ley, M. Levi, and Y. Kagan, �??Progress in externally modulated AM CATV transmission systems,�?? J. Lightwave Technol. 11, 82-105, (1993).
    [CrossRef]
  2. R. Sadhwani, B. Jalali, �??Adaptive CMOS predistortion linearizer for fiber-optic links,�?? J. Lightwave Technol. 21, 3180-3193, (2003).
    [CrossRef]
  3. J. Basak, R. Sadhwani, B. Jalali, �??WDM pilot tone technique for analogue optical links,�?? Electron. Lett. 39, 1083-1084, (2003).
    [CrossRef]
  4. R. H. Stolen and J. E. Bjorkholm, �??Parametric amplification and frequency conversion in optical fibers,�?? J. Quantum Electron. 18, 1062-1072, (1982).
    [CrossRef]
  5. H. Taga, �??Long distance transmission experiments using WDM technology,�?? J. Lightwave Technol. 14, 1287-98, (1996).
    [CrossRef]
  6. Forghieri, F. Tkach, R.W., Chrapyvy, A.R., �??WDM systems with unequally spaced channels,�?? J. Lightwave Technol. 13, 889-897, (1995).
    [CrossRef]
  7. Forghieri, F., Tkach, R.W. Chraplyvy, A.R., Marcuse, D., �??Reduction of four-wave mixing crosstalk in WDM systems using unequally spaced channels,�?? Photon. Technol. Lett. 6, 754-756, (1994).
    [CrossRef]
  8. M. W. Maeda, W. B. Sessa, W. I. Way, A. Yi-Yan, L. Curtis, R. Spicer, and R. I. Laming, �??The effect of four-wave mixing in fibers on optical frequency-division multiplexed systems,�?? J. Lightwave Technol. 8, 1402-1408, (1990).
    [CrossRef]
  9. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  10. H. Takahashi and K. Inoue, �??Cancellation of four-wave mixing by use of phase shift in dispersive fiber inserted into a zero-dispersion transmission line,�?? Opt. Lett. 20, 860-862, (1995).
    [CrossRef] [PubMed]
  11. M. E. Mahric, F. S. Yang, M.-C. Ho, and L. G. Kazovsky, �??High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,�?? J. Lightwave Technol. 17, 210-215, (1999).
    [CrossRef]
  12. J. Kim, O. Boyraz, J. H. Lim, M. N. Islam, �??Gain enhancement in cascaded fiber parametric amplifier with quasi-phase matching: theory and experiment,�?? J. Lightwave Technol. 19, 247-251, (2001).
    [CrossRef]

Electron. Lett. (1)

J. Basak, R. Sadhwani, B. Jalali, �??WDM pilot tone technique for analogue optical links,�?? Electron. Lett. 39, 1083-1084, (2003).
[CrossRef]

J. Lightwave Technol. (7)

M. Nazarathy, J. Berger, J. Ley, M. Levi, and Y. Kagan, �??Progress in externally modulated AM CATV transmission systems,�?? J. Lightwave Technol. 11, 82-105, (1993).
[CrossRef]

R. Sadhwani, B. Jalali, �??Adaptive CMOS predistortion linearizer for fiber-optic links,�?? J. Lightwave Technol. 21, 3180-3193, (2003).
[CrossRef]

H. Taga, �??Long distance transmission experiments using WDM technology,�?? J. Lightwave Technol. 14, 1287-98, (1996).
[CrossRef]

Forghieri, F. Tkach, R.W., Chrapyvy, A.R., �??WDM systems with unequally spaced channels,�?? J. Lightwave Technol. 13, 889-897, (1995).
[CrossRef]

M. W. Maeda, W. B. Sessa, W. I. Way, A. Yi-Yan, L. Curtis, R. Spicer, and R. I. Laming, �??The effect of four-wave mixing in fibers on optical frequency-division multiplexed systems,�?? J. Lightwave Technol. 8, 1402-1408, (1990).
[CrossRef]

M. E. Mahric, F. S. Yang, M.-C. Ho, and L. G. Kazovsky, �??High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,�?? J. Lightwave Technol. 17, 210-215, (1999).
[CrossRef]

J. Kim, O. Boyraz, J. H. Lim, M. N. Islam, �??Gain enhancement in cascaded fiber parametric amplifier with quasi-phase matching: theory and experiment,�?? J. Lightwave Technol. 19, 247-251, (2001).
[CrossRef]

J. Quantum Electron. (1)

R. H. Stolen and J. E. Bjorkholm, �??Parametric amplification and frequency conversion in optical fibers,�?? J. Quantum Electron. 18, 1062-1072, (1982).
[CrossRef]

Opt. Lett. (1)

Photon. Technol. Lett. (1)

Forghieri, F., Tkach, R.W. Chraplyvy, A.R., Marcuse, D., �??Reduction of four-wave mixing crosstalk in WDM systems using unequally spaced channels,�?? Photon. Technol. Lett. 6, 754-756, (1994).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Basic concept of the Optical-domain Post Distortion Linearizer. (b) Experimental setup. LD: laser diode. SLM: spatial light modulator. DSF: dispersion shifted fiber. EDFA: erbium doped fiber amplifier. PC: personal computer.

Fig. 2.
Fig. 2.

Simulation of FWM suppression for (a) static and (b) adaptive phase control techniques. Red coloring indicates suppression > 20 dB. An adaptive phase adjustment can provide precision and agility to phase variations at many wavelengths.

Fig. 3.
Fig. 3.

Optical spectrum measured (a) before and (b) after the Optical-domain Post Distortion Linearizer shows >20 dB suppression. (c) FWM power vs. relative input phase illustrates the sensitivity of the nonlinear attenuation to variations in phase.

Equations (14)

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d A s , c dz = [ ( A s , c 2 + 2 k s , c A k 2 ) A s , c + 2 A 1 A 2 A c , s * e i Δ kz ]
d A 1 , 2 dz = [ ( A 1 , 2 2 + 2 k 1 , 2 A k 2 ) A 1 , 2 + 2 A 2,1 * A s A c e i Δ kz ] .
d A s , c dz = i [ ( k s , c + 2 γ P p ) A s , c + γ P p e i 2 ϕ po A c , s * ]
d A p dz = i γ P p A p
[ A s ( z ) A c * ( z ) ] = [ e i ϕ p 0 0 e i ϕ p ] [ a b b * a * ] [ A s 0 e + i φ s 0 A c 0 e i φ c 0 ]
a = cosh ( gz ) + i κ 2 g sinh ( gz )
b = i γ P p g e i 2 ϕ p 0 sinh ( gz )
κ = Δ k + 2 γ P p
g = ( γ P p ) 2 ( κ 2 ) 2 .
A s ( z ) 2 = a 2 A s 0 2 + b 2 · A c 0 2 + 2 a b A s 0 A c 0 cos ( φ s 0 + φ c 0 + ϕ a ϕ b )
ϕ a = tan 1 ( κ 2 g tan ( g z ) )
ϕ b = 2 φ p 0 + π 2 .
L = 1 g arcsin [ A c 0 2 A s 0 2 ( γ A p 0 2 g ) 2 ( κ 2 g ) 2 + 1 ] 1 2
φ s 0 + φ c 0 2 φ p 0 + ξ = ( 2 n + 1 ) π n = 0,1 , 2

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