Adaptive optical post distortion linearization

Jason Chou; Ozdal Boyraz; Bahram Jalali

doi:10.1364/OPEX.13.005711

Adaptive optical post distortion linearization

Jason Chou, Ozdal Boyraz, and Bahram Jalali

Optics Express
Vol. 13,
Issue 15,
pp. 5711-5718
(2005)
•doi: 10.1364/OPEX.13.005711

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Jason Chou, Ozdal Boyraz, and Bahram Jalali, "Adaptive optical post distortion linearization," Opt. Express 13, 5711-5718 (2005)

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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.

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References

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Publication

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 and B. Jalali, “Adaptive CMOS predistortion linearizer for fiber-optic links,” J. Lightwave Technol. 21, 3180–3193, (2003).
[Crossref]
J. Basak, R. Sadhwani, and B. Jalali, “WDM pilot tone technique for analogue optical links,” Electron. Lett. 39, 1083–1084, (2003).
[Crossref]
R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” J. Quantum Electron. 18, 1062–1072, (1982).
[Crossref]
H. Taga, “Long distance transmission experiments using WDM technology,” J. Lightwave Technol. 14, 1287-98, (1996).
[Crossref]
F. Forghieri, R.W. Tkach, and A.R. Chrapyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897, (1995).
[Crossref]
F. Forghieri, R.W. Tkach, A.R. Chraplyvy, and D. Marcuse, “Reduction of four-wave mixing crosstalk in WDM systems using unequally spaced channels,” Photon. Technol. Lett. 6, 754–756, (1994).
[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]
G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
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]
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, and 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]

2003 (2)

R. Sadhwani and B. Jalali, “Adaptive CMOS predistortion linearizer for fiber-optic links,” J. Lightwave Technol. 21, 3180–3193, (2003).
[Crossref]

J. Basak, R. Sadhwani, and B. Jalali, “WDM pilot tone technique for analogue optical links,” Electron. Lett. 39, 1083–1084, (2003).
[Crossref]

2001 (1)

J. Kim, O. Boyraz, J. H. Lim, and 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]

1999 (1)

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]

1996 (1)

H. Taga, “Long distance transmission experiments using WDM technology,” J. Lightwave Technol. 14, 1287-98, (1996).
[Crossref]

1995 (2)

F. Forghieri, R.W. Tkach, and A.R. Chrapyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897, (1995).
[Crossref]

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]

1994 (1)

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

1993 (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]

1990 (1)

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]

1982 (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” J. Quantum Electron. 18, 1062–1072, (1982).
[Crossref]

Agrawal, G. P.

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

Basak, J.

J. Basak, R. Sadhwani, and B. Jalali, “WDM pilot tone technique for analogue optical links,” Electron. Lett. 39, 1083–1084, (2003).
[Crossref]

Berger, J.

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]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” J. Quantum Electron. 18, 1062–1072, (1982).
[Crossref]

Boyraz, O.

Chraplyvy, A.R.

Chrapyvy, A.R.

F. Forghieri, R.W. Tkach, and A.R. Chrapyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897, (1995).
[Crossref]

Curtis, L.

Forghieri, F.

F. Forghieri, R.W. Tkach, and A.R. Chrapyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897, (1995).
[Crossref]

Ho, M.-C.

Inoue, K.

Islam, M. N.

Jalali, B.

J. Basak, R. Sadhwani, and B. Jalali, “WDM pilot tone technique for analogue optical links,” Electron. Lett. 39, 1083–1084, (2003).
[Crossref]

R. Sadhwani and B. Jalali, “Adaptive CMOS predistortion linearizer for fiber-optic links,” J. Lightwave Technol. 21, 3180–3193, (2003).
[Crossref]

Kagan, Y.

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]

Kazovsky, L. G.

Kim, J.

Laming, R. I.

Levi, M.

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]

Ley, J.

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]

Lim, J. H.

Maeda, M. W.

Mahric, M. E.

Marcuse, D.

Nazarathy, M.

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]

Sadhwani, R.

J. Basak, R. Sadhwani, and B. Jalali, “WDM pilot tone technique for analogue optical links,” Electron. Lett. 39, 1083–1084, (2003).
[Crossref]

R. Sadhwani and B. Jalali, “Adaptive CMOS predistortion linearizer for fiber-optic links,” J. Lightwave Technol. 21, 3180–3193, (2003).
[Crossref]

Sessa, W. B.

Spicer, R.

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” J. Quantum Electron. 18, 1062–1072, (1982).
[Crossref]

Taga, H.

H. Taga, “Long distance transmission experiments using WDM technology,” J. Lightwave Technol. 14, 1287-98, (1996).
[Crossref]

Takahashi, H.

Tkach, R.W.

F. Forghieri, R.W. Tkach, and A.R. Chrapyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897, (1995).
[Crossref]

Way, W. I.

Yang, F. S.

Yi-Yan, A.

Electron. Lett. (1)

J. Basak, R. Sadhwani, and 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 and 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]

F. Forghieri, R.W. Tkach, and A.R. Chrapyvy, “WDM systems with unequally spaced channels,” J. Lightwave Technol. 13, 889–897, (1995).
[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)

Other (1)

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

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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.

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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.

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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.

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Equations (14)

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\frac{d A_{s, c}}{dz} = iγ [({∣ A_{s, c} ∣}^{2} + 2 \sum_{k \neq s, c} {∣ A_{k} ∣}^{2}) A_{s, c} + 2 A_{1} A_{2} A_{c, s}^{*} e^{- i Δ kz}]

\frac{d A_{1, 2}}{dz} = iγ [({∣ A_{1, 2} ∣}^{2} + 2 \sum_{k \neq 1, 2} {∣ A_{k} ∣}^{2}) A_{1, 2} + 2 A_{2,1}^{*} A_{s} A_{c} e^{- i Δ kz}] .

\frac{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}^{*}]

\frac{d A_{p}}{dz} = i ∙ γ P_{p} ∙ A_{p}

[\begin{matrix} A_{s} (z) \\ A_{c}^{*} (z) \end{matrix}] = [\begin{matrix} e^{i ∙ ϕ_{p}} & 0 \\ 0 & e^{- i ∙ ϕ_{p}} \end{matrix}] ∙ [\begin{matrix} a & b \\ b^{*} & a^{*} \end{matrix}] ∙ [\begin{matrix} ∣ A_{s 0} ∣ ∙ e^{+ i ∙ φ_{s 0}} \\ ∣ A_{c 0} ∣ ∙ e^{- i ∙ φ_{c 0}} \end{matrix}]

a = \cosh (gz) + i ∙ \frac{κ}{2 g} \sinh (gz)

b = i ∙ \frac{γ P_{p}}{g} ∙ e^{i ∙ 2 ϕ_{p 0}} ∙ \sinh (gz)

κ = Δ k + 2 γ P_{p}

g = \sqrt{{(γ P_{p})}^{2} - {(\frac{κ}{2})}^{2}} .

{∣ A_{s} (z) ∣}^{2} = {∣ a ∣}^{2} ∙ {∣ A_{s 0} ∣}^{2} + {∣ b ∣}^{2} \cdot {∣ 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} (\frac{κ}{2 ∣ g ∣} \tan (∣ g ∣ z))

ϕ_{b} = 2 φ_{p 0} + \frac{π}{2} .

L = \frac{1}{∣ g ∣} \arcsin {[\frac{{∣ A_{c 0} ∣}^{2}}{{∣ A_{s 0} ∣}^{2}} {(\frac{γ {∣ A_{p 0} ∣}^{2}}{∣ g ∣})}^{2} - {(\frac{κ}{2 ∣ g ∣})}^{2} + 1]}^{- \frac{1}{2}}

φ_{s 0} + φ_{c 0} - 2 φ_{p 0} + ξ = (2 n + 1) π n = 0,1, 2 \dots

Abstract

References

2003 (2)

2001 (1)

1999 (1)

1996 (1)

1995 (2)

1994 (1)

1993 (1)

1990 (1)

1982 (1)

Agrawal, G. P.

Basak, J.

Berger, J.

Bjorkholm, J. E.

Boyraz, O.

Chraplyvy, A.R.

Chrapyvy, A.R.

Curtis, L.

Forghieri, F.

Ho, M.-C.

Inoue, K.

Islam, M. N.

Jalali, B.

Kagan, Y.

Kazovsky, L. G.

Kim, J.

Laming, R. I.

Levi, M.

Ley, J.

Lim, J. H.

Maeda, M. W.

Mahric, M. E.

Marcuse, D.

Nazarathy, M.

Sadhwani, R.

Sessa, W. B.

Spicer, R.

Stolen, R. H.

Taga, H.

Takahashi, H.

Tkach, R.W.

Way, W. I.

Yang, F. S.

Yi-Yan, A.

Electron. Lett. (1)

J. Lightwave Technol. (7)

J. Quantum Electron. (1)

Opt. Lett. (1)

Photon. Technol. Lett. (1)

Other (1)

Cited By

Figures (3)

Equations (14)

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