Abstract

The nonlinear propagation of a partially coherent continuous-wave laser beam in single-mode optical fibers is investigated both theoretically and experimentally, with a special attention to the zero-dispersion wavelength region where modulation instability is expected. Broadband asymmetric spectral broadening is reported experimentally and found in fairly good agreement with a numerical Schrödinger simulation including a phase-diffusion model for the partially coherent beam. This model shows in addition that the underlying spectral broadening mechanism relies not only on modulation instability but also on the generation of high-order soliton-like pulses and dispersive waves. The coherence degradation which results from these ultrafast phenomena is confirmed by autocorrelation measurement.

© 2004 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear fiber optics, (Optics and Photonics, 3rd ed., Ac. Press, San Diego, 2001).
  2. D. A. Chestnut and J. R. Taylor, “Gain-flattened fiber Raman amplifiers with nonlinearity-broadened pumps,” Opt. Lett. 28, 2294–2296 (2003).
    [Crossref] [PubMed]
  3. Tim J. Ellingham, Juan D. Ania- Castañón, O. Shtyrina, Michail P. Fedoruk, and Sergei K. Turitsyn, “CW Raman pump broadening using modulational instability,” In Nonlinear Guided Waves and their Applications, paper MC42, (March 28–31, Toronto, Canada, 2004).
  4. A. K. Abeeluck, C. Headley, and C. G. Jorgensen, “A fiber-based, high-power supercontinuum light source,” In Optical Fiber Communication, paper TuK5, (February 22–27, Los Angeles, California, 2004).
  5. F. Vanholsbeeck, S. Coen, Ph. Emplit, C. Martinelli, and T. Sylvestre, “Cascaded Raman generation in optical fibers : Influence of chromatic dispersion and Rayleigh back-scattering”, Opt. Lett. 29, 998–1000 (2004).
    [Crossref] [PubMed]
  6. J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear dispersion-shifted fibers,” Appl. Phys. B 77, 211–218 (2003).
    [Crossref]
  7. S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
    [Crossref] [PubMed]
  8. S. Ryu, “Change of field spectrum of signal light due to fibre nonlinearities and chromatic dispersion in long-haul coherent systems using in-line optical amplifiers,” Electron. Lett. 28, 2212 (1992).
    [Crossref]
  9. M. Lax, “Classical noise. V. Noise in self-substained oscillators,” Phys. Rev. 160, 290–307 (1967).
    [Crossref]
  10. A. V. Husakou and J. Hermann, “Supercontinuum generation, four-wave mixing and fission of higher-order solitons in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 2171–2182 (2002).
    [Crossref]
  11. C. H. Henry, “Theory of the linewidth of SC Lasers,” IEEE J. Quant. Electron. 18, 259–264 (1982).
    [Crossref]
  12. D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, “Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601 (2004).
    [Crossref]
  13. P. K. A. Wai, C. R. Menuyk, H. H. Chen, and Y. C. Lee, “Soliton at the zero-dispersion wavelength of a single-mode fiber,” Opt. Lett. 12, 628–630, (1987).
    [Crossref] [PubMed]
  14. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
    [Crossref] [PubMed]
  15. G. R. Boyer and X. F. Carlotti, “Pulse-spreading minimization in single-mode optical fibers,” Phys. Rev. A 38, 5140–5148 (1988).
    [Crossref] [PubMed]
  16. J. C. Bouteiller, “Linewidth predictions for Raman fibre lasers,” Electron. Lett. 39, 1511–1512 (2003).
    [Crossref]

2004 (2)

F. Vanholsbeeck, S. Coen, Ph. Emplit, C. Martinelli, and T. Sylvestre, “Cascaded Raman generation in optical fibers : Influence of chromatic dispersion and Rayleigh back-scattering”, Opt. Lett. 29, 998–1000 (2004).
[Crossref] [PubMed]

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, “Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601 (2004).
[Crossref]

2003 (3)

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear dispersion-shifted fibers,” Appl. Phys. B 77, 211–218 (2003).
[Crossref]

D. A. Chestnut and J. R. Taylor, “Gain-flattened fiber Raman amplifiers with nonlinearity-broadened pumps,” Opt. Lett. 28, 2294–2296 (2003).
[Crossref] [PubMed]

J. C. Bouteiller, “Linewidth predictions for Raman fibre lasers,” Electron. Lett. 39, 1511–1512 (2003).
[Crossref]

2002 (1)

1995 (2)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref] [PubMed]

1992 (1)

S. Ryu, “Change of field spectrum of signal light due to fibre nonlinearities and chromatic dispersion in long-haul coherent systems using in-line optical amplifiers,” Electron. Lett. 28, 2212 (1992).
[Crossref]

1988 (1)

G. R. Boyer and X. F. Carlotti, “Pulse-spreading minimization in single-mode optical fibers,” Phys. Rev. A 38, 5140–5148 (1988).
[Crossref] [PubMed]

1987 (1)

1982 (1)

C. H. Henry, “Theory of the linewidth of SC Lasers,” IEEE J. Quant. Electron. 18, 259–264 (1982).
[Crossref]

1967 (1)

M. Lax, “Classical noise. V. Noise in self-substained oscillators,” Phys. Rev. 160, 290–307 (1967).
[Crossref]

Abeeluck, A. K.

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear dispersion-shifted fibers,” Appl. Phys. B 77, 211–218 (2003).
[Crossref]

A. K. Abeeluck, C. Headley, and C. G. Jorgensen, “A fiber-based, high-power supercontinuum light source,” In Optical Fiber Communication, paper TuK5, (February 22–27, Los Angeles, California, 2004).

Agrawal, G. P.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

G. P. Agrawal, Nonlinear fiber optics, (Optics and Photonics, 3rd ed., Ac. Press, San Diego, 2001).

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref] [PubMed]

Anderson, D.

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, “Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601 (2004).
[Crossref]

Ania- Castañón, Juan D.

Tim J. Ellingham, Juan D. Ania- Castañón, O. Shtyrina, Michail P. Fedoruk, and Sergei K. Turitsyn, “CW Raman pump broadening using modulational instability,” In Nonlinear Guided Waves and their Applications, paper MC42, (March 28–31, Toronto, Canada, 2004).

Bouteiller, J. C.

J. C. Bouteiller, “Linewidth predictions for Raman fibre lasers,” Electron. Lett. 39, 1511–1512 (2003).
[Crossref]

Boyer, G. R.

G. R. Boyer and X. F. Carlotti, “Pulse-spreading minimization in single-mode optical fibers,” Phys. Rev. A 38, 5140–5148 (1988).
[Crossref] [PubMed]

Carlotti, X. F.

G. R. Boyer and X. F. Carlotti, “Pulse-spreading minimization in single-mode optical fibers,” Phys. Rev. A 38, 5140–5148 (1988).
[Crossref] [PubMed]

Cavalcanti, S. B.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Chen, H. H.

Chestnut, D. A.

Coen, S.

Ellingham, Tim J.

Tim J. Ellingham, Juan D. Ania- Castañón, O. Shtyrina, Michail P. Fedoruk, and Sergei K. Turitsyn, “CW Raman pump broadening using modulational instability,” In Nonlinear Guided Waves and their Applications, paper MC42, (March 28–31, Toronto, Canada, 2004).

Emplit, Ph.

Fedoruk, Michail P.

Tim J. Ellingham, Juan D. Ania- Castañón, O. Shtyrina, Michail P. Fedoruk, and Sergei K. Turitsyn, “CW Raman pump broadening using modulational instability,” In Nonlinear Guided Waves and their Applications, paper MC42, (March 28–31, Toronto, Canada, 2004).

Headley, C.

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear dispersion-shifted fibers,” Appl. Phys. B 77, 211–218 (2003).
[Crossref]

A. K. Abeeluck, C. Headley, and C. G. Jorgensen, “A fiber-based, high-power supercontinuum light source,” In Optical Fiber Communication, paper TuK5, (February 22–27, Los Angeles, California, 2004).

Helczynski-Wolf, L.

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, “Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601 (2004).
[Crossref]

Henry, C. H.

C. H. Henry, “Theory of the linewidth of SC Lasers,” IEEE J. Quant. Electron. 18, 259–264 (1982).
[Crossref]

Hermann, J.

Husakou, A. V.

Jorgensen, C. G.

A. K. Abeeluck, C. Headley, and C. G. Jorgensen, “A fiber-based, high-power supercontinuum light source,” In Optical Fiber Communication, paper TuK5, (February 22–27, Los Angeles, California, 2004).

Jørgensen, C. G.

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear dispersion-shifted fibers,” Appl. Phys. B 77, 211–218 (2003).
[Crossref]

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref] [PubMed]

Lax, M.

M. Lax, “Classical noise. V. Noise in self-substained oscillators,” Phys. Rev. 160, 290–307 (1967).
[Crossref]

Lee, Y. C.

Lisak, M.

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, “Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601 (2004).
[Crossref]

Martinelli, C.

Menuyk, C. R.

Nicholson, J. W.

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear dispersion-shifted fibers,” Appl. Phys. B 77, 211–218 (2003).
[Crossref]

Ryu, S.

S. Ryu, “Change of field spectrum of signal light due to fibre nonlinearities and chromatic dispersion in long-haul coherent systems using in-line optical amplifiers,” Electron. Lett. 28, 2212 (1992).
[Crossref]

Semenov, V.

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, “Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601 (2004).
[Crossref]

Shtyrina, O.

Tim J. Ellingham, Juan D. Ania- Castañón, O. Shtyrina, Michail P. Fedoruk, and Sergei K. Turitsyn, “CW Raman pump broadening using modulational instability,” In Nonlinear Guided Waves and their Applications, paper MC42, (March 28–31, Toronto, Canada, 2004).

Sylvestre, T.

Taylor, J. R.

Turitsyn, Sergei K.

Tim J. Ellingham, Juan D. Ania- Castañón, O. Shtyrina, Michail P. Fedoruk, and Sergei K. Turitsyn, “CW Raman pump broadening using modulational instability,” In Nonlinear Guided Waves and their Applications, paper MC42, (March 28–31, Toronto, Canada, 2004).

Vanholsbeeck, F.

Wai, P. K. A.

Yan, M. F.

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear dispersion-shifted fibers,” Appl. Phys. B 77, 211–218 (2003).
[Crossref]

Yu, M.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Appl. Phys. B (1)

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, “Pulsed and continuous-wave supercontinuum generation in highly nonlinear dispersion-shifted fibers,” Appl. Phys. B 77, 211–218 (2003).
[Crossref]

Electron. Lett. (2)

S. Ryu, “Change of field spectrum of signal light due to fibre nonlinearities and chromatic dispersion in long-haul coherent systems using in-line optical amplifiers,” Electron. Lett. 28, 2212 (1992).
[Crossref]

J. C. Bouteiller, “Linewidth predictions for Raman fibre lasers,” Electron. Lett. 39, 1511–1512 (2003).
[Crossref]

IEEE J. Quant. Electron. (1)

C. H. Henry, “Theory of the linewidth of SC Lasers,” IEEE J. Quant. Electron. 18, 259–264 (1982).
[Crossref]

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

Opt. Lett. (3)

Phys. Rev. (1)

M. Lax, “Classical noise. V. Noise in self-substained oscillators,” Phys. Rev. 160, 290–307 (1967).
[Crossref]

Phys. Rev. A (3)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref] [PubMed]

G. R. Boyer and X. F. Carlotti, “Pulse-spreading minimization in single-mode optical fibers,” Phys. Rev. A 38, 5140–5148 (1988).
[Crossref] [PubMed]

Phys. Rev. E (1)

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, “Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601 (2004).
[Crossref]

Other (3)

G. P. Agrawal, Nonlinear fiber optics, (Optics and Photonics, 3rd ed., Ac. Press, San Diego, 2001).

Tim J. Ellingham, Juan D. Ania- Castañón, O. Shtyrina, Michail P. Fedoruk, and Sergei K. Turitsyn, “CW Raman pump broadening using modulational instability,” In Nonlinear Guided Waves and their Applications, paper MC42, (March 28–31, Toronto, Canada, 2004).

A. K. Abeeluck, C. Headley, and C. G. Jorgensen, “A fiber-based, high-power supercontinuum light source,” In Optical Fiber Communication, paper TuK5, (February 22–27, Los Angeles, California, 2004).

Supplementary Material (1)

» Media 1: AVI (1864 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) Temporal intensity and (b) power spectrum of a PC laser beam in a single-mode optical fiber at three propagation distances (z=0, red, z=300m, green, and z=3100 m, blue). The entire sequence can be viewed as a movie (avi, 1865 kb). PC wave’s parameters are λ=1555 nm, P=600 mW, Δf=50 GHz. Fiber’s parameters are β 2=-5.5.10-28s2m-1, β 3=1.15.10-40s3m-1, β 4=-2.85.10-55s4m-1, λ0=1549 nm, γ=2W-1km-1, α=4.6.10-5m-1. [Media 1]

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Fig. 2.
Fig. 2.

Ouput/Input spectral widths ratio of a PC wave after 3100 m of propagation in a single-mode optical fiber. Solid lines: analytical prediction Eq. (4), Crosses and circles: numerical results.

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Fig. 3.
Fig. 3.

(a) Experimental and (b) simulated spectra for increasing pump power. blue : output, from bottom to top (a) P=0.8, 1, 1.4, and 1.8 W and (b) P=0.4, 0.5, 0.7, 0.9 W. Green : normal dispersion P=1.4 W. Red: input at (a) 0.8 W and (b) 0.4 W.

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Fig. 4.
Fig. 4.

(a) Experimental and (b) theoretical intensity autocorrelation functions for same increasing power levels as in Fig. 3. Red line: Input. Blue lines: Output.

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Equations (5)

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

∂ A ∂ z + i β 2 2 ∂ 2 A ∂ t 2 − β 3 6 ∂ 3 A ∂ t 3 − i β 4 24 ∂ 4 A ∂ t 4 + α 2 A = i γ ∣ A ∣ 2 A
A P ( t ) = P 0 × exp ( i φ ( t ) )
Γ ( t , z ) = < A P * ( t , z ) A P ( t , z ) >
Δ Ω = 4 ( γ P ∣ β 2 ∣ ) 1 ⁄ 2
δ ω = − 3 β 2 β 3 + 4 β 3 γ P 3 β 2 2 .

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