Abstract

An investigation is made of the effects of initial or dynamically induced chirping on the linear propagation characteristics of pulses in optical fibers. It is shown that under certain conditions the chirping will give rise to a splitting of the initial pulse into two separating subpulses. The necessary conditions for pulse splitting to occur are established analytically and corroborated by numerical computations.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, Nonlinear Fibers (Academic, San Diego, Calif., 1995).
  2. B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
    [Crossref]
  3. J. M. Hickman, A. S. L. Gomes, and C. B. de Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–31507 (1992).
    [Crossref]
  4. L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
    [Crossref]
  5. D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
    [Crossref] [PubMed]

2000 (1)

L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
[Crossref]

1992 (1)

J. M. Hickman, A. S. L. Gomes, and C. B. de Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–31507 (1992).
[Crossref]

1988 (1)

B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
[Crossref]

1987 (1)

D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
[Crossref] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fibers (Academic, San Diego, Calif., 1995).

Anderson, D.

L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
[Crossref]

D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
[Crossref] [PubMed]

Berntson, A.

L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
[Crossref]

de Araujo, C. B.

J. M. Hickman, A. S. L. Gomes, and C. B. de Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–31507 (1992).
[Crossref]

Desaix, M.

L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
[Crossref]

Gomes, A. S. L.

J. M. Hickman, A. S. L. Gomes, and C. B. de Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–31507 (1992).
[Crossref]

Hall, B.

L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
[Crossref]

Helczynski, L.

L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
[Crossref]

Hickman, J. M.

J. M. Hickman, A. S. L. Gomes, and C. B. de Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–31507 (1992).
[Crossref]

Jaskorzynska, B.

B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
[Crossref]

Lisak, M.

L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
[Crossref]

D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
[Crossref] [PubMed]

Schadt, D.

B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
[Crossref]

IEEE J. Quantum Electron. (1)

B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
[Crossref]

Phys. Rev. A (1)

D. Anderson and M. Lisak, “Analytic study of pulse broadening in dispersive optical fibers,” Phys. Rev. A 35, 184–187 (1987).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

J. M. Hickman, A. S. L. Gomes, and C. B. de Araujo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547–31507 (1992).
[Crossref]

Phys. Scr. (1)

L. Helczynski, B. Hall, D. Anderson, M. Lisak, A. Berntson, and M. Desaix, “Cross phase modulation induced pulse splitting—the optical axe,” Phys. Scr. T84, 81–84 (2000).
[Crossref]

Other (1)

G. P. Agrawal, Nonlinear Fibers (Academic, San Diego, Calif., 1995).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Qualitative picture showing the competition between pulse broadening and pulse separation.

Fig. 2
Fig. 2

Numerical simulations demonstrating the effects of (a) increasing chirp strength, β[1:0.2:1.6,2:1:5], and (b) chirp width, τ1/τ0[1:0.2:2,3], on the linear pulse-splitting process after a propagation of 1LD.

Fig. 3
Fig. 3

Numerical simulation of the linear optical axe, showing clear pulse splitting in the time and frequency domains. Parameters used are β=4 and τ1/τ0=0.8.

Fig. 4
Fig. 4

Result of a numerical simulation, showing a contour plot of the dynamical evolution of optical pulse splitting caused by initial nonmonotonic chirping. The contours range from 40% to 90% levels of the input signal intensity. Parameters used are β=4 and τ1/τ0=0.8.

Fig. 5
Fig. 5

Experimentally obtained pulse splitting: (a) Splitting caused by cross-phase modulation with a strong copropagating pulse. (b) Linear case. Here splitting is caused by initial self-phase-modulationlike chirping.

Equations (26)

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

iΨx=k022Ψτ2,
τn-+ τn|ψ(x, τ)|2dτ-+|ψ(x, τ)|2dτ.
τ=a0+a1x,τ2=b0+b1x+b2x2.
a0=-+ τ|ψ(0, τ)|2dτ-+|ψ(0, τ)|2dτ,
a1=k02Im -+[dψ(0, τ)/dτ]ψ*(0, τ)dτ-+|ψ(0,τ)|2dτ,
b2=k022-+|dψ(0, τ)/dτ|2dτ-+|ψ(0, τ)|2dτ.
dσdx<dτdx,
a1>b2-a12a1>b2/2.
(Δω)2ω2-ω2,
ω=-+ ω|ψ˜(x, ω)|2dω-+|ψ˜(x, ω)|2dω,
ω2=-+ ω2|ψ˜(x, ω)|2dω-+|ψ˜(0, τ)|2dω,
a1=2τ0I00dϕ0dτexp(-τ2/τ02)dτ,
b2=4τ0I00τ2τ04+dϕ0dτ2exp(-τ2/τ02)dτ,
τ0I0=0 A02dτ.
a1=4πβτ0,b2=4(1+4β2τ02).
41+41-2πβ2τ02<0.
1+4β2τ*3τ14τ0-4πτ*<0,1τ*2=1τ02+1τ12.
τ1τ0<216π2-11/21.8.
βcrit=2τ12τ*24π-τ0τ*-1/2.
iψx=k022ψτ2+U(x, τ)ψ,
d2τdx2=k0-+(U/τ)ψ(x, τ)|2dτ-+|ψ(x, τ)|2dτ.
ψG+exp-[τ-τ(0)]22τˆ02,
d2ydx2=-2γ exp(-y2),
y=ττˆ01+τ12τˆ02-1/2,γ=k0τ121+τˆ02τ12-3/2.
12dydx2-γ exp(-y2)=W,
limxdydx=2W  limxdτdx=-2k0N1+τˆ02τ12-1/4.

Metrics