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  • Vol. 28, Iss. 23 — Dec. 1, 2003
  • pp: 2363–2365

Modulational instability and space time dynamics in nonlinear parabolic-index optical fibers

Stefano Longhi  »View Author Affiliations


Optics Letters, Vol. 28, Issue 23, pp. 2363-2365 (2003)
http://dx.doi.org/10.1364/OL.28.002363


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Abstract

Beam propagation in multimode graded-index parabolic optical fibers in the presence of group-velocity dispersion and Kerr nonlinearity is theoretically investigated. It is shown that a modulational instability arising from the periodic spatial focusing of the beam takes place regardless of the sign of fiber dispersion, leading to a highly nonlinear space–time dynamics and the generation of ultrashort optical pulses.

© 2003 Optical Society of America

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

Citation
Stefano Longhi, "Modulational instability and space time dynamics in nonlinear parabolic-index optical fibers," Opt. Lett. 28, 2363-2365 (2003)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-23-2363


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References

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  14. It is remarkable that there exist exact nonlinear periodic solutions to Eq. 1. Indeed, if E(x, y,ξ)= F(x,y)exp(-isξ) is a nonlinear guided mode of the fiber, where the mode profile F(x,y) and corresponding propagation constant s are found as the nonlinear eigenmode and the eigenvalue of the equation (1/2k0)∇2F- (k0g/2)r2F+(n2k0/n0)|F|2F=sF, one can show that an exact periodic solution to Eq. 1 is given by Es(x,y,ξ)=1―a(ξ)F(x―a y―a) ×exp[-is∫ξ0ʹa2(x)-ik0 2ada dxr2, where the scaling function a=a(x) is periodic, with period p/g, given by a(x)= a02 cos 2(gx)+sin 2(gx)1/2, and a0=a(0) is an arbitrary scaling constant. For simplicity, an approximate Gaussian solution given by Eq. 2 is considered here.

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