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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 12 — Dec. 1, 2013
  • pp: 3260–3271

Instability of the split-step method for a signal with nonzero central frequency

T. I. Lakoba  »View Author Affiliations

JOSA B, Vol. 30, Issue 12, pp. 3260-3271 (2013)

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We obtain analytical conditions for the occurrence of numerical instability (NI) of a split-step method when the simulated solution of the nonlinear Schrödinger equation is close to a plane wave with nonzero carrier frequency. We also numerically study such an instability when the solution is a sequence of pulses rather than a plane wave. The plane-wave-based analysis gives reasonable predictions for the frequencies of the numerically unstable Fourier modes but overestimates the instability growth rate. The latter is found to be strongly influenced by the randomness of the signal’s profile: The more randomly it varies during the propagation, the weaker is the NI. Using an example of a realistic transmission system, we demonstrate that our single-channel results can be used to predict occurrences of NI in multichannel simulations. We also give an estimate for the integration step size for which NI, while present, will not affect simulation results for such systems. Using that estimate may lead to a significant saving of computational time.

© 2013 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons

ToC Category:
Fiber Optics and Optical Communications

Original Manuscript: June 24, 2013
Revised Manuscript: October 18, 2013
Manuscript Accepted: October 18, 2013
Published: November 20, 2013

T. I. Lakoba, "Instability of the split-step method for a signal with nonzero central frequency," J. Opt. Soc. Am. B 30, 3260-3271 (2013)

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