The mechanism of the polarizational mode instability in birefringent fiber optics

Yi A. Li, Keith Promislow

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

We show that the soliton solutions of the integrable Manakov equation exhibit an instability under arbitrarily small Hamiltonian perturbations. The instability arises from eigenvalues embedded in the essential spectrum of the associated linearized operators; these eigenvalues are dislodged by smooth perturbations. Specifically we consider perturbations which arise in fiber optics as a result of birefringence, including the so-called four-wave mixing term. Employing the Evans function and a Dirichlet expansion on the stable manifold of the linearized system, we obtain rigorous perturbation results and compute the stability diagram of the fast wave for all physical values of the birefringent parameters, using a novel numerical scheme derived from the Dirichlet expansion.

Original languageEnglish
Pages (from-to)1351-1373
Number of pages23
JournalSIAM Journal on Mathematical Analysis
Volume31
Issue number6
DOIs
StatePublished - 2000

Keywords

  • Dirichlet expansion
  • Evans function
  • Polarization mode instability
  • Traveling waves

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