title: Higher-order modulation instability in nonlinear fiber optics.
abstract: We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves.
authors.affiliation: Tampere University of Technology, Optics Laboratory, FI-33101 Tampere, Finland.
authors.forename: Miro
authors.initials: M
authors.lastname: Erkintalo
authors.forename: Kamal
authors.initials: K
authors.lastname: Hammani
authors.forename: Bertrand
authors.initials: B
authors.lastname: Kibler
authors.forename: Christophe
authors.initials: C
authors.lastname: Finot
authors.forename: Nail
authors.initials: N
authors.lastname: Akhmediev
authors.forename: John M
authors.initials: JM
authors.lastname: Dudley
authors.forename: Goëry
authors.initials: G
authors.lastname: Genty