Parametric amplification and modulational instabilities in dispersive nonlinear directional couplers with relaxing nonlinearity

S. Trillo, S. Wabnitz, G. I. Stegeman, Ewan M Wright

Research output: Contribution to journalArticle

69 Citations (Scopus)

Abstract

We investigate the effects of a nonlinearity with a finite response time, combined with group-velocity dispersion and self-phase modulation, on the parametric amplification and modulational instability exhibited by light propagating in a nonlinear directional coupler. A linear-stability analysis of the nonlinear coupled-mode equations describing propagation in the coupler furnishes simple general expressions for the bandwidth of the spatial growth rate of an initially weak modulation for the case in which the carrier propagates in either the symmetric or the antisymmetric mode of the coupler. New types of scalar and vectorial modulational instabilities of the nonlinear Schrodinger equation are predicted, in both the normal- and the anomalous-dispersion regimes. The physical origin of these instabilities is the interplay among linear coupling, parametric four-photon mixing, and Raman scattering.

Original languageEnglish (US)
Pages (from-to)889-900
Number of pages12
JournalJournal of the Optical Society of America B: Optical Physics
Volume6
Issue number5
DOIs
StatePublished - 1989

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directional couplers
nonlinearity
couplers
group velocity
phase modulation
coupled modes
nonlinear equations
Raman spectra
scalars
bandwidth
modulation
propagation
photons

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Atomic and Molecular Physics, and Optics

Cite this

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abstract = "We investigate the effects of a nonlinearity with a finite response time, combined with group-velocity dispersion and self-phase modulation, on the parametric amplification and modulational instability exhibited by light propagating in a nonlinear directional coupler. A linear-stability analysis of the nonlinear coupled-mode equations describing propagation in the coupler furnishes simple general expressions for the bandwidth of the spatial growth rate of an initially weak modulation for the case in which the carrier propagates in either the symmetric or the antisymmetric mode of the coupler. New types of scalar and vectorial modulational instabilities of the nonlinear Schrodinger equation are predicted, in both the normal- and the anomalous-dispersion regimes. The physical origin of these instabilities is the interplay among linear coupling, parametric four-photon mixing, and Raman scattering.",
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AU - Wabnitz, S.

AU - Stegeman, G. I.

AU - Wright, Ewan M

PY - 1989

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N2 - We investigate the effects of a nonlinearity with a finite response time, combined with group-velocity dispersion and self-phase modulation, on the parametric amplification and modulational instability exhibited by light propagating in a nonlinear directional coupler. A linear-stability analysis of the nonlinear coupled-mode equations describing propagation in the coupler furnishes simple general expressions for the bandwidth of the spatial growth rate of an initially weak modulation for the case in which the carrier propagates in either the symmetric or the antisymmetric mode of the coupler. New types of scalar and vectorial modulational instabilities of the nonlinear Schrodinger equation are predicted, in both the normal- and the anomalous-dispersion regimes. The physical origin of these instabilities is the interplay among linear coupling, parametric four-photon mixing, and Raman scattering.

AB - We investigate the effects of a nonlinearity with a finite response time, combined with group-velocity dispersion and self-phase modulation, on the parametric amplification and modulational instability exhibited by light propagating in a nonlinear directional coupler. A linear-stability analysis of the nonlinear coupled-mode equations describing propagation in the coupler furnishes simple general expressions for the bandwidth of the spatial growth rate of an initially weak modulation for the case in which the carrier propagates in either the symmetric or the antisymmetric mode of the coupler. New types of scalar and vectorial modulational instabilities of the nonlinear Schrodinger equation are predicted, in both the normal- and the anomalous-dispersion regimes. The physical origin of these instabilities is the interplay among linear coupling, parametric four-photon mixing, and Raman scattering.

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