title: Three-wave interaction in two-component quadratic nonlinear lattices.
abstract: We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that energy conversion and pulse propagation known from three-wave interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained in non-phase-matched lattices by tilting the interacting plane waves with respect to each other.
authors.affiliation: Department of Physics and Center of Mathematical Sciences, University of Madeira, 9000 Funchal, Portugal.
authors.forename: V V
authors.initials: VV
authors.lastname: Konotop
authors.forename: M D
authors.initials: MD
authors.lastname: Cunha
authors.forename: P L
authors.initials: PL
authors.lastname: Christiansen
authors.forename: C B
authors.initials: CB
authors.lastname: Clausen