title: Nonlocal description of X waves in quadratic nonlinear materials.
abstract: We study localized light bullets and X waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multidimensional nonlinear waves. For X waves we show that a local cascading limit in terms of a nonlinear Schrödinger equation does not exist-one needs to use the nonlocal description, because the nonlocal response function does not converge toward a function. Also, we use the nonlocal theory to show that the coupling to the second harmonic is able to generate an X shape in the fundamental field despite having anomalous dispersion, in contrast to the predictions of the cascading limit.
authors.affiliation: Department of Mathematics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark. P.V.Larsen@mat.dtu.dk
authors.forename: P V
authors.initials: PV
authors.lastname: Larsen
authors.forename: M P
authors.initials: MP
authors.lastname: Sørensen
authors.forename: O
authors.initials: O
authors.lastname: Bang
authors.forename: W Z
authors.initials: WZ
authors.lastname: Królikowski
authors.forename: S
authors.initials: S
authors.lastname: Trillo