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Phys. Rev. E 73, 036614 (2006) [10 pages]

Nonlocal description of X waves in quadratic nonlinear materials

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P. V. Larsen* and M. P. Sørensen
Department of Mathematics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark

O. Bang
COM•DTU, Department of Communications, Optics & Materials, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark

W. Z. Królikowski
Laser Physics Centre and ARC Centre of Excellence for Ultrahigh-Bandwidth Devices for Optical Systems, Research School of Physical Sciences, Australian National University, Canberra, Australian Capital Territory 0200, Australia

S. Trillo
Department of Engineering, University of Ferrara, Via Saragat 1, 44100 Ferrara, Italy and Istituto Nazionale de Fisica della Materia (INFM)-RM3, Via delle Vasca Navale, 00146 Roma, Italy

Received 23 December 2005; published 22 March 2006

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 δ 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.

© 2006 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.73.036614
DOI:
10.1103/PhysRevE.73.036614
PACS:
03.50.De, 05.45.Yv, 42.65.Jx, 42.65.Tg

*Electronic address: P.V.Larsen@mat.dtu.dk

 
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