Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation

Hervé Leblond, David Kremer, and Dumitru Mihalache Laboratoire de Photonique d’Angers, Université d’Angers, 2 Bd. Lavoisier, 49045 Angers Cedex 01, France Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125, Romania Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania Abstract By using a reductive perturbation method, we derive from Maxwell-Bloch equations, a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media, without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method, and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the tranverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.