Dynamics of collapse of optical pulses in Kerr medium

Issue title: Atomic and molecular nonlinear optics: Theory, Experiment and Computation A homage to the pioneering work of Stanisław Kielich (1925-1993)

Guest editors: G. Maroulis, T. Bancewicz, B. Champagne and A.D. Buckingham

Article type: Research Article

Authors: Long, V. Cao^a | Leoński, W.^a | Viet, H. Nguyen^b

Affiliations: [a] Institute of Physics, Zielona Góra University, ul. Prof. Szafrana 4a, 65-516 Zielona Góra, Poland | [b] Soltan Institute for Nuclear Studies, Hoża 69, 00-681 Warsaw, Poland

Abstract: We consider the propagation of optical pulses in Kerr medium in the presence of a harmonic potential for 2D case in framework of Variational Approximation (VA). We will use two types of trial function: gaussian and hyperbolic secant ones. We will show that if the value of the nonlinearity parameter reaches a certain critical value the pulse collapses. This collapse corresponds to the physical situation when the self-focusing effect dominates over the dispersion and diffraction. We show that our analytical results are confirmed by several numerical calculations which are in excellent agreement with those of the VA predictions. By the analogy between the propagation equation and Gross-Pitajevski equation for Bose-Einstein condensates (BECs) we can transfer obtained results to the case of BEC placed in a external harmonic potential. It follows that in both of cases the wave collapse can appear.

DOI: 10.3233/JCM-2010-0333

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 10, no. 3-6, pp. 465-472, 2010