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3 Computational Methods in Science and Technology

3 2010

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School of Optics in Vinh University: A Short History

Long Van C.

Computational Methods in Science and Technology

2010

Vol. spec. iss. (2)

xx-xx

Propagation of Ultrashort Pulses in a Nonlinear Medium

Long Van C., Dinh Thuan B., Goldstein P., Viet Hung N., Hoai Son D.

Computational Methods in Science and Technology

2010

Vol. spec. iss. (2)

xx-xx

In this paper, using a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium derived in [8] we study in the specific case of Kerr media. An obtained ultrashort pulse propagation equation which is called Generalized Nonlinear Schrödinger Equation usually has a very complicated form and looking for its solutions is usually a “mission impossible”. Theoretical methods to solve this equation are effective only for some special cases. As an example we describe the method of a developed elliptic Jacobi function expansion. Several numerical methods of finding approximate solutions are simultaneously used. We focus mainly on the following methods: Split-Step, Runge-Kutta and Imaginary-time algorithms. Some numerical experiments are implemented for soliton propagation and interacting high order solitons. We consider also an interesting phenomenon: the collapse of solitons.

Nonlinear Optics of Photons and Atoms

Long Van C., Xuan Khoa D., Trippenbach M.

Computational Methods in Science and Technology

2010

Vol. spec. iss. (2)

xx-xx

In this presentation we intend to focus on the exchange of experience between nonlinear optics (optical pulse and beam propagation in nonlinear media) and atom optics (dynamics of coherent waves generated from Bose-Einstein condensates). A common ground here is the nonlinear Schrödinger equation, which with the proper substitution of variables describes both types of phenomena. In nonlinear optics it is a light propagation equation that relates the signal at the end of the nonlinear crystal to the signal at the input face of the medium. In Bose-Einstein condensate dynamics it is the called the Gross-Pitaevskii equation. We will discuss various types of phenomena which have realisations both in the nonlinear optics and atom optics. We will concentrate our consideration on soliton formation, which is a challenge to fundamental and applied research in these two domains of physics.