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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.

Soliton pairing of two coaxially co-propagating mutually incoherent 1-D beams in Kerr type media.

Medhekar S., Sarkar K. R., Paltami P. P.

Optica Applicata

2007

Vol. 37, nr 3

243-259

In this paper, we have developed a theory (using parabolic equation approach) of coupled propagation of two coaxially co-propagating and mutually incoherent bright 1-D beams in Kerr type media. We have provided a detailed account of the propagation behavior and condition of formation of spatial soliton pairs for various coupling coefficients ( = 1, 2/3, 2) when wavelengths and widths of the beams are the same/different. We have also identified conditions for a distinct type of coupled propagation. Our simple and straightforward theory presents many features of co-propagating beams which are in agreement with the features reported earlier using coupled nonlinear Schrödinger equation (NLSE). The paper adds to the understanding of coupled propagation by revealing many additional features not reported earlier.