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Nonlinear Optics of Photons and Atoms

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

Computational Methods in Science and Technology

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2010

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Vol. spec. iss. (2)

xx-xx

EN

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.

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Propagation Technique for Ultrashort Pulses III: Pulse Splitting of Ultrashort Pulses in a Kerr Medium

Long V. C., Viet H. N., Trippenbach M., Xuan K. D.

Computational Methods in Science and Technology

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2008

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Vol. 14, nr 1

21-26

EN

Impact of such terms as third order dispersion, self-steepening and stimulated Raman scattering on evolution of ultrashort pulses is considered in detail. Under influence of these effects, pulse did not maintain its initial shape. Pulse splits into constituents, its spectrum also evolving into several bands which are known as optical shock and self-frequency shift phenomena. We concluded that when the input peak power is large enough, dynamics of pulse splitting will be complicated. Our numerical simulations were in good agreement with experimental results.

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Propagation Technique for Ultrashort Pulses. II: Numerical Methods to Solve the Pulse Propagation Equation

Long V. C., Viet H. N., Trippenbach M., Xuan K. D.

Computational Methods in Science and Technology

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2008

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Vol. 14, nr 1

14-19

EN

We presented the numerical technique to approximately solve the pulse propagation equation. Two efficient methods for this problem, the Split-Step Fourier and the fourth order Runge-Kutta methods are considered. Their high accuracy are shown by comparison with analytical solutions in some particular situations. Our numerical experiments are implemented for soliton propagation and interacting high order solitons. We also numerically investigate an important technique to create ultrashort pulses, which is known as the pulse compression. It is based on high order soliton propagation in Kerr media when the effect of stimulated Raman scattering is taken into account.

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Propagation Technique for Ultrashort Pulses. I: Propagation Equation for Ultrashort Pulses in a Kerr Medium

Long V. C., Viet H. N., Trippenbach M., Xuan K. D.

Computational Methods in Science and Technology

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2008

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Vol. 14, nr 1

5-11

EN

In this work we investigated propagation of ultrashort laser pulses in dispersive nonlinear media. We derived a general propagation equation of pulses which includes the linear and nonlinear effects to all orders. We studied in the specific case of Kerr media and obtained an ultrashort pulse propagation equation called a Generalized Nonlinear Schrödinger Equation. The impact of the third order dispersion, the higher-order nonlinear terms self-steepening, and stimulated Raman scattering are explicitly analyzed.

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Nieliniowa optyka atomów

Trippenbach M., Infeld E.

Postępy Fizyki

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2007

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T. 58, z. 2

55-65

EN

Research on nonlinear atom optics is reviewed. The original methods used to obtain Bose-Einstein condensates (BEC) in experiments at JILA and MIT are briefly described. Experimental realization of BEC in atomic gases led to the discovery of interesting new phenomena. It transpired that atoms can exhibit photon-like collective behavior. Indeed, many classical nonlinear optical effects were duplicated using atoms, e.g. four wave mixing, parametric processes as well as soliton propagation and metamorphosis. Nonlinear optics and BEC are theoretically much more similar than one might expect for such disparate fields. Indeed, in the experiments covered here, atoms and photons often change places.

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Can a variational approach describe pulse splitting in a dispersion managed system?

Infeld E, Matuszewski M, Shino C, Trippenbach M

Optica Applicata

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2006

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Vol. 36, nr 4

s. 575--580

EN

When looking for solitons in nonlinear systems, it is often useful to have a simplifying tool. One such tool is the variational method. On the other hand, in the presence of fast oscillations, the wavefunction of the system can split into two distinct parts. This is not describable by the classical variational method. Edwards et al., (J. Phys. B 38(4), 2005, pp. 363–76), introduced a hybrid variational analysis which can describe the dynamics in one selected direction more accurately. However, it remained to be seen how well this method describes the dynamics of solitons, in particular their splitting and subsequent recombining. Here we investigate an application of the hybrid variational analysis to a two dimensional system with dispersion management, where such splitting is known to occur. We conclude that indeed agreement is good. This could encourage wider use of the hybrid method.