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Femtosecond Light Wave Packets

100%
Radzewicz C., Trippenbach M., Band Y., Krasinski J.
Acta Physica Polonica A
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1998
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vol. 93
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issue 1
237-251
EN
We analyze propagation of ultra short light pulses in a transparent, dispersive, nonlinear medium. A general formula for femtosecond wave packet evolution is developed and applied to specific problems. Theoretical and experimental results for wave packet distortion by lenses, wave packet rotation in birefringent media and group velocity matching in sum frequency generation are presented. Numerical results for splitting of femtosecond wave packets in dispersive Kerr media are also presented.
2
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On Existence of Solitons for the 3rd Harmonic of a Light Beam in Planar Waveguides

100%
Cao Long V., Goldstein P., Trippenbach M.
Acta Physica Polonica A
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2004
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vol. 105
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issue 5
437-444
EN
We consider equations governing propagation of a monochromatic laser beam coupled to its third harmonic in a nonlinear medium. The system proves to be non-integrable in the sense of Painleve. However it is partially integrable for all values of its parameters. We further check the possibility of solving the equations by the Hirota bilinear method. The system is found to be solvable this way provided that the complex phase of the third harmonics is equal to tripled phase of the fundamental mode (modulo i) and also the amplitudes of these modes are in special proportion. This result corresponds to the previously known condition of existence of the sech soliton solutions. Furthermore, the Hirota scheme is found to work only for exact resonance, i.e. for the ratio of the dispersion coefficients equal to the ratio of frequencies. Finally, all these conditions may only be satisfied for single envelope solitons of the cubic Schrödinger type.
3
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Bose-Einstein Condensates in Optical Lattices

100%
Wasilewski W., Trippenbach M., Rzążewski K.
Acta Physica Polonica A
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2002
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vol. 101
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issue 1
47-60
EN
We study an ultracold dilute gas of bosonic atoms in an optical lattice induced by intersecting laser beams. As a first approximation we neglect confining potential and atom-atom interactions. In this case the Gross-Pitaevskij equation reduces to simple Mathieu equation. Upon choosing periodic boundary conditions this problem has well known periodic solution. This simple picture allows to demonstrate localization of the wave packet and formation of the band structure. We calculate spectrum of the excited states as a function of the strength of modulating potential and using a standard adiabaticity criterion we predict the most efficient way to ramp up optical lattice, without higher state excitation. Finally, we discuss the influence of the atom-atom interaction (nonlinearity) on the adiabaticity of the process.
4
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Nonlinear Effects with Ultrashort Laser Pulses

100%
Wasylczyk P., Wasilewski W., Trippenbach M., Radzewicz C.
Acta Physica Polonica A
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2002
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vol. 101
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issue 1
89-104
EN
Propagation of an intense femtosecond laser pulse through a transparent nonlinear medium such as dielectric leads to a number of phenomena. In our experiment we observed complex spatial, spectral, and temporal structures appearing in the initially smooth femtosecond laser pulse when the pulse power is comparable to or higher than the critical power for self-focusing. We have also developed a complete, 3-dimensional theoretical model to describe the observed phenomena.
5
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Harmonically Trapped Classical Gas under Critical Rotation

76%
Chwedeńczuk J., Ziń P., Trippenbach M., Dąbrowska B., Gajda M., Rzążewski K.
Acta Physica Polonica A
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2003
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vol. 104
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issue 5
399-407
EN
We study one- and two-dimensional systems of two interacting particles in a time dependent harmonic potential. In a case of one-dimensional geometry a frequency of the potential varies periodically, while in the two-dimen- sional~case the harmonic potential rotates with a constant angular velocity. We show that depending on the driving frequency the distance between the particles can either explode or stay bound. Repulsive interaction can prevent the explosion, which seems quite counter-intuitive. Our work is related to Ecole Normale Supérieure experiment and shows that the effect found there is purely classical.
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