On Existence of Solitons for the 3rd Harmonic of a Light Beam in Planar Waveguides

• Authors: V. Cao Long , P. Goldstein , M. Trippenbach
• Languages of publication: EN

Abstracts

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.

Keywords

EN

42.81.Dp

Discipline

• 42.81.Dp: Propagation, scattering, and losses; solitons

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2004
• Volume: 105
• Issue: 5
• Pages: 437-444

Dates

published

2004-05

received

2003-12-04

accepted

2004-04-26

Contributors

author

V. Cao Long

• Institute of Physics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

author

P. Goldstein

• The Andrzej Soltan Institute for Nuclear Studies, Hoża 69, 00-681 Warsaw, Poland

author

M. Trippenbach

• Institute of Experimental Physics, Optics Division, Warsaw University, Hoża 69, 00-681 Warsaw, Poland

References

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Identifiers

DOI

10.12693/APhysPolA.105.437