Exact solution to solitary wave equations of light interacting with two-level atomic systems

智 藤井, 敏雄 伊東

A. S. Rosenthal, Talal Ghannam

The exact electric polarization operator of the Maxwell-Bloch equations for a three-level Λ-type system is derived without assuming equality of the transition dipole moments. Numerical solution of the resulting solitary wave equations yields a richer spectrum than found earlier for identical dipole moments [Hioe and Grobe, Phys. Rev. Lett.73, 2559 (1994)]. The two components of the new solitary waves each have a zero-pulse area and take the form of modulated oscillations.

Alidou Mohamadou, Étienne Wamba, Daniel Lissouck +1 more

The matter-wave solutions of Bose-Einstein condensates with three-body interaction are examined through the one-dimensional Gross-Pitaevskii equation. By using a modified lens-type transformation and a further extension of the tanh-function method we obtain the exact analytical solutions which describe the propagation of kink-shaped solitons, anti-kink-shaped solitons, and other families of solitary waves. We realize that the shape of a kink solitary wave depends on both the scattering length and the parameter of atomic exchange with the substrate. The stability of the solitary waves is examined using analytical and numerical methods. Our results can also be applied to nonlinear optics in the presence of cubic-quintic media.

P. van der Straten, Harold J. Metcalf

Maciej Janowicz, Martin Holthaus

Running-wave solutions to three systems of partial differential equations describing wave propagation in atomic media in the kinetic limit have been obtained. Those systems include approximations to (i) standard two-level Maxwell–Bloch equations; (ii) equations describing processes with saturated absorption in three-level systems and (iii) equations describing processes with reversed saturation in four-level systems. It has been shown that in all three cases kink-like solitary waves can emerge if the dynamical equation for the intensity includes a linear contribution to the Lambert–Beer law. Those solitary waves can propagate with either sub- or superluminal velocity of the edge of the kink, and in a direction which can be either the same as or opposite to that of the carrier wave. In addition, simple qualitative information about the behaviour of waves near the wavefronts has been obtained.

Thierry Colin, Boniface Nkonga