Some Remarks on Quasi-Solitons in Optical Fibers

In this paper a unique analysis of solitary waves corresponding to the solutions of the non-linear cubicquintic Schr6dinger equation for optical fibers is performed. These results imply that for an intensitysquared dependent refractive index, the behavior of the solitary waves is at most quasi-soliton. In our context there is not soliton behavior so that the existence of Raman solitons is not possible. However, under certain conditions it is reasonable to expect the existence of Raman quasi-solitons in the anomalous- dispersion regime.The mathematical aspects involved are emphasized because the theoretical research is very important in the context of non-linear optics to clarify various, often confusing ideas derived from certain experimental works.

Relativistic Multiple Scattering Theory

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].