Effects of spatial dispersion on Self--induced transparency in two--level media

TL;DR

This paper investigates how dispersion affects self-induced transparency (SIT) solitons in two-level media, revealing new phenomena like pulse stopping and superluminal motion depending on frequency ratios and medium properties.

Contribution

It provides a detailed analysis of dispersion effects on SIT, introducing new insights into pulse velocity control and stopping mechanisms based on frequency ratios and medium broadening.

Findings

Pulse stopping occurs when pulse energy is fully absorbed.

Superluminal motion predicted in amplifying media at resonance.

Pulse velocity depends on the ratio of pulse to atomic transition frequency.

Abstract

We study the effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - $x=\omega/\omega_0$. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above unity, while for the inhomogeneously broadened systems it appears irrespective of the value of $x$. Analysis performed on the basis of Mcall\& Hahn \textit{Area theorem} implies that pulse stopping is achieved when Ber's absorption coefficient approaches infinity, that is, pulse energy is fully absorbed in the medium. In the case of amplifying media super-luminal motion is predicted as in the case of resonance. However, there is a lowest value in the frequency ratio below which the pulse velocity tends to the sub-luminal region. These new features of the SIT phenomenon open novel ways on how it may be exploited for the control of electromagnetic wave radiation in two-level media. This may be achieved by varying frequency ratio.