Generation of a pilot phase pulse during the propagation of slow elliptically polarized pulses in a medium under coherent population trapping

Propagation of elliptically polarized light pulses in a medium of two-level atoms with degenerate energy levels under coherent population trapping has been studied within the density-matrix formalism and reduced Maxwell’s equation. It has been shown that ellipticity pulses and the orientation angle of the polarization ellipse move with a deceleration. The analytical expression for the group velocity of an arbitrary $J \rightarrow J$ dark transition ($J$ is an integer) has been derived. In addition, a previously unknown effect of forced phase modulation under the variation of the spatial orientation of the polarization ellipse has been discovered. This phase modulation includes a pilot pulse passing through the medium at the speed of light in vacuum and a slow pulse moving synchronously with the pulse of the orientation angle.