Normal modes for electromagnetically induced transparency in a lambda system of degenerate energy levels

This paper presents an analytical study of the formation of normal modes of probe light for electromagnetically induced transparency in a lambda system of quantum transitions between $^3\mathrm{P}_0$, $^3\mathrm{P}_1^0$ and $^3\mathrm{P}_2$ levels in the case of an elliptically polarised control field and inhomogeneous broadening. The normal modes are elliptically polarised waves with identical polarisation ellipse eccentricities but different electric vector rotation directions. The mode eccentricities are only determined by the control field polarisation ellipse eccentricity. The major axis of the polarisation ellipse of one of the normal modes is parallel to the major axis of the control light polarisation ellipse, whereas the major axis of the polarisation ellipse of the other normal mode is perpendicular to it. The former type of mode has a higher group velocity than does the latter type of mode, and both velocities depend on control light polarisation ellipse eccentricity and intensity. Probe light with an arbitrary elliptical polarisation is the sum of normal modes which propagate independently of each other. Since the modes differ in group velocity, a probe pulse entering the medium splits into two components, each of which is a normal mode. The fraction of energy in each normal mode depends only on polarisation characteristics of coupled fields and is independent of their intensity.