We analyze exact non-EIT type solutions to the equations for propagation of fast-light pulses through a resonant medium. We examine instabilities encountered attaining superluminal group velocities with an ultra-short rather than adiabatic or cw probe.
We investigate the weak probe pulse propagation through the atomic medium, in the presence of the strong control laser field, under the regime of the electromagnetically induced transparency (EIT). These fields couple to the medium by forming the 3-level ladder configuration. We focus on two distinct cases: closed system, which is a non-degenerate, and open system, where the middle level is 3-fold degenerate, and the additional levels are coupled to the other levels only via spontaneous emission. The spatio-temporal profile of the probe pulse envelope is obtained by using the formalism of Maxwell-Bloch equations with the help of the Fourier transform method. We study the influence of the control field Rabi frequency, the spectral half-width of the initial pulse and decay rates on the propagation of the probe pulse. Several important pulse parameters are also calculated and discussed. It is shown that the group velocity of light can be controlled in such a manner that one can switch from slow to fast light and vice versa when changing the control Rabi frequency and spectral pulse half-width. Moreover, the possibility of replacing the open with an effective closed system is also discussed.
We have examined the propagation of femtosecond laser pulses in an absorbing dye solution through a short to a long range of propagation distance. The transmitted pulses show strong spectral shift and a superluminal to subluminal transition in the propagation velocity keeping its initial shape almost intact. It is verified that the peak velocity is well described by a modified group velocity v(S) defined within the framework of the saddle-point method as well as by a recent prediction of the net group delay of surviving frequency.
We theoretically study the propagation through a resonant absorbing medium of a time-dependent perturbation modulating the amplitude of a continuous wave (cw). Modeling the medium as a two-level system and linearizing the Maxwell-Bloch equations for the perturbation, we establish an exact analytical expression of the transfer function relating the Fourier transforms of the incident and transmitted perturbations. It directly gives the gain and the phase shift undergone in the medium by a harmonic modulation. For the case of a pulse modulation, it enables us to determine the transmission time of the pulse center of mass (group delay), evidencing the relative contributions of the coherent and incoherent (population) relaxations. We show that the group delay has a negative value (fast light) fixed by the coherent effects when the cw intensity is small compared to the saturation intensity and becomes positive (slow light) when this intensity increases, before attaining a maximum that cannot exceed the population relaxation time. The analytical results are completed by numerical determinations of the shape of the transmitted pulses in the different regimes.