We find the Lax pair for a system of reduced Maxwell-Bloch equations that describes the propagation of two-component
extremely short electromagnetic pulses through the medium containing two-level quantum particles
with arbitrary dipole moments.
The solutions of the reduced Maxwell-Bloch equations for an anisotropic two-level medium, which describe the propagation of electromagnetic pulses having a duration from a few field oscillations, are studied. An influence of the permanent dipole moment of the quantum transition on dynamics of the pulses and their spectrum is considered.
The distinctive features of passing of the two-component extremely short pulses through the nonlinear media are discussed. The equations considered describe the propagation in the two-level anisotropic medium of the electromagnetic pulses consisting of ordinary and extraordinary components and an evolution of the transverse-longitudinal acoustic pulses in a crystal that contains the paramagnetic impurities with effective spin S = 1/2. The solutions decreasing exponentially and algebraically are studied.
The distinctive features of the propagation of the two-component electromagnetic pulses in an anisotropic media are studied in the frameworks of the system of equations of the resonance of long and short waves. It is shown that an interaction of the light with the quantum systems, which have a constant dipole momentum nonequal to zero, occurs not only in the usual mode of the self-induced transparency, but also in two new modes. In the first one (supertransparency), the pulse propagation causes the significant change of the population density of quantum levels, while its group velocity remains close to linear one. In the second mode (extraordinary transparency), the group velocity of the pulse changes significantly, but the population of the levels is practically invariable. It is also noted that the largest change of the population takes place, if the carrier frequency of the solitons is less than the resonant frequency, at that the detuning value depends on the duration of the pulses.