Rigorous theory of self-induced transparency in the case of a double resonance in a three-level medium

A study is made of steady-state ultrashort electromagnetic radiation pulses of two different wavelengths propagating at the same velocity in a three-level medium under exact resonance conditions. It is shown that such pulses (simultons) correspond to the soliton solutions of the corresponding generalized reduced Maxwell–Bloch equations which thus represent a new example of a system of evolution equations that can be solved exactly by the inverse scattering method. A full characterization of a simulton requires the knowledge of its duration and phase and also of a twodimensional vector (called the internal polarization vector) with the components equal to the relative amplitudes of the pulses forming a simulton. Collision of two different simultons generally changes their polarizations. An expression is obtained for the angle of rotation of the polarization vectors as a function of the simulton amplitudes and their initial polarizations.