Propagation of ultrashort pulses of polarised radiation in a resonant medium

An analysis is made of the coherent interaction of a short pulse of polarised electromagnetic radiation with a medium in which the energy levels are degenerate in respect of the angular momentum projection. In the case of the j_a = 1 → j_b = 0 transition it is found, without recourse to the approximation of slowly varying envelopes, that the system of the Maxwell – Bloch equations has an exact solution in the form of a steady-state solitary wave of duration equal to half the period of emission as a result of the investigated atomic transition. A new solution is obtained, in addition to a simple generalisation corresponding to a polarised video pulse. When the populations of the excited states with different projections of the angular momentum are different, the spherical components of the vector representing the electric field intensity do not behave proportionately: if one of them corresponds to a unipolar spike of the electric field, the other component is a variable-sign solitary wave.