Joint Effect of the Dipole–Dipole Interaction and Constant Dipole Moment on the Shape of the Field Pulse without an Envelope

Abstract

An integrable model is proposed for a two-level medium with a constant dipole moment, which describes the evolution of electromagnetic field pulses without an envelope with account for the dipole–dipole interaction. In the nearest neighbor approximation, this interaction is taken into account in the form of quadratic dispersion. It is found that such a generalization of the reduced Maxwell–Bloch equations preserves the complete integrability. It is shown using the obtained exact soliton solutions as examples that the joint effect of quadratic dispersion and the constant dipole moment has a number of unique features and provides new opportunities for controlling the shape of field pulses. In particular, it is found that the shape and amplitude of a field pulse depend on the signs of the dipole–dipole interaction as well as on the sign of the constant dipole moment.