The polychromatic laser guide star (PLGS) is one of the solutions proposed to extend the sky coverage by large telescopes to 100% by enabling a complete knowledge of all perturbation orders of the wavefront. The knowledge of the tip–tilt is deduced from the monitoring of the chromatic components of the PLGS, from 330nm to the visible or near infrared. Here we study the original scheme to create the PLGS by resonant excitation of the mesospheric sodium by two pulsed lasers (tens of kilohertz repetition rate, tens of watts average power, tens of nanoseconds pulse duration), at 589 and 569nm , respectively. The efficiency of this process is investigated numerically by means of both Bloch equation and rate equation models. The influence of numerous laser parameters is studied. In the best case, having optimized all laser parameters, the return flux at 330nm should not exceed 7×104photons/s/m2 for 2×18W laser average power at the mesosphere. This maximum is obtained for a modeless laser whose spot diameter corresponds to 4 times the diffraction limit. For a diffraction-limited spot, the return flux falls down to 4×104photons/s/m2 .