Vector Area Theorem mapping in crystals and polarization stability of SIT-solitons

The stability of polarization, areas, and number of self-induced transparency (SIT)-solitons at the output from the LaF_3:Pr^{3+} crystal is theoretically studied versus the polarization direction and the area of the input linearly polarized laser pulse. For this purpose the Vector Area Theorem is rederived and two-dimensional Vector Area Theorem map is obtained. The map is governed by the crystal symmetry and takes into account directions of the dipole matrix element vectors of the different site subgroups of optically excited ions. The Vector Area Theorem mapping of the time evolution of the laser pulse allows one to highlight soliton polarization properties.