Vectorial Karhunen-Loeve modes for the description of the polarization transverse pattern dynamics in lasers and their classification based on the characterization of the singular points

Vectorial Karhunen-Loeve modes are introduced for the description of the polarization transverse pattern dynamics of the Zeeman multitransverse mode laser with a large Fresnel number and anisotropic cavity. Some approaches for the classification of these modes are presented based on the characterization of the mode function behaviour in the vicinity of the singular points in the transverse plane. The results of numerical experiments show that for the regimes with rotating patterns these modes are closely connected with A n catastrophe functions of complex argument x ± iy, where x, y are the transverse coordinates.