Transverse polarization laser dynamics: vector modes of Karhunen-Loeve and their classification using catastrophe theory

Summary form only given. It is known that the sensible basis for description of the system dynamics is to be that a few modes contain most of the dynamics. This basis can be built using the Karhunen-Loeve modes. To describe complex spatio-temporal laser dynamics we have used the Karhunen-Loeve procedure in which it is necessary to calculate the eigenvectors and eigenvalues of the correlation matrix 2/spl times/2, obtained via the time-averaging of the product of the vector field components values at two different points. The laser dynamics are mostly described by the modes having the sum of their eigenvalues near to 1.