POLARIZATION INSTABILITY IN LASERS .1. MODEL AND STEADY-STATES OF NEODYMIUM-DOPED FIBER LASERS

The aim of this paper is to provide a vectorial model which can describe the dynamics of the two transverse held polarizations presented by an optical fiber laser. These dynamics are supposed to take their origin from the interaction between the propagating field and the atoms: an assumption based on the existence of a transverse distribution of dipole moments and which leads to a vectorial atomic polarization. Also, and as we have considered a frequency for each field polarization, a longitudinal dependence of the population inversion must be taken into account. A double Fourier expansion (transverse and longitudinal) of the material variables is then needed and the resulting model is analyzed using the bifurcation theory: the existence of all stationary states is fully expressed in the parameter space. The stability of these states and the system dynamic is studied in the following paper [Phys. Rev. A 52, 4243 (1995)].