Abstract
Propagation of a mixture of modes of a laser beam through a saturable nonlinear medium has been studied using JWKB method and the paraxial ray approximation. Two second order nonlinear coupled differential equations for the beam width parameters resembling equations of coupled nonlinear oscillators of unit mass are obtained. A scalar potential of the system has been formulated whose analysis yields some valuable information like existence of two critical values of the potential within which bound state of the system exists. From the stability analysis it has been found that the stable beam propagation depends on the ratio of intensities of the two modes. A threshold of power is defined. When beam power is above the threshold value the propagation is stationary.
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