In this paper, we will elaborate on our new ducting model which is developed for describing the propagation of laser beams in nonlinear Kerr media. In this model, it is assumed that the Gaussian beam shape remains unchanged during its propagation inside the nonlinear medium and using the aberration-free theory, the variable form refractive index has been obtained. The refractive index of the nonlinear medium is obtained in the form of refractive index of ducting media. Therefore, by applying the ray matrix of a ducting medium with variable elements along the propagation direction, one can find the laser beam parameters. To this end, the resulted relations for the beam radius and radius of curvature should be numerically solved along the propagation direction. The used method for solving these relations is also presented. The proposed model can be used for describing the propagation of continuous wave or pulsed laser beams.

Keywords: Nonlinear optics, Wave propagation, Self-phase modulation

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