Gaussian beam evolution in nonlinear inhomogeneous fibres

Abstract

The paper analyzes the Gaussian beam (GB) evolution in nonlinear fibers in the framework of paraxial complex geometrical optics (PCGO). This method reduces the problem of Gaussian beam diffraction in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, PCGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to the other methods of nonlinear optics such as: variational method approach, method of moments and beam propagation method. It is shown that the PCGO method readily supplies the solution of Nonlinear Schrödinger Equation (NLS) for self-focusing fiber with a focusing refractive profile.

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