In this paper, propagation of an electromagnetic beam wrapped around the axis of a thin axisymmetric wave guide embedded in a square law medium, depending on a \beta^2 parameter small enough to make the \beta^{2n} terms negligible for n\geq 2 has been analyzed. To solve Maxwell's equations in this wave guide, a paraxial approximation of the wave equations, satisfied by the electric and magnetic components of the electromagnetic field, has been used. The solutions of the corresponding paraxial wave equations describe beam propagation by a series expansion of Gaussian modes.
