New method to get fundamental Gaussian beam's perturbation solution and its global property

Using a multi-variable series method, we successfully investigated the global property of perturbation description for fundamental Gaussian beam. We explicitly proved that as long as the perturbation parameter s≠0, although it includes the Gaussian factor exp Mathametic experssion (ρ and ζ are normalized cylindrical polar coordinates defined in the text), the complete perturbation solution for fundamental Gaussian beam always diverges. © 2008 Springer-Verlag.