Abstract: Laser beam propagation in the media with complex quadratic index of refraction n = n₀ + n₂r²/ r_e² was investigated. The expressions of beam radius, W(z) and curvature of its wave front, R(z)^-1 were obtained. The self-similar (s.s.) mode (perfect guiding) will occure after propagation distance larger than a characteristic length z_c, only if n₂₁≠0. The s.s. mode is a eigenmode of media, its propagation parameters W, R^-1 are dependent on n₂, but independent of the initial value W₀, R₀^-1. At the end, s. s. mode is a Gaussian spherical wave, not the plane wave.