How to make a uniform beam produce self-focusing or self-defocusing effects

In the research of self-focusing and self-defocusing phenomena, it is generally known that the used nonlinear optical material possesses the coefficient of nonlinear refractive index n2(r), which is usually uniform in spacial distribution, that is, n2(r) is all the same in the material. Therefore in order to obtain the desired self-focusing or self-defocusing, the radial distribution of incident beam intensity I(r) must be Gaussian form and uniform beam can't cause self-focusing or self-defocusing. In addition, for the material n2 < 0, self-focusing is obtainable, but self-defocusing isn't. Otherwise, for the material n2 < 0, only self-defocusing can be obtained.