In this paper, the paraxial Gaussian beam width evolution equation, which is obtained by means of variational approach, is simplified, the affection of the potentially functional spurious root, which arises from the Taylors series expansion of the strongly nonlocal nonlinear material response function, is eliminated, and the formulae of the paraxial Gaussian optical beam .

The propagation of paraxial Gaussian beam in three-dimensional strongly nonlocal media is disccussed with a variational approach.

Transmission characteristics of nonparaxial Gaussian beam;

The axial intensity of nonparaxial Gaussian beams diffracted by a small aperture;

The closed-form expressions for the intensity of resulting beam for the coherent and incoherent combinations of non-paraxial off-axis Gaussian beams have been derived with some interesting special cases,such as the far-field expressions,on-axis intensity,paraxial approximation expressions for coherent and incoherent combinations of non-paraxial off-axis Gaussian beams.