By using the angular spectrum representation, the propagation law of the second intensity moment are given for the axially symmetric paraxial and nonparaxial scalar beam.

Transmission characteristics of nonparaxial Gaussian beam;

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

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.