Starting from the vectorial Rayleigh-Sommerfeld diffraction integrals and taking the vectorial nonparaxial flattened Gaussian beams as an example,the transversal intensity of vectorial nonparaxial flattened Gaussian beams is studied.

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.