Based on the vector angular spectrum method and the stationary phase method
and the fact that a circular aperture function can be expanded into a finite
sum of complex Gaussian functions, the analytical vectorial structure of a
four-petal Gaussian beam (FPGB) diffracted by a circular aperture is derived in
the far field. The energy flux distributions and the diffraction effect
introduced by the aperture are studied and illustrated graphically. Moreover,
the influence of the f-parameter and the truncation parameter on the
nonparaxiality is demonstrated in detail. In addition, the analytical formulas
obtained in this paper can degenerate into un-apertured case when the
truncation parameter tends to infinity. This work is beneficial to strengthen
the understanding of vectorial properties of the FPGB diffracted by a circular
aperture