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Based on the vector angular spectrum method and the stationary phase methodand the fact that a circular aperture function can be expanded into a finitesum of complex Gaussian functions, the analytical vectorial structure of afour-petal Gaussian beam (FPGB) diffracted by a circular aperture is derived inthe far field. The energy flux distributions and the diffraction effectintroduced by the aperture are studied and illustrated graphically. Moreover,the influence of the f-parameter and the truncation parameter on thenonparaxiality is demonstrated in detail. In addition, the analytical formulasobtained in this paper can degenerate into un-apertured case when thetruncation parameter tends to infinity. This work is beneficial to strengthenthe understanding of vectorial properties of the FPGB diffracted by a circularaperture.

Vectorial structure of a hard-edged-diffracted four-petal Gaussian beam in the far field