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

TL;DR

This paper analytically investigates the vectorial structure and diffraction effects of a four-petal Gaussian beam passing through a circular aperture, revealing how aperture and parameters influence nonparaxiality and beam properties.

Contribution

It derives an analytical vectorial model for the far-field diffraction of a four-petal Gaussian beam by a circular aperture, including effects of aperture truncation and nonparaxiality.

Findings

Energy flux distributions are characterized and visualized.

Aperture truncation influences diffraction and beam structure.

Formulas reduce to un-apertured case as truncation parameter increases.

Abstract

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.