Analytical vectorial structure of non-paraxial four-petal Gaussian beams in the far field

TL;DR

This paper analytically investigates the vectorial structure of non-paraxial four-petal Gaussian beams in the far field, revealing how their petal pattern evolves and depends on the beam order, enhancing understanding of their electromagnetic properties.

Contribution

It provides a detailed analytical description of the far-field vectorial structure of non-paraxial FPGBs using electromagnetic representations, which was not previously detailed.

Findings

FPGBs evolve into multiple small petals in the far field.

The number of petals depends on the input beam order.

The vectorial structure clarifies electromagnetic properties of FPGBs.

Abstract

The analytical vectorial structure of non-paraxial four-petal Gaussian beams(FPGBs) in the far field has been studied based on vector angular spectrum method and stationary phase method. In terms of analytical electromagnetic representations of the TE and TM terms, the energy flux distributions of the TE term, the TM term, and the whole beam are derived in the far field, respectively. According to our investigation, the FPGBs can evolve into a number of small petals in the far field. The number of the petals is determined by the order of input beam. The physical pictures of the FPGBs are well illustrated from the vectorial structure, which is beneficial to strengthen the understanding of vectorial properties of the FPGBs.