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

摘要

The analytical vectorial structure of non-paraxial four-petal Gaussianbeams(FPGBs) in the far field has been studied based on vector angular spectrummethod and stationary phase method. In terms of analytical electromagneticrepresentations of the TE and TM terms, the energy flux distributions of the TEterm, the TM term, and the whole beam are derived in the far field,respectively. According to our investigation, the FPGBs can evolve into anumber of small petals in the far field. The number of the petals is determinedby the order of input beam. The physical pictures of the FPGBs are wellillustrated from the vectorial structure, which is beneficial to strengthen theunderstanding of vectorial properties of the FPGBs.