Analytical vectorial structure of truncated modified Laguerre–Gaussian beam in the far field

Based on the vectorial angular spectrum representation of Maxwell equations and the method of stationary phase, analytical expressions are derived for the TE term, TM term and whole energy flux of a hard-edged diffracted modified Laguerre–Gaussian beam (MLGBs) in the far field, respectively. It is shown that the evolutive energy flux not only depends on the beam order, initial waist width but also relates to the truncated parameter. Furthermore, influences of the truncated parameter on the discrepancies of energy flux distributions between paraxial and non-paraxial cases are also analyzed for different selections of the initial beam width.

► Analytical expressions are derived for the energy flux of a truncated modified Laguerre–Gaussian beam in the far field.
► The energy flux not only depends on the beam order, initial waist width but also relates to the truncated parameter.
► Influences of the truncated parameter on energy flux distributions between paraxial and non-paraxial cases are also analyzed.