Vectorial structure of Hermite–Laguerre–Gaussian beam in the far field

Starting from Maxwell's equations, a Hermite–Laguerre–Gaussian (HLG) beam is decomposed into the TE and TM terms by using the vector angular spectrum representation. By means of the method of stationary phase, the analytical TE and TM terms are presented in the far field. The energy flux distributions of the TE and TM terms are also investigated and depicted in the far field. The influences of the additional angle parameter and Gaussian waist width on the vectorial structure and energy flux pattern of HLG beam are also investigated. This research reveals the internal vectorial structure of HLG beam and may provide a new approach to the manipulation of laser beams.