Vectorial structure of the far field of an elegant Hermite–Gaussian beam

Based on the vector angular spectrum method and the method of stationary phase, an analytical expression for the vectorial structure of the far field of an elegant Hermite–Gaussian beam is derived. The analytical formulae of the energy flux distributions of the TE term, the TM term, and the whole beam are presented in the far field. Analytical expressions for the ratios of the powers of the TE and TM terms to those of the elegant Hermite–Gaussian beam are obtained without any approximation. The physical pictures of the far field of an elegant Hermite–Gaussian beam are demonstrated and compared with those of the far field of the corresponding standard Hermite–Gaussian beam. This research reveals the internal vectorial structure of the far field of an elegant Hermite–Gaussian beam from an alternative viewpoint.

► Far field of an elegant Hermite–Gaussian beam is investigated from the vectorial structure.
► Contributions of the TE and TM terms to the elegant Hermite–Gaussian beam are also examined.
► Physical pictures of elegant and standard Hermite–Gaussian beams are compared in the far field.
► Reveals the discrepancy between these above two kinds of beams.