Vectorial Structural Property of a Cylindrical Vector Laguerre-Gaussian Beam in the Far-field Regime
Y-Q. Xu and G-Q. Zhou
The two cases of a cylindrical vector Laguerre-Gaussian beam result from the exchange of the transverse electric (TE) fields in the source plane. Based on the angular spectrum representation and the method of stationary phase, the analytical expressions for the energy flux of the vectorial structure; namely, the TE and the transverse magnetic (TM) terms of cylindrical vector Laguerre-Gaussian beams with two cases are derived in the far-field regime. In the far-field, the ratios of the power of the TE and TM terms to that of the cylindrical vector Laguerre-Gaussian beam are analytically presented. Based on the second-order and the fourth-order moments, analytical formulae of the far-field divergence angles and the kurtosis parameters of the TE term, the TM term, and the cylindrical vector Laguerre-Gaussian beam are derived, respectively. The vectorial structures of the two cases of the cylindrical vector Laguerre-Gaussian beam have different energy flux distributions. In the case of n ± 1 ≠ 1; however, they have the same power, the same far-field divergence angle, and the same kurtosis parameter. The influences of the radial mode number, the azimuthal mode number, and the Gaussian waist size on the energy fluxes, the powers, the far-field divergence angles, and the kurtosis parameters of the cylindrical vector Laguerre-Gaussian beam and its vectorial structure are illustrated by numerical examples.
Keywords: Laser beam, cylindrical vector, Laguerre-Gaussian beam, energy flux, far-field divergence angle, kurtosis parameter, vectorial structure