Vectorial Structure of an Elegant Laguerre-Gaussian Beam in the Far-field Regime
Based on the vectorial structure of an optical beam and the method of stationary phase, the analytical expressions for the vectorial structure of the even and the odd elegant Laguerre-Gaussian beams are derived in the far-field regime, respectively. The analytical formulae of the energy flux distributions of the transverse electric (TE) term, the transverse magnetic (TM) term and the whole beam of the even and the odd elegant Laguerre-Gaussian beams are presented in the far-field. The ratios of the powers of the TE and TM terms to the power of the elegant Laguerre-Gaussian beam are also derived. The physical pictures of the far-field of elegant Laguerre-Gaussian beams are demonstrated and compared with those of the far-field of the corresponding standard Laguerre-Gaussian beams. This research reveals the abundant and interesting internal details of the far-field of the elegant Laguerre-Gaussian beam.
Keywords: Elegant Laguerre-Gaussian beam, vectorial structure, far-field, transverse electric (TE), transverse magnetic (TM)