Beam shape coefficient calculation for a Gaussian beam: localized approximation, quadrature and angular spectrum decomposition methods.

Three methods for calculating the beam shape coefficients (the quadrature, the angular spectrum decomposition (ASD), and the localized approximation methods) are studied. The normalized associated Legendre function is employed in the calculation so as to prevent overflow. The two-dimensional integrations in the quadrature and the ASD methods are developed to the one-dimensional integration to speed up the calculation. The Gaussian beams reconstructed with different methods are compared, showing the difference in the remodeling effects of these methods. The reason for the presence of pseudodistribution in the localized model is given.