Speed up the beam shape coefficient evaluation by using scalar spherical wave expansion and scalar translational addition theorem

The work proposes a two-step indirect method for evaluating the beam shape coefficients (BSCs) of the electromagnetic (EM) field of shaped beams. The spherical wave expansion of the EM field is based on the expansion of the scalar potential function so that the BSCs of the EM field are obtained as the linear combinations of the BSCs of the potential function. By using the scalar translational addition theorem, the BSCs of the potential function in the particle coordinate system are obtained from those in the beam system. The beams having circular profile and carrying no topological charge are considered in the work. The method simplifies the formulation of the BSCs and speeds up the numerical calculations. The numerical results for the Gaussian beam validate the method in evaluating the BSCs and reproducing the beam field in both accuracy and efficiency.