Error analysis of the Gaussian beam summation method for ultra wide-band radiation in inhomogeneous medium

We address issues related to the accuracy of the beam summation method (BSM) for ultra wideband (UWB) radiation in inhomogeneous medium. In the BSM, the field is expanded using a lattice of beam propagators that are tracked locally in the medium. As a test bed for the accuracy of the BSM, we derive a solution for a beam in a general plane stratified medium which is valid beyond the paraxial regime. We then use it to derive bounds on the error away from the beam axis, and to obtain rules for optimizing the choice of the parameters in the BSM.