Multistep method for wide-angle beam propagation

Abstract

A new beam-propagation method is presented whereby the Padé approximant wide-angle propagation operator is factored into a series of simpler Padé (1, 1) operators, thus leading naturally to a multistep method whose component steps are each solvable by using readily available paraxiallike solution techniques. The resulting method allows accurate approximations to true Helmholtz propagation while incurring only a modest numerical penalty. In addition, the tridiagonal form of the component steps allows the straightforward use of the previously reported transparent boundary condition.