New method for nonparaxial beam propagation

A new method for solving the wave equation is presented that is nonparaxial and can be applied to wide-angle beam propagation. It shows very good stability characteristics in the sense that relatively larger step sizes can be taken. An implementation by use of the collocation method is presented in which only simple matrix multiplications are involved and no numerical matrix diagonalization or inversion is needed. The method is hence faster and is also highly accurate.