A single scatter improvement for beam propagation methods

The beam propagation methods are widely used in numerical simulations of optical waveguides that change gradually in the propagation direction. However, their accuracy is still limited if the one-way models are used over a large propagation distance. The single scatter approximation can be used to improve the accuracy of the beam propagation method, but its usual discrete form is not convenient for numerical implementation. We obtain an improved one-way equation as the continuous limit of the discrete single scatter approximation. Alternative discretization of this equation leads to efficient numerical implementations with the same improved accuracy.