Boundary conditions for the finite difference beam propagation method based on plane wave solutions of the Fresnel equation

A technique for constructing the finite difference schemes of the beam propagation method at the boundary of the computational window retains the propagation matrices within longitudinal homogeneous sections. The involvement of only the refractive indexes and mesh parameters helps the approach to avoid tedious adjustments, reducing computational time. The schemes do not depend on the computed fields and facilitate a similar treatment of both interior and boundary points. The method can be easily implemented for both two- and three-dimensional structures.