Transparent boundary condition for the beam propagation method

A new boundary condition is presented for use in beam propagation calculations that passes outgoing radiation freely with minimum reflection coefficient (as low as 3×10^-8). In conjunction with a standard Crank-Nicholson finite difference scheme, the assumption that the radiation field behaves as a complex exponential near the boundary is shown to result in a specific transparent boundary condition algorithm. In contrast to the commonly used absorber method, this algorithm contains no adjustable parameters, and is thus problem independent. It is shown to be accurate and robust for both two- and three-dimensional problems