A new preconditioner based on paraxial approximation for stable and efficient reflective beam propagation method

We present a preconditioner based on the paraxial approximation for the square-root operator to realize a stable and efficient iterative scheme in the reflective beam propagation method. The new preconditioner is shown to be highly effective in facilitating robust, efficient, and accurate solutions for computation of reflected and transmitted fields due to index discontinuities along optical waveguides, due primarily to the improvement on the condition number of the operator used.