Noniterative vectorial beam propagation method with a smoothing digital filter

This is the authors' abstract. We don't add key points for this paper.

The alternating direction implicit (ADI) technique is used in the numerical solution scheme for each longitudinal step, in the well-known vectorial beam propagation method (VBPM). It is used to reduce the linear-system matrix into a set of tridiagonal ones, which can then be solved by Thomas algorithm. Solutions using standard (Crank-Nicolson) VBPM for step-index waveguides contain small oscillations, which can significantly reduce the accuracy of the solutions. We show that this "noise" can be removed by a properly tailored low-pass digital filter in the spatial frequency domain. Results become as accurate as those obtained by iterative techniques. Examples deal first with the scaler LP/sub 01/ mode and a Gaussian field in a single-mode fiber converging to the vector HE/sub 11/ mode. Second, with an optimized Ti:LiNbO/sub 3/ bent waveguide using MgO. Finally, with a rib waveguide where advantages related to the use of the digital filter become very evident.