Beam-propagation algorithm based on the method of lines

We extend the method of lines [ ItohT., ed., Numerical Techniques for Microwave and Millimeter Wave Passive Structures ( Wiley, New York, 1989), pp. 381– 446] for application as a beam-propagation algorithm with absorbing boundary conditions. We thus avoid reflections from the computational window edges. The new algorithm has in principle none of the restrictions of standard beam-propagation methods (propagation under paraxial conditions in low-contrast media and relatively small propagation steps) and is applied to planar waveguides with high-refractive-index steps (e.g., straight or S-bend slab waveguides) and to rib waveguides.