A Three-Dimensional Multistep Horizontally Wide-Angle Beam-Propagation Method Based on the Generalized Douglas Scheme

A three-dimensional horizontally wide-angle beam-propagation method is formulated on the basis of the multistep method for higher order Pade approximants, together with the alternating-direction implicit scheme. The fourth-order accurate finite-difference formula is used to enhance the efficiency of the method. The effectiveness is demonstrated through the analyses of a tilted step-index waveguide and a multimode interference coupler