3-D semivectorial bidirectional marching solver with fourth-order accuracy for optical waveguides

In this paper, we develop and analyze a new, to the best of our knowledge, semivectorial bidirectional operator marching method with fourth-order accuracy (Bi-OMM4) for three-dimensional optical waveguides. The fourth-order semivector exponential scheme reproduces the exact reformulations for equations with pairs of bidirectional reflection operators based on the Dirichlet-to-Neumann (DtN) mapping. Implementations for large range step sizes in both directions are presented, and exact bidirectional range marching formulas are derived for each range-independent segment. The study compares the results obtained from the Bi-OMM4 with the fourthorder bidirectional beam propagation method based on the finite difference scheme (FD-Bi-BPM4) and the bidirectional operator marching method with second-order accuracy (Bi-OMM2) to validate the accuracy and effectiveness of Bi-OMM4 by analyzing several examples of uniform and longitudinally varying waveguides. The results show that the Bi-OMM4 is numerically faster than the FD-Bi-BPM4 by almost seven times for different transverse grid sampling points, and it offers higher accuracy than Bi-OMM2 without a significant increase in computation resources. (c) 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.